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DYNAMIC ECONOMETRIC MODELS OF HOUSEHOLD VEHICLE OWNERSHIP AND UTILIZATION

bY FRED LAIRES MANNERING B.S.C.E.

U n i v e r s i t y of Saskatchewan (1976)

M.S.C.E.

Purdue U n i v e r s i t y (197 9)

Submitted t o t h e Department of C i v i l Engineering i n p a r t i a l f u l f i l l m e n t of t h e r e q u i r e m e n t s f o r t h e d e g r e e of

DOCTOR OF PHILOSOPHY

at t h e MASSACHUSETTS INSTITUTE OF TECHNOLOGY

May 1983

S i g n a t u r e of Author Department of C i v i l E n g i n e e r i n g

C e r t i f i e d by C l i f f o r d Winston Thesis Supervisor Accepted by F r a n c o i s M. M. Morel Chairman, D e p a r t m e n t a l Committee on G r a d u a t e S t u d e n t s of t h e Department of C i v i l E n g i n e e r i n g

DYNAMIC ECONOMETRIC MODELS OF HOUSEHOLD

VEHICLE OWNERSHIP AND UTILIZATION

FRED LAIRES MANNERING Submitted t o t h e Department of C i v i l E n g i n e e r i n g on May 3 , 1983 i n p a r t i a l f u l f i l l m e n t of t h e Requirements f o r t h e Degree of Doctor of Philosophy i n C i v i l Engineering ABSTRACT T h i s t h e s i s p r e s e n t s a t h e o r e t i c a l and e m p i r i c a l assessment of t h e demand f o r motor v e h i c l e s i n t h e U.S. The a n a l y s i s was undert a k e n a t t h e household l e v e l , and f u l l e x p l i c i t c o n s i d e r a t i o n was given t o t h e i n t e r r e l a t i o n s h i p s between t h e h o u s e h o l d ' s c h o i c e s of q u a n t i t y of v e h i c l e s t o own, t y p e s of v e h i c l e s t o own ( d e f i n e d by make, model and v i n t a g e ) , and t h e e x t e n t t o which t h e s e v e h i c l e t y p e s a r e u t i l i z e d . Moreover, t h e dynamic a s p e c t s of t h e h o u s e h o l d ' s v e h i c l e m e r s h i p and u t i l i z a t i o n d e c i s i o n were accounted f o r by viewing dynamics a s t h e e v o l u t i o n of household t a s t e s . Based on fundamentally d i f f e r e n t economic t h e o r i e s r e l a t i n g t o t h e manner i n which households a d d r e s s t h e i n t e r t e m p o r a l n a t u r e of t h e i r v e h i c l e owner s h i p problem, two dynamic econometric models of v e h i c l e ownership and u t i l i z a t i o n were d e r i v e d . The d e r i v e d models were e s t i m a t e d w i t h a n a t i o n a l household samp l e i n which a l l r e l e v a n t v e h i c l e ownership i n f o r m a t i o n was a v a i l a b l e f o r t h e same households f o r a two-and-one-half y e a r p e r i o d , December 1977 t o June 1980. The r e s u l t i n g model e s t i m a t i o n s s u g g e s t t h a t v e h i c l e demand c o n d i t i o n s f a v o r t h e s u r v i v a l of t h e domestic automobile i n d u s t r y . This i s r e f l e c t e d by t h e f i n d i n g t h a t households have an i n h e r e n t p r e f e r e n c e toward GM and Ford p r o d u c t s , and t o a l e s s e r e x t e n t , C h r y s l e r and AMC p r o d u c t s , a s opposed t o foreign-made v e h i c l e s . However, t o e x p l o i t t h i s p r e f e r e n c e , domestic m a n u f a c t u r e r s must be a b l e t o o f f e r r e a s o n a b l y c o m p e t i t i v e models,both i n terms of performance and c a p i t a l costs.

Thesis Supervisor: Title:

D r . C l i f f o r d Winston P r o f e s s o r of C i v i l E n g i n e e r i n g

Acknowledgements

S e v e r a l p e o p l e were i n s t r u m e n t a l t o t h e d e v e l o p m e n t of t h i s thesis.

F i r s t I w i s h t o acknowledge my a d v i s o r , C l i f f W i n s t o n , f o r

p r o v i d i n g s u b s t a n t i v e i n s i g h t and g u i d a n c e .

Also, t h e a d v i c e and

comments of Ann F r i e d l a e n d e r and Dan McFadden were v i t a l t o t h i s thesis.

I n a d d i t i o n , t h a n k s a r e due t o Moshe Ben-Akiva

and S t e v e

Lerman f o r t h e i r a s s i s t a n c e t h r o u g h o u t my s t a y a t M.I.T. I would a l s o l i k e t o acknowledge t h e s u p p o r t p r o v i d e d by my p a r e n t s o v e r t h e many y e a r s of my e d u c a t i o n .

T h e i r c o n c e r n and

I am a l s o i n d e b t e d t o J i l l S h i r l e y

u n d e r s t a n d i n g was h i g h l y v a l u e d .

f o r h e r g e n e r a l s u p p o r t a n d h e r w i l l i n g n e s s t o l i s t e n and comment on many of t h e t h e o r e t i c a l and e m p i r i c a l p r o b l e m s t h a t a r o s e d u r i n g t h e e v o l u t i o n of t h i s t h e s i s .

Many s t u d e n t s i n t h e T r a n s p o r t a t i o n

Systems D i v i s i o n , p a s t a n d p r e s e n t , p r o v i d e d e n c o u r a g e m e n t and a s u i t a b l e r e s e a r c h environment.

Their contribution i n t h i s regard

i s deeply appreciated. F i n a l l y , I would l i k e t o t h a n k Connie Choquet f o r h e r a s s i s t a n c e i n t h e p r e p a r a t i o n of t h i s t h e s i s .

Her t y p i n g s k i l l s made t h e l a s t

few weeks of t h e t h e s i s e x p e r i e n c e a r e l a t i v e p l e a s u r e .

T&U Abstract

OF CONTENTS

..................................... Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . .

T a b l e of

..................... CHAPTER 2 . C R I T I C A L REVIEW OF PREVIOUS RESEARCH . . . . . . . . . 2.1 Aggregate Models . . . . . . . . . . . . . . . . . . . . CHAPTER 1.

INTRODUCTION

........ .... Disaggregate Models . . . . . . . . . . . . . 2.2.1 Household L e v e l o f Ownership Models . . 2.2.2 Household Vehicle Type Choice Models . 2.2.3 Household V e h i c l e Utili'zation Models . 2.2.4 Joint Disaggregate Models . . . . . . . 2.2.5 S u m m a r y of t h e C u r r e n t Work . . . . . . 2.1.1 2.1.2

2.2

CHAPTER 3

.

3.3

3.4

4.2 4.3 4.4

. . . . . . . .

... ... . . . ... ... . . . . . . ...

THEORETICAL MODELS OF HOUSEHOLD VEHICLE OWNERSHIP ANDUTILIZATION

3.3.2

4.1

. . . . . . . .

. . . . 3.2.2 D e r i v a t i o n of t h e I n d i r e c t U t i l i t y F u n c t i o n . 3 . 2 . 3 D y n a m i c D i s c r e t e C h o i c e M o d e l of V e h i c l e Q u a n t i t y and V e h i c l e Type . . . . . . . . . The I n t e r t e m p o r a l Dynamic Model . . . . . . . . . . 3.3.1 T h e U t i l i t y F u n c t i o n a l . . . . . . . . . . .

3.2

CHAPTER 4

Stock Adjustment Models Comprehensive Aggregate Models

. . . . . . . . . . . . T h e H o u s e h o l d ' s V e h i c l e Ownershi'p P r o b l e m . The R e s t r i c t e d Dynamic Model . . . . . . . . 3 . 2 . 1 The Dynamic U t i l i z a t i o n Equation . .

3.1

. . . .

. . . .

. . . .

. . . . . . . .

. . . . . . . .

4 . 3

9 11

11 12

13 14 15 19 21 22

24 24 27 28 31 32 34

T h e I n t e r t e m p o r a l M o d e l a n d t h e Maximum P r i n c i p l e

35 40

......

44

.

50

.............

50

E s t i m a b l e M o d e l s and E c o n o m e t r i c P r o c e d u r e s

.

2

.

COMPARATIVE ANALYSIS OF AVAILABLE DISAGGREGATE DATA Cross-Sectional Household Data

. . . . . . . . . . . . . . . . . . Vehicle Attribute Files . . . . . . . . . . . . . . . . Descripti-on o f D a t a Used i n E s t i m a t i o n . . . . . . . . . Household P a n e l D a t a

(Continued) 4

56 58 59

TABLE OF CONTENTS (CONTINUED)

5.5

........... F i n a l Empirical Specifi'cations . . . . . . . . . . . . . Type Choice Models: S i n g l e - V e h i c l e Households . . . . . Type Choice Models: Two-Vehlcle Households . . . . . . S i n g l e - V e h i c l e Households . V e h i c l e U t i l l ' z a t i o n Models: V e h i c l e U t i l i z a t i o n Models: Two-Vehicle Households . .

5.7

Household V e h l c l e Demand R e s p o n s i v e n e s s

CHAPTER 5

.

5.1 5.2 5.3 5.4

EMPIRICAL E S T I ' M A T I ~AND RESULTS

5.7.1 5.7.2 5.7.3 5.8 CHAPTER 6

O v e r a l l Household ResponsTveness Household R e s p o n s i v e n e s s by V e h i c l e Make Responsiveness t o Manufacturer Offerings

Model S p e c i f i c a t i o n T e s t s

.

APPENDIX A

APPENDIX B

REFERENCES

SUMMARY AND CONCLUSIONS

. .

........ ........

. . . . . . . . . . . . . . . . . . . . . . .

...............

63 63 66 80 89 98

112 112 116 121 126 136

DERIVATION OF THE RESTRICTED DYNAMIC UTILTZATION EQUATION

139

DERIVATTON OF THE INTERTEMPORAL DYNAMIC UTILIZATION EQUATION

142

......................

...................... ............................

146

CHAPTER 1.

INTRODUCTION

H % s t o r i c a l l y , a u t o m o b i l e sales i n t h e U. S

. have

been c h a r a c t e r -

i z e d by a c y c l i c a l p a t t e r n t h a t h a s had a s t r o n g e f f e c t on t h e p r o f i t a b i l i t y and v i a b i l i t y of

automobile manufacturers.

I n more r e c e n t

y e a r s , s i n c e t h e e n e r g y shock of 1979, t h e r e h a s been c o n c e r n t h a t a f u n d a m e n t a l s h i f t i n t h e demand f o r new a u t o m o b i l e s h a s o c c u r r e d . T h i s concern h a s i t s b a s i s i n t h e f a c t t h a t a u t o m o b i l e sales have been d e p r e s s e d f o r t h e t h r e e y e a r s f o l l o w i n g t h e 1979 e n e r g y s h o c k , an u n u s u a l l y l o n g t i m e f o r a t y p i c a l downward s a l e s c y c l e .

The i m p l i c a -

t i o n of a f u n d a m e n t a l downward s h i f t i n t h e demand f o r new a u t o m o b i l e s i s t h a t some d o m e s t i c m a n u f a c t u r e r s may n o t s u r v i v e , a n d i t w i l l b e

n e c e s s a r y f o r t h e i n d u s t r i a l b a s e of t h e U.S. economy t o a d j u s t accordingly. The c u r r e n t s t a t e of t h e U.S. presented i n r e l a t i v e l y short order.

a u t o m o b i l e m a r k e t can be E s s e n t i a l l y , sales of d o m e s t i c

new c a r s r e a c h e d a r e s p e c t a b l e 9 . 3 m i l l i o n u n i t s d u r i n g t h e 1978 c a l e n d a r y e a r w i t h i m p o r t s a l e s a c c o u n t i n g f o r less t h a n 1 8 p e r c e n t of t o t a l sales.

A t t h e t i m e , i t appeared as though t h e d o m e s t i c i n d u s -

t r y had s u c c e s s f u l l y rebounded f r o m t h e 1975 r e c e s s i o n and w a s o f f e r i n g a competitive product l i n e .

However, w i t h t h e e n e r g y shock of J u n e

1979 and t h e c o r r e s p o n d i n g i n c r e a s e s i n f u e l p r i c e s , d o m e s t i c new c a r s a l e s began a s t e a d y d e c l i n e w i t h 8 . 3 , 6 . 6 , 6.2 and 5 . 7 m i l l i o n u n i t s b e i n g s o l d i n t h e 1979, 1 9 8 0 , 1 8 9 1 , and 1982 c a l e n d a r y e a r s r e s p e c t i v e l y . A l s o , t h e p r o p o r t i o n of t o t a l s a l e s a t t r i b u t a b l e

t o f o r e i g n manufact-

u r e r s i n c r e a s e d s t e a d i l y t o n e a r l y 29 p e r c e n t i n c a l e n d a r y e a r 1982,

d e s p i t e t h e v o l u n t a r y import r e s t r i c t i o n s assumed by t h e Japanese m a n u f a c t u r e r s i n A p r i l 1981. L a r g e l y a s a r e s u l t of changing consumer demand d u r i n g t h i s p e r i o d , C h r y s l e r has been f l i r t i n g w i t h bankruptcy and b o t h Ford and

GM have r e c o r d e d r e c o r d l o s s e s .

To d a t e , t h e r e d o e s n o t appear t o be

any s t r o n g i n d i c a t i o n s t h a t t h e r e c e n t p l i g h t of t h e domestic automobile i n d u s t r y i s improving. The o b j e c t i v e of t h e c u r r e n t work i s t o a s s e s s t h e consumer's demand f o r automobiles and t h e manner i n which t h i s demand has changed over time. analysis.

Three a s p e c t s of consumer demand a r e c r i t i c a l t o t h e F i r s t , t h e d e t e r m i n a t i o n of whether or n o t consumer's v a l u a -

t i o n s of v e h i c l e a t t r i b u t e s , such a s f u e l e f f i c i e n c y and c a p i t a l c o s t s , have changed over time w i l l p r o v i d e v a l u a b l e i n s i g h t i n t o t h e underl y i n g d e t e r m i n a n t s of t h e c u r r e n t s t a t e of t h e v e h i c l e market.

Second,

t h e e s t i m a t i o n of e x i s t i n g consumer v a l u a t i o n s of v e h i c l e a t t r i b u t e s

w i l l be u s e f u l i n d e t e r m i n i n g t h e f i n a n c i a l v i a b i l i t y of domestic automobile m a n u f a c t u r e r s .

Finally, establishing the inherent prefer-

e n c e s of consumers f o r s p e c i f i c makes of automobiles ( e . g . Ford, GM, and s o on) w i l l be an i m p o r t a n t concern i n a s s e s s i n g t h e r e c o v e r y p o t e n t i a l of s p e c i f i c automobile manufacturers. To a c h i e v e t h e s e o b j e c t i v e s , t h e c u r r e n t work d e r i v e s and e s t i m a t e s , a t t h e household l e v e l , dynamic econometric models of automobile demand t h a t account f o r t h e household c h o i c e s of v e h i c l e q u a n t i t y (number of v e h i c l e s t o own), v e h i c l e t y p e (by make, model, and v i n t a g e ) , and v e h i c l e u t i l i z a t i o n ( v e h i c l e m i l e s of t r a v e l ) .

These

models a r e e s t i m a t e d w i t h n a t l o n a l d a t a c o v e r i n g t h e t i m e b e f o r e , d u r i n g , and a f t e r t h e J u n e 1979 e n e r g y s h o c k ,

Therefore, t h e empirical

e s t i m a t i o n s w i l l provide valualjle informatfon r e l a t i n g t o t h e determin a n t s of t h e c u r r e n t s t a t e of t h e U . S .

automobile market.

Moreover,

t h e results w i l l b e u s e f u l i n a n a l y z i n g t h e f u t u r e f i n a n c i a l p r o s p e c t s of d e m e s t i c m a n u f a c t u r e r s . T h i s t h e s i s i s o r g a n i z e d i n t h e f o l l o w i n g manner.

Chapter 2

p r e s e n t s a c r i t i c a l r e v i e w of p r e v i o u s a u t o m o b i l e demand r e s e a r c h . The o b j e c t i v e of t h e c h a p t e r i s t o emphasize t h e i n a d e q u a c i e s of p r e v i o u s work i n a d d r e s s i n g t h e h o u s e h o l d v e h i c l e ownership d e c i s i o n making p r o c e s s .

I n C h a p t e r 3 , two p l a u s i b l e t h e o r i e s of h o u s e h o l d

v e h i c l e o w n e r s h i p b e h a v i o r a r e d i s c u s s e d and used a s a b a s i s t o d e r i v e e c o n o m e t r i c a l l y e s t i m a b l e models,

C h a p t e r 4 summarizes a number o f

d a t a s o u r c e s t h a t a r e s u i t a b l e f o r e s t i m a t i n g t h e models d e r i v e d i n C h a p t e r 3 , and p r o v i d e s r e a s o n s f o r s e l e c t i n g and a d e s c r i p t i o n of t h e d a t a a c t u a l l y u s e d f o r model e s t i m a t i o n . The e m p i r i c a l work i s p r e s e n t e d i n C h a p t e r 5 a l o n g w i t h i n t e r p r e t a t i o n s of t h e r e s u l t s .

Finally,

C h a p t e r 6 summarizes t h e m a j o r f i h d i n g s o f t h e Wmk and p r o v i d e s i n s i g h t 2 n t o t h e f u t u r e of t h e d o m e s t i c a u t o m o b i l e i n d u s t r y ,

CHAPTER 2.

CRITICAL REVIEW OF PREVIOUS RESEARCH

I n r e c e n t y e a r s , a l a r g e number of v e h i c l e r e l a t e d r e s e a r c h e f f o r t s have been u n d e r t a k e n i n a n a t t e m p t t o a n a l y z e p a r t i c u l a r i s s u e s r e l a t i n g t o m a r k e t b e h a v i o r and t o p r o v i d e p r o j e c t i o n s of f u t u r e m a r k e t conditions.

The f a c t o r s m o t i v a t i n g p a s t r e s e a r c h e f f o r t s h a v e v a r i e d

considerably over t h e y e a r s , a p p a r e n t l y i n response t o p r e v a i l i n g economic o r r e g u l a t o r y c o n d i t i o n s .

The t r a d i t i o n a l m o t i v a t i o n h a s b e e n

t o p r o v i d e i n f o r m a t i o n t o t h e v e h i c l e i n d u s t r y and government t h a t r e l a t e s t o t h e demand f o r new v e h i c l e s and t h e e f f e c t of v e h i c l e p r i c i n g p o l i c i e s on demand ( s e e R i c h a r d s o n e t a l . (1979) )

.

More r e c e n t l y ,

t h e m o t i v a t i n g f o r c e s h a v e expanded from new v e h i c l e demand p r i c i n g i s s u e s t o i n c l u d e c o n c e r n s r e l a t i n g t o a i r p o l l u t i o n and e n e r g y consumption ( s e e R i c h a r d s o n e t a l . (1980, 1 9 8 2 ) ) .

The a i r p o l l u t ' i o n

c o n c e r n s e v o l v e d o u t of t h e government r e g u l a t i o n s of t h e l a t e S i x t i e s and e a r l y S e v e n t i e s .

Energy consumption became a r e l e v a n t i s s u e a f t e r

t h e p e t r o l e u m s u p p l y d i s r u p t i o n s of 1 9 7 3 and 1979 and t h e new v e h i c l e f u e l e f f i c i e n c y s t a n d a r d s e s t a b l i s h e d by t h e government i n t h e midSeventies. Although t h e m o t i v a t i o n s of r e s e a r c h e f f o r t s have v a r i e d n o t i c e a b l y , two u n d e r l y i n g c o n c e r n s h a v e s e r v e d as a f o c u s f o r a l l v e h i c l e market r e s e a r c h :

1 ) v e h i c l e demand and 2) v e h i c l e u s a g e .

In this

c o n t e x t , v e h i c l e demand may b e viewed as t h e t y p e s (make, model and v i n t a g e ) and q u a n t i t i t i e s of v e h i c l e s e n t e r i n g and s u r v i v i n g i n t h e n a t i o n a l v e h i c l e f l e e t , while v e h i c l e usage r e l a t e s t o b o t h t h e type (e.g.

c i t y , highway) and e x t e n t of v e h i c l e u s e .

Once v e h i c l e demand

and usage concerns a r e determined, t h e i s s u e s d i s c u s s e d above can b e r e a d i l y addressed.

I n comparing v a r i o u s v e h i c l e r e l a t e d r e s e a r c h

e f f o r t s , a d i s t i n c t i o n can be i d e n t i f i e d by c o n s i d e r i n g t h e manner and e x t e n t t o which t h e u n d e r l y i n g concerns of v e h i c l e demand and usage have been a d d r e s s e d .

A t t h e household l e v e l (viewed h e r e a s t h e primary v e h i c l e consumption u n i t ) t h r e e a s p e c t s of v e h i c l e demand and usage a r e v i t a l t o v e h i c l e r e l a t e d r e s e a r c h work.

F i r s t , t h e l e v e l of household v e h i c l e

ownership ( i . e . , number of v e h i c l e s owned) i s c r i t i c a l n o t o n l y due t o the shear

q u a n t i t y of v e h i c l e s owned, b u t a l s o because v e h i c l e

r e p l a c e m e n t b e h a v i o r , e x t e n t of v e h i c l e s p e c i a l i z a t i o n by t y p e , and v e h i c l e u t i l i z a t i o n b e h a v i o r v a r y g r e a t l y w i t h r e s p e c t t o ownership level.

Second, t h e r e i s s t r o n g t h e o r e t i c a l e v i d e n c e t o s u g g e s t t h a t

households s e l e c t v e h i c l e t y p e s and e x t e n t of v e h i c l e u s a g e j o i n t l y . I n t h i s s e n s e a household can be viewed a s s e l e c t i n g v e h i c l e t y p e s w i t h some e x p e c t a t i o n of t h e e x t e n t of t h e i r f u t u r e u s e .

The j o i n t n e s s

of t h e t y p e and usage d e c i s i o n s i s a v i t a l a s p e c t of v e h i c l e demand and usage modeling.

F i n a l l y , t h e dynamic b e h a v i o r of household v e h i c l e

t y p e and usage d e c i s i o n s i s an i m p o r t a n t concern, s i n c e by t h e i r n a t u r e , household v e h i c l e t a s t e s ( p r e f e r e n c e s f o r v e h i c l e a t t r i b u t e s ) e v o l v e over t i m e a s p a s t d e c i s i o n s and f u t u r e e x p e c t a t i o n s a f f e c t current v e h i c l e r e l a t e d choices. I n t h e f o l l o w i n g review, p r e v i o u s r e s e a r c h w i l l b e c a t e g o r i z e d by modeling approach, and c r i t i q u e d w i t h i n t h e v e h i c l e demand and usage framework d e s c r i b e d above.

2.1

A g g r e g a t e Models A g g r e g a t e models h a v e been t h e p r i m a r y v e h i c l e m a r k e t m o d e l i n g

r e s e a r c h a p p r o a c h f o r many y e a r s .

Such models g e n e r a l l y u s e t i m e series

d a t a of a g g r e g a t e v e h i c l e sales, p r i c e s , and p r e v a i l i n g s o c f o economic c o n d i t i o n s i n t h e model c a l i b r a t i o n p r o c e s s ;

t h e y d o n o t ex-

p l i c i t l y a d d r e s s t h e h o u s e h o l d as t h e d e c i s i o n making u n i t , b u t i n s t e a d c o n s i d e r t h e a g g r e g a t e b e h a v i o r of h o u s e h o l d s . The i n i t i a l m o t i v a t i o n , t o p r o v i d e new v e h i c l e d e m a n d / p r i c i n g i n f o r m a t i o n t o b e n e f i t i n d u s t r i a l and g o v e r n m e n t a l p o l i c y d e v e l o p m e n t , s e r v e d as a c a t a l y s t f o r a number of p i o n e e r i n g a g g r e g a t e r e s e a r c h efforts.

These p i o n e e r i n g works, which i n c l u d e Roos and Von S o z l i s k i

( 1 9 3 9 ) , F a r r e l l (19541, and Boulding (1955) l e d t o t h e development of t h e c l a s s i c s t o c k a d j u s t m e n t model, which h a s s e r v e d as a Gasis f o r much of t h e a g g r e g a t e modeling work s i n c e t h e 1 9 5 0 ' s . 2.1.1

S t o c k Adjustment Models

S t o c k a d j u s t m e n t models r e p r e s e n t a n a t t e m p t t o c a p t u r e t h e dynamic a s p e c t s of v e h i c l e c h o i c e a t an a g g r e g a t e l e v e l .

The p r i n c i p l e

u n d e r l y i n g t h e s t o c k a d j u s t m e n t model i s t h a t a t any g i v e n t i m e some d e s i r e d s t o c k of v e h i c l e s e x i s t s ; however, d u e t o t h e t r a n s a c t i o n s costs associated with entering t h e vehicle market, t h i s desired stock i s r e a l i z e d only gradually over t i m e .

T h i s t h e o r y i m p l i e s t h a t due

t o t r a n s a c t i o n s c o s t s , h o u s e h o l d s may n o t change t h e i r v e h i c l e s t o c k s

a t once e v e n i f t h e y d i f f e r from d e s i r e d s t o c k s . j u s t m e n t models assume t h e f o l l o w i n g form:

I n g e n e r a l s t o c k ad-

where: X i s t h e new v e h f c l e demand i n a s p e c i f i e d p e r i o d of t i m e ; t St-l

i s the stock i n t h e preceding t i m e period; S

*

t

i s the desired

s t o c k and i s a f u n c t i o n of v e h i c l e p r i c e s , socioeconomic c o n d i t i o n s , and s o on; 8 i s t h e r a t e of d e p r e c i a t i o n of o l d s t o c k ( i . e . ,

8s

t-1

r e p r e s e n t s r e p l a c e m e n t demand); and k i s t h e a d j u s t m e n t c o e f f i c i e n t r e p r e s e n t i n g t h e f r a c t i o n of t h e d e s i r e d change i n ownership t a k i n g p l a c e i n one t i m e p e r i o d . S t o c k a d j u s t m e n t m o d e l s w e r e f i r s t a p p l i e d t o v e h i c l e demand by Chow (19571, N e r l o v e ( 1 9 5 7 ) , and Brems (1957).

These e a r l y works l e d

t o a series of r e s e a r c h e f f o r t s t h a t a p p l i e d t h e same b a s i c a p p r o a c h , s u c h a s t h e work of S u i t s ( 1 9 5 8 ) , Houthakker and T a y l o r ( 1 9 7 0 ) , Hamburger ( 1 9 6 7 ) , Evans ( 1 9 6 9 ) , S c h a e s s l e r and Smith ( 1 9 7 4 ) , W e s t i n ( 1 9 7 5 ) , and

Eastwood and Anderson (1976).

Although c l a s s i c s t o c k a d j u s t m e n t models c a n b e e a s i l y d e v e l o p e d from r e a i l y a v a i l a b l e d a t a , t h e y h a v e a number of c r i t i c a l d e f i c i e n c i e s . F i r s t , t h e y do n o t a c c o u n t f o r t h e j o i n t n e s s of v e h i c l e c h o i c e and u t i l i z a t i o n . Next, t h e b e h a v i o r a l d i f f e r e n c e a s s o c i a t e d w i t h household ownership l e v e l s i s n o t a d e q u a t e l y a d d r e s s e d .

Finally, t h e i r treatment

of t h e dynamic a s p e c t s o f h o u s e h o l d v e h i c l e ownership ( t h e e v o l u t i o n of v e h i c l e r e l a t e d t a s t e s ) i s r e s t r i c t e d by t h e u s e of a g g r e g a t e d a t a and t h e l i m i t e d t i m e p e r i o d o v e r which s u c h d a t a w e r e o b t a i n e d . 2.1.2

Comprehensive A g g r e g a t e Models

As t h e f a c t o r s m o t i v a t i n g v e h i c l e market r e s e a r c h expanded t o i n c l u d e i s s u e s r e l a t e d t o e n e r g y consumption and a i r p o l l u t i o n , more

e l a b o r a t e models t h a n t h e c l a s s i c s t o c k a d j u s t m e n t models were developed. Such comprehensive a g g r e g a t e models g e n e r a l l y had t h e i r t h e o r e t i c a l f o u n d a t i o n based on t h e s t o c k a d j u s t m e n t approach, b u t were expanded t o i n c l u d e v e h i c l e demand by s i z e c l a s s ( a g g r e g a t e s of makes, models, and v i n t a g e s ) , v e h i c l e u t i l i z a t i o n , and v e h i c l e s c r a p p a g e r a t e s by model Again a g g r e g a t e t i m e series d a t a were used f o r e s t i m a t i o n .

year.

Examples of comprehensive a g g r e g a t e models i n c l u d e t h e works of B u r r i g h t and Evans (1975), Whorf (1975), Kulash (1975), S c h i n e and Loxley ( 1 9 7 7 ) , Wharton (1977), C a s s e l l a (1978), Luckey (1978) and K e n d a l l (1978). The b a s i c translate

d e f i c i e n c i e s of t h e c l a s s i c s t o c k a d j u s t m e n t models

d i r e c t l y t o comprehensive a g g r e g a t e models; i n a d e q u a t e

c o n s i d e r a t i o n of b e h a v i o r a l d i f f e r e n c e s by household v e h i c l e ownership l e v e l s , non-existent

o r s u p e r f i c i a l t r e a t m e n t of t h e i n t e r r e l a t i o n s h i p

between v e h i c l e c h o i c e and u t i l i z a t i o n , a n d l i m i t e d t r e a t m e n t

of t h e

dynamic a s p e c t s of changing consumer t a s t e s .

2.2

D i s a g g r e g a t e Models D i s a g g r e g a t e models of v e h i c l e ownership, which a r e g e n e r a l l y

e s t i m a t e d w i t h household l e v e l d a t a , w e r e developed t o c o r r e c t deficien-cies models.

observed i n t r a d i t i o n a l s t o c k adjustment b a s e d a g g r e g a t e

The u s e of d i s a g g r e g a t e approaches corresponded r o u g h l y t o

t h e development of d i s c r e t e c h o i c e modeling methods, which a r e t h e primary e c o n o m e t r i c t e c h n i q u e s of d i s a g g r e g a t e v e h i c l e ownership modeling. Existing disaggregate analyses are c l a s s i f i e d here i n t o four

c a t e g o r i e s ; 1 ) h o u s e h o l d l e v e l of ownership models ( i , e . , number of v e h i c l e s owned), 2) h o u s e h o l d v e h i c l e t y p e c h o i c e models ( i . e , , make, model, and v i n t a g e ) , 3) v e h i c l e u t i l i z a t i o n m o d e l s , and 4) j o T n t d i s a g g r e g a t e models, t h a t attempt t o account f o r t h e i n t e r r e l a t i o n s h i p s between l e v e l , t y p e , and u t T l 2 z a t i o n .

The m a j o r r e s e a r c h works

i n e a c h o f t h e s e c a t e g o r i e s are reviewed below. 2.2.1

Household L e v e l o f Ownership Models

L e v e l of ownership models were m o t i v a t e d , t o a l a r g e e x t e n t by u r b a n t r a n s p o r t a t i o n modeling r e q u i r e m e n t s imposed by f e d e r a l m a n d a t e s i n t h e mid-1970's,

and b y e n e r g y consumption c o n c e r n s .

The m a j o r

t h r u s t of s u c h modeling e f f o r t s h a s been t o a c c o u n t f o r t h e d i f f e r e n t t r a v e l b e h a v i o r e x h i b i t e d by h o u s e h o l d s a t d i f f e r e n t v e h i c l e o w n e r s h i p levels.

P i o n e e r i n g v e h i c l e level c h o i c e models w e r e concerned w i t h es-

t i m a t i n g t h e p r o b a b i l i t y of a household mqning a s p e c i f i c number of vehicles.

T h i s was a c h i e v e d by e s t i m a t i n g t h e u t i l i t y a s s o c i a t e d

w i t h v a r i o u s ownership l e v e l s ,

Such works g e n e r a l l y u t i l i z e d a

d i s c r e t e c h o i c e model of t h e m u l t i n o m i a l l o g i t form i n which v e h i c l e o w n e r s h i p l e v e l u t i l i t i e s were a f u n c t i o n of s u c h f a c t o r s as a u t o m o b i l e p r i c e , h o u s e h o l d income, and h o u s e h o l d t r a v e l a c c e s s i b i l i t y . of models of t h i s t y p e i n c l u d e t h o s e u d B u r n s , Go!ob,

and

Examples

Nicolaidis

(19761, and Golob and Burns (1978). S u b s e q u e n t v e h i c l e ownership l e v e l models viewed t h e h o u s e h o l d d e c i s i o n of v e h i c l e ownership t o b e d e t e r m i n e d j o i n t l y w i t h o t h e r transportation related decisions.

Examples of t h i s i n c l u d e t h e j o i n t

work t r i p mode c h o i c e and v e h i c l e ownership l e v e l model o f Lerman and

Ben-Akiva

(1976), and t h e j o i n t l o c a t i o n and t y p e of r e s i d e n c e , work

t r i p mode c h o i c e and v e h i c l e ownership l e v e l model of Lerman (1976). Both of t h e s e models were of t h e multinomial l o g i t form.

In later

work, T r a i n (1980) e s t i m a t e d a work t r i p mode choice and v e h i c l e ownership l e v e l model along t h e same l i n e s a s t h e Lerman and Ben-Akiva work, b u t used a s e q u e n t i a l l o g i t model t o a l l e v i a t e p o s s i b l e I1independence of i r r e l e v a n t a l t e r n a t i v e s " (IIA) v i o l a t i o n s . U n f o r t u n a t e l y , t h e owner s h i p l e v e l models, w h i l e overcoming t h e i n a b i l i t y of t r a d i t i o n a l a g g r e g a t e models t o account f o r b e h a v i o r a l d i f f e r e n c e s by household ownership l e v e l , s t i l l s u f f e r from a number of major shortcomings.

F i r s t , t h e models do n o t i n c o r p o r a t e v e h i c l e

t y p e (make, model, and v i n t a g e ) i n f o r m a t i o n .

Therefore, i s s u e s r e l a t i n g

t o v e h i c l e t y p e s p e c i a l i z a t i o n by household l e v e l and subsequent energy and a i r p o l l u t i o n i n f o r m a t i o n t h a t can be d e r i v e d only from t h e c h a r a c t e r i s t i c s of i n d i v i d u a l v e h i c l e t y p e s ( e . g . , engine emissions)

,

can n o t be a s s e s s e d .

fuel

efficiency,

Second, t h e l a c k of v e h i c l e

t y p e c o n s i d e r a t i o n p r e c l u d e s e v a l u a t i o n of t h e j o i n t r e l a t i o n s h i p between v e h i c l e t y p e and u t i l i z a t i o n .

F i n a l l y , t h e models a r e s t a t i c , e s t i m a t e d

w i t h c r o s s s e c t i o n a l d a t a , and completely i g n o r e t h e e f f e c t of changing t a s t e s on household v e h i c l e c h o i c e and usage d e c i s i o n s . 2.2.2

Household V e h i c l e Type Choice Models

D i s a g g r e g a t e t y p e c h o i c e models were motivated by t h e need t o determine s p e c i f i c components of v e h i c l e demand s o t h a t t h e p r o p a g a t i o n of new v e h i c l e t e c h n o l o g i e s , such a s h i g h f u e l e f f i c i e n c y v e h i c l e s , could be determined i n t h e n a t i o n a l v e h i c l e f l e e t .

In t h i s regard,

t y p e c h o i c e models were developed t o overcome some of t h e d e f i c i e n c i e s of b o t h a g g r e g a t e s t o c k a d j u s t m e n t models and d i s a g g r e g a t e ownership l e v e l models by e x p l i c i t l y a c c o u n t i n g f o r t h e v e h i c l e t y p e c h o i c e a s p e c t of t h e household d e c i s i o n making p r o c e s s . The e a r l i e s t d i s a g g r e g a t e t y p e choice work w a s t h a t of Laye and T r a i n (1976, 1 9 7 9 ) , i n which t h e y e s t i m a t e a multinomial l o g i t model and p r o v i d e f o r household c h o i c e among t e n new v e h i c l e c l a s s e s ( i . e . a g g r e g a t e s of make and model), conditioned on t h e f a c t t h a t t h e p u r c h a s e of a new v e h i c l e i s t o be made.

I n subsequent work, Manski and Sherman

(1980) e s t i m a t e t r u e t y p e c h o i c e models i n which households s e l e c t s p e c i f i c makes, models, and v i n t a g e s from both new and used v e h i c l e market o f f e r i n g s .

The model i s

of t h e multinomial l o g i t form, and

d i f f e r e n t t y p e choice models were e s t i m a t e d f o r d i f f e r e n t ownership l e v e l s , i n r e c o g n i t i o n of t h e b e h a v i o r a l d i f f e r e n c e s among household ownership l e v e l s , a s d i s c u s s e d e a r l i e r .

Moreover, t h e Manski/

Sherman model made an a t t e m p t t o c a p t u r e t h e dynamic behavior of household v e h i c l e ownership by i n c l u d i n g a lagged dummy v a r i a b l e i n t h e u t i l i t y f u n c t i o n of t h e v e h i c l e t y p e s owned i n t h e p r e c e d i n g time period.

The model was e s t i m a t e d w i t h c r a s s s e c t i o n a l d a t a t h a t

i n c l u d e d i n f o r m a t i o n on household v e h i c l e h o l d i n g s and socioeconomic condit i o n s . The a t t e m p t t o c a p t u r e dynamic behavior by i n c l u s i o n of t h e lagged dummy v a r i a b l e h a s no t h e o r e t i c a l j u s t i f i c a t i o n and i s n o t an a p p r o p r i a t e method of a d d r e s s i n g t h e e v o l u t i o n of household vehicle tastes.

To a s s e r t t h a t household t a s t e s a r e determined only

from t h e ownership of s p e c i f i c v e h i c l e t y p e s i s c l e a r l y a s i m p l i f i c a t i o n

16

of t h e p r o c e s s , as

c u r r e n t and e x p e c t e d f u e l c o s t s and t h e

c h a r a c t e r i s t i c s of v e h i c l e s owned b y t h e household can a l s o be expected i o i n f l u e n c e tastes.

T h e r e f o r e , a l t h o u g h t h e u s e of s u c h

dummy v a r i a b l e s h a s b e e n found t o have s u b s t a n t i a l s t a t i s t i c a l s i g n i f i c a n c e , t h e y a r e an, i m p r e c i s e measure o f dynamic b e h a v i o r . A s i d e from t h i s p o i n t , t h e M a n s k i / ~ h e r m a n model s u f f e r s from two a d d i t i o n a l weaknesses.

F i r s t , t h e i n t e r a c t i o n between v e h i c l e t y p e

c h o i c e and u t i l i z a t i o n i s n o t t a k e n i n t o a c c o u n t .

Since t h e choice

of v e h i c l e t y p e s i s made j o i n t l y w i t h u s e , t h e a b s e n c e of a t y p e c h o i c e / usage i n t e r a c t i o n i s a

serious limitation.

S e c o n d , t h e manner

i n which m u l t i v e h i c l e h o u s e h o l d s a r e a d d r e s s e d i s i n a d e q u a t e , a s t h e y deploy t h e concept of a composite v e h i c l e ( i . e . ,

a fictitious vehicle

comprised of t h e b e s t a t t r i b u t e s o f t h e t r u e h o u s e h o l d v e h i c l e t y p e s ) , which h a s n o

theoretical justification.

Moreover, t h e f a c t t h a t m u l t i -

v e h i c l e h o u s e h o l d s a c c o u n t f o r o v e r 80% of t o t a l h o u s e h o l d v e h i c l e h o l d i n g s i n t h e U n i t e d S t a t e s (Mannering ( 1 9 8 1 ) ) makes t h e i m p o r t a n c e o f p r o p e r t h e o r e t i c a l t r e a t m e n t of t h e m u l t i v e h i c l e h o u s e h o l d o b v i o u s . I n an a t t e m p t t o overcome some o f t h e d e f i c i e n c i e s of t h e Manski and Sherman work, B e r k o v e c and R u s t (1981) e s t i m a t e a n e s t e d l o g i t model i n which h o u s e h o l d s a r e assumed t o f i r s t s e l e c t a c l a s s of v e h i c l e t y p e , and t h e n a s p e c i f i c v e h i c l e t y p e w i t h i n t h e c l a s s chosen.

The work p r e -

s e n t s a t h e o r e t i c a l framework f o r p r o p e r l y a d d r e s s i n g v e h i c l e t y p e and u s a g e i n t e r a c t i o n s , b u t t h e e m p i r i c a l work does n o t c o n s i d e r t h i s i n t e r action.

Moreover, Berkovec and R u s t used t h e same t h e o r e t i c a l l y

q u e s t i o n a b l e l a g g e d dummy v a r i a b l e , as d i d Manski and Sherman, t o

account f o r t h e dynamics of household b e h a v i o r .

(Again, t h e y had

only c r o s s s e c t i o n a l d a t a w i t h i n f o r m a t i o n on v e h i c l e h o l d i n g s i n t h e preceding y e a r ) .

I n summary, t h e Berkovec and Rust work, by i t s u s e of

a s e q u e n t i a l l o g i t model a s opposed t o a s i n g l e - l e v e l m u l t i n o m i a l l o g i t model, can be considered a s t a t i s t i c a l improvement over t h e Manski/ Sherman models ( a s i t a l l e v i a t e s same of t h e p o s s i b l e I I A v i o l a t i o n s ) , b u t n o t a t h e o r e t i c a l improvement.

Moreover, Berkovec and Rust only

c o n s i d e r s i n g l e v e h i c l e households i n t h e i r a n a l y s i s , t h e r e b y p r o v i d i n g no i n s i g h t i n t o t h e b e h a v i o r of m u l t i v e h i c l e households, which a r e t h e dominant s e c t o r i n t h e U.S. market. Whereas t h e Manski/Sherman and Berkovec/Rust models were s t r u c t u r e d such t h a t t h e d e c i s i o n t o a c q u i r e a c a r and t h e t y p e of c a r acq u i r e d were considered j o i n t l y , t h e work of Hocherman , P r a s h k e r Ben-Akiva structure.

,

and

(1982) s e p a r a t e t h e two d e c i s i o n s w i t h a n e s t e d l o g i t The Hocherman models were e s t i m a t e d w i t h a 1978 c r o s s -

s e c t i o n a l sample of I s r a e l i households.

Due t o t h e s m a l l p e r c e n t a g e

of m u l t i v e h i c l e households i n I s r a e l , o n l y s i n g l e v e h i c l e households were considered i n t h e a n a l y s i s .

S t a t i s t i c a l l y , the nested s t r u c t u r e

proposed by Hocherman a p p e a r s t o be an improvement over t h e

an ski/

Sherman s t r u c t u r e , a s a g r e a t e r number of v e h i c l e a t t r i b u t e s were found t o s i g n i f i c a n t l y i n f l u e n c e t h e choice of v e h i c l e type (make, model, and vintage).

The shortcomings of t h e Hocherman model i n c l u d e t h e non-

c o n s i d e r a t i o n of v e h i c l e type and usage i n t e r a c t i o n s and t h e t h e o r e t i c a l l y q u e s t i o n a b l e t r e a t m e n t of t h e dynamics of household v e h i c l e ownership.

Again, t h e t r e a t m e n t of dynamics i n t h e Hocherman work i s

based on t h e lagged dummy v a r i a b l e approach used by Pfanski and Sherman, w i t h t h e r e s u l t b e i n g t h e same Smprecise measure of changing tastes. With a s t r u c t u r e s i m i l a r t o t h a t developed by Hocheman, P r a s h k e r , and Ben-Akiva, Hensher and M a n s f i e l d (1982) e s t i m a t e d a n e s t e d l o g i t a c q u i s i t i o n c h o i c e / t y p e c h o i c e model u s i n g A u s t r a l i a n d a t a .

Only

t h r e e c l a s s e s ( a g g r e g a t e s of t y p e ) of v e h i c l e s were c o n s i d e r e d , and t h e s e were c l a s s i f i e d by v e h i c l e f u e l

efficiency (i.e.

low, medium, and h i g h ) .

Aside from t h i s v e r y l i m i t e d c h o i c e of v e h i c l e t y p e , t h e t r e a t m e n t of dynamics was v i r t u a l l y n o n - e x i s t e n t

a s was t h e e f f e c t o f : 1 ) t h e v e h i c l e

t y p e and usage i n t e r a c t i o n s and 2) t h e c h o i c e of ownership l e v e l . 2.2.3

Household V e h i c l e U t i l i z a t i o n Models

V e h i c l e u t i l i z a t i o n models were motivated l a r g e l y by t h e nedd t o f o r e c a s t energy consumption.

U t i l l z a t i o n models can be c a t e g o r i z e d

i n t o t h o s e based on t h e d i s c r e t e c h o i c e of i n d i v i d u a l t r i p s and t h o s e t h a t view v e h i c l e m i l e s of t r a v e l a s a continuous v a r i a b l e . C l a s s i c examples of t h e d i s c r e t e choice approach t o v e h i c l e u t i l i z a t i o n i n c l u d e t h e modeling systems developed by Cambridge S y s t e m a t i c s (1976, 1979).

These modeling systems were e s t i m a t e d w i t h

r e g i o n a l d a t a samples ( e . g . Washington, San F r a n c i s c o ) .

The d e t e r -

m i n a t i o n of v e h i c l e u t i l i z a t i o n (VMT) was d e r i v e d from work t r i p and non-work t r i p modal c h o i c e models (e. g. choice of d r i v e a l o n e , shared r i d e , o r t r a n s i t ) and non-work t r i p g e n e r a t i o n and d e s t i n a t i o n choice models,

U n f o r t u n a t e l y , such a modeling approach i s d e f i c i e n t i n a number

of i m p o r t a n t ways.

F i r s t , t h e t r e a t m e n t of t h e i n t e r a c t i o n s between

v e h i c l e ownership l e v e l , v e h i c l e t y p e , and v e h i c l e u t i l i z a t i o n a r e

v i r t u a l l y ignored.

N e x t , t h e dynamic a s p e c t s i n f l u e n c i n g v e h i c l e

ownership and t h e i r i m p a c t on v e h i c l e u t i l i z a t i o n a r e n o t a d d r e s s e d . F i n a l l y , s u c h an a p p r o a c h d o e s n o t a s s i g n u t i l i z a t i o n (VMT) t o s p e c i f i c v e h i c l e s w i t h i n m u l t i v e h i c l e households.

This last p o i n t i s a

p o t e n t i a l l y s e r i o u s f l a w s i n c e f u e l consumption i s a f u n c t i o n of t h e e x t e n t t o which s p e c i f i c v e h i c l e t y p e s (make, model, and v i n t a g e )

are u s e d . The m o d e l i n g of v e h i c l e m i l e s of t r a v e l a s a c o n t i n u o u s v a r i a b l e a t t h e h o u s e h o l d l e v e l h a s b e e n u n d e r t a k e n by o n l y a few r e s e a r c h e r s . An example of t y p i c a l work i n t h i s a r e a i s t h e h o u s e h o l d VMT model e s t i m a t e d by C h a r l e s R i v e r A s s o c i a t e s (1978).

Unfortunately, t h e

C h a r l e s R i v e r work s u f f e r s from t h e same weaknesses as t h e d i s c r e t e c h o i c e a p p r o a c h e s d i s c u s s e d above.

I n a n e f f o r t t o overcome some of t h e

w e a k n e s s e s of p r e v i o u s h a u s e h o l d v e h i c l e u t i l i z a t i o n m o d e l s , Mannering (1983) e s t i m a t e d a model of v e h i c l e u s e i n m u l t i v e h i c l e h o u s e h o l d s i n which u t i l i z a t i o n was a s s i g n e d t o s p e c i f i c h o u s e h o l d v e h i c l e s .

The

model was e s t i m a t e d w i t h n a t i o n a l U.S. d a t a c o l l e c t e d d u r i n g t h e months of September, O c t o b e r , and November, 1979, and an e q u a t i o n s y s t e m was e s t i m a t e d t o model t h e a l l o c a t i o n of v e h i c l e u s e t o i n d i v i d u a l household v e l l i c l e s .

A l t h o u g h t h e model p r o v i d e s p o t e n t i a l l y u s e f u l

i n s i g h t i n t o v e h i c l e u s e i n m u l t i v e h i c l e households, t h e treatment of t h e i n t e r r e l a t i o n s h i p s between l e v e l , t y p e , and u t i l i z a t i o n are l i m i t e d , and t h e dynamic a s p e c t s o f v e h i c l e ownership are n o t a d d r e s s e d .

2,2,4

J o i n t D i s a g g r e g a t e Models

In r e c o g n i t i o n of t h e f a c t t h a t t h e household v e h i c l e c h o i c e s of l e v e l , t y p e , and u t i l i z a t i o n a r e i n t e r r e l a t e d , a number of r e s e a r c h e f f o r t s have a t t e m p t e d t o e x p l i c i t l y account f o r t h e s e interrelationships.

P e r h a p s t h e e a r l i e s t work i n t h i s d i r e c t i o n i s

t h e simultaneous number of c a r s , new o r used c a r choice model of Johnson (1978).

The Johnson s p e c i f i c a t i o n was of t h e m u l t i n o m i a l

l o g i t form a n d , a l t h o u g h h i s d e f i n i t i o n of v e h i c l e type was r a t h e r crude (new o r u s e d ) , t h e f a c t t h a t t h e r e l a t i o n s h i p between v e h i c l e l e v e l and t y p e was accounted f o r i s s i g n i f i c a n t .

Johnson made no

attempt t o account f o r dynamic b e h a v i o r .

In more r e c e n t work, Booz, A l l e n

& Hamilton (1983) e s t i m a t e a n e s t e d

l o g i t s t r u c t u r e w i t h c h o i c e of l e v e l and choice of type (make, model, and v i n t a g e ) ,

The t y p e c h o i c e model f o l l o w s t h a t of Manski and

Sherman (1980) and t h e l e v e l choices of z e r o , one, o r two v e h i c l e s a r e considered.

The Booz, A l l e n , & Hamilton s p e c i f i c a t i o n i n d i c a t e d

t h a t t h e e f f e c t of t y p e c h o i c e on l e v e l choice i s minimal.

T h i s some-

what c o u n t e r i n t u i t i v e f i n d i n g may be e x p l a i n e d by a number of d e f i c i e n c i e s i n t h e model s t r u c t u r e .

F i r s t , v e h i c l e u t i l i z a t i o n was i n -

c o r r e c t l y viewed a s an exogenous v a r i a b l e i n t h e t y p e c h o i c e s p e c i f i c a tions.

T h i s of c o u r s e s h o u l d be t r e a t e d a s an endogenous v a r i a b l e and

be e x p l i c i t l y modeled a s s u c h .

Perhaps more i m p o r t a n t l y , t h e dynamic

a s p e c t s of t h e v e h i c l e ownership problem were v i r t u a l l y ignored i n Booz, A l l e n & Hamilton work.

The only known work t h a t a t t e m p t s t o account f o r a l l of t h e i-ntera c t i o n s between v e h i c l e l e v e l , t y p e , and u t i l i z a t i o n , i s t h a t of T r a i n and Lohrer (1982).

T h e i r modeling system i n c l u d e s household c h o i c e s o f :

1 ) v e h i c l e l e v e l f o r z e r o , one, and two v e h i c l e s , 2) v e h i c l e t y p e d e f i n e d by c l a s s e s ( a g g r e g a t e s of make, model, and v i n t a g e ] , and

3 ) v e h i c l e u t i l i z a t i o n (aver a one-year p e r i o d ) of t h e chosen v e h i c l e class i n miles.

Although t h e T r a i n and Lohrer e f f o r t r e p r e s e n t s - an

advance i n t h a t t h e i n t e r r e l a t i o n s h i p s between t h e c r i t i c a l a s p e c t s of household v e h i c l e ownership a r e e x p l i c i t l y accounted f o r , t h e work s u f f e r s from two c r i t i c a l d e f i c i e n c i e s ,

F i r s t , by c o n s i d e r i n g o n l y

a g g r e g a t e s of v e h i c l e makes, models, and v i n t a g e s ( c l a s s e s ) , p o t e n t i a l l y r i c h i n f o r m a t i o n on v e h i c l e a t t r i b u t e s and v e h i c l e brand p r e f e r ences i s ignored.

Second, T r a i n and Lohrer u s e t h e same dummy v a r i a b l e

t o c a p t u r e t h e dynamics of v e h i c l e ownership a s d i d Manski and Sherman (1980) ( i . e . i n t h i s c a s e , one i f t h e

v e h i c l e c l a s s was n o t owned

i n t h e p r e c e d i n g time p e r i o d and z e r o o t h e r w i s e ) .

The f a u l t s of t h i s

approach t o dynamics i n a t r u e t y p e c h o i c e model ( i . e .

choice among

makes, models, and v i n t a g e s ) have been d i s c u s s e d a t l e n g t h e a r l i e r . I n a c l a s s c h o i c e model of t h e T r a i n and Lohrer v a r i e t y , t h i s d u m y v a r i a b l e approach t o dynamics i s even l e s s v a l i d s i n c e changes i n t h e t y p e (make, model, o r v i n t a g e ) of a v e h i c l e owned w i t h i n t h e same c l a s s i s simply n o t accounted f o r i n t h e model s t r u c t u r e .

2.2.5

Summary of t h e Current Work

The o b j e c t i v e of t h e r e s e a r c h p r e s e n t e d h e r e i n i s t o overcome what a r e thought t o be t h e c r i t i c a l d e f i c i e n c i e s of p r e v i o u s work

u n d e r t a k e n i n t h e a u t o m o b i l e demand a r e a .

To a c h i e v e t h i s , a

d i s a g g r e g a t e , h o u s e h o l d l e v e l m o d e l i n g approach i s u s e d .

It s h o u l d

b e c l e a r from t h e p r e c e d i n g l i t e r a t u r e r e v i e w t h a t a d i s a g g r e g a t e approach o f f e r s many a d v a n t a g e s , a s opposed t o t r a d i t i o n a l a g g r e g a t e a p p r o a c h e s , i n t e r m s of e x p l a i n i n g u n d e r l y i n g b e h a v i o r .

Also, t h e

c u r r e n t r e s e a r c h v i e w s t h e dynamic a s p e c t s of h o u s e h o l d v e h i c l e owners h i p as t h e e v o l u t i o n o f h o u s e h o l d t a s t e s .

From t h i s v i e w , e s t i m a b l e

models a r e d e r i v e d u s i n g a p p r o p r i a t e economic t h e o r y r e l a t i n g t o t a s t e changes.

F i n a l l y , e x p l i c i t account i s given t o t h e i n t e r r e l a t i o n s h i p s

between t h e h o u s e h o l d c h o i c e s of q u a n t i t y of v e h i c l e s , v e h i c l e t y p e (make, m o d e l , and v i n t a g e ) , and v e h i c l e u t i l i z a t i o n . It i s a s s e r t e d t h a t t h e c u r r e n t work, by a d d r e s s i n g t h e w e a k n e s s e s

of p r e v i o u s a u t o m o b i l e demand r e s e a r c h , w i l l p r o v i d e v a l u a b l e i n s i g h t i n t o h o u s e h o l d v e h i c l e o w n e r s h i p b e h a v i o r and t o t h e f i n a n c i a l v i a b i l i t y of d o m e s t i c a u t o m o b i l e m a n u f a c t u r e r s .

CHAPTER 3.

THEORETICAL MODELS OF HOUSEHOLD VEHICLE OWNERSHIP AND UTILIZATION

T h i s c h a p t e r i s comprised of f o u r p r i m a r y s e c t i o n s .

In the

f i r s t s e c t i o n , a g e n e r a l d i s c u s s i o n of t h e h o u s e h o l d ' s v e h i c l e owners h i p problem i s g i v e n .

The o b j e c t i v e h e r e i s t o p r e s e n t t h e r e a d e r

w i t h an i n t u i t i v e s e n s e of t h e dimensions of t h e household v e h i c l e ownership d e c i s i o n .

The f o l l o w i n g two s e c t i o n s a r e devoted t o t h e

development of a l t e r n a t e t h e o r i e s of household v e h i c l e ownership behavior.

Based on t h e s e t h e o r i e s , e c o n o m e t r i c a l l y e s t i m a b l e

models a r e d e r i v e d .

The f i n a l s e c t i o n d e s c r i b e s e c o n o m e t r i c pro-

c e d u r e s t h a t a r e used i n t h e e v e n t u a l e s t i m a t i o n o f t h e d e r i v e d models. 3.1

The Household ' s V e h i c l e Ownership Problem I n g e n e r a l , household c h o i c e s of v e h i c l e q u a n t i t y , v e h i c l e

t y p e and v e h i c l e u t i l i z a t i o n a r e made w i t h t h e i n t e n t of a c h i e v i n g some o p t i m a l p a t t e r n of t r i p g e n e r a t i n g a c t i v i t i e s given t h r e e a r e a s of concern:

1) socioeconomic f a c t o r s , 2 ) exogenous economic c o n d i t i o n s

and 3) dynamic c o n s i d e r a t i o n s .

Socioeconomic f a c t o r s comprise a

b r o a d r a n g e of c h a r a c t e r i s t i c s , such a s household income and household compositio?,that needs.

a f f e c t household a c t i v i t i e s and v e h i c l e ownership

Exogenous economic c o n d i t i o n s i n c l u d e t h e c o s t of petroleum

p r o d u c t s and v e h i c l e p r i c e s i n new and u s e d c a r m a r k e t s .

The dynamic

c o n s i d e r a t i o n s of t h e h o u s e h o l d ' s v e h i c l e ownership problem a r i s e from t h e e v o l u t i o n of household t a s t e s over t i m e .

T h i s concept of changing

household t a s t e s , which h a s been virtually overlooked i n p r e v i o u s

a u t o m o b i l e demand l i t e r a t u r e , f o r m s t h e EasTs f o r t h e model d e r i v a t i o n s p r e s e n t e d i n t h i s work. I n t u i t i v e l y , t a s t e c h a n g e s can b e e x p e c t e d t o a r i s e from a number of s o u r c e s . and c o l l e c t i n g

In p a r t i c u l a r , h o u s e h o l d s can b e viewed as l e a r n i n g

i n f o r m a t i o n from p a s t e x p e r i e n c e s w i t h a s p e c i f i c

v e h i c l e o r make of v e h i c l e , t h e r e b y forming a b a s i s f o r t a s t e c h a n g e s . O t h e r s o u r c e s of t a s t e c h a n g e s i n c l u d e t h o s e r e s u l t i n g from a d v e r t i s i n g and t h e i n f o r m a t i o n c o l l e c t e d from c o n t a c t w i t h o t h e r v e h i c l e owners. Although t h e r e i s a n abundance of economic l i t e r a t u r e t h a t a d d r e s s e s t h e i s s u e of a c c o u n t i n g f o r t a s t e changes i n u t i l i t y f u n c t i o n s ( s e e , f o r example, P e s t o n ( 1 9 6 7 ) , Gorman ( 1 9 6 7 ) , F i s h e r and S h e l l ( 1 9 6 9 ) , P o l l a k and Wales ( 1 9 6 9 ) , P o l l a k ( 1 9 7 0 ) , P h l i p s (1972) and Lluch (1974)) ,, e s s e n t i a l l y , two b a s i c a p p r o a c h e s have b e e n used.

The f i r s t a p p r o a c h

w a s t h a t used by b o t h P e s t o n (1967) and Gorman (1967).

T h e i r work

c o n s i d e r s u t i l i t y f u n c t i o n s of t h e form

where t h e x ' s r e p r e s e n t q u a n t i t i e s of t h e commodities t h a t are consumed, and t h e A and 6 ' s a r e p a r a m e t e r s .

To i n t r o d u c e t a s t e c h a n g e s , ; t h e

e x p o n e n t s i n E q u a t i o n (1) a r e p e r m i t t e d t o b e f u n c t i o n s of t i m e s u c h that 'it x '2t Ut - A X l t 2 t

u n d e r t h e a s s u m p t i o n t h a t t h e consumer i s l e a r n i n g from p a s t e x p e r i e n c e s , t h i s approach a d o p t s t h e f o l l o w i n g l e a r n i n g f u n c t i o n s

(see Peston (1967)):

where t h e s u b s c r i p t s t-1 d e n o t e consumption i n t h e p r e c e d i n g t i m e p e r i o d . Although t h i s a p p r o a c h h a s t h e a d v a n t a g e of e x p l i c i t l y a c c o u n t i n g f o r

t a s t e c h a n g e s , i t s u f f e r s f r o m t h e f a c t t h a t t h e f u n c t i o n a l form used makes t h e d e r i v a t i o n of e s t i m a b l e commodity demand e q u a t i o n s e x c e e d i n g l y d i f f i c u l t , i f not impossible. With l i m i t a t i o n s of t h e P e s t o n t y p e t a s t e change f o r m u l a t i o n i n mind, a more f r u i t f u l a p p r o a c h was developed and a p p l i e d by F i s h e r and S h e l l ( 1 9 6 9 ) , P o l l a k and Wales ( 1 9 6 9 ) , and P o l l a k ( 1 9 7 0 ) .

The

s t a r t i n g p o i n t f o r t h i s a p p r o a c h i s t o c o n s i d e r u t i l i t y f u n c t i o n s of t h e following fonn

where t h e x ' s r e p r e s e n t q u a n t i t i e s of t h e c o m o d i t i e s t h a t are consumed i and a

i

and bit d e n o t e p a r a m e t e r s , w i t h t h e l a t t e r c o n t r o l l i n g f o r t a s t e

changes o v e r t i m e .

I n t h i s r e g a r d , t h e t a s t e change p a r a m e t e r b

b e any f u n c t i o n o f t i m e o r p a s t consumption.

it

can

Unlike t h e Peston type

t a s t e change f o r m u l a t i o n , a c c o u n t i n g f o r t a s t e changes i n t h e manner i m p l i e d by E q u a t i o n ( 4 ) p e r m i t s t h e d e r i v a t i o n of dynamic commodity demand e q u a t i o n s w i t h r e l a t i v e ease ( s e e P o l l a k and Wales (1969) and P o l l a k (1970)).

F o r t h i s r e a s o n , t h e a n a l y s i s of v e h i c l e ownership

i n t h i s s t u d y f o l l o w s from t h e i d e a e x p r e s s e d i n E q u a t i o n ( 4 ) .

To i n c o r p o r a t e t a s t e changes i n t h e case of household v e h i c l e ownership, t h e c u r r e n t a n a l y s i s assumes t h a t such changes a r e determined s o l e l y by p a s t d e c i s i o n s .

S p e c i f i c a l l y , i t i s assumed t h a t t a s t e changes

a r e determined by t h e p a s t u t i l i z a t i o n of s p e c i f i c v e h i c l e s o p e r a t e d by t h e household.

T h i s i m p l i e s t h a t t h e household can b e viewed a s

developing " h a b i t s " of v e h i c l e ownership based on i t s p a s t e x p e r i e n c e s w i t h s p e c i f i c v e h i c l e s ( i . e . e x t e n t of u t i l i z a t i o n ) . v a r i a b l e i s defined, Sit,

If a state

t h a t summarizes p a s t u t i l i z a t i o n r e l e v a n t t o

v e h i c l e i a t time t , t h e n t a s t e changes can be i n t r o d u c e d i n t o t h e f u n c t i o n a l form of Equation C4) by t h e simple l i n e a r e x p r e s s i o n

where 0

i

and ai a r e p a r a m e t e r s .

The p r e c i s e d e f i n i t i o n of t h e s t a t e

v a r i a b l e , a l o n g w i t h t h e development of a l t e r n a t i v e dynamic v e h i c l e ownership models t h a t account f o r t a s t e changes, i s given i n t h e n e x t section.

3.2

The R e s t r i c t e d Dynamic Model The r e s t r i c t e d dynamic model p e r m i t s households t o c o n s i d e r

t h e e f f e c t s of p a s t behavior on c u r r e n t t a s t e s b u t assumes t h a t t h e y d o n o t c o n s i d e r t h e e f f e c t t h a t c u r r e n t consumption w i l l have on f u t u r e utility.

T h i s somewhat u n r e a l i s t i c assumption w i l l be r e l a x e d l a t e r

w i t h t h e i n t e r t e m p o r a l dynamic model, b u t t h e c o s t of t h i s r e l a x a t i o n i n terms of a d d i t i o n a l l i m i t a t i o n s t h a t must be imposed on t h e d e c i s i o n making p r o c e s s w i l l be shown t o be h i g h . I n t h e development of t h e r e s t r i c t e d dynamic model, a f o u r - s t e p

procedure i s used i n which t h e household's

c h o i c e s of v e h i c l e q u a n t i t y ,

v e h i c l e t y p e , and v e h i c l e u t i l i z a t i o n a r e viewed as contemporaneous. The p r o c e d u r e b e g i n s by s p e c i f y i h g a dynamic u t i l i z a t i o n e q u a t i o n which i s then transformed t o be measurable i n a l l v a r i a b l e s .

Using t h e

d e r i v e d dynamic u t i l i z a t i o n e q u a t i o n , Roy's I d e n t i t y i s a p p l i e d t o r e c o v e r t h e corresponding i n d i r e c t u t i l i t y f u n c t i o n .

F i n a l l y , a dynamic

d i s c r e t e c h o i c e model of v e h i c l e q u a n t i t y and v e h i c l e t y p e i s o b t a i n e d from t h e i n d i r e c t u t i l i t y f u n c t i o n 3.2.1.

The Dynamic U t i l i z a t i o n Equation

To develop a p p r o p r i a t e household v e h i c l e ownership models, t a s t e changes a r e i n c o r p o r a t e d d i r e c t l y i n t o t h e demand e q u a t i o n ( i n t h i s c a s e t h e u t i l i z a t i o n e q u a t i o n ) a s opposed t o t h e more t r a d i t i o n a l method d e s c r i b e d e a r l i e r of f i r s t i n c o r p o r a t i n g t a s t e changes i n t h e d i r e c t u t i l i t y f u n c t i o n and t h e n d e r i v i n g t h e corresponding demand e q u a t i o n s . The advantages of a d d r e s s i n g t a s t e changes i n t h i s manner w i l l become a p p a r e n t a s t h e model d e r i v a t i o n s a r e p r e s e n t e d . To b e g i n , c o n s i d e r a household s e l e c t i n g only one v e h i c l e from t h e s e t of a v a i l a b l e v e h i c l e t y p e s (make, model, and v i n t a g e ) . m u l t i v e h i c l e ownership c a s e w i l l be addressed l a t e r .

The

I f i t i s assumed

t h a t t a s t e changes a r e determined by p r e v i o u s c h o i c e s o n l y , t h e n t h e dynamic u t i l i z a t i o n e q u a t i o n can be w r i t t e n a s

x

it

= T

i

+Bi(It - .Cit) + ai S i t ,

where x

it

come, Cit

i s t h e r a t e of u t i l i z a t i o n of v e h i c l e i , I i s t h e r a t e of v e h i c l e o p e r a t i n g c o s t ,

, a t time t , and T ~ Bi,

and ct a r e parameters. i

'it

i s t h e r a t e of i n -

t

is t h e s t a t e v a r i a b l e

Recall t h a t the s t a t e

v a r i a b l e i s i n t e n d e d t o "summarize" p a s t u t i l i z a t i o n r e l e v a n t t o v e h i c l e i.

Consequently, i t i s n o t measurable i n t h e t r a d i t i o n a l s e n s e and

t h e r e f o r e must be e l i m i n a t e d from t h e u t i l i z a t i o n e q u a t i o n i n o r d e r f o r t h i s e q u a t i o n t o be e s t i m a b l e . To e l i m i n a t e t h e s t a t e v a r i a b l e from Equation (6), c o n s i d e r t h e a c c o u n t i n g r e l a t i o n s h i p ( a t any time t ) f o r v a r i a b l e i

where J

it

i s t h e g r o s s a d d i t i o n of u t i l i z a t i o n from v e h i c l e c h o i c e s ,

(i.e. and 6i i s a c o n s t a n t r a t e of d e p r e c i a t i o n of S it of p a s t e x p e r i e n c e s w i t h t h e v e h i c l e i ) .

the depreciation

In t h i s analysis,

Jit

is

d e f i n e d t o be a l i n e a r f u n c t i o n of t h e u t i l i z a t i o n of v e h i c l e i , and t h e u t i l i z a t i o n of v e h i c l e s of t h e same make a s v e h i c l e i.

These

l a t t e r v a r i a b l e s c a p t u r e t h e n o t i o n of t r a n s f e r e n c e of ownership experi e n c e between v e h i c l e s of t h e same make (2.e. brand l o y a l t y ) . . Jit

Thus,

can be d e f i n e d a s

where x

it

i s t h e u t i l i z a t i o n of v e h i c l e i , x f i s t h e u t i l i z a t i o n of a it

v e h i c l e ( n o t i n c l u d i n g v e h i c l e i ) t h a t i s t h e same make a s v e h i c l e i .

Givenxhis d e f i n i t i o n , n o t e t h t t h e g e n e r a l s o l u t i o n t o Equation (7)

T h i s i n d i c a t e s t h a t t h e s t a t e v a r i a b l e a t any t i m e t i s e q u a l t o t h e sum of t h e d i s c o u n t e d e x p e r i e n c e s ( a s d e f i n e d by E q u a t i o n ( 8 ) ) ) of v e h i c l e i . Given t h e above r e l a t i o n s h i p s , i t i s d e s i r a b l e f o r e s t i m a t i o n p u r p o s e s t o t r a n s f o r m E q u a t i o n (6) i n t o a d i s c r e t e t i m e framework. Thus, E q u a t i o n ( 6 ) i s r e d e f i n e d f o r v e h i c l e i as

xi t = T i + F i ( I t

where x

it

-Cit)+a? i it,

i s t h e accumulated u t i l i z a t i o n of v e h i c l e i

time i n t e r v a l ,

I

t

i s t h e i n t e r v a l household income,

over t h e d i s c r e t e

'it

is the interval

c o s t of o p e r a t i n g v e h i c l e i , T ~ Bi, , and ai a r e p a r a m e t e r s , and

2i t

is

d e f i n e d as t h e mean v a l u e of t h e s t a t e v a r i a b l e o v e r t h e t i m e i n t e r v a l . A t t e n t i o n can now be g i v e n t o removing a b l e , from E q u a t i o n ( 1 0 ) .

?i t '

which i s n o t measur-

The p r o c e d u r e t h a t i s u s e d t o d o t h i s i s

somewhat t e d i o u s , and t h e r e f o r e i s p r e s e n t e d i n Appendix A.

A s shown

i n t h i s a p p e n d i x , t h e t r a n s f o r m e d e q u a t i o n can be w r i t t e n as

where t h e A ' s a r e p a r a m e t e r s , lit = Tt i 30

-

Cit,

and a l l o t h e r v a r i a b l e s

a r e as defined previously. equation

Note t h a t t h i s e q u a t i o n i s a dynamic

of v e h i c l e u t i l i z a t i o n t h a t i s measurable i n a l l v a r i a b l e s ,

s i n c e t h e unmeasurable s t a t e v a r i a b l e has been removed. 3.2.2.

D e r i v a t i o n of t h e I n d i r e c t U t i l i t y Function

Given t h e dynamic u t i l i z a t i o n e q u a t i o n s p e c i f i e d above, i t i s p o s s i b l e t o d e r i v e t h e c o r r e s p o n d i n g dynamic i n d i r e c t u t i l i t y f u n c t i o n implied by Roy's I d e n t i t y .

where V

it

That i s

i s t h e dynamic i n d i r e c t u t i l i t y f u n c t i o n and p

it

is the unit

R w , d e f i n e t h e o p e r a t i n g c o s t of

p r i c e of v e h i c l e u t i l i z a t i o n . v e h i c l e ownership a s

tit where r and

n

it

= mi t Pi t '

(13

i s t h e t y p i c a l v e h i c l e u t i l i z a t i o n of v e h i c l e i i n p e r i o d t

i s a parameter.

Thus, u s i n g Equations ( l l ) , ( 1 2 ) , and ( 1 3 ) , i t

can be shown ( s e e , f o r example, Hausman (1981)) t h a t t h e i n d i r e c t u t i l i t y f u n c t i o n i s of t h e form

,

3.2.3

Dynamic D i s c r e t e Choice Model o f V e h i c l e Q u a n t i t y and V e h i c l e Type

The d e r i v a t i o n p r o v i d e d above i s v a l i d f o r h o u s e h o l d s t h a t choose The a n a l y s i s i s now e x t e n d e d t o i n c l u d e m u l t i -

t o own one v e h i c l e .

v e h i c l e ownership c h o i c e . It i s assumed t h a t h o u s e h o l d s choose t h e q u a n t i t y of v e h i c l e s t o own, n , and t h e t y p e of v e h i c l e t o own, i , s u c h t h a t t h e i r i n d i r e c t T h a t i s , a household w i l l s e l e c t

u t i l i t y f u n c t i o n s a r e maximized. n ' v e h i c l e s of t y p e i ' n

( i . e . make, model, and v i n t a g e of e a c h of t h e n '

vehicles)

iff

2

Vnti

Y

Vni

n

n , . in .

n

The p r o b a b i l i t y of s e l e c t i n g n ' and i ' i s n

P n'i

=Prob[V n

n'i' n

> v -

'

n, in].

ni,

Decomposing t h e i n d r e c t u t i l i t y f u n c t i o n i n t o a s y s t e m a t i c component,

-

, and

Vni

n

a random component, E ni n

,

such t h a t

V n , i a r e j o i n t l y distributed with a generalni n n i z e d e x t r e m e v a l u e d i s t r i b u t i o n , we can o b t a i n a n e s t e d o r s e q u e n t i a l

and assu.ming t h a t

E

l o g i t model s u c h t h a t

where P n

'

i s t h e m a r g i n a l p r o b a b i l i t y of n 1 v e h i c l e s being s e l e c t e d ,

and P i s t h e p r o b a b i l i t y of a v e h i c l e t y p e b e i n g s e l e c t e d i 1In1 n c o n d i t i o n a l on n ' . A s shown by McFadden (1979) t h e s e p r o b a b i l i t i e s

t h e m e a n i n d i r e c t u t i l i t y , v a r i e s only o v e r n , a n d G , , where7 nr7 lnIn v a r i e s over n and i 5 i s a parameter, n'

and Ln i s t h e i n c l u s i v e v a l u e .

Given t h e above r e l a t i o n s h i p s , a l l t h a t remains i s t o s p e c i f y t h e f u n c t i o n a l form of t h e i n d i r e c t u t i l i t y f u n c t i o n .

Tn t h i s s t u d y ,

we a r e f o r c e d f o r e m p i r i c a l r e a s o n s t o c o n s i d e r o n l y one and two v e h i c l e households.

The a p p r o p r i a t e i n d i r e c t u t i l i t y f u n c t i o n f o r t h e

one v e h i c l e household i s g i v e n by Equation (14).

I n t h e c a s e of a two-

v e h i c l e household, t h e o p e r a t i n g c o s t s of i t s v e h i c l e p o r t f o l i o i a r e defined as:

where p

1 it

2 and pit

a r e t h e o p e r a t i n g c o s t s of v e h i c l e 1 and 2 r e s p e c t i v e l y ,

i n vehicle p o r t f o l i o i, r i n t h e p o r t f o l i o , and n

i

it

i s t h e t y p i c a l u t i l i z a t i o n of e a c h v e h i c l e

i s a parameter.

Thus, i t can be shown t h a t t h e

i n d i r e c t u t i l i t y f u n c t i o n f o r p o r t f o l i o i is:

where t h e s u p e r s c r i p t T r e p r e s e n t s t h e combination of v e h i c l e s comprising portfolio

i.

The dynamic u t i l i z a t i o n e q u a t i o n s c o r r e s p o n d i n g t o

t h i s i n d i r e c t u t i l i t y f u n c t i o n ( i . e . Equation (22)) a r e of t h e form

For t h e r e s t r i c t e d dynamic c a s e , t h e complete system 05 equat i o n s d e s c r i b i n g t h e household's

c h o i c e of v e h i c l e q u a n t i t y , v e h i c l e t y p e ,

and v e h i c l e u t i l i z a t i o n a r e now d e f i n e d .

The s t r u c t u r e of t h e a c t u a l

e s t i m a b l e forms of t h e s e e q u a t i o n s w i l l b e given i n a l a t e r s e c t i o n .

3.3

The I n t e r t e m p o r a l Dynamic Model The i n t e r t e m p o r a l approach d i f f e r s from t h e r e s t r i c t e d dynamic

approach i n t h a t households a r e now assumed t o c o n s i d e r t h e e f f e c t s of c u r r e n t consumption on f u t u r e u t i l i t y . holds

T h i s i m p l i e s t h a t house-

t a k e i n t o account t h e e f f e c t t h a t c u r r e n t consumption w i l l have

on f u t u r e t a s t e changes.

Hence, t h e i n t e r t e m p o r a l model i s based on a

s u b s t a n t i a l l y d i f f e r e n t and somewhat more r e a l i s t i c d e c i s i o n making

p r o c e s s t h a n t h a t upon which t h e r e s t r i c t e d dynamic model i s b a s e d . The u n f o r t u n a t e d i s a d v a n t a g e of t h e i n t e r t e m p o r a l model i s t h a t a number of s t r o n g assumptions must 6 e made t o a r r i v e a t t r a c t a b l e results.

These assumptions and t h e complete d e r i v a t i o n of t h e i n t e r -

t e m p o r a l dynamic model a r e p r e s e n t e d below. 3.3.1

The U t i l i t y F u n c t i o n a l

The o b j e c t i v e h e r e i s t o d e r i v e models t h a t can be e m p i r i c a l l y e v a 1 u a t e d . T ~ a c h i e v e t h i s , i t i s n e c e s s a r y t o d e f i n e an i n t e r t e m p o r a l u t i l i t y f u n c t i o n t h a t i s t h e sum of p r e s e n t and f u t u r e i n s t a n t a n e o u s u t i l i t i e s ( i . e . u t i l i t i e s a t any p o i n t i n t i m e ) .

I n reducing t h e

i n t e r t e m p o r a l u t i l i t y t o a sum of i n s t a n t a n e o u s u t i l i t i e s , i t i s i m p e r a t i v e t h a t t h e p o s t u l a t e s s e t f o r t h by Koopmans (1960) be d i s c u s s e d . To b e g i n , Koopmans' n o t a t i o n i s adopted by d e f i n i n g a sequence of commodity p u r c h a s e s over time as a program and d e n o t i n g i t . 1X

=

(xl,

X2,

x3

...

X4

...I

=

( x ~ , ~ x= )

...

where x ' s a r e consumption v e c t o r s and t h e s u b s c r i p t s 1, 2 , 3 , t o d i s c r e t e time periods.

(24)

...

refer

Note t h a t Equation (24) i m p l i e s t h a t e a c h

program i s assumed t o extend over an i n f i n i t e f u t u r e .

I n t h e c a s e of

household v e h i c l e ownership, t h e i n f i n i t e f u t u r e assumption may n o t be e n t i r e l y u n r e a l i s t i c s i n c e households t e n d t o s u r v i v e from generat i o n t o generation. Using t h e above n o t a t i o n , t h e p r e v i o u s l y s t a t e d o b j e c t i v e i s t o d e f i n e a u t i l i t y f u n c t i o n f o r a l l p o s s i b l e programs ( i . e .

f o r a l l Ix),

such t h a t t h i s u t i l i t y , U ( x) i s a s i m p l e f u n c t i o n of t h e i n s t a n t a n e o u s 1

1 1.' u2 (x2) ,

u t i l i t i e s u (x )

... ,

To a c h i e v e t h i s , t h e fo l l . 0 ~ -

ut ( x t ) .

i n g f o u r p o s t u l a t e s must be a c c e p t e d

( s e e Koopmans (1960) and

Koopmans, Diamond, and Williamson ( 1 9 6 4 ) ) , P 1 ( E x i s t e n c e and C o n t i n u i t y ) : There e x i s t s a c o n t i n u o u s u t i l i t y .) f u n c t i o n U( x ) , which i s d e f i n e d f o r a l l lx = (x , x 2 , such t h a t , &or a l l t , xt i s a p o i n t of a boundea convex X of t h e n d i m e n s i o n a l commodity s p a c e .

..

A d e t a i l e d d i s c s s i o n on t h e e x i s t e n c e and c o n t i n u i t y p o s t u l a t e

i s p r e s e n t e d i n Koopmans (1960). P2 ( S e n s i t i v i t y ) : There e x i s t f i r s t p e r i o d consumption v e c t o r s x 1p x i and a program x from t h e second p e r i o d on, s u c h t h a t 2 u (xl, 2x) > u ( x i , 2x)

.

T h i s p o s t u l a t e r e q u i r e s u t i l i t y t o be changed when consumption

i s changed i n some s p e c i f i e d t i m e p e r i o d .

This p o s t u l a t e e x c l u d e s t h e

p o s s i b i l i t y t h a t a consumer a t t a c h e s u t i l i t y only t o a consumption l e v e l exceeding some minimum v a l u e ,

Thus, b o t h p o s t u l a t e s P 1 and P2 a r e n o t

very r e s t r i c t i v e o r u n r e a l i s t i c . P3 (Limited Noncomplementarity) f o r a l l x I ' x 1, 1 2x9 2 ~ ' (P3a) (P3b)

x') 2 U ( X ~ , ~ X ' ) 1'2 U(X~,~X 2 )U ( X ~ , ~ Xi m ' ) p l i e s U(xl1'2 x) 2 U ( X ; , ~ X ~ ) U(xl , 2 x ) ~U ( X ; , ~ X ) i m p l i e s U(x

P3a s t a t e s t h a t d i f f e r e n t consumption programs u n d e r t a k e n a f t e r t h e f i r s t p e r i o d do n o t a f f e c t consumption p r e f e r e n c e s i n t h e f i r s t p e r i o d . P3b s t a t e s t h a t d i f f e r e n t consumption p a t t e r n s i n t h e f i r s t p e r i o d do n o t a f f e c t t h e p r e f e r e n c e o r d e r i n g s comsumption programs c o n s i d e r e d from t h e second p e r i o d onward.

P o s t u l a t e P3 i s n o t t e r r i b l y

r e l a i s t i c s i n c e t h e r e i s n o r e a s o n t o b e l i e v e t h a t t h e complementarity of goods does n o t e x t e n d over more t h a n one time p e r i o d .

I n t h e case

of v e h i c l e ownership modeling, w i t h n o t i o n s of brand l o y a l t y cons i d e r e d , i t i s c l e a r t h a t t h i s p o s t u l a t e does n o t have a h i g h d e g r e e of N e v e r t h e l e s s , acceptance of P3 i s c r i t i c a l s i n c e t h e i n t e r -

realism.

temporal u t i l i t y f u n c t i o n can b e w r i t t e n a s

where v ( u l ,

U ) i s a continuous and 2

i n c r e a s i n g f u n c t i o n of t h e

in-

s t a n t a n e o u s u t i l i t y f u n c t i o n a t tTme t = l (u ) , and t h e i n t e r t e m p o r a l 1 u t i l i t y f u n c t i o n a s s o c i a t e d w i t h a l l consumption sequences s t a r t i n g from p e r i o d t = 2 ( u ~ ( ~ x ) ) I. n o r d e r f o r Equation (25) t o become u s e f u l i n t h e d e r i v a t i o n of t h e i n t e r t e m p o r a l model, i t i s n e c e s s a r y t o drop t h e time s u b s c r i p t s from t h e i n s t a n t a n e o u s and i n t e r t e m p o r a l u t i l i t y funct i o n s t h e r e b y w r i t i n g Equation (25) a s

To a c h i e v e t h e t r a n s for m t i o n from Equation (25) t o Equation (26) t h e f o l l o w i n g p o s t u l a t e must be a c c e p t e d .

P4 ( S t a t i o n a r i t y ) :

F o r a given x

U(X~,~X 2 )U(x 1 , 2 ~ 1 ) i f f

1

x , 2 ~ ,' 2 U( 2X) 2 U ( 2 ~ ' ) and a l l

The i m p l i c a t i o n of t h i s p o s t u l a t e i s t h a t t h e p a s s a g e of t i m e i s n o t p e r m i t t e d t o have an e f f e c t on p r e f e r e n c e s .

Koopmans, Diamond

and Williamson (1964) p r o v i d e t h e f o l l o w i n g c l a r i f i c a t i o n s of t h i s postulate.

P 4 s t a t e s t h a t f o r some x

1

and a l l 2 x ,

2

x ' , program A ( s e e

below) i s a t l e a s t a s good a s program B i f and only i f program C i s a t

,

least a s good as program D where: Period Program A

B C

D

I n w o r d s , t h e o r d e r i n g s of programs d i f f e r i n g o n l y from t h e second p e r i o d onward w i l l n o t b e a f f e c t e d by a d v a n c i n g t h e t i m i n g of s u c h programs by one p e r i o d .

Similarly, the

posEponement of programs

w i l l n o t a f f e c t e x i s t i n g o r d e r i n g p r o v i d i n g common consumption v e c t o r s

are used t o f i l l i n t e r i m t i m e p e r i o d s .

The p r o o f of how P 4 p e r m i t s

E q u a t i o n s (25) t o b e t r a n s f o r m e d i n t o E q u a t i o n (26) i s g i v e n e l s e where ( s e e P h l i p s ( 1 9 7 4 ) ) . The r e a d e r i s r e f e r r e d t o Koopmans (1960) and Koopmans, Diamond, and Williamson (1964) f o r a d d i t i o n a l t e c h n i c a l d e t a i l s r e g a r d i n g t h e p o s t u l a t e s d e s c r i b e d above. the

What i s i m p o r t a n t t o t h i s s t u d y i s t h a t

a c c e p t a n c e o f t h e Koopmans p o s t u l a t e s p e r m i t s t h e r e c u r s i v e

i n t e r t e m p o r a l u t i l i t y f u n c t i o n , E q u a t i o n ( 2 6 ) , t o be w r i t t e n .

A s an

a d d i t i o n a l p o i n t , n o t e t h a t t h e i t e r a t i v e a p p l i c a t i o n of E q u a t i o n (26) gives

where t h e f u n c t i o n s u(xl)

u(x j , 2

l e v e l s a s s o c i a t e d d t h a program,

... r e p r e s e n t

instantaneous u t i l i t y

1"

U l t i m a t e l y , t o d e r i v e an i n t e r t e m p o r a l model o f h o u s e h o l d v e h i c l e o w n e r s h i p , i t i s d e s i r a b l e t o h a v e an i n t e r t e m p o r a l u t i l i t y functional,

i n c o n t i n u o u s time', of t h e form, 03

This equation implies t h a t t h e intertemporal u t i l i t y function i s defined as a d i s c o u n t e d sum of a l l f u t u r e o n e - p e r i o d i n s t a n t a n e o u s u t i l i t i e s . To a r r i v e a t E q u a t i o n (28)

,

t h e m a j o r r e s t r i c t i o n of " a d d i t i v i t y "

t i m e must b e added t o t h e f o u r p o s t u l a t e s d e s c r i b e d e a r l i e r .

over

This

r e s t r i c t i o n , of c o u r s e , i m p l i e s t h a t t h e m a r g i n a l r a t e of s u b s t i t u t i o n between two a d j a c e n t p e r i o d s i s i n d e p e n d e n t of f u t u r e p e r i o d d e c i s i o n s . It i s c l e a r t h a t a d d i t i v i t y i s a v e r y s t r o n g r e s t r i c t i o n . F i n a l l y , t h e d i s c o u n t f u n c t i o n a p p e a r i n g i n E q u a t i o n (28) c a p t u r e s t h e n o t i o n of " i m p a t i e n c e " , advanced t i m i n g of consumption.

which i s t h e p r e f e r e n c e f o r

The f a c t t h a t t h e d i s c o u n t f u n c t i o n

assumes t h e form e-yt where y i s c o n s t a n t o v e r t i m e , i s t i e d t o t h e work of S t r o t z ( 1 9 5 6 ) .

S t r o t z h a s shown t h a t a c o n s i s t e n t p l a n n e r

must s u b s t i t u t e f o r h i s t r u e d i s c o u n t f u n c t i o n (which may assume any form),

a d i s c o u n t f u n c t i o n whose r a t e of change wer t i m e i s c o n s t a n t ,

b e f o r e maximizing h i s i n t e r t e m p o r a l u t i l i t y .

Although t h e S t r o t z r e s u l t

is powerful i n t h a t i t provides a u t i l i t y f u n c t i o n a l t h a t l e n d s i t s e l f t o t h e d e v e l o p m e n t of t r a c t a b l e models, t h e r e are r e a s o n s t o s u s p e c t t h a t t h e s t r a t e g y of c o n s i s t e n t p l a n n i n g i s n e v e r e n t i r e l y a c h i e v e d .

The p r i m a r y r e a s Q n i s t h a t S t r o t z ' s d e r i y a t i o n s assume t h a t f u t u r e

If i'n f a c t t h e p l a n n e r ' s e x p e c t a t i o n s

e v e n t s are known w i t h c e r t a i n t y .

of f u t u r e s a t i s f a c t i o n s a r e n o t r e a l i z e d , t h e u s e of a c o n s t a n t d i s c o u n t f u n c t i o n w i l l n o t be v a l i d .

Moreover, even i f a l l e x p e c t a t i o n s were

r e a l i z e d , t h e p o s s i b i l i t y t h a t i m p a t i e n c e may change over t i m e w i l l r e sult i n a y that varies. A s t h e p o s t u l a t e s and o t h e r a s s u m p t i o n s d i s c u s s e d i n t h i s s e c t i o n

i n d i c a t e , t h e p r i c e of o b t a i n i n g a u t i l i t y f u n c t i o n a l of t h e form i n d i c a t e d i n E q u a t i o n (28) i s h i g h i n t e r m s of t h e r e s t r i c t i o n s t h a t m u s t be imposed.

However, w i t h t h e s e r e s t r i c t i o n s a c c e p t e d , i t w i l l be

shown i n t h e f o l l o w i n g s e c t i o n t h a t an i n t e r t e m p o r a l model of v e h i c l e q u a n t i t y , t y p e , and u t i l i z a t i o n c h o i c e can b e r e a d i l y d e r i v e d .

3.3.2

The I n t e r t e m p o r a l Model and t h e Maximum P r i n c i p l e

The i n t e r t e m p o r a l n a t u r e of t h e h o u s e h o l d ' s v e h i c l e ownership problem l e n d s i t s e l f t o dynamic o p t i m i z a t i o n t e c h n i q u e s and i n p a r t i c u l a r t h e Maximum g r i n c i p l e .

To i l l u s t r a t e t h i s , t h e h o u s e h o l d ' s o p t i m i z a t i o n

problem can b e viewed as c o n s i s t i n g of t h e maximization of i t s p r e s e n t d i s c o u n t e d v a l u e of u t i l i t y

MaxU=

r

u ( ~ , x ) e -d~t ,~

(29)

0

where u ( S , x ) i s t h e t i m e i n v a r i a n t i n s t a n t a n e o u s u t i l i t y f u n c t i o n , x d e n o t e s v e h i c l e u t i l i z a t i o n , S i s a s t a t e v a r i a b l e as d e f i n e d i n t h e r e s t r i c t e d dynamic m o d e l , and y i s t h e d i s c o u n t r a t e .

This equation

follows from Equation ( 2 8 ) , w i t h a l l t h e r e s t r i c t i o n s n e c e s s a r y t o w r i t e

t h a t equation, applying,

I n d e t e r m i n i n g an o p t i m a l v e h i c l e ownership

program f o r t h e h o u s e h o l d , t h e Maximum P r i n c i p l e w i l l p r o v i d e t h e necessary conditions.

Specifically,

t h e household's v e h i c l e ownership

problem c a n b e f o r m u l a t e d i n t e r m s of a H a m i l t o n i a n a s

max H(S, x , $, y , z ) = ii(S , x )

where Ij, i s a c o s t a t e v a r i a b l e ,

S

+

$S

+

yf ( x , z ) ,

i s t h e t i m e r a t e of change i n t h e s t a t e

v a r i a b l e , f d e n o t e s a v e c t o r of e q u a t i o n s of m o t i o n , y d e n o t e s a v e c t o r of c o s t a t e v a r i a b l e s t h a t c o r r e s p o n d t o f , and z i s a v e c t o r of o t h e r s t a t e v a r i a b l e s t h a t r e l a t e t o t h e v e h i c l e ownership d e c i s i o n ( f o r example, h o u s e h o l d w e a l t h ) .

The economTc i n t e r p r e t a t i o n of t h e

H a m i l t o n i a n i s s i m p l y t h e c u r r e n t f l o w of u t i l i t y from a l l s o u r c e s , i n c l u d i n g t h o s e r e a l i z e d i m m e d i a t e l y , u ( S , x ) , and t h o s e a n t i c i p a t e d ,

$s + yf ( x , z ) . Unfortunately, solving t h e household's intertemporal v e h i c l e ownership problem by d i r e c t m a x i m i z a t i o n of t h e H a m i l t o n i a n i s e x c e e d i n g l y d i f f i c u l t i f not impossible.

T h e r e f o r e , an i n d i r e c t p r o c e d u r e t h a t

p a r a l l e l s t h e p r o c e d u r e u s e d i n t h e d e r i v a t i o n of t h e r e s t r i c t e d dynamic model, i s f o l l o w e d . T h a t i s , a n i n t e r t e m p o r a l dynamic u t i l i z a t i o n equat i o n i s s p e c i f i e d and t h e n t r a n s f o r m e d s o t h a t a l l i n d e p e n d e n t v a r i a b l e s a r e measurable.

The r e s u l t i n g e q u a t i o n i s u s e d w i t h R o y r s I d e n t i t y t o

derive a correspcnding intertemporal i n d i r e c t u t i l i t y function. F i n a l l y , t h e i n d i r e c t u t i l i t y f u n c t i o n i s u s e d t o d e r i v e a dynamic i n t e r t e m p o r a l d i s c r e t e c h o i c e model of v e h i c l e q u a n t i t y and v e h i c l e t y p e .

To b e g i n , t h e i n t e r t e m p o r a l dynamic u t i l i z a t i o n e q u a t i o n i s s p e c i f i e d as

where

I)

it

f s t h e Hamiltonian c o s t a t e v a r i a b l e as defined i n Equation (30),

i s a p a r a m e t e r , and a l l o t h e r v a r i a b l e s a r e a s d e f i n e d f o r t h e Wi r e s t r i c t e d dynamic model.

The economic i n t e r p r e t a t i o n of

I)

it

is that

i t i s t h e i m p l i c i t v a l u e a t t a c h e d t o a m a r g i n a l u n i t of t h e s t a t e v a r i -

able S it'

The i n c l u s i o n of $

it

d i s t i n g u i s h e s t h e i n t e r t e m p o r a l from

t h e r e s t r i c t e d dynamic u t i l i z a t i o n e q u a t i o n i n t h a t now, i n t h e i n t e r t e m p o r a l c a s e , t h e e f f e c t t h a t c u r r e n t consumption h a s on f u t u r e u t i l i t y i s e n t e r e d i n t o t h e h o u s e h o l d ' s o p t i m i z a t i o n problem.

This p o i n t

w i l l become c l e a r e r below, It s h o u l d be n o t e d t h a t E q u a t i o n (31) h a s two unmeasurable v a r i -

ables,

'it

and S

it'

The s t a t e v a r i a b l e ,

'ity

can b e e l i m i n a t e d f r o m t h e

e q u a t i o n by t h e method used i n t h e r e s t r i c t e d dynamic model d e r i v a t i o n , w h i l e an a n a l o g o u s p r o c e d u r e can b e used t o e l i m i n a t e $ it e l i m i n a t i o n of

I)

it

.

Specifically,

can b e a c h i e v e d by b e g i n n i n g w i t h t h e c a n o n i c a l

e q u a t i o n f o r m a x i m i z a t i o n of t h e H a m i l t o n i a n ( f o r e a c h t )

o r (from E q u a t i o n (.30))

,

D i f f e r e n t i a t i n g Equation (7) w i t h r e s p e c t t o S

i

and s u b s t i t u t i n g t h e

r e s u l t i n t o Equation (33) y i e l d s

To proceed f u r t h e r , i t i s n e c e s s a r y t o s p e c i f y a f u n c t i o n a l form f o r t h e time i n v a r i a n t i n s t a n t a n e o u s u t i l i t y f u n c t i o n , u.

A convenient

f u n c t i o n a l form i n t h i s r e g a r d , due t o i t s l i n e a r f i r s t o r d e r d e r i v a tives,

i s a quadratic specification.

Therefore, i f the instantaneous

u t i l i t y function i s defined a s

then Equation (34) can be w r i t t e n a s

-.

-.

where 6 , c , and B a r e p a r a m e t e r s and t h e time s u b s c r i p t h a s been reintroduced.

Using E q u a t i o n s ( 7 ) , ( 3 1 ) , and ( 3 6 ) , a dynamic i n t e r -

temporal u t i l i z a t i o n e q u a t i o n can be d e r i v e d w i t h o u t t h e s t a t e and a s s o c i a t e d Hamiltonian c o s t a t e v a r i a b l e s .

As shown i n Appendix B ,

the r e s u l t i n g intertemporal u t i l i z a t i o n equation is

where A 's a r e f u n c t i o n s of t h e s t r u c t u r a l p a r a m e t e r s , and a l l o t h e r i

t e r m s a r e as p r e v i o u s l y d e f i n e d .

I n comparing t h i s - u t i l i z a t i o n

e q u a t i o n w i t h t h e r e s t r i c t e d dynamic u t i l i z a t i o n e q u a t i o n , t h e m a j o r empirical d i s t i n c t i o n i s t h a t t h i s equation contains v a r i a b l e s t h a t a r e l a g g e d o v e r b o t h one and two t i m e

periods.

This i s t r u e despite

the f a c t t h a t the i n i t i a l behavioral postulates s e t f o r t h t o derive t h e s e e q u a t i o n s were q u i t e d i f f e r e n t . Given E q u a t i o n ( 3 7 ) , t h e d e r i v a t i o n of t h e i n t e r t e m p o r a l i n d i r e c t u t i l i t y f u n c t i o n and t h e c o m p l e t e model of v e h i c l e q u a n t i t y t y p e , and u t i l i z a t i o n c o n s i s t s of a s t r a i g h t f o r w a r d a p p l i c a t i o n of t h e p r o c e d u r e s u s e d t o d e r i v e t h e r e s t r i c t e d dynamic system. 3.4

E s t i m a b l e Models and E c o n o m e t r i c P r o c e d u r e s

In t h i s s e c t i o n , e s t i m a b l e f o r m s of t h e e q u a t i o n s d e r i v e d i n S e c t i o n s 3 . 2 and 3 . 3 a r e p r e s e n t e d a l o n g w i t h a d e s c r i p t i o n of a p p r o p r i a t e e c o n o m e t r i c e s t i m a t i o n p r o c e d u r e s . To b e g i n , c o n s i d e r t h e f o l l o w i n g s t o c h a s t i c i n d i r e c t u t i l i t y f u n c t i o n which i s b a s e d on t h e r e s t r i c t e d dynamic model E q u a t i o n s (14) and ( 2 2 ) .

For one v e h i c l e :

f o r two v e h i c l e s :

where Z i s a v e c t o r of household c h a r a c t e r i s t i c s b e l i e v e d t o i n f l u e n c e v e h i c l e ownership d e c i s i o n s ; 0 i s a v e c t o r of e s t i m a b l e p a r a m e t e r s ; v ' s a r e unobserved household characteristics; Yli

and Ypi

a r e v e c t o r s of

1 2 o b s e r v a b l e household and v e h i c l e c h a r a c t e r i s t i c s i n f l u e n c i n g v e h i c l e ownership d e c i s i o n s ;

'i

1 and Ri2 a r e parameter v e c t o r s ;

E

li

and E

2i2t

a r e unobserved v e h i c l e a t t r i b u t e s ; and a l l o t h e r v a r i a b l e s a r e a s p r e vious l y defined

.

Under t h e assumption t h a t t h e E~~

' s and E~~

's are j o i n t l y dis2 t r i b u t e d w i t h a g e n e r a l i z e d extreme v a l u e d i s t r i b u t i o n , i t can be shown

1

t h a t t h e models of l e v e l c h o i c e and type choice g i v e n i n Equations (19) and (20) r e s p e c t i v e l y a r e based on i n d i v i d u a l household maximization of t h e i n d i r e c t u t i l i t y f u n c t i o n given above.

Applying Roy's I d e n t i t y

t o Equation ( 3 8 ) , t h e s t o c h a s t i c u t i l i z a t i o n e q u a t i o n s a r e of t h e form:

f o r one v e h i c l e , and

f o r two v e h i c l e s , m = 1 , 2 , where a l l o t h e r v a r i a b l e s a r e a s p r e v i o u s l y d e f i n e d . S t o c h a s t i c e s t i m a b l e e q u a t i o n s f o r t h e i n t e r t e m p o r a l model a r e achieved by t h e same procedure a s t h e one o u t l i n e d above. Note t h a t t h e modeling system c o n s i s t i n g of Equations ( 1 9 ) , ( 2 0 ) , (39) and (40) c o n s t i t u t e a d i s c r e t e / c o n t i n u o u s model of v e h i c l e q u a n t i t y , t y p e , and u t i l i z a t i o n c h o i c e .

The econometric consequences of a d i s c r e t e /

c o n t i n u o u s model s t r u c t u r e have been t h e s u b j e c t of c o n s i d e r a b l e r e s e a r c h i n recent years.

I n i t i a l t h e o r e t i c a l contributions i n t h i s area include

t h o s e of Heckman (1976, 1978, 1979)

.

More r e c e n t t h e o r e t i c a l and

e m p i r i c a l c o n t r i b u t i o n s i n c l u d e t h o s e of Hay (1980), Dubin and McFadden (1981), and McFadden and Winston (1981).

I n t h e modeling system p r e s e n t e d

above, t h e d i s c r e t e / c o n t i n u o u s s t r u c t u r e i s an i s s u e i n t h e e s t i m a t i o n of Equations (39) and ( 4 0 ) , s i n c e a s t a t i s t i c a l

c o r r e l a t i o n between

v e h i c l e s p e c i f i c a t t r i b u t e s and t h e a d d i t i v e e r r o r terms i n t h e dynamic u t i l i z a t i o n e q u a t i o n s w i l l be p r e s e n t .

I n t u i t i v e l y , some c o r r e l a t i o n

can be e x p e c t e d t o e x i s t between unobservables a f f e c t i n g v e h i c l e t y p e c h o i c e and t h o s e a f f e c t i n g u t i l i z a t i o n .

For example,

t h e unobserved e f f e c t s t h a t t e n d t o i n c r e a s e usage (e.g.

p l e a s u r e of

d r i v i n g ) w i l l a d v e r s e l y a f f e c t t h e p r o b a b i l i t y of s e l e c t i n g an o l d ,

d e c r e p i t v e h i c l e from which l i t t l e d r i v i n g p l e a s u r e can be d e r i v e d . S i m i l a r l y , t h e unobserved e f f e c t s t h a t i n c r e a s e t h e u t i l i t y of s e l e c t i n g a newer model v e h i c l e (e.g.

t h e need f o r v e h i c l e r e l i a b i l i t y )

may i n c r e a s e t h e e x t e n t t o which i s i s u s e d .

Such c o r r e l a t i o n i m p l i e s

t h a t o r d i n a r y l e a s t s q u a r e s w i l l l e a d t o b.:ased

and t o i n c o n s i s t e n t

e s t i m a t e s of t h e utilization e q u a t i o n p a r a m e t e r s . 5 a l l e v i a t e t h i s problem

,

c o n s i d e r , f o r example, a r e w r i t t e n form of t h e one-vehicle

r e s t r i c t e d dynamic u t i l i z a t i o n e q u a t i o n (Equation (39)) c o n d i t i o n i n g on t h e cholce of v e h l c l e type i,

where n i s t h e t o t a l number of v e h i c l e t y p e s i n t h e c h o i c e s e t ; $kit i s a dummy v a r i a b l e whi'ch is one when k = i and z e r o o t h e r w i s e .

To o b t a i n c o n s i s t e n t e s t i m a t e s of t h i s e q u a t i o n study, t h e c h o i c e dummies (Gkit)

i n the current

i n Equation (41) a r e r e p l a c e d by t h e A

e s t i m a t e d p r o b a b i l i t i e s from t h e d i s c r e t e choice t y p e models,

'it

T h i s method of a d d r e s s i n g t h e endogeneity of v e h i c l e t y p e a t t r i b u t e s i n t h e u t i l i z a t i o n e q u a t i o n s ( a g a i n , r e s u l t i n g fromthe d i s c r e t e l c o n t i n uous model s t r u c t u r e ) was f i r s t proposed by Dubin and McFadden (1981). Another i s s u e t h a t l s of concern t o t h e econometric e s t i m a t i o n of t h e proposed modeling system i s t h e p o s s i b l e p r e s e n c e of s e r i a l correlation. 'it

Should s . e r i a l c o r r e l a t i o n of e r r o r t e r n s e x i s t , t h e n t h e

used i n t h e e s t i m a t i o n of t h e u t i l i z a t i o n e q u a t i o n w i l l be c o r r e l a t e d

w i t h t h e a d d i t i v e e r r o r term, s i n c e P utilization.

it

i s i n f l u e n c e d by lagged

A l s o , t h e l a g g e d u t i l i z a t i o n s used as e x p l a n a t o r y

v a r i a b l e s i n t h e u t i l i z a t i o n equation w i l l be c o r r e l a t e d with t h e n

e r r o r term.

A s o l u t i o n t o t h i s problem would be t o r e g r e s s P

it

and x

it-1

on exogenous v a r i a b l e s t h e r e b y e n a b l i n g l e a s t s q u a r e s e s t i m a t i o n of t h e A

h

u t i l i z a t i o n e q u a t i o n , which w i l l now i n c l u d e f' c o n s i s t e n t parameter e s t i m a t e s .

h

it

and x

it-1 '

t o produce

Unfortunately, t h i s procedure i s n o t

f e a s i b l e i n t h e a n a l y s i s u n d e r t a k e n i n t h i s s t u d y due t o t h e e x c e p t i o n a l l y l a r g e number of v e h i c l e t y p e a l t e r n a t i v e s ( 5 ' s ) . As a f u r t h e r c o m p l i c a t i o n , a c c o u n t i n g f o r s e r i a l c o r r e l a t i o n i n t h e p r e s e n c e of l a g g e d endogenous v a r i a b l e s i n t h e d i s c r e t e c h o i c e model

of v e h i c l e t y p e i s e x c e e d i n g l y d i f f i c u l t .

Although t h e o r e t i c a l

work i n t h i s a r e a h a s been u n d e r t a k e n by Heckman (1981), o n l y a s i m p l e b i n a r y p r o b i t d l s c r e t e c h o i c e model h a s b e e n c o n s i d e r e d .

Moreover,

Heckman's work i n d i c a t e s t h a t th.e t r e a t m e n t of s e r i a l c o r r e l a t i o n i n t h e p r e s e n c e of a l a g g e d endogenous v a r i a b l e i n a dynamic d i s c r e t e c h o i c e c o n t e x t r e q u i r e s an a p p r o x i m a t i o n of i n i t i a l c o n d i t i o n s , which i n t h e v e h i c l e ownershTp c a s e i s an i m p o s s i b l e d a t a r e q u i r e m e n t .

In

any e v e n t e x t e n s i o n s of Heckman's work t o a m u l t i n o m i a l l o g i t ' s t r u c t u r e s u c h as t h e one proposed h e r e a r e l i k e l y t o b e e x t r e m e l y d i f f i c u l t , As a result of t h e d i f f i c u l t i e s i n a d d r e s s i n g t h e s e r i a l c o r r e l a t i o n problem, t h e c u r r e n t s t u d y i s f o r c e d t o assume t h a t d i s t u r b a n c e s

are s e r i a l l y i n d e p e n d e n t .

It s h o u l d be p o i n t e d o u t , however, t h a t

r e a s o n a b l e g e n e r a l arguments c a n b e made t o s u p p o r t t h e v a l i d i t y of t h i s assumption.

'For example, P o l l a k and Wales (1969) a r g u e t h a t

t h e r e i s n o r e a s o n t o assume s e r i a l c o r r e l a t i o n i n w o d e l s which depend on consumption i n prevl'ous p e r i o d s ,

T h e i r argument i s based on t h e f a c t

t h a t s e r i a l c o r r e l a t i o n can be e x p e c t e d , f o r example, i f a h i g h e r l e v e l of consumption of a good y e s t e r d a y i s a s s o c i a t e d w i t h a h i g h e r l e v e l of consumption t o d a y ,

However, i f lagged consumption i s i n c l u d e d i n

t h e model, t h e n t h i s r e l a t i o n s h i p i s c a p t u r e d s i n c e a h i g h e r l e v e l of y e s t e r d a y ' s e r r o r term i m p l i e s a h i g h e r l e v e l of y e s t e r d a y ' s consumption, which i n t u r n i m p l i e s a h i g h e r v a l u e of lagged consumption i s used t o p r e d i c t t o d a y ' s consumption.

Consequently, t h e e f f e c t s of s e r i a l c o r r e l a -

t i o n a r e negated.

A f i n a l point relate6 c h o i c e model. ( e . g. Ford)

t o t h e e s t i m a t i o n of t h e d i s c r e t e t y p e

I n t h i s a n a l y s i s , t h e t y p e of v e h i c l e i s d e f i n e d by make

, model

( e . g. Mustang)

, and

v i n t a g e ( e , g. 1967).

With t h i s

d e f i n i t i o n , t h e household t h e o r e t i ' c a l l y h a s thousands of c h o i c e s a v a i l a b l e , and i f e v e r y one was i n c l u d e d i n t h e e s t i m a t i o n , t h e c o m p u t a t i o n a l burden would be e x c e s s i v e .

F o r t u n a t e l y , t h e c h o i c e of

assuming t h e d i s t u r b a n c e s of t h e d i s c r e t e c h o i c e model t o be j o i n t l y d i s t r i b u t e d w i t h a g e n e r a l i z e d extreme v a l u e d i s t r i b u t i o n p e r m i t s c o n s i s t e n t e s t i m a t i o n of p a r a m e t e r s u s i n g a sub-sample of t h e a v a i l a b l e c h o i c e s e t ( s e e McFadden (1978)).

A number of e m p i r i c a l t e s t s r e l a t i n g

t o t h e s u i t a b i l i t y of t h e assumed l o g i t t y p e c h o i c e s t r u c t u r e a r e p r e s e n t e d i n Chapter 5 ,

CHAPTER 4.

COMPARATIVE ANALYSIS OF AVAIZBLE DTSAGGREGATE DATA

I n t h e U. S. c o n t e x t , a number of household l e v e l d a t a s o u r c e s c a n b e used i n e s t i m a t i n g m o d e l s of t h e household v e h i c l e ownership d e c i s i o n s of q u a n t i t y , t y p e , and u t i l i z a t i o n of v e h i c l e s . T h i s , c h a p t e r f i r s t c l a s s i f i e s s u c h d a t a s o u r c e s i n t o c r o s s - s e c t i o n a l and p a n e l d a t a , and p r e s e n t s an o v e r v i e w and q u a l i t a t i v e d i s c u s s i o n r e l a t i n g t o t h e i r u s e f u l n e s s as a b a s i s f o r h o u s e h o l d v e h i c l e owners hi^ m o d e l i n g . d i s c u s s i o n of v e h i c l e t y p e a t t r i b u t e f i l e s i s p r e s e n t e d .

Next, a Such f i l e s

are used t o c m p l e m e n t h o u s e h o l d d a t a and t h e y i n c l u d e i n f o r m a t i o n on d i f f e r e n t v e h i c l e makes, m o d e l s , and v i n t a g e s ( e . g .

1974 Ford P i n t o )

,

s u c h as p r i c e , h o r s e p o w e r , l u g g a g e c a p a c i t y , s e a t i n g c a p a c i t y , and o t h e r a t t r i b u t e s t h a t may i n £ l u e n c e v e h i c l e ownership c h o i c e s .

Finally,

t h e c h a p t e r c o n c l u d e s w i t h a b r i e f d i s c u s s i o n of t h e d a t a u s e d i n t h e e m p i r i c a l a n a l y s i s u n d e r t a k e n i n t h i s work. 4.1

Cnoss- S e c t i o n a l Household Data

A summary of t h e c h a r a c t e r i s t i c s of f o u r m a j o r cross-sectional household l e v e l d a t a s o u r c e s i s p r e s e n t e d i n T a b l e 1.

The f o l l o w i n g

p a r a g r a p h s p r e s e n t a d i s c u s s i o n of t h e s e s o u r c e s . P e r h a p s one of t h e f i r s t d a t a s o u r c e s s u i t a b l e f o r household v e h i c l e ownership m o d e l i n g was t h e d a t a c o l l e c t e d by t h e Survey R e s e a r c h C e n t e r (SRC) d u r i n g t h e w i n t e r of 1976.

I n c i d e n t l y , t h i s n a t c o n d l random

sample of 1200 h o u s e h o l d s was u s e d i n t h e e s t i m a t i o n of t h e Manski and Sherman (1980) v e h i c l e t y p e c h o i c e m o d e l s .

The d a t a i s one of t h e

e a r l i e s t known s a m p l e s t o i n c l u d e i n f o r m a t i o n on t h e model y e a r of e a c h v e h i c l e c u r r e n t l y h e l d , a l o n g w i t h a code i'ndi'cating m a n u f a c t u r e r (make)

50

T a b l e 1.

Summary of Household L e v e l D a t a S o u r c e s Cross-Sectional SRC -

Sample S i z e

1200

Collection Dates

W i n t e r '76

Sample Type

National Rand om

NPTS

NTS -

17949 1095 Apr ' 77 May/June t o Mar . I 7 8 '78

4081 ~uv/Dec '78

National Rand om

National Random

.

National Random

Information

A. S o c i o Economic

B.

1.

Income

2.

Family S i z e

3.

Ages of Members

4.

E d u c a t i m of Members

5.

Employment S t a t u s of Members

6.

Sex of Members

7.

Ge o g r a p h i c L o c a t i o n

Vehicle Belated

a ) V e h i c l e s Owned at t i m e of Collection

I.

Model Year

2.

Make

4,

U t i l i z a t i o n (VMT)

5.

Vehicle Options ( e . g . No. of c y l i n d e r s )

6.

Vehicle Purchase Date

b ) V e h i c l e s Owned one Year Prior t o Collection

1. Model Year 2.

Make

3.

Model

X X X Table continued next page

*

See T e x t

NIECS

Table 1 (Continued)

4.

U t i l i z a t i o n (VMT)

5,

V e h i c l e Options ( e . g . No. of c y l i n d e r s )

6.

V e h i c l e P u r c h a s e Date

SRC -

NPTS

(Table 1 continued on n e x t page)

NTS X

NIECS X

X

Sample S i z e Collection Dates

Sample Type

In£ ormat i on A.

S o c i o Economic

1. Income

B.

2.

Family S i z e

3.

Ages of Members

4.

Education a£ Members

5.

Employment S t a t u s of Members

6.

Sex of Members

7.

Geographic Location

Vehicle Related a ) V e h i c l e s Owned a t time of Collect ion

1. Model Year 2.

Make

3.

Model

4.

U t i l i z a t i o n (VMT)

5.

V e h i c l e Options ( e . g . No. of C y l i n d e r s )

6.

V e h i c l e Purchase Date

June ' 7 9 t o De c , "80 National Rand om

Low Income S e a t t l e /Denver

and, i n t h e c a s e of domestic c a r s , t h e v e h i c l e model ( e . g . P i n t o ) . There a r e two maj or f a u l t s w i t h t h l s d a t a .

Fi'rst

,

a s implied above,

v e h i c l e model i n f o r m a t i o n w a s n o t c o l l e c t e d f o r f o r e i g n makes. T h i s c l e a r l y l i m i t s t h e u s e f u l n e s s of t h e d a t a i n s t u d y i n g a number of major c o n c e r n s , such as causes of import market p e n e t r a t i o n .

Second,

t h e d a t a c o n t a i n s no i n f o r m a t i o n on t h e v e h i c l e s owned p r i o r t o t h e survey d a t e .

The absence of t h i s i n f ormat i o n p r e c l u d e s any a n a l y s i s

of t h e dynamics of household v e h i c l e ownership ( i . e . t h e e v o l u t i o n of household v e h i c l e r e l a t e d t a s t e s ) . Another s i g n i f i c a n t c r o s s - s e c t i o n a l d a t a s o u r c e i s t h e 1977 Nationwide P e r s o n a l T r a n s p o r t a t i o n study-(NPTS).

T h i s s u r v e y was

conducted by t h e Bureau of t h e Census under t h e s p o n s o r s h i p of t h e Department of T r a n s p o r t a t i o n .

Data was c o l l e c t e d n a t i o n a l l y from t h e

p e r i o d c o v e r i n g A p r i l 1977 t o 'March 1978.

U n f o r t u n a t e l y , t h e NPTS

d a t a s h a r e s a c r i t i c a l d e f i c i e n c y w i t h t h e SRC d a t a i n t h a t informat i o n on t h e v e h i c l e s owned p r i o r t o t h e survey d a t e was n o t c o l l e c t e d . D e s p i t e t h i s r a t h e r s e r i o u s d e f i c i e n c y , t h e i n c r e d i b l e s i z e of t h e NPTS sample (17,949 households) makes i t a d e s i r a b l e d a t a s o u r c e f o r s t a t i c modeling of household v e h i c l e ownership.

To d a t e , t h i s s o u r c e

i s n o t known t o have been used i n any d i s a g g r e g a t e v e h i c l e ownership

study

. The most w i d e l y used d a t a set a p p e a r s t o be t h e N a t i o n a l

T r a n s p o r t a t i o n Survey (NTS) which w a s c o l l e c t e d i n May and June 1978 by Cambridge S y s t e m a t i c s I n c o r p o r a t e d f o r t h e N a t i o n a l S c i e n c e Foundat i o n (both t h e Berkovec and Rust c1981) and T ~ a i nand Lohrer (1982)

works u s e t h i s d a t a s o u r c e ) .

The sample c o n s i s t s of 1095 h o u s e h o l d s

which were chosen on a n a t i o n w i d e b a s i s .

The v a l u e of t h i s d a t a

s o u r c e l i e s i n t h e f a c t t h a t i t was t h e f l r s t s o u r c e t o i n c l u d e i n f o r m a t i o n on v e h i c l e s owned p r i o r t o t h e t i m e t h e s u r v e y was c o l l e c t e d .

I n t h i s c a s e , i n f o r m a t i o n on a l l v e h i c l e s owned d u r i n g t h e one-year p e r i o d p r e c e d i n g t h e s u r v e y d a t e was o b t a f n e d . t h i s data permits the explicit

The a v a i l a b i l i t y of

a n a l y s i s of t h e dynamic a s p e c t s of

t h e v e h i c l e owner s h i p problem. I n a more r e c e n t s u r v e y , t h e N a t i o n a l r n t e r i m Energy Consumpt i o n Study

(NIECS), r e l e v a n t v e h l c l e r e l a t e d i n f o r m a t i o n was c o l l e c t e d

from 4 , 0 8 1 h o u s e h o l d s .

T h i s s u r v e y w a s conducted by t h e U.S. Department

of Energy i n t h e F a l l of 1978 t o o b t a i n i n f o r m a t i o n on e n e r g y consumption i n the residential sector.

As was t h e c a s e w i t h t h e NTS d a t a ,

i n f o r m a t i o n on a l l v e h i c l e s owned d u r i n g t h e one-year p e r i o d p r e c e d i n g t h e s u r v e y d a t e was o b t a i n e d ,

However, f o r a t l e a s t two r e a s o n s ,

t h e NIECS d a t a is s u p e r i o r t o t h e NTS d a t a i n i t s a b i l i t y t o a d d r e s s t h e h o u s e h o l d v e h i c l e ownership problem, t h e NIECS d a t a i s a s u b s t a n t i a l a d v a n t a g e .

F i r s t , t h e s h e e r s i z e of This s i z e advantage permits

e x p l o r a t i o n of v e h i c l e ownership b e h a v i o r by s p e c i f i c segments o f t h e population.

For example, a s u f f i c i e n t number of o b s e r v a t i o n s on house-

h o l d s owning t h r e e and f o u r v e h i c l e s may b e a v a i l a b l e i n t h e l a r g e r d a t a s e t , t h e r e b y p e r m i t t i n g e s t i m a t i o n t h a t c o u l d n o t h a v e been undert a k e n i n t h e s m a l l e r d a t a sample.

The second a d v a n t a g e i s t h a t t h e

c o n f i d e n c e i n t e r v a l s on model p a r a m e t e r estimates w i l l g e n e r a l l y b e

smaller f o r t h e l a r g e r d a t a s e t , t h e r e b y p r o v i d i n g more p r e c i s e

estimates.

To d a t e , o n l y t h e Boaz, A l l e n , & Hamilton (1983) s t u d y

have used t h e NIECS d a t a f o r y e h i c l e ownership m o d e l i n g . 4.2

Household P a n e l D a t a

A t least two h o u s e h o l d p a n e l d a t a s o u r c e s c o n t a i n i n g v e h i c l e r e l a t e d i n f o r m a t i o n a r e known t o e x i s t .

These are t h e Household T r a n s -

p o r t a t i o n P a n e l (HTP) and t h e S e a t t l e and Denver Experiments (SI'ME/DIME).

Income M a i n t e n a n c e

A summary of t h e c h a r a c t e r i s t i c s c o n t a i n e d

i n t h e s e d a t a s o u r c e s i s p r e s e n t e d i n T a b l e 1. The h o u s e h o l d t r a n s p o r t a t i o n p a n e l was i n i t i a t e d by t h e Department of Energy t o p r o v i d e a follow-up s u r v e y ( r e l a t i v e t o t h e NIECS sample) w i t h i n f o r m a t i o n on v e h i c l e u t i l i z a t i o n .

This panel

i n i t i a l l y c o n s i s t e d of p r e v i o u s l y surveyed NIECS h o u s e h o l d s who owned a t l e a s t one v e h i c l e . The s u r v e y s t r a t e g y was t o d i v i d e t h e e l i g i b l e

h o u s e h o l d s of t h e NIECS sample i n t o s i x g r o u p s , and t o c o l l e c t monthly i n f o r m a t i o n on v e h i c l e s owned, f u e l consumed, and m i l e s d r i v e n . The p a n e l w a s . i n i t i a t e d i n J u n e 1979, and one group was b r o u g h t i n t o t h e sample e a c h month f o r a two-month r e p o r t i n g p e r i o d .

Starting

i n December 1979, t h e s e g r o u p s were r e t u r n e d t o t h e sample, one e a c h month, f o r a f i n a l two-month r e p o r t i n g p e r i o d .

To e x t e n d

t h e s u r v e y beyond November 1979, a n o t h e r n a t i o n a l random sample w a s c o l l e c t e d ( i . e . non-NIECS h o u s e h o l d s ) and segmented t o c r e a t e a d d i t i o n a l h o u s e h o l d g r o u p s which w e r e a g a i n i n t r o d u c e d i n t o t h e s u r v e y i n t h e same manner.

D a t a i s a v a i l a b l e from t h i s p a n e l t o December 1980.

The HTP i s a n e x t r e m e l y r i c h d a t a s o u r c e f o r v e h i c l e o w n e r s h i p modeling, a s a l l r e l e v a n t v e h i c l e r e l a t e d information i s i n c l u d e d .

Moreover, when t h e HTP d a t a is l i n k e d w i t h t h e c o r r e s p o n d i n g o b s e r v a t i o n s i n t h e e a r l i e r NIECS s u r v e y , a two-and-one-half

year vehicle

ownership h i s t o r y c a n b e c o n s t r u c t e d f o r e a c h h o u s e h o l d .

This i s

p a r t i c u l a r l y v a l u a b l e i n t h e a s s e s s m e n t of t h e dynamic a s p e c t s of household v e h i c l e ownership.

The HTP d a t a h a s n o t been used i n any

p r e v i o u s v e h i c l e ownership s t u d y . The S e a t t l e and Denver Income Maintenance e x p e r i m e n t s were s u r v e y s conducted t o a s s e s s t h e f e a s i b i l i t y of a n e g a t i v e income t a x program t h a t p r o v i d e s a minimum g u a r a n t e e d income t o e l i g i b l e f a m i l i e s . The s u r v e y e d f a m i l i e s w e r e d i v i d e d i n t o two r o u g h l y

equal groups,

w i t h one group r e c e i v i n g v a r i o u s l e v e l s of g u a r a n t e e d income and t h e o t h e r group u s e d a s t h e s t u d y c o n t r o l . t h e S t a n f o r d R e s e a r c h I n s t i t u t e (SRI)

,

The s u r v e y was conducted by and i n a l l , 2,042 f a m i l i e s

were e n r o l l e d between 1970 and 1 9 7 1 i n S e a t t l e , and 2 , 7 5 8 f a m i l i e s were e n r o l l e d between 1 9 7 1 and 1972 i n Denver.

Eligibility i n the

s u r v e y was l i m i t e d t o low income f a m i l i e s ( i . e . t o t a l income l e s s t h a n $11,000 i n 1 9 7 1 ) .

I n f o r m a t i o n on p a r t i c i p a t i n g f a m i l i e s was

c o l l e c t e d on a q u a r t e r l y b a s i s t h r o u g h t h e e a r l y months of 1978. The p r i m a r y a t t r a c t i o n of t h e SIME/DIME d a t a b a s e i s t h a t i n f o r m a t i o n on s p e c i f i c h o u s e h o l d s i s a v a i l a b l e f o r a s e v e n - y e a r period.

Moreover, t h e r a t e of a t t r i t i o n (always a c o n c e r n w i t h p a n e l

d a t a of t h i s t y p e ) was k e p t t o a minimum ( s e e Spiegleman and Yaeger (1979)).

The m a j o r d i s a d v a n t a g e a s s o c i a t e d w i t h t h e SIME/DIME d a t a

i s t h a t i n f o r m a t i o n on t h e make and m o d e l of v e h i c l e s owned and t h e e x t e n t t o which s u c h v e h i c l e s a r e used i s n o t a v a i l a b l e .

It i s

f r u s t r a t i n g t o know t h a t v e h i c l e make and model i n f o r m a t i o n was a c t u a l l y c o l l e c t e d b u t n e v e r coded onto d a t a f i l e s ,

Recovering

such i n f o r m a t i o n i s v i r t u a l l y impossTble s i n c e a l l work on t h e p r o j e c t t e r m i n a t e d d u r i n g t h e summer of 1982.

The t o t a l absence of v e h i c l e

u t i l i z a t i o n d a t a , and t h e f a c t t h a t only. low lncome h.ouseholds a r e c o n s i d e r e d , f u r t h e r l i m i t s t h e a p p l i c a b i l i t y of t h e sIMX / D I N E s u r v e y t o v e h i c l e ownership modeling.

4.3

Vehicle A t t r i b u t e F i l e s

A s mentioned e a r l i e r , v e h i c l e attribute f i l e s a r e used t o complement household d a t a .

Such f i l e s c o n t a l n i n f o r m a t i o n r e l a t i n g

t o t h e a t t r i b u t e s of s p e c i f i c v e h i c l e makes, models, and v i n t a g e s , One of t h e e a r l i e s t v e h i c l e a t t r i b u t e f i l e s was t h a t assembled by Cambridge S y s t e m a t i c s (1978) and s u b s e q u e n t l y used i n t h e v e h i c l e t y p e c h o i c e r e s e a r c h o f M a n s k i a n d s h e m a n (1980) and Berkovec and Rust (1981).

T h i s f i l e c o n t a i n s a t t r i b u t e i n f o r m a t i o n on over 750

v e h i c l e s from t h e model y e a r s 1967-1978.

The v e h i c l e a t t r i b u t e s

c o n t a i n e d i n t h i s f i l e i n c l u d e v e h i c l e p r i c e ( a s of June 1978) , v e h i c l e weight, f u e l e f f i c i e n c y (NPG)

, turning

r a d i u s , e s t i m a t e of

s e a t i n g s p a c e , 0-60 mph a c c e l e r a t i o n t i m e i n s e c o n d s , i n t e r i o r n o i s e l e v e l s , and luggage s p a c e .

Although r e a s o n a b l y d e t a i l e d , t h e Cambridge

S y s t e m a t i c ' s v e h i c l e a t t r i b u t e f i l e s u f f e r s from two weaknesses. i n f o r m a t i o n on t h e e n g i n e

First,

s i z e of a s p e c i f i c make and model i s ex-

c l u d e d , and i n s t e a d t h e a t t r i b u t e s of t h e model's most p o p u l a r e n g i n e s i z e a r e assumed.

S i n c e e n g i n e o p t i o n s f o r p a r t i c u l a r v e h f c l e models

can have a s u b s t a n t i a l impact on a number of v e h i c l e a t t r i b u t e s

e . g . a c c e l e r a t i o n , horsepower, and f u e l e f f i c i e n c y ) , t h e assumption of t h e most p o p u l a r e n g i n e s i z e can b e q u i t e i m p r e c i s e .

Second,

t h e Cambridge S y s t e m a t i c s ' f i l e h a s many m i s s i n g v e h i c l e models and v i n t a g e s f o r f o r e i g n m a n u f a c t u r e r s , t h e r e b y l i m i t i n g i t s usef u l n e s s t o v e h i c l e ownership modeling. I n r e c o g n i t i o n of t h e d e f i c i e n c i e s of t h e Cambridge S y s t e m a t i c s Hamilton i (1983) c o n s t r u c t e d v e h i c l e a t t r i b u t e f i l e , Booz, A l l e n , ? a v e h i c l e a t t r i b u t e f i l e t h a t provfded i n f o r m a t i o n on engine o p t i o n s and expanded t h e number of f o r e i g n v e h i c l e models and v i n t a g e s considered.

The r e s u l t i n g f i l e c o n s i s t e d of over 2700 v e h i c l e s covering

t h e model y e a r s ( v i n t a g e s ) from 1969 t o 1979 and contained i n f o r m a t i o n on e n g i n e s i z e (displacement i n c u b i c i n c h e s and number of c y l i n d e r s ) , wheel b a s e , w e i g h t , h e i g h t , f r o n t and r e a r s e a t i n g room, luggage s p a c e , horsepower, v e h i c l e p r i c e a s of November 1978, Consumer ~ e p o r t ' s maintenance i n d e x , f u e l e f f i c i e n c y (mpg)

,

t h e EPA roominess f a c t o r ,

and s e a t i n g c a p a c i t y by number of p a s s e n g e r s .

This vehicle atrribute

i n r o m a t i o n was compiled from t h e Oak Ridge N a t i o n a l L a b o r a t o r i e s v e h i c l e d e s c r i p t i o n d a t a , t h e Automotive News market d a t a book i s s u e , Ward's Automotive Almanac, Consumer R e p o r t s ' automotive i s s u e s , and t h e Red Book of r e t a i l c a r p r i c e s .

It i s s t r d n g l y suspected t h a t t h i s

v e h i c l e a t t r i b u t e f i l e i s t h e most complete f i l e i n e x i s t e n c e .

4.4

D e s c r i ~ t i o nof Data Used i n E s t i m a t i o n For t h e purposes of t h e c u r r e n t s t u d y , t h e N a t i o n a l I n t e r i m

Energy Consumption Survey (NIECS) and t h e Household T r a n s p o r t a t i o n P a n e l (HTP) ( b o t h of which were d i s c u s s e d a t l e n g t h e a r l i e r ) were

combined t o p r o v i d e household samples c a p a b l e of e s t i m a t i n g t h e t h e o r e t i c a l models d e r i v e d ih t h e p r e c e d i n g c h a p t e r .

The s t r a t e g y

was t o s e l e c t t h e Household T r a n s p o r t a t i o n P a n e l Groups f i r s t e n t e r i n g i n J u n e , J u l y and August 1979 (and r e t u r n i n g t o t h e p a n e l i n Decemb e r 1979, and J a n u a r y and February 1980 -respectively) households w i t h t h e i r c o r r e s p o n d i n g NIECS i n f o r m a t i o n . of t h e s e two

and l i n k t h e s e The combination

s u r v e y s p r o v i d e s v e h i c l e ownership i n f o r m a t i o n f o r t h e

same households ( a t o t a l of 962 households) from t h e f a l l of 1977 t o t h e s p r i n g of 1980, With t h e l i n k a g e of t h e two s u r v e y s completed, t h e r e s u l t i n g d a t a was o r g a n i z e d i n t o f i v e d i s c r e t e t i m e i n t e r v a l s of a s i x - m o n t h duration ( t h i s i s i l l u s t r a t e d I n Figure 1 ) .

Thus, household v e h i c l e

h o l d i n g s ( q u a n t i t y and t y p e ) a r e known a s of December 1977, w i t h c o r r e s p o n d i n g u t i l i z a t i o n accumulated o v e r t h e J a n u a r y 1978 t o J u n e 1978 p e r i o d , h o l d i n g s a s of June 1978, w i t h c o r r e s p o n d i n g u t i l i z a t i o n from J u l y 1978 t o December 1978, and s o on f o r December 1978, June 1979, and December 1979.

However, t h e forthcoming e m p i r i c a l a n a l y s i s

i s f o r c e d t o b e g i n w i t h t h e v e h i c l e h 0 3 d i n s a s of December 1978 s i n c e

t h i s was t h e f i r s t t i m e p e r i o d f o r which one and two t i m e p e r i o d u t i l i z a t i o n l a g s could b e i n c o r p o r a t e d , a s r e q u i r e d f o r t h e r e s t r i c t e d and i n t e r t e m p o r a l models d e r i v e d i n t h e p r e c e d i n g c h a p t e r .

Hence i n

t h e a c t u a l e s t i m a t i o n s c o n t a i n e d h e r e i n , t h r e e t i m e p e r i o d s were u s e d : (1)

v e h i c l e h o l d i n g s a s of December 1978 w i t h u t i l i z a t i o n from

J a n u a r y 1979 t o June 1979; (2) v e h i c l e h o l d i n g s a s of June 1979, w i t h u t i l i z a t i o n from J u l y 1979 t o December 1979; (3) v e h i c l e h o l d i n g s

a s of December 1979, w i t h u t 2 l i z a t i o n from J a n u a r y 1980 t o June 1980. It s h o u l d be n o t e d t h a t t h e s e p e r i - o d s . r e s p e c t i v e l y c a p t u r e household

v e h i c l e ownership b e h a v i o r b e f o r e , d u r i n g , and a f t e r t h e June 1979 e n e r g y shock. To supplement t h e c r o s s - s e c t i o n a l time s e r i e s household d a t a , t h e Booz, A l l e n 6 Hamilton v e h i c l e a t t r i b u t e f i l e was used a s a b a s f s f o r creati'ng an expanded a t t r i , b u t e f l l e t h a t would be s u i t a b l e f o r t h e t i m e p e r i o d s over which household d a t a was a v a i l a b l e .

In

summary, t h e Booz, Allen 6 Hamilton a t t r i b u t e f i l e w a s modified as follows:

(1) a t t r i b u t e i n f o r m a t i o n on 1980 model y e a r v e h i c l e s was

added s i n c e such v e h i c l e s were a v a i l a b l e t o t h e household sample i n t h e f a l l of 1979; ( 2 ) t h e Red Book r e t a i l c a r v a l u e s were added t o i n c l u d e v a l u e s a s of December 1977, J u n e 1978, December 1978, June 1979, and December 1979; and (3) v e h i c l e a t t r i b u t e s of t h e pre-1969 model y e a r v e h i c l e s were added t o match t h o s e v e h i c l e s a c t u a l l y owned by t h e household sample, The combination of t h e household and v e h i c l e a t t r i b u t e f i l e s d e s c r i b e d above, p r o v i d e a s u f f i c i e n t l y d e t a i l e d d a t a b a s e f o r e s t i m a t i o n of t h e v e h i c l e ownership and u t i l i z a t i o n models proposed i n t h e p r e c e d i n g chapter.

A l l items considered,

t h e d a t a b a s e used

i n t h i s s t u d y i s a r g u a b l y t h e r i c h e s t and most complete d a t a s o u r c e ever

used i n t h e a n a l y s i s of household v e h i c l e ownership b e h a v i o r .

CHAPTER 5 .

EMPIRICAL ESTIPLATION AND 'RESULTS

T h i s c h a p t e r p r e s e n t s t h e e s t i m a t i o n r e s u l t s of v e h h l e owners h i p models of t h e form d e r i v e d i n Chapter 3 ,

Also, t o a s s e s s t h e

c u r r e n t and f u t u r e p r o s p e c t s of household v e h i c l e denand, a number of

a p p l i c a t i o n s of t h e e s t i m a t e d models a r e p r e s e n t e d . The o r g a n i z a t i o n of t h l s c h a p t e r i s a s f o l l o w s .

F i r s t , a number

of p o i n t s a r e d i s c u s s e d r e l a t i n g t o t h e d i f f e r e n c e s between t h e t h e o r e t i c a l models d e r i v e d i n Chapter 3 and t h e f i n a l s p e c i f i c a t i o n s used i n emprrical est3mation.

Next, t h e e s t i m a t i o n r e s u l t s of t h e t y p e

c h o i c e , u t i l i z a t i o n , and l e v e l cho?ce models a r e p r e s e n t e d and t h e Z r implications are evaluated,

Following t h i s , an assessment of v e h i c l e

demand r e s p o n s i v e n e s s i s g i v e n , based on s e v e r a l a p p l i c a t i o n s of t h e e s t i m a t e d models.

F i n a l l y , t h e c h a p t e r concludes w i t h a number of

s p e c i f i c a t i o n t e s t s performed t o d e t e r m i n e t h e v a l i d i t y of t h e e c o n o m e t r i c approach used i n model e s t i m a t i o n . 5.1

F i n a l Empirical S p e c i f i c a t i o n s There a r e a number of estimation c o n s i d e r a t i o n s t h a t determined

t h e f i n a l model s p e c i f i c a t i o n s .

The f i r s t concern r e l a t e s t o t h e

e s t i m a t i o n of t h e i n d i r e c t u t i l i t y and u t i l i z a t i o n e q u a t i o n p a r a m e t e r s ( t h e A's

i n Equations (38),

s u b s c r i p t e d by i.

(391, and ( 4 0 ) ) which have been up t o now

Given t h e l a r g e number of v e h i c l e t y p e a l t e r n a t i v e s

a v a i l a b l e t o t h e household, T t i s e m p i r i c a l l y n e c e s s a r y t o c o n s t r a i n t h e s e p a r a m e t e r s t o be e q u a l a c r o s s a v a i l a b l e v e h i c l e a l t e r n a t i v e s .

m

a s i m i l a r v e i n , t y p i c a l u t i l i z a t i o n ( r . ' s i n Equation ( 3 8 ) ) i s lt

n o t p e ~ m i t t e dt o vary a c r o s s i , a g a i n d u e t a t h e l a r g e number of a v a i l a b l e v e h i c l e alternatiyes, The n e x t i s s u e c o n c e r n s t h e e s t i m a t i o n of t h e t y p e c h o i c e models and of t h e e s t i m a t i o n of a number of t e r m s a p p e a r i n g i n t h e i n d i r e c t u t i l i t y f u n c t i o n , s p e c i f i c a l l y Z'B, A31t-l

v t , n r t , A 2 1 t , Ao, and

( s e e Equation ( 3 8 ) ) .

I n p r a c t i c e t h e s e terms w i l l v a r y a c r o s s -A2 P it. Unfortunately , a l t e r n a t i v e s s i n c e t h e y a r e m u l t i p l i e d by e

a l l o w i n g t h e s e terms t o v a r y a c r o s s a l t e r n a t i v e s would make e s t i m a t i o n d i f f i c u l t , i f n o t i m p o s s i b l e , s i n c e , f o r example, e q u a t i o n d i s t r u b a n c e , i s n o t known.

v

t'

the utilization

To r e s o l v e t h i s problem and t o

r e t a i n a l o g i t s t r u c t u r e , c o n s l d e r a r e w r i t t e n form of t h e t o t a l e r r o r term

a p p l y i n g a T a y l o r s e r i e s expansion around t h e mean o p e r a t i n g p r i c e P

t

i f h i g h e r o r d e r t e r m s a r e assumed n o t t o c o n t r i b u t e s i g n i f i c a n t l y , t h e e r r o r term becomes

This assumption

i s reasonable t o the extent t h a t there i s a r e l a t i v e l y

s m a l l v a r i a n c e i n o p e r a t i n g p r i c e s (1i.e. p r i c e p e r g a l l o n

+ vehicle -A2

miles per gallon).

With t h i s assumption a c c e p t e d , t h e term

does n o t v a r y a c r o s s a l t e r n a t i v e s . Aoy

Trt,

A2q7 A3 I't-1' and Z'B

V

t

e

Pf

S i m i l a r l y , t h e remaining terms

can a l s o be e l i m i n a t e d from t h e i n d i r e c t

u t i l i t y function. The n e x t t w o p o i n t s r e l a t e t o i n f o r m a t i o n t h a t was o b t a i n e d from i n i t i a l e s t i m a t i o n of t h e t y p e c h o i c e and u t i l i z a t i o n models, F i r s t , r e c a l l t h a t - i n t h e t y p e c h o i c e model a number of terms a r e -A P m u l t i p l i e d by e t . During e s t i m a t i o n of t h e t y p e c h o i c e models i t was found t h a t t h e l o g - l i k e l i h o o d a t convergence was r e l a t i v e l y i n s e n s i t i v e t o v a l u e s of -A2.

I n f a c t , v a l u e s of -A

2

i n t h e r a n g e of -3.0

t o +13.0 d i d n o t r e s u l t i n s i g n i f i c a n t d i f f e r e n c e s i n t h e l o g l i k e l i hood a t convergence o r i n parameter e s t i m a t e s . t h e e s t i m a t i o n s c a r r i e d out h e r e , -A

2

Consequently, f o r a l l

was s e t e q u a l t o -.I.

This i s

a t h e o r e t i c a l l y p l a u s i b l e v a l u e i n addition t o being s t a t i s t i c a l l y w i t h i n t h e r a n g e of a d m i s s i b l e v a l u e s t h a t maximize t h e l o g - l i k e l i h o o d . The second p o i n t concerns t h e dynamic s t r u c t u r e of t h e e m p i r i c a l models.

I n i t i a l e s t i m a t i o n s of s p e c i f i c a t i o n s t h a t

i n c o r p o r a t e d lagged o p e r a t i n g c o s t and lagged income v a r i a b l e s y i e l d e d h i g h l y i n s i g n i f i c a n t and s m a l l parameter e s t i m a t e s f o r t h e s e v a r i a b l e s . T h i s s u g g e s t s t h a t a t h e o r e t i c a l model which i s based on a s t a t e v a r i a b l e summarizing p a s t u t i l i z a t i o n s and a c o n s t a n t r a t e of s t a t e d e p r e c i a t i o n may n o t be a p p r o p r i a t e f o r a n a l y z i n g household v e h i c l e ownership.

I n p a r t i c u l a r , i t appears t h a t t h e assumption of a c o n s t a n t

r a t e of s t a t e d e p r e c i a t i o n i s h i g h l y q u e s t i o n a b l e s i n c e e m p i r i c a l e v i dence i n d i c a t e s t h a t t h e s t a t e v a r l a l j l e may a c t u a l l y a p p r e c i a t e i n some p e r i o d s .

T h i s was found t o be t h e c a s e l m e d 2 a t e l y f o l l o w i n g t h e

energy c r i s i s d u r i n g t h e s l m e r of 1979, a s households v a l u e d p r e - c r i s i s h a b i t s more h i g h l y t h a n c r i s i s h a b i t s .

Tn any e v e n t , t h e d e p r e c i a t i o n

r a t e a p p e a r s t o be h i g h l y i r r e g u l a r and i n c o n s i s t e n t w i t h t h e c o n s t a n t r a t e assumed i n t h e t h e o r e t i c a l d e r i v a t i o n s .

In order t o r e s o l v e t h i s

problem, t h e e s t i m a t e d models excluded lagged o p e r a t i n g c o s t and lagged income v a r i a b l e s .

A s such, t h e f i n a l s p e c i f i c a t i o n s a c t u a l l y e s t i m a t e d

a r e more i n l i n e w i t h t h e h a b i t f ormatlon t a s t e change work of P o l l a k and Wales (1969) and P o l l a k (1970). F h a l l y , t o s t a t f s t i , c a l l y t e s t f o r s t r u c t u r a l s t a b i l i t y of v e h i c l e l e v e l , t y p e , and u t i l i ' z a t i o n model p a r a m e t e r s over time, d a t a from v a r i o u s time p e r i o d s w a s pooled t o r e - e s t i m a t e model p a r a m e t e r s . I n s o d o i n g , t h e f a c t t h a t t h e r e may be two o r t h r e e o b s e r v a t i o n s from t h e same household was n o t accounted f o r .

A s p o i n t e d o u t by

Chamberlain ( 1 9 8 0 ) , accounting f o r household s p e c i f i c e f f e c t s i n pooled time s e r i e s d a t a t e n d s t o be d 2 f f i c u l t f o r d i s c r e t e models. S i n c e t h e r e e x i s t s t h e p o s s i b i l i t y of omitted v a r i a b l e b i a s i f t h i s e f f e c t i s n o t account f o r , t h e r e s u l t s of t h e combined time p e r i o d e s t i m a t i o n s , which w i l l be p r e s e n t e d i n forthcoming s e c t i o n s , should b e viewed w f t h some cauti'on.

5.2

T v ~ eChoice Models: Sinnle-Vehicle Households The s i n g l e v e h i c l e household t y p e c h o i c e model s p e c i f i e s t h e

p r o b a b i l T t p of t h e household s e l e c t i n g a s p e c i f i c v e h i c l e t y p e ,

defined by v e h i c l e make ( e . g . C h e y r o l e t ) , model ( e . g , C o r v e t t e ) , and v i n t a g e (e.g.

1 9 7 5 ) , c o n d i t i o n e d on t h e f a c t t h a t one and o n l y one

v e h i c l e i s s e l e c t e d ( t h e v e h i c l e l e v e l o r q u a n t i t y choice model w i l l be p r e s e n t e d l a t e r ) .

With t h e v e h i c l e a t t r i b u t e f i l e prepared f o r

t h i s s t u d y ( s e e t h e prev*ous c h a p t e r f o r a d e s c r i p t i o n ) , t h e household t h e o r e t i c a l l y can s e l e c t from w e l l over 2000 d i f f e r e n t v e h i c l e type a l t e r n a t i v e s .

S i n c e t h e computational burdens of p r o v i d i n g s o

many a l t e r n a t i v e s i n t h e e s t i m a t i o n p r o c e s s would be e x c e s s i v e , a sampling of a v a i l a b l e a l t e r n a t i v e s w a s undertaken s i n c e c o n s i s t e n t parameter e s t i m a t e s can be o b t a i n e d from such a procedure p r o v i d i n g a l o g i t s t r u c t u r e i s used ( s e e t h e d i s c u s s i o n p r e s e n t e d i n S e c t i o n 3 . 4 ) . For t h e e m p i r i c a l a n a l y s i s c a r r i e d out h e r e , t h e h o u s e h o l d ' s c h o i c e s e t included t e n v e h i c l e type a l t e r n a t i v e s .

I n t h e case where a house-

hold owned a v e h i c l e ( o r v e h i c l e s ) i n t h e preceding p e r i o d , t h i s v e h i c l e ( o r v e h i c l e s ) w a s i n c l u d e d among t h e t e n a l t e r n a t i v e s .

Also,

a s a n o t e , i n o r d e r t o t e s t f o r t h e r o b u s t n e s s of t h i s sampling proc e d u r e , models were e s t i m a t e d w i t h c h o i c e s e t s of e i g h t , twenty, and t h i r t y a l t e r n a t i v e v e h i c l e t y p e s and v i r t u a l l y no change i n parameter e s t i m a t e s was found. With t h e above p o i n t s i n mind, a t t e n t i o n can now be given t o t h e p r e c i s e s p e c i f i c a t i o n of t h e i n d i r e c t u t i l i t y f u n c t i o n . the indirect u t i l i t y function

Although

d e r i v e d e a r l i e r (Equation 38) completely

s p e c i f i e s t h e dynamic a s p e c t of t h e v e h i c l e ownership d e c i s i o n , t h e in v e c t o r of o b s e r v a b l e household and v e h i c l e c h a r a c t e r i s t i c s (Y' li 1 Equation ( 3 8 ) ) i n f l u e n c i n g v e h i c l e t y p e c h o i c e s t i l l must be s p e c i f i e d .

The c o m p l e t e l i s t of e x p l a n a t o r y v a r i a b l e s u l t i m a t e l y u s e d i n model e s t i m a t i o n i s p r e s e n t e d i n T a b l e 2 a l o n g w i t h t h e i r summary s t a t i s t i c s . A l s o , t h e r e s u l t i n g model parameteT e s t i m a t e s f o r d i s t i n c t and combined t i m e p e r i o d s are g i v e n i n T a b l e 3.

To s t r u c t u r e t h e d i s c u s s i o n of t h e

e x p l a n a t o r y v a r i a b l e s e l e c t i o n p r o c e s s and t h e r e s u l t i n g p a r a m e t e r estimates, f o u r c a t e g o r i e s of v a r i a b l e s are p r e s e n t e d : 1 ) v e h i c l e c o s t

v a r i a b l e s , 2) dynamic components, 3 ) g e n e r a l v e h i c l e c h a r a c t e r i s t i c s , and 4) b r a n d ( v e h i c l e make) p r e f e r e n c e v a r i a b l e s . V e h i c l e Cost V a r i a b l e s E s s e n t i a l l y , two components of v e h i c l e c o s t s can b e e n v i s i o n e d , o p e r a t i n g c o s t s and c a p i t a l c o s t s .

I n t h i s a n a l y s i s o p e r a t i n g c o s t s are

measured as t h e f u e l c o s t p e r m i l e ( d e t e r m i n e d by d i v i d i n g t h e p r e v a i l i n g p e r g a l l o n p r i c e of f u e l by t h e f u e l e f f i c i e n c y of t h e v e h i c l e t y p e a l t e r n a t i v e measured i n m i l e s p e r g a l l o n ) m u l t i p l i e d by t h e t y p i c a l o r e x p e c t e d u t i l i z a t i o n measured as m i l e s a c c u m u l a t e d o v e r r e s p e c t i v e six-month t i m e p e r i o d s ,

The r e s u l t i s t h e t o t a l e x p e c t e d

f u e l o p e r a t i n g c o s t s i n c u r r e d d u r i n g a six-month t i m e p e r i o d .

In enter-

i n g o p e r a t i n g c o s t s i n t h e s p e c i f i c a t i o n , t h e t e r m i s d i v i d e d by a n n u a l h o u s e h o l d income t o s u p p o r t t h e h y p o t h e s i s t h a t o p e r a t i n g c o s t s s h o u l d b e less o n e r o u s t o h i g h income h o u s e h o l d s . Over t h e t h r e e six-month t i m e p e r i o d s w i t h which models w e r e e s t i m a t e d ( p e r i o d s b e f o r e , d u r i n g , and a f t e r t h e J u n e 1979 e n e r g y s h o c k ) , t h e a v e r a g e p e r g a l l o n f u e l p r i c e i n c r e a s e d from $0.72 t o $ 1 . 1 7 , making t h i s o v e r a l l time span p a r t i c u l a r l y i n t e r e s t i n g i n studying t h e e f f e c t s of r a p i d l y e s c a l a t i n g o p e r a t i n g c o s t s .

The p a r a m e t e r estimates o f t h e

Table 2 .

V a r i a b l e s Used i n S i n g l e - V e h i c l e Type Choice Models (Means f o r Chosen A l t e r n a t i v e s ) PIU) la PRD 2b Hean Xean

PRD 3' Xean

PIRO

.0201

.0259

.03304

CAPO

.2120

.2070

.2080

F r o n t 2r.d r e a r s h o u l d e r room ( i n . ) F o r h o u s e h o l d s w i t h 3 o r more members

GFRSR

38.55

38.30

38.35

American Motors D m y ( 1 i f AMC, 0 otherwise)

AMC

.0380

.0352

.0302

Ford d m y ( 1 i f F o r d , 0 o t h e r w i s e )

FORD

.2742

.2734

.2702

C h r y s l e r dummy ( 1 i f C h r y s l e r , 0 o t h e r w i s e )

CHRY S

.I265

.I271

.I264

F o r e i g n c a r dummy ( 1 i f f o r e i g n c a r , 0 otherwise)

FORN

.0875

.0861

.0906

Horsepower + e n g i n e d i s p l a c e m e n t ' CCI) For h o u s e h o l d s w i t h h e a d s 35 y e a r s o l d o r less

ETE CH

.I871

.I885

.I906

Luggage s p a c e ( f t ' ) f o r household w i t h f o u r o r more members

GLUG:1

3.605

3.592

3.547

2 y r s o l d o r newer

WAG

.2100

.I980

.2060

vehicle 8 y r s old or older

OLDAG

.3520

.3750

.3681

345

361

364

Variable (Fuel c o s t ($/mi) Income (S/yr)

Elnemonic

*

V e h i t l e C a p i t a l Cost Incone ( S i y r )

d t-ypical u t - i l i z a t i o n (mi) ) +

+

1 P e r i o d l a g g e d u t i l i z a t i o n (mi.) Same v e h i c l e 2 P e r i o d l a g g e d u t i l i z a t i o n (mi.) Same v e h i c l e 1 P e r i o d l a g g e d u t i l i z a t i o n (mi.) S i m i l a r nzke v s h i c l e 2 P e r i o d l a g g e d u t i l i z a t i o n (mi.) S i m i l a r make v e h i c l e F r o n t and r e a r s h o u l d e r room ( i n . ) F o r h o u s e h o l d s w i t h 2 o r l e s s members

New v e h i c l e dummy

- vehicle

Old v e h i c l e dummy

-

Number of o b s e r v a t i o n s

-

Table 2 (continued)

% e r i o d 1 i s type c h o i c e a s of December 1 9 7 8 , w i t h u t i l i z a t i o n from J a n . 1979 t o June 1979. The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $0.72 p e r g a l l o n . b ~ e r i o d2 i s t y p e c h o i c e a s of J u n e 1979, w i t h u t i l i z a t i o n from June 1979 t o Dec. 1980. The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $0.96 p e r g a l l o n . 'period 3 i s t y p e c h o i c e a s of December 1 9 7 9 , w i t h u t i l i z a t i o n from J a n . 1980 t o J u n e 1980. The mean f u e l p r i c e i n t h i s six-month period i s $1.17 p e r g a l l o n . d ~ y p i c a ul t i l i z a t i o n i s d e t e r m i n e d by a p p l y i n g t h e f o l l o w i n g e q u a t i o n s f o r s i n g l e v e h i c l e households: Typical u t i l i z a t i o n ( r

It

) = 2684 +457.8

+

.05294

*

*

number of household members

income ( $ / ~ r )

For two v e h i c l e h o u s e h o l d s T y p i c a l u t i l i z a t i o n of e a c h v e h i c l e ( r Z t ) = 3331

+

household membes+ .04686

151.1

+

*

number of

income ( $ / v r )

The p a r a m e t e r s i n t h e s e e q u a t i o n s were e s t i m a t e d by o r d i n a r y l e a s t s q u a r e s u s i n g a v e r a g e u t i l i z a t i o n s d e r i v e d from a l l a v a i l a b l e p e r i o d s i n t h e household sample.

Table 3.

Type Choice Model Parameter E s t i m a t e s ( S t a n d a r d E r r o r s i n p a r e n t h e s e s ) : S i n g l e V e h i c l e Households 1 1 1 L c r c e m ~ ~ ~ Hudcl ~rnl.

LFHSR

FORD

FOHN

l'crltwl 1

I'crlod 2

I'erlod 3 --

I'urloJ163

Alll'er!odtl_

-21.17 (11.91)

-23.40 (7.91)

-31.41 (7.85)

-26.20 (6.57)

-25.08 (5.01)

I

HcuLrlt:Lcd Hc,'l~: l

-

.

I'rrlud 1

L'el.LcwI 2

Pcrid 3

I'erindu 1 b 3

All I ' ~ ~ . L , , ~ I J

-23.70 (11.30)

-23.56 (7.88)

-31.93 (7.44)

-27.6 (6.21)

-25.85 (4.84)

t h e o p e r a t i n g c ~ s vt a r i a b l e (PTRQ) a r e g i v e n i n Table 3 , and i t i s c l e a r t h a t t h e s e parameters a r e c o r r e c t l y sl'gned (i, e , i n c r e a s e d o p e r a t i n g c o s t s have a n e g a t i v e e f f e c t on v e h i c l e s e l e c t i o n p r o b a b i l i ~ i e s ) and s t a t i s t f c a l l y s i g n i f i c a n t i n a l l t h r e e time p e r i o d s ,

Also, f t should

be noted t h a t t h e magnitude of t h e PIRO parameter i n c r e a s e s n o t i c e a b l y from time p e r i o d 1 t o time p e r i o d 3 i n b o t h t h e r e s t r i c t e d and i n t e r temporal models, i n d i c a t i n g t h a t households' v a l u a t i o n of o p e r a t i n g c o s t s h a s been i n c r e a s i n g over t i m e .

As a f i n a l point, other ~ p e r a t i n g

c o s t s t h a t may be presumed t o i n f l u e n c e t h e v e h i c l e type decis?on, such a s i n s u r a n c e c o s t s , maintenance c o s t s , and a c c i d e n t repa?r c o s t s , were n o t i n c l u d e d i n t h e s p e c i f i c a t i o n p r i m a r i l y due t o t h e una v a i l a b i l i t y of such d a t a . The o t h e r important component of v e h i c l e c o s t s i s t h e c a p i t a l cost.

T h i s v a r i a b l e (CAPO) i s e n t e r e d i n t o t h e s p e c i f i c a t i o n as t h e

p r e v a i l i n g Red Book p r i c e of t h e v e h i c l e t y p e , d i v i d e d by household income t o r e f l e c t t h e b e l i e f t h a t c a p i t a l c o s t s a r e l e s s onerous t o h i g h income households.

A s T a b l e 3 i n d i c a t e s , t h e CAPO parameter

e s t i m a t e s a r e p r o p e r l y s i g n e d and s t a t i s t i c a l l y s i g n i f i c a n t f o r b o t h t h e i n t e r t e m p o r a l and r e s t r i c t e d models i n a l l time p e r i o d s .

In

terms of parameter magnitudes, t h e impact of t h e c a p i t a l c o s t s a p p e a r t o be f a i r l y s t a b l e o v e r t i m e . With t h e PIRO and CAPO parameter e s t i m a t e s , i t i s p o s s i b l e t o c a l c u l a t e t h e m a r g i n a l r a t e of s u b s t i t u t i o n (MRS) of o p e r a t i n g and capital costs.

A s i n d i c a t e d i n T a b l e 4 , t h e amount t h a t a household

i s w i l l i n g t o pay i n terms of i n c r e a s e d c a p i t a l c o s t s f o r a one-cent

T a b l e 4 . M a r g i n a l R a t e s of S u b s t i t u t i o n of O p e r a t i n g and C a p i t a l Costs . ( F r i c e w i l l i n g t o pay f o r l c / m i d e c r e a s e i n o p e r a t i n g c o s t s ) and Implied Annualized Discount F a c t o r s : S i n g l e V e h i c l e Households (Standard E r r o r s i n Farentheses) Interte~nporalModel Period 2

Period 3

Period 1 6 3

A l l Periods

Period 1

Period 2

Period 3

Periods 1 6 3

A l l Periodr

4409

4501

4559

4483

4486

4409

4501

4559

4483

4486

(15.5)

19.8 (7.8)

15.6 (5.0)

19.2 (5.5)

I

Income Typical Hem

-.

Restricted Hddel

Period 1

.

ion

Discount

p e r m2le d e c r e a s e i n o p e r a t i n g c ~ s t sCip c o n s t a n t d o l l a r s ) evaluated a t t h e p o p u l a t i o n mean, h a s i n c r e a s e d s u b s t a n t i a l l y over t i m e , These e s t i m a t e d m a r g i n a l r a t e s of s u b s t i t u t i o n prov2de some additional i n t e r e s t i n g information.

For example, i f a d r i v i n g r a t e of

4500 m i l e s p e r six-month p e r i o d i s assumed, then a $45 s a v i n g s can be expected f o r a one-cent r e d u c t i o n i n v e h i c l e o p e r a t i n g c o s t s .

Further,

i f a c o n s t a n t v e h i c l e d e p r e c i a t i o n r a t e of 9 p e r c e n t i s assumed a l o n g w i t h a d i s c o u n t r a t e of 3 p e r c e n t , t h e n t h e semi-annual i s 12 p e r c e n t of t h e p u r c h a s e p r i c e .

c a p i t a l cost

Given t h e s e assumptions, t h e

" r a t i o n a l " household could be expected t o pay $375 ( i . e . f o r a one c e n t p e r m i l e r e d u c t i o n i n o p e r a t i n g c o s t s .

$45

+

12%)

As indicated

i n Table 4 , t h e 'MRS e s t i m a t e s a r e r e a s o n a b l y c o n s i s t e n t w i t h t h i s example.

The f a c t t h a t t h e e s t i m a t e d m a r g i n a l r a t e s of s u b s t i t u t i o n

r e p o r t e d h e r e a r e i n c r e a s i n g o v e r t i m e most l i k e l y i n d i c a t e s an i n c r e a s e , among households, i n expected f u e l p r i c e s and/or a h i g h e r v a l u a t i o n of f u t u r e r e d u c t i o n s i n o p e r a t i n g expenses. I n a r e l a t e d m a t t e r , household d i s c o u n t f a c t o r s were c a l c u l a t e d and t h e r e s u l t a n t v a l u e s a r e a l s o p r e s e n t e d i n Table 4.

It should be

n o t e d t h a t t h e d i s c o u n t f a c t o r s p r e s e n t e d i n Table 4 i m p l i c i t l y i n c l u d e t h e t r u e d i s c o u n t r a t e p l u s expected v e h i c l e d e p r e c i a t i o n .

As s u c h ,

e s t i m a t e d d i s c o u n t f a c t o r s i n t h e v i c i n i t y of 15-30% can be c o n s i d e r e d p l a u s i b l e i n t h e s e n s e t h a t a n n u a l o p e r a t i n g and c a p i t a l c o s t s w i l l be equal.

The f a c t t h a t t h e d i s c o u n t f a c t o r s a r e d e c l i n i n g over t i m e

a g a i n r e f l e c t s h o u s e h o l d s t i n c r e a s e d v a l u a t i o n of v e h i c l e o p e r a t i n g costs.

I n g e n e r a l , t h e s e r e s u l t s i n d 2 c a t e t h a t households a r e

74

d i s c o u n t i n g t h e impacts of f u t u r e o p e r a t i n g c o s t s a t r a t e s t h a t a r e l e s s t h a n t h o s e r a t e s i n d i c a t e d b e f o r e t h e energy shock.

In a sense,

t h e y a r e becoming l e s s myopic and more aware of f u t u r e c o s t s . Dynamic Components A s i n d i c a t e d i n t h e d e r i v a t i o n s g i v e n i n Chapter 3 , t h e dynamic components of t h e v e h i c l e t y p e c h o i c e model a r e r e p r e s e n t e d by t h e lagged u t i l i z a t i o n s of t h e same v e h i c l e ( i . e . i n d i c a t i n g t h a t t h e v e h i c l e had been owned and o p e r a t e d i n p r e c e d i n g p e r i o d s ) o r of a v e h i c l e of a s i m i l a r make.

R e c a l l t h a t t h e u t i l i z a t i o n of a v e h i c l e of a s i m i l a r

make a t t e m p t s t o c a p t u r e t h e n o t i o n of brand l o y a l t y , d e f i n e d as t h e accumulation of i n f o r m a t i o n through d r i v i n g and ownership e x p e r i e n c e , on p a r t i c u l a r v e h i c l e makes ( b r a n d s ) .

A s i n d i c a t e d i n Table 3 , t h e

p a r a m e t e r e s t i m a t e s of a l l t h e dynamic components, X T 1 , XT2, XPT1, and XPT2

a r e properly

s i g n e d ( i . e . p a s t ownership h a s a p o s i t i v e e f f e c t

on t h e p r o b a b i l i t y of v e h i c l e s e l e c t i o n ) and s t a t i s t i c a l l y s i g n i f i c a n t a c r o s s time p e r i o d s .

111 terms of p a r a m e t e r magnitudes, t h e lagged

u t i l i z a t i o n s of t h e same v e h i c l e ( x T ~ ,XT2) a r e s u b s t a n t i a l l y l a r g e r t h a n t h o s e of a s i m i l a r make v e h i c l e (XPT1, XPT2), a s was i n i t i a l l y expected. Perhaps t h e most i n t e r e s t i n g a s p e c t of t h e dynamic component parameter e s t i m a t e s i s t h a t t h e y draw t h e o n l y e m p i r i c a l d i s t i n c t i o n between t h e i n t e r t e m p o r a l and r e s t r i c t e d models. i n t e r t e m p o r a l model c o n t a i n s t h e two-period and XPT2, and t h e r e s t r i c t e d model d o e s n o t . XPT2

Specifically, the

lagged u t i l i z a t i o n s , XT2 The i n c l u s i o n of XT2 and

i n t h e model s t r u c t u r e produce c o r r e c t l y s i g n e d and s t a t i s t T c a l l y 75

s i g n i f i c a n t corresponding parameter e s t i m a t e s t h e r e b y i n d i c a t f n g t h a t t h e i n t e r t e m p o r a l model may be j u s t i f i e d .

However, t h e %on-dynamic''

component parameter e s t i m a t e s a r e v i r t u a l l y i d e n t i c a l as r e f l e c t e d i'n t h e r e s u l t s p r e s e n t e d i n Table 3 .

Subsequently, t h e s u b s t a n t i v e

c o n c l u s i o n s t h a t can be drawn from t h e e s t i m a t i o n r e s u l t s a r e q u i t e s i m i l a r f o r b o t h t h e i n t e r t e m p o r a l and r e s t r i c t e d models. General V e h i c l e C h a r a c t e r i s t i c s General v e h i c l e c h a r a c t e r i s t i c s can be c l a s s i f i e d i n t o t h r e e c a t e g o r i e s ; 1 ) dimensions, 2 ) performance, and 3 ) r e l i a b i l f t y .

Vehicle

dimensions can be i n c l u d e d i n t h e model es-timation t o r e f l e c t t h e e f f e c t t h a t s e a t i n g c a p a c i t y , cargo s t o r a g e a r e a , passenger comfort, and m a n e u v e r a b i l i t y w i l l have on t h e c h o i c e of v e h i c l e t y p e s .

I n terms of

d a t a , i n f o r m a t i o n i s a v a i l a b l e on f r o n t and r e a r s e a t s h o u l d e r rooms ( s e a t i n g c a p a c i t y ) , luggage s p a c e (cargo s t o r a g e a r e a ) , v e h i c l e weight ( a proxy f o r r i d e c o m f o r t ) , and v e h i c l e wheel b a s e ( a proxy f o r maneuverability).

I n t h e f i n a l e s t i m a t i o n s , only s h o u l d e r room and luggage

space were found t o produce s i g n i f i c a n t r e s u l t s .

The s h o u l d e r room

v a r i a b l e was d e f i n e d a s t h e summation of f r o n t and r e a r s e a t s p a c e , and s e p a r a t e parameters were e s t i m a t e d f o r householdswith two o r fewer members (WRSR) and f o r households w i t h t h r e e o r more members.

This

s e p a r a t i o n s u p p o r t s t h e h y p o t h e s i s t h a t l a r g e r households w i l l v a l u e s e a t i n g c a p a c i t y more t h a n s m a l l e r households. Indeed, t h e e s t i m a t i o n s p r e s e n t e d i n Table 3 i n d i c a t e t h a t t h e parameters a r e p r o p e r l y s i g n e d (i.e.

s e a t i n g c a p a c i t y h a s a p o s i t i v e impact on t h e p r o b a b i l i t y of

v e h i c l e s e l e c t i o n ) , s t a t i s t i c a l l y s i g n i f i c a n t , and, i n f a c t , t h e

GFRSX p a r a m e t e r i s s u b s t a n t i a l l y l a r g e r i n magnitude t h a n t h e LFRSR parameter, a s expected,

A l s o , i t a p p e a r s t h a t household v a l u a t i o n s

of s e a t i n g c a p c i t y have i n c r e a s e d s l i g h t l y over t i m e . The luggage s p a c e v a r i a b l e , GLUG1, was d e f i n e d a s a v a i l a b l e c a r g o s p a c e i n c u b i c f e e t , and was s p e c i f i e d o n l y f o r h o u s e h o l d s w i t h f o u r o r more members.

The h y p o t h e s i s h e r e i s t h a t luggage s p a c e i s i m p o r t a n t

o n l y f o r r e a s o n a b l y l a r g e - s i z e d h o u s e h o l d s . Luggage s p a c e was found t o have l i t t l e e f f e c t on t h e v e h i c l e t y p e c h o i c e d e c i s i o n s of s m a l l e r households.

Although t h e GLUGl v a r i a b l e i s c o r r e c t l y s i g n e d , i t i s n o t

h i g h l y s i g n i f i c a n t , s t a t i s t i c a l l y , i n most time p e r i o d s .

Also, t h e

magnitude of t h e GLUGl p a r a m e t e r e s t i m a t e i n c r e a s e s over t i m e . The n e x t c a t e g o r y of g e n e r a l v e h i c l e c h a r a c t e r i s t i c s i s t h e performance c a t e g o r y .

U n f o r t u n a t e l y , t h e amount of p e r f o r m a n c e - r e l a t e d

d a t a a v a i l a b l e i s somewhat l i m i t e d .

As aproxy f o r vehicle acceleration,

horsepower d i v i d e d v e h i c l e weight was i n c l u d e d i n i n i t i a l s p e c i f i c a t i o n s , b u t i m p r o p e r l y s i g n e d and s t a t i s t i c a l l y i n s i g n i f i c a n t p a r a m e t e r e s t i m a t e s resulted.

This i s not s u r p r i s i n g since i t i s t h e engine's torque, n o t

horsepower, t h a t d e t e r m i n e s t h e a c c e l e r a t i o n c a p a b i l i t y of t h e v e h i c l e . The f a c t t h a t horsepower and t o r q u e a r e c o r r e l a t e d , t o some e x t e n t , provided i n i t i a l j u s t i f i c a t i o n f o r considering such a v a r i a b l e , b u t t h e e s t i m a t i o n r e s u l t s i n d i c a t e t h a t t h e horsepower/weight v a r i a b l e i s inappropriate.

The o n l y performance v a r i a b l e found t o y i e l d r e a s o n a b l e

r e s u l t s was d e f i n e d as t h e 'horsepower

d i v i d e d by e n g i n e d i s p l a c e m e n t

(ETECH).E x p l o r a t i o n of a u t o m o t i v e r o a d t e s t s i n d i c a t e d t h a t t h i s v a r i a b l e

i s h i g h l y c o r r e l a t e d w i t h both. e n g i n e t o r q u e and t h e c o r n e r i n g power of t h e v e h i c l e (measured by l a t e r a l a c c e l e r a t i o n ) .

The ETECH v a r i a b l e

was d e f i n e d o n l y f o r households which had household heads of 35 y e a r s of age o r l e s s .

The b e l i e f h e r e i s t h a t performance i s h i g h l y v a l u e d

among young households. signed

The ETECH parameter e s t i m a t e s a r e p r o p e r l y

in a l l time p e r i o d s and r e a s o n a b l y s i g n i f i c a n t s t a t i s t i c a l l y , The f i n a l c a t e g o r y of v e h i c l e c h a r a c t e r i s t i c s i s r e l i a b z l i t y .

Accurate measures of r e l i a b i l i t y a r e d i f f i c u l t t o o b t a i n . s o u r c e i s Consumer Reports

One p o s s i b l e

where survey r e s u l t s from maintenance and

r e a p i r experiences a r e tabulated,

Unfortunately,

a v a i l a b l e f o r a r e l a t i v e l y s m a l l percentage

such

information is

of t h e t o t a l number of

d i f f e r e n t makes, models, and v i n t a g e s of ~ e h i c l e sa v a i l a b l e t o t h e household, and as s u c h , could n o t be used i n model e s t i m a t i o n .

U1-

t i m a t e l y , v e h i c l e age w a s used as a proxy f o r r e l i a b i l i t y , s i n c e i t i s known t h a t t h e g e n e r a l r e l i a b i l i t y of v e h i c l e s d e c l i n e s w i t h o v e r time.

Two v e h i c l e age dummy v a r i a b l e s were found t o produce t h e most s a t i s factory r e s u l t s :

NEWAG which w a s s p e c i f i e d only f o r v e h i c l e s two

y e a r s old o r l e s s , and OLDAG which was s p e c i f i e d f o r v e h i c l e s e i g h t y e a r s old o r o l d e r .

I n b o t h c a s e s , t h e parameter e s t i m a t e s were

p r o p e r l y s i g n e d ( i . e . newer y e h i c l e s a r e more d e s i r a b l e and o l d e r v e h i c l e s a r e l e s s ) and f a i r l y s i g n i f i c a n t , s t a t i s t i c a l l y .

I n terms

of p a r a -

meter magnitudes, i t appears a s though o l d e r v e h i c l e s were becoming l e s s - onerous over time w h i l e t h e d e s i r a b i l i t y of newer v e h i c l e s remained r e l a t i v e l y c o n s t a n t .

Brand P r e f e r e n c e V a r i a b l e s It should be n o t e d t h a t i n t h i s s t u d y a d i s t i n c t i o n between brand l o y a l t y and brand p r e f e r e n c e Is drawn.

The p r o c e s s t h r o u g h which b r a n d

l o y a l t y i s developed c o n s i s t s of t h e accumulation of informati'on, t h r o u g h d r i v i n g and ownership e x p e r i e n c e , on p a r t i c u l a r v e h i c l e makes (brands)

.

Given t h i s p r o c e s s , t h e r e i s n o r e a s o n t o s u s p e c t t h a t

any one make of v e h i c l e w i l l have a h i g h e r d e g r e e of brand l o y a l t y t h a n a n o t h e r , s i n c e t h i s would u n r e a l i s t i c a l l y imply t h a t l e a r n i n g p r o c e s s e s d i f f e r a c c o r d i n g t o v e h i c l e make.

Brand p r e f e r e n c e i s

d e f i n e d a s a tendency t o p u r c h a s e a s p e c i f i c make of v e h i c l e .

This

tendency may be i n f l u e n c e d by t h e e x t e n t of t h e make's d e a l e r n e t w o r k , reapir costs,

p a r t s a v a i l a b i l i t y , and s o on.

I n t h e models e s t i m a t e d

h e r e , brand l o y a l t y i s c a p t u r e d by t h e XPTT and XPT2 v a r i a b l e s d e s c r i b e d earlier.

On t h e o t h e r hand, brand p r e f e r e n c e (expected t o d i f f e r among

makes) i s c a p t u r e d by a s e r i e s of v e h i c l e make dummies. I n a l l , brand p r e f e r e n c e i s r e p r e s e n t e d by f o u r v e h i c l e make dummy v a r i a b l e s i n c l u d i n g p r o d u c t s produced by; American Motors (AMC), Ford (FORD) , C h r y s l e r (CHRYS) , and a durmny v a r i a b l e f o r a l l f o r e i g n makes (FORN)

.

I n s e l e c t i n g t h e s e v a r i a b l e s , G e n e r a l Motors p r o d u c t s are

i m p l i c i t l y normalized t o z e r o .

The parameter e s t i m a t e s p r e s e n t e d i n

T a b l e 3 i n d i c a t e t h a t American M o t o r s , C h r y s l e r and F o r e i g n V e h i c l e s have a lower brand p r e f e r e n c e t h a n GM p r o d u c t s , w h i l e Ford v e h i c l e s have t h e h i g h e s t brand p r e f e r e n c e .

I n terms of parameter m a g n i t u d e s , f o r e i g n

makes have f a r and away t h e w o r s t brand p r e f e r e n c e .

This f a c t suggests

t h a t d o m e s t i c m a n u f a c t u r e r s have an i n h e r e n t advantage o v e r f o r e i g n

79

producers i n t h i s r e g a r d ,

Also n o t e t h a t American Motors, C h r y s l e r ,

and f o r e i g n m a n u f a c t u r e r s appear t o have d e c l i n i n g brand p r e f e r e n c e s over t i m e , which i n d i c a t e s an i n c r e a s i n g c o m p e t i t i v e advantage f o r b o t h GM and Ford. Structural Stability To t e s t f o r t h e s t a b i l i t y of parameter e s t i m a t e s over t i m e , a number of l i k e l i h o o d r a t i o t e s t s were made. s t a t i s t i c s i n d i c a t e ( s e e Table 3)

As t h e r e s u l t a n t

x2

t h e h y p o t h e s i s of parameter s t a b i l i t y ,

over a l l time p e r i o d s , can be r e e j e c t e d a t confidence l e v e l s of 80% and 14% f o r t h e i n t e r t e m p o r a l and r e s t r i c t e d models r e s p e c t i v e l y .

I f just

t h e f i r st and t h i r d p e r i o d s a r e c o n s i d e r e d , t h e r e b y e l i m i n a t i n g t h e r e l a t i v e l y u n s t a b l e p e r i o d when t h e , e n e r g y shock i n i t i a l l y o c c u r r e d , i t i s found t h a t t h e h y p o t h e s i s of s t r u c t u r a l s t a b i l i t y can be r e j e c t e d at t h e 71% confidence l e v e l f o r t h e i n t e r t e m p o r a l model, and a t t h e 14% l e v e l f o r t h e r e s t r i c t e d model.

Therefore, i t i s apparent t h a t , i n

b o t h of t h e above t e s t s , s t r u c t u r a l s t a b i l i t y can only b e r e j e c t e d a t r e l a t i v e l y low confidence l e v e l s .

5.3

Type Choice Models :

Two-Vehicle Households

The two-vehicle household t y p e c h o l c e model s p e c i f i e s t h e p r o b a b i l i t y of s e l e c t i n g a p o r t f o l i o of s p e c i f i c v e h i c l e t y p e s .

In

t h i s c a s e each a l t e r n a t i v e p o r t f o l i o c o n s i s t s of two v e h i c l e s d e f i n e d hy make, model, and v i n t a g e .

Again, due t o t h e l a r g e number of two-

v e h i c l e c o m b i n a t i o n s ( p o r t f o 1 i o s ) t h e o r e t i c a l l y a v a i l a b l e t o t h e household f o r s e l e c t i o n , a sample of t e n v e h i c l e p o r t f o l i o s was s e l e c t e d a t random f o r model e s t i m a t i o n purposes, as was done i n t h e e s t i m a t i o n

80

of t h e s i n g l e - v e h i c l e h o u s e h o l d t y p e c h o i c e models.

A l s ~ ,t h e p r e c i s e

s p e c i f i c a t i o n of t h e t y p e c h o i c e i n d i r e c t u t i l i t y f u n c t i o n was d e t e r mined by a p r o c e d u r e s i m i l a r t o t h a t f o l l o w e d i n t h e c a s e of t h e s i n g l e v e h i c l e household.

The c o m p l e t e l i s t of e x p l a n a t o r y v a r i a b l e s u l t i m a t e l y

used i n model e s t i m a t i o n i s p r e s e n t e d i n T a b l e 5 a l o n g w i t h t h e i r c o r r e s p o n d i n g summary s t a t i s t i c s .

The r e s u l t i n g model p a r a m e t e r estimates

f o r d i s t i n c t and combined t i m e p e r i o d s are g i v e n i n T a b l e 6.

A discussion

of t h e e x p l a n a t o r y v a r i a b l e s e l e c t i o n p r o c e s s and t h e r e s u l t i n g p a r a m e t e r

estimates i s g i v e n below. V e h i c l e Cost V a r i a b l e s Both o p e r a t i n g (PIRO) and c a p i t a l c o s t v a r i a b l e s (CAPO) are s p e c i f i e d e x a c t l y as i n t h e s i n g l e v e h i c l e t y p e c h o i c e m o d e l , w i t h t h e e x c e p t i o n b e i n g t h a t t h e c o s t s a r e now summed o v e r b o t h v e h i c l e s comprising the portfolio.

A s Table 6 i l l u s t r a t e s , t h e r e s u l t i n g parameter

e s t i m a t e s a r e p r o p e r l y s i g n e d and s t a t f s t i c a l l y s i g n i f i c a n t i n a l l t i m e periods.

These r e s u l t s i n d i c a t e t h a t f o r b o t h t h e i n D e r t e m p o r a 1 and

r e s t r i c t e d m o d e l s , h o u s e h o l d ' s v a l u a t i o n s of o p e r a t i n g c o s t s have i n c r e a s e d o v e r t i m e w h i l e t h e i r v a l u a t i o n s of c a p i t a l c o s t s have d e c r e a s e d over t i m e .

T h i s i s r e f l e c t e d i n t h e c a l c u l a t e d m a r g i n a l r a t e s of

s u b s t i t u t i o n e v a l u a t e d a t t h e p o p u l a t i o n mean, p r e s e n t e d i n T a b l e 7 . As t h i s t a b l e shows, t h e p r i c e t h a t t w o - v e h i c l e h o u s e h o l d s are w i l l i n g t o pay f o r a 1~p e r m i l e d e c r e a s e i n o p e r a t i n g c o s t s h a s i n c r e a s e d n o t i c e a b l y o v e r t h e t h r e e t i m e p e r i o d s f o r which models w e r e e s t i m a t e d . C o r r e s p o n d i n g l y , h o u s e h o l d s ' d i s c o u n t f a c t o r s have d e c r e a s e o v e r t i m e . The g e n e r a l f i n d i n g s d e s c r i b e d above a r e e s s e n t i a l l y i d e n t i c a l

T a b l e 5. V a r i a b l e s Used i n Two-Vehicle Type Choice Models (Means f o r Chosen A l t e r n a t i v e s )

PRD la PRD 2b Mean Mean

PRD 3' Mean

PIRO

.02557

.03485

.04315

C a p i t a l c o s t of b o t h v e h i c l e s f Income C$/yr)

CAPO

.2993

.3029

.2939

1 p e r i o d l a g g e d u t i l i z a t i o n (mi.) of same vehicles i n vehicle p o r t f o l i o

XT1

10720

9185

9261

2 p e r i o d lagged u t i l i z a t i o n (mi.) of same vehicles i n vehicle p b r t f o l i o

XT2

7990

8794

8113

1 p e r i o d l a g g e d u t i l i z a t i o n (mi.) of s i m i l a r make v e h i c l e s i n p o r t f o l i o

XPTl

380.2

298.1

335.3

2 p e r i o d l a g g e d u t i l i a a t i o n (mi.) of s i m i l a r make v e h i c l e s i n p o r t f o l i o

XPT2

856.9

746.5

527.6

F r o n t and r e a r s h o u l d e r room summed over b o t h v e h i c l e s

FRSR

212.5

215.2

213.0

Pickup t r u c k duunny

PICK

.I361

.I114

.I271

Number of American Motors c a r s i n p o r t f o l i o

AMC

.07101

.0629

.0553

Number of Fords i n portfolio

FORD

.5237

.5229

.5083

Number of C h r y s l e r s i n p o r t f o l i o

CHRYS

.2426

.2429

.2597

Number of f o r e i g n c a r s i n p o r t f o L i o

FORN

.2929

.2686

.2983

Number of v e h i c l e s 2 y r s o l d o r newer i n portfolio

PWAG

.2278

.I943

.2265

Number o f v e h i c l e s 8 yrs o l d o r o l d e r i n portfollo

OLDAG

.5110

.6600

.6436

338

350

362

Mnemonic

Variable

*

(Fuel c o s t ($/mi) .of both v e h i c l e s t y p i c a l u t i l i z a t i o n d ) i Income C$/yr)

--

Number o f o b s e r v a t i o n s

% e r i o d 1 i s t y p e c h o i c e a s of December 1978, w i t h u t i l i z a t i o n from J a n . 1979 t o June 1979.The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $0.72 p e r g a l l o n . b ~ e r i o d2 i s t y p e c h o i c e a s of June 1979, w i t h u t i l i z a t i o n from J u n e 1979 t o Dec. 1980. The mean f u e l p r i c e i n t h i s six-month p e r i o d is $0.96 p e r g a l l o n .

(continued)

Table 5.

(continued)

'period 3 i s t y p e c h o i c e a s of December 1 9 7 9 , w i t h u t i l i z a t i o n from J a n . 1980 t o J u n e 1980. The x e a n f u e l p r i c e i n t h i s six-month p e r i o d i s $1.17 p e r g a l l o n . d ~ y p i c a lu t i l i z a t i o n i s d e t e r m i n e d by a p p l y i n g t h e f o l l o w i n g e q u a t i o n s f o r s i n g l e v e h i c l e households: Typical u t i l i z a t i o n (rlt)

= 2684 +457.8

+

.05294

*

*

number of h o u s e h o l d members

income ( $ / ~ r )

F o r two v e h i c l e h o u s e h o l d s T y p i c a l u t i l i z a t i o n of e a c h v e h i c l e ( r 2 t ) = 3331

+

h o u s e h o l d m e m b e s + .04686

151.1

+

*

number of

income ( $ / y r )

The p a r a m e t e r s i n t h e s e e q u a t i o n s were e s t i m a t e d by o r d i n a r y l e a s t s q u a r e s u s i n g average u t i l i z a t i o n s derived from a l l a v a i l a b l e p e r i o d s i n t h e household sample.

Table 6.

Type Choice Model Parameter Estimates (Standard Errors in Parentheses): Two-Vehicle Households

-

I n t e r t e r ~ ~ p o r eMcwlcl l

YlHO

K c s t r i c t c d Hodel

Ycrlod 1

L'eriod 2

-13.19 (13.32)

-22.45 (12.71)

-20.183 (8.44)

-18.41 (7.15)

-18.71 (6.10)

-1.57 (.407)

-1.35 (.469)

-1.61 (. 376)

(.271)

-

CAPO

1.ug 1.1 kc lllluod eL Zero

-- --.

.

-

lrrg I.lkcl lhood :tt Corlvurgcnce

~.

I

-12.49 (13.27)

-22.119 (12.60)

-20.15 (8.46)

-18.17 (7.15)

-18.66 (6.09)

-2.21 (.659)

-1.49 (.405)

-1.33 (.469)

-1.62 (.377)

-1.56 (.272)

.

1

Table 7 . M a r g i n a l R a t e s of S u b s t i t u t i o n of O p e r a t i n g and C a p i t a l Costs ( P r i c e W i l l i n g t o pay f o r 1 ~ / m id e c r e a s e i n o p e r a t i n g c o s t s ) and I m p l i e d Annualized D i s c o u n t F a c t o r s : Two V e h i c l e Households (Standard E r r o r s i n Parentheses) I

I n t e r t e m p o r e l Hcdel Period 1

Heen T y p i c a l 8 4 f o r Each Veh Diecount IFectore 32'9) (percent)

P"

Period 2

Period 3

Pericda 163

A l l Puriodb

4869

4881

4860

4860

14.0 (8.1)

13.2 (6.4)

17.4 (7.7)

16.7 (6.0)

R e s t r i c t e d Model Period 2

Period 3

P e r i o d s 163

Alllr

. 4845

4869

4881

4860

4860

(38.0)

13.2 (7.6)

13.2 (6.4)

17.8 (7.9)

16.9 (6.1)

Period 1

I

t o t h o s e found and d i s c u s s e d i n t h e c a s e of t h e s i n g l e y e h i c l e household. Dynamic Components The dynamic components of t h e two-vehicle

t y p e c h o i c e model a r e

r e p r e s e n t e d by t h e lagged u t i l i z a t i o n s of t h e same v e h i c l e s i n t h e vehicle portfolio (i.e.

t h o s e v e h i c l e s owned i n t h e p r e c e d i n g t i m e

p e r i o d s ) and t h e lagged u t i l i z a t i o n s of s i m i l a r make v e h i c l e s i n t h e vehicle portfolio.

A s i n d i c a t e d i n Table 6 , t h e parameter e s t i m a t e s of

t h e u t i l i z a t i o n v a r i a b l e s (XT1, XT2, XPT1, XPT2) a r e g e n e r a l l y c o r r e c t l y s i g n e d and s t a t i s t i c a l l y s i g n i f i c a n t .

I n comparing i n t e r t e m p o r a l and

r e s t r i c t e d models, t h e d i s t i n g u i s h i n g v a r i a b l e s (XT2 and XF'T2) g e n e r a l l y p r o v i d e s t a t i s t i c a l l y s i g n i f i c a n t parameter e s t i m a t e s , l e n d i n g s u p p o r t t o t h e s u p e r i o r i t y of t h e i n t e r t e m p o r a l model.

However, a s i n t h e s i n g l e

v e h i c l e household c a s e , t h e r e s u l t a n t d i f f e r e n c e s between t h e common parameter e s t i m a t e s of t h e i n t e r t e m p o r a l and r e s t r i c t e d models i s q u i t e small. General Vehicle C h a r a c t e r i s t i c s I n terms of v e h i c l e dimensions, only t h e f r o n t and r e a r d h o u l d e r room, summed over b o t h v e h i c l e s , (FRSR) was found t o produce s t a t i s t i c a l l y significant results.

A s can be seen i n T a b l e 6 , t h e PRSR parameter

e s t i m a t e s a r e p r o p e r l y s i g n e d ( i . e . more s h o u l d e r room h a s a p o s i t i v e e f f e c t on t h e p o r t f o l i o ' s s e l e ~ t i o np r o b a b i l i t y ) and r e l a t i v e l y s t a b l e over t i m e .

Also, i t should be n o t e d t h a t i n t e r i m e s t i m a t i o n s i n d i c a t e d

l i t t l e , i f any, d i f f e r e n c e i n t h e v a l u a t i o n s t h a t households of d i f f e r e n t s i z e s p l a c e d on t h e s h o u l d e r room v a r i a b l e , hence o n l y one parameter e s t i m a t e f o r a l l households was made. 86

For v e h i c l e performance, none of t h e horsepower, w e i g h t , o r e n g i n e displacement v a r i a b l e s (or combinations t h e r e o f ) . w e r e found t o produce s t a t i s t i c a l l y acceptable r e s u l t s .

The one performance r e l a t e d v a r i a b l e

i n c l u d e d i n t h e e s t i m a t i o n was a pickup t r u c k v a r i a b l e (PICK) i n d i c a t i n g t h e number of pickup t r u c k s i n t h e p o r t f o l i o .

The h y p o t h e s i s h e r e i s

t h a t two-vehicle households a r e l i k e l y t o f i n d t h e s p e c i a l i z e d performance of a pickup t r u c k d e s i r a b l e i n a v e h i c l e p o r t f o l i o .

'In f a c t ,

t h i s h y p o t h e s i s i s supported i n b o t h t h e i n t e r t e m p o r a l and r e s t r i c t e d models f o r t h e f i r s t and t h i r d time p e r i o & a s r e f l e c t e d by t h e p o s i t i v e PICK parameter e s t i m a t e s . shock (Period 2 )

,

However, d u r i n g t h e p e r i o d of t h e energy

t h e PICK parameter e s t i m a t e s a r e n e g a t i v e i n d i c a t i n g

t h a t pickup t r u c k s were u n d e s i r a b l e .

T h i s s i g n change may have been

caused by t h e h o u s e h o l d ' s c u r t a i l m e n t of v e h i c u l a r t r i p s t h a t r e q u i r e d t h e u s e of pickup t r u c k s (e.g. moving of a p p l i a n c e s , and s o o n ) . F i n a l l y , f o r t h e r e l i a b i l i t y c h a r a c t e r i s t i c s of t h e v e h i c l e p o r t f o l i o , v e h i c l e age was used

a s a proxy f o r r e l i a b i l i t y

s i m i l a r t o t h a t used i n t h e s i n g l e - v e h i c l e

i n a manner

type choice e s t i m a t i o n s .

The

c o n s t r u c t e d v a r i a b l e s NEWAG ( t h e number of v e h i c l e s i n t h e p o r t f o l i o 2 y e a r s o l d o r newer) and OLDAG ( t h e number of v e h i c l e s 8 y e a r s o l d o r

o l d e r ) produced c o r r e c t l y s i g n e d parameter e s t i m a t e s t h a t were g e n e r a l l y statistically significant.

The r e s u l t s i n d i c a t e ( s e e Table 6 ) t h a t t h e

d e s i r a b i l i t y of newer v e h i c l e s h a s i n c r e a s e d over time w h i l e t h e u n d e s i r a b i l i t y of o l d e r v e h i c l e s h a s d e c l i n e d over time.

This f i n d i n g

i m p l i e s t h a t v e h i c l e s i n t h e 3 t o 7 y e a r o l d range have become g e n e r a l l y l e s s d e s i r a b l e over time.

Brand P r e f e r e n c e V a r i a b l e s Brand p r e f e r e n c e i s a c c o u n t e d f o r by i n c l u d i n g variables d e f i n e d as t h e number o f : American M o t o r s v e h i c l e s i n t h e v e h i c l e p o r t f o l i o (AMC)

, Ford

p r o d u c t s i n t h e p o r t f o l i o (FORD),

t h e p o r t f o l i o (CHRYS), and f o r e i g n - a d e (FORN).

Chrysler products i n

vehicles i n the portfolio

The e s t i m a t i o n r e s u l t s are i n g e n e r a l agreement w i t h t h o s e

o b t a i n e d i n t h e s i n g l e - v e h i c l e household c a s e .

That i s , f o r e i g n

p r o d u c e r s have a brand p e r f e r n c e d i s a d v a n t a g e r e l a t i v e t o a l l d o m e s t i c m a n u f a c t u r e r s , and Ford and GM h a v e a brand p r e f e r e n c e a d v a n t a g e over b o t h C h r y s l e r and AMC. Structural Stability

A number of l i k e l i h o o d r a t i o t e s t s were u n d e r t a k e n t o t e s t t h e s t a b i l i t y of t h e model e s t i m a t g o v e r t i m e .

The

x2

s t a t i s t i c s presented

i n T a b l e 6 i n d i c a t e t h a t i t i s p o s s i b l e t o r e j e c t t h e h y p o t h e s i s of p a r a m e t e r s t a b i l i t y f o r t h e i n t e r t e m p o r a l and r e s t r i c t e d models a t t h e 95% and 46% c o n f i d e n c e l e v e l s r e s p e c t i v e l y when a l l p e r i o d s are c o n s i d e r e d , and a t t h e 88% and 14% c o n f i d e n c e l e v e l s r e s p e c t i v e l y when t h e second (energy shock) p e r i o d i s e l i m i n a t e d .

These t e s t r e s u l t s

i n d i c a t e t h a t a l t h o u g h t h e h y p o t h e s i s o f s t r u c t u r a l s t a b i l i t y can b e r e j e c t e d w i t h g r e a t e r c o n f i d e n c e i n t h e two-vehicle t o t h e o n e - v e h i c l e household c a s e p r e s e n t e d e a r l i e r . level

c a s e as opposed The c o n f i d e n c e

a t which s t r u c t u r a l s t a b i l i t y can b e r e j e c t e d i s n o t e x c e p t i o n -

a l l y high.

5.4

Yehfcle U t i l i z a t i o n Models:

Sfngle-Vehlcle H o u s e h ~ l d s

The v e h i c l e u t i l i z a t i o n model' s p e c i f i e s ' t h e number ~ f mi.1e.s d r i v e n by t h e h ~ u s e h o l dover a s i k - m o n t h time p e r i o d .

The d e t e r m i n a n t s

of v e h i c l e u t i l i z a t i o n can be c l a s s i f l e d i n t o t h r e e c-ategories: 1 ) o p e r a t i n g c o s t s , 2) dyanmic a s p e c t s , and 3) t r i p g e n e r a t i o n v a r i a b l e s . The t h e o r e t i c a l d e r i v a t i o n s g i v e n i n Chapter 3 ( s e e Equation ( 3 9 ) ) comp l e t e l y s p e c i f y t h e o p e r a t i n g and dynamic c o s t v a r i a b l e s ,

What r e m a i n s ,

t h e n , i s t h e s p e c i f i c a t i o n of t h e t r i p g e n e r a t i o n v a r i a b l e s ( i . e . t h e

Z' v e c t o r i n Equation ( 3 9 ) ) .

The l i s t of e x p l a n a t o r y v a r i a b l e s u t i m a t e -

l y used i n model e s t i m a t i o n i s g i v e n i n Table 8 along w i t h t h e i r corresponding summary s t a t i s t i c s .

A l s o , t h e r e s u l t i n g parameter e s t i m a t e s

f o r d i s t i n c t and combined time p e r i o d s a r e p r e s e n t e d i n Table 9 .

The

d i s c u s s i o n below f o c u s e s on t h e e x p l a n a t o r y v a r i a b l e s e l e c t i o n p r o c e s s and an i n t e r p r e t a t i o n of t h e r e s u l t i n g parameter e s t i m a t e s , Operatfng Costs The o p e r a t i n g c o s t v a r i a b l e (PIRO) i s d e f i n e d , as i n t h e model d e r i v a t i o n s , a s t h e f u e l c o s t p e r mfle m u l t i p l i e d by t h e t y p i c a l u t i l ization.

S i n c e o p e r a t i n g c o s t i s a f u n c t i o n of v e h i c l e type ( i . e . f u e l

e f f i c i e n c y i n m i l e s p e r g a l l o n ) , a n d h e n c e i s endogenous, c o n s i s t e n t parameter e s t i m a t e s a r e o b t a i n e d by t h e procedure d e t a i l e d i n S e c t i o n 3 . 4 ( s e e Equation ( 4 1 ) ) .

The r e s u l t i n g PIRO parameter e s t i m -

a t e s a r e , i n most c a s e s , p r o p e r l y signed and s t a t i s t i c a l l y s i g n i f i c a n t

.

The e x c e p t i o n o c c u r s d u r i n g t h e energy shock (Period 2) as t h e e s t i m a t e s are not s t a t i s t i c a l l y s i g n i f i c a n t i n e i t h e r the intertemporal or r e s t r i c t e d models, and t h e parameter e s t i m a t e i n t h e r e s t r i c t e d model

T a b l e 8. V a r i a b l e s Used i n S i n g l e V e h i c l e U t i l i z a t i o n Models FXD la DRD 2 Variable Fuel cost ($/mi)

*

t y p i c a l u t i l i z a t i o n (mi)

Income ( $ l y r )

b

?IID 3'

Mnemonic

Mean

Nean

Nean

PIRO

190.6

256.2

317.4

10

12970

14130

15120

1 p e r i o d l a g g e d u t i l i z a t i o n (mi.) Same v e h i c l e 2 period lagged u t i l i z a t i o n (mi.) Same v e h i c l e 1 p e r i o d l a g g e d u t i l i z a t i o n (mi.) S i m i l a r make v e h i c l e 2 period lagged u t i l i z a t i o n (mi.) S i m i l a r make v e h i c l e Urban d m y ( 1 i f u r b a n l o c a t i o n , 0 otherwise) N o r t h e a s t dummy ( 1 i f N o r t h e a s t l o c a t i o n , 0 otherwise)

- NEST

.2464

.2493

.2308

Age dummy (1 i f head of h o u s e h o l d 5 0 yrs old or l e s s , 0 o t h e w i s e )

HAGE

.5159

.5291

.5165

Number of h o u s e h o l d w o r k e r s

NWORK

.6754

.8809

.8929

345

361

364

--

Number of o b s e r v a t i o n s

% e r i o d 1 i s t y p e c h o i c e a s o f December 1978, w i t h u t i l i z a t i o n from J a n . 1979 t o June 1979. The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $0.72 p e r g a l l o n . b ~ e r i o d2 i s t y p e c h o i c e a s of J u n e 1979, w i t h u t i l i z a t i o n from J u n e 1979 t o Dec. 1980. The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $0.96 p e r g a l l o n . $ e r i o d 3 i s t y p e c h o i c e a s o f December 1979, w i t h u t i l i z a t i o n from J a n . 1980 t o J u n e 1980. The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $1.17 p e r g a l l o n . d ~ y p i c a lu t i l i z a t i o n i s d e t e r m i n e d by a p p l y i n g t h e f o l l o w i n g e q u a t i o n s f o r s i n g l e v e h i c l e households: Typical u t i l i z a t i o n ( r

It

)

=

2684 +457.8

+

.05294

*

*

number of household members

income ( $ / y r )

(Continued)

Table 8

(Continued)

For two v e h i c l e households T y p i c a l u t i l i z a t i o n of e a c h v e h i c l e ( r 2 t ) = 3331

+

household membels+ ,04686

151.1

+

*

number of

income ( $ / y r )

The p a r a m e t e r s i n t h e s e e q u a t i o n s were e s t i m a t e d by o r d i n a r y l e a s t s q u a r e s u s i n g a v e r a g e u t i l i z a t i o n s d e r i v e d from a l l a v a i l a b l e p e r i o d s i n t h e household sample.

Table 9.

U t i l i z a t i o n Model P a r a m e t e r E s t i m a t e s ( S t a n d a r d E r r o r s i n P a r e n t h e s e s ) : S i n g l e - V e h i c l e Households

InLerLreporal Model

K r s t r l c t e d Model

1

I

Perlod 1 --

Perlod 2

Period 3

Periods 1 6 3

A l l Perlodv

-9.67 (3.18)

-1.12 (2.91)

-2.36 (1.70)

-4.98 (1.14)

-4.22 (1.12)

Period I

Perid 2

Period 3

Perlala 1 6 3

A l l Perlrxls

-8.36 (3.3J)

1.55 (3.76)

-3.67 (1.86)

-4.93 (1.23)

-4.22 (1.33) -

XP1 -

XP2

UHO

-

-..

NEAST

.038 (.Ole)

.OO8 (.021)

.007 .015

.019 (.011)

.022 (.011)

.356 (.026)

.704 (.052)

.521 (.026)

.432 (.Ole)

.486 (-019)

i s improperly signed ( i . e . higher o p e r a t i n g c o s t s i n c r e a s e t h e e x t e n t

of v e h i c l e u t i l i z a t i o n ) .

T h l s can b e e x p l a i a e d by tke f u e l s u p p l y

c o n s t r a i n a s and f u e l s t a t i o n q u e u e i n g t h a t p r e v a i l e d d u r i n g t h i s t i m e period.

The combination of t h e s e two f a c t o r s a p p e a r s t o h a v e

d e t e r m i n e d t h e e x t e n t of v e h i c l e u t i l i z a t i o n i n t h i s p e r i o d , as opposed t o t h e more t r a d i t i o n a l d e t e r m i n a t e s of v e h i c l e u s e ,

m

t e r m s of p a r a m e t e r m a g n i t u d e s , i t a p p e a r s as t h o u g h t h e

i m p o r t a n c e of o p e r a t i n g c o s t s i n d e t e r m i n i n g v e h i c l e u t i l i z a t i o n h a s d e c l i n e d over t i m e .

T h i s i s s u p p o r t e d by t h e o p e r a t i n g c o s t - u t i l i z a t i o n

(VMT) e l a s t i c i t y estimates ( e v a l u a t e d a t t h e p o p u l a t i o n mean) p r e s e n t e d i n T a b l e 10.

Note t h a t i n t h i s t a b l e t h e s h o r t - r u n e l a s t i c i t r e s a r e

o b t a i n e d d i r e c t l y from t h e e q u a t i o n estimates w h e r e a s t h e long-run e l a s t i c i t i e s are o b t a i n e d by assuming t h a t s t e a d y - s t a t e u t i l i z a t r o n i s achieved ( i . e .

x

t

= x

t-1

= x

t-2

...).

A s e x p e c t e d , long-run e l a s t r c i t i e s

tend t o b e l a r g e r than short-run e l a s t i c i t i e s . t h a t b o t h s h o r t - r u n and long-run

It i s c l e a r , however,

o p e r a t i n g c o s t e l a s t i c i t i e s have

t e n d e d t o d e c l i n e over t i m e . Dynamic A s p e c t s The dynamic a s p e c t s i n c l u d e , as s p e c i f i e d by t h e d e r i v a t i o n s i n Chapter 3 , lagged u t i l i z a t i o n of t h e same v e h i c l e ( i . e .

i f owned and

o p e r a t e d i n p r e v i o u s t i m e p e r i o d s ) and lagged u t i l i z a t i o n of a s i m i l a r make v e h i c l e ( i . e .

i f t h e c u r r e n t v e h i c l e w a s n o t owned p r e v i o u s l y b u t

a v e h i c l e of t h e same make was owned p r e v i o u s l y ) .

S i n c e t h e s e dynamic

v a r i a b l e s a r e v e h i c l e s p e c i f i c , t h e procedure described i n Section 3.4 i s applied

i n e s t i m a t i o n (see Equation ( 4 1 ) ) .

A s can b e s e e n i n T a b l e 9 ,

Table 10,

U t i l i z a t i o n E l a s t i c i t i e s (Standard E r r o r s i n Parentheses): S i n g l e - V e h i c l e Households

I n t e r t e m p o r a l Model Elasticitv

.o,nc (3hort-run,)

I

Period 2

Period 3

Periods 1 6 3

A l l I'erlodu

(.134)

,078 ( .188)

-.260 ( .136)

-.281 (.070)

-.22R (.072)

,049 (.035)

,108 (.052)

.020 (.067)

.025 (.054)

.063 (.036)

-.279 (-074)

-.522 (.208)

.264 (.615)

-.541 (.284)

-.495 ( . 123)

.168 (.081)

.078 (.226)

.052 (.111)

Period 2

Period 3

Periods 1 6 3

All Periods

-.3RY (.128)

-.a61 (.146)

-.I73 (.125)

-.284 (.065)

-.228 ( .060)

.I00 (.050)

.058 (.052)

-.nu7 (.05U)

.044 (.032)

I ' erid -- -

OpecaL Lng -.911 Costs (.288) (L.O~I~-~IIII)

1

-.212 (.507)

-.257 (.l86)

-.446 (.102)

.201 (.l8l)

-.a11 (.074)

.069 (.050)

-..--.. . ..

11,C',l,,C

(I.ong-run)

R e s t r i c t e d Model

I

I

Period 1

-.336

-----

.

.2.14 (.117)

.060 ( .043)

-- -.---.

-----

.(I69 (.014)

-- -

---

..-

-.444 (. 140) -- - - - -- -- -..--.

.I11 (.063)

.I34 ( .066)

t h e s e v a r i a b l e s ( X I , X2, 33'1, and XP2) a l l p r o d u c e p r o p e r l y s i g n e d and g e n e r a l l y s t a t i s t i c a l l y s i g n i f i c a n t parameter e s t i m a t e s ,

Tn terms of

p a r a m e t e r m a g n i t u d e s , t h e r e seems t o be a c o n s i d e r a b l e amount of i n s t a b i l i t y over t i m e , w i t h no s t r o n g p a t t e r n s i n d i c a t e d .

A statistical

t e s t of t h e s t r u c t u r a l s t a b i l i t y of t h e u t i l i z a t i o n e q u a t i o n s w i l l be presented s h o r t l y . When i n t e r p r e t i n g t h e d i f f e r e n c e s 2n e m p i r i c a l f i t of t h e i n t e r t e m p o r a l and r e s t r i c t i v e models, t h e same q u a l i t a t i v e c o n c l u s i o n s made i n t h e t y p e c h o i c e models can be made h e r e . ables distinguishing

That i s , a l t h o u g h t h e v a r i -

t h e i n t e r t e m p o r a l model (X2 and 8 P 2 ) p r o d u c e

s t a t i s t i c a l l y s i g n i f i c a n t p a r a m e t e r e s t i m a t e s , t h e impact t h a t t h e s e a d d i t i o n a l v a r i a b l e s have on t h e p a r a m e t e r e s t i m a t e s of v a r i a b l e s s h a r e d by b o t h models i s n o t g r e a t . Trip Generation Variables The f a c t o r s d e t e r m i n i n g household t r i p g e n e r a t i o n i n c l u d e t h o s e r e l a t i n g t o w e a l t h , g e o g r a p h i c l o c a t i o n , and l i f e c y c l e .

To r e p r e s e n t

w e a l t h , t h e h o u s e h o l d ' s a n n u a l income (TO) i s i n c l u d e d i n t h e c a t i o n as s u g g e s t e d by t h e d e r i v a t i o n s in C h a p t e r 3. income p a r a m e t e r estimates

specifi-

As expected, the

were g e n e r a l l y p r o p e r l y s i g n e d i n d i c a t i n g

t h a t h o u s e h o l d s w i t h h i g h e r incomes t e n d t o d r i v e more t h a n t h o s e w i t h lower incomes.

The magnitudes of t h e income p a r a m e t e r e s t i m a t e s d e c l i n e

o v e r t i m e r e f l e c t i n g t h e d e c l i n i n g i m p o r t a n c e of income i n d e t e r m i n i n g utilization.

T h i s i s f u r t h e r s u b s t a n t i a t e d by t h e d e c l i n i n g m a g n i t u d e s

of b o t h long-run

and s h o r t - r u n i n c o m e / u t i l i z a t i o n e l a s t i c i t y e s t i m a t e s

( i n t e r p r e t e d a t t h e p o p ~ ~ l a t i omean) n a s shown i n T a b l e 1 0 .

Other v a r i a b l e s a f f e c t i n g v e h i c l e u t i l i z a t i o n r e l a t e t o geographic l o c a t i o n .

I n t u i t i v e l y , t h e g e n e r a t i o n of t r i p s r e q u i r i n g

v e h i c l e u s e w i l l v a r y widely from urban t o r u r a l r e s i d e n t i a l l a c a t i o n , a s w e l l a s from one r e g i o n of t h e country t o a n o t h e r ,

Ih t h e f i n a l

model e s t i m a t i o n , two geographic v a r i a b l e s were 'included.

The f i r s t i s

a dummy v a r i a b l e (URB) d e f i n e d only f o r households r e s i d i n g i n an urban area.

expected, t h e parameter e s t i m a t e of t h i s v a r i a b l e i s nega-

As

t i v e i n d i c a t i n g t h a t urban households tend t o d r i v e l e s s t h a n t h e i r rural

counterparts.

T h i s e s t i m a t e r e f l e c t s t h e f a c t t h a t urban house-

h o l d s have g r e a t e r a c c e s s i b i l i t y t o a l t e r n a t e modes of t r a v e l (e.g.

bus),

t h e urban s p a t i a l d i s t r i b u t i o n r e q u i r e s l e s s v e h i c u l a r t r i p s t o s a t i s f y household a c t i v i t i e s , and t h e t r a n s p o r t a t i o n i n f r a s t r u c t u r e i s l e s s conducive t o automobile t r a v e l ( e . g. c o n g e s t i o n , p a r k i n g l i m i t a t i o n s , and s o o n ) . over time

The URB parameter e s t i m a t e s seem t o be r e a s o n a b l y s t a b l e

.

The second geographic l o c a t i o n v a r i a b l e (NEAST) i s d e f i n e d o n l y f o r households l i v i n g i n t h e n o r t h e a s t e r n p o r t i o n of t h e U.S.

Initially,

i t was expected t h a t n o r t h e a s t e r n households would t r a v e l l e s s due

t o t h e h i g h e r p o p u l a t i o n d e n s i t i e s and t h e g e n e r a l l y poorer q u a l i t y of t h e highway t r a n s p o r t a t i o n network.

However, i t was found t h a t t h e

NEAST parameter e s t i m a t e s were n o t always signed a s e x p e c t e d , and t h e s t a t i s t i c a l s i g n i f i c a n c e of t h e r e s u l t s was n o t p a r t i c u l a r l y h i g h . should be noted t h a t o t h e r r e g i o n a l v a r i a b l e s were considered i n t h e e s t i m a t i o n b u t t h e r e s u l t s were not s a t i s f a c t o r y . The f i n a l t r i p g e n e r a t i o n v a r i a b l e s r e l a t e t o t h e h o u s e h o l d ' s

96

It

l i f e cycle.

S p e c i f i c a l l y , l ? f e c y c l e v a r i a b l e s s h o u l d c a p t u r e com-

p o n e n t s of t h e t r i p g e n e r a t i o n p r o c e s s t h a t v a r y by t h e s t a g e of househ o l d development ( e . g . p r e s e n c e of c h i l d r e n , working p a r e n t s , r e t i r e d p a r e n t s , and s o on)

.

U l t i m a t e l y , two l i f e c y c l e v a r i a b l e s were i n c l u d e d

i n t h e e s t i m a t i o n s ; t h e head of t h e h o u s e h o l d t s a g e (HAGE] and t h e number of h o u s e h o l d w o r k e r s (NWORK).

The HAGE v a r i a b l e a t t e m p t s t o c a p t u r e t h e

f a c t t h a t "older" households tend t o g e n e r a t e fewer v e h i c u l a r t r i p s . The HAGE v a r i a b l e i s d e f i n e d o n l y f o r h o u s e h o l d s w i t h h e a d s f i f t y y e a r s old o r l e s s .

The EL4GE p a r a m e t e r e s t i m a t e s a r e p r o p e r l y s i g n e d and

s t a t i s t i c a l l y s i g n i f i c a n t (see Table 9 ) .

The p a r a m e t e r magnitudes i n d i -

c a t e t h a t t h e e f f e c t of t h e HAGE v a r i a b l e on u t i l i z a t i o n h a s t e n d e d t o d e c l i n e over time. The r e m a i n i n g l i f e c y c l e v a r i a b l e (NWO'RK) was e x p e c t e d t o p r o duce p o s i t i v e parameter e s t i m a t e s ( i . e . the higher t h e vehicle u t i l i z a t i o n ) .

t h e h i g h e r t h e number of w o r k e r s ,

Tn most t i m e p e r i o d s , t h i s e x p e c t a -

t i o n w a s b o r n e o u t . However, d u r i n g t h e e n e r g y shock ( P e r i o d 2 ) n e g a t i v e and s t a t i s t i c a l l y i n s i g n i f i c a n t p a r a m e t e r e s t i m a t e s r e s u l t e d .

This

i s p r o b a b l y due t o t h e f u e l s u p p l y c o n s t r a i n t s which seem t o l e a d t o a g e n e r a l "breakdown" of u t i l i z a t i o n model e s t i m a t i o n s . Structural Stability To t e s t f o r t h e s t r u c t u r a l s t a b i l i t y of t h e u t i l i z a t i o n e q u a t i o n s o v e r t i m e , a number of Chow t e s t s were conducted.

When a l l p e r i o d s were

c o n s i d e r e d , it w a s found t h a t t h e h y p o t h e s i s of s t r u c t u r a l s t a b i l i t y c o u l d be r e j e c t e d a t h i g h l e v e l s of c o n f i d e n c e i n e x c e s s of 99% f o r b o t h t h e i n t e r t e m p o r a l and r e s t r i c t e d model s p e c i f i c a t i o n s ( s e e t h e

F - s t a t i s t i c s i n Table 9 ) ,

However, when t h e f u e l s u p p l y c o n s t r a i n e d

second p e r i o d i s n o t i n c l u d e d i n t h e Chow t e s t s , t h e h y p o t h e s i s of s t r u c t u r a l s t a b i l i t y can be r e j e c t e d e a s i l y f o r t h e r e s t r i c t e d model b u t o n l y a t t h e 80% c o n f i d e n c e l e v e l f o r t h e i n t e r t e m p o r a l model.

These

r e s u l t s s e e m t o i n d i c a t e t h a t t h e u t i l i z a t i o n model i s s u b s t a n t i a l l y l e s s s t a b l e over t i m e t h a n t h e c o r r e s p o n d i n g v e h i c l e t y p e c h o i c e model ( s e e Section 5.2)

5.5

,

V e h i c l e U t i l i z a t i o n Models:

Two-Vehicle Households

The two v e h i c l e household u t i l i z a t i o n e q u a t i o n s s p e c i f y t h e number of m i l e s d r i v e n by t h e household on e a c h of t h e two v e h i c l e s comprising t h e household's v e h i c l e p o r t f o l i o .

The model e s t i m a t i o n s

were based on t h e u t i l i z a t i o n e q u a t i o n d e r i v e d ?n C h a p t e r 3 ( E q u a t i o n (40)).

Again, as w a s t h e c a s e i n t h e s i n g l e - v e h i c l e h o u s e h o l d model,

t h e e s t i m a t i o n procedure d e t a i l e d i n Section 3.4 w a s a p p l i e d t o o b t a i n c o n s i s t e n t p a r a m e t e r e s t i m a t e s i n t h e p r e s e n c e of t h e d i s c r e t e l c o n t i n u o u s model s t r u c t u r e .

The complete l i s t of e x p l a n a t o r y v a r i a b l e s u l t i m a t e l y

used i n model e s t i m a t i o n i s g i v e n i n T a b l e 11 a l o n g w i t h t h e i r c o r r e s ponding summary s t a t i s t i c s .

I n a d d i t i o n , t h e r e s u l t i n g parameter

e s t i m a t e s f o r d i s t i n c t and combined t i m e p e r i o d s a r e p r e s e n t e d i n Table 12.

A n i n t e r p r e t a t i o n of t h e r e s u l t i n g model e s t i m a t e s i s g i v e n

below. Operating Costs The o p e r a t i n g c o s t v a r i a b l e (PITO) i s d e f i n e d as t h e c o m b i n a t i o n of t h e t o t a l f u e l e x p e n s e s ( i . e . f u e l

c o s t s m u l t i p l i e d by t y p i c a l

u t i l i z a t i o n ) of b o t h v e h i c l e s c o m p r i s i n g t h e h o u s e h o l d ' s v e h i c l e 98

Table 11. V a r i a b l e s Used i n Two-Vehicle U t i l i z a t i o n Models

PRD 2b Me an

Variable F u e l c o s t ( $ / m i . ) of b o t h v e h i c l e s T y p i c a l u t i l i z a t i o n (mi.ld

PRD 3' Yean

554.0

*

Income (S/yr)

1 p e r i o d l a g g e d u t i l i z a t i o n (mi.) of same v e h i c l e s i n v e h i c l e p o r t f o l i o 2 p e r i o d lagged u t i l i z a t i o n (mi.) of same v e h i c l e s i n v e h i c l e p o r t f o l i o

1 p e r i o d lagged u t i l i z a t i o n (mi.) of similar make v e h i c l e s i n p o r t f o l i o 2 p e r i o d lagged u t i l i z a t i o n (d.) of s i m i l a r make v e h i c l e i n p o r t f o l i o Urban dummy ( 1 i f u r b a n l o c a t i o n , 0 otherwise) N o r t h e a s t dummy ( 1 i f n o r t h e a s t l o c a t i o n , 0 otherwise) Age dummy (1 i f household head 50 y r s o l d o r l e s s , 0 otherwise)

WGE

N d e r of household workers New v e h i c l e dummy (1 i f newer v e h i c l e of p a i r , 0 otherwise) B d e r of o b s e r v a t i o n s

Y e r i o d 1 i s type c h o i c e a s of December 1978, w i t h u t i l i z a t i o n from Jan. 1979 t o June 1979,The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $0.72 p e r g a l l o n . b ~ e r i o d2 i s t y p e c h o i c e a s of J u n e 1979, w i t h u t i l i z a t i o n from J u n e 1979 t o Dec. 1980. The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $0.96 p e r g a l l o n . $ e r i o d 3 i s t y p e c h o i c e a s of December 1979, w i t h u t i l i z a t i o n from J a n . 1980 t o J u n e 1980. The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $1.17 p e r g a l l o n .

(Continued)

Table 11.

(Continued)

d ~ y p i c a ul t i l i z a t i o n i s d e t e r m i n e d by a p p l y i n g t h e f o l l o w i n g e q u a t i o n s f o r s i n g l e v e h i c l e households : Typical u t i l i z a t i o n (rlt)

=

2684 f 4 5 7 . 8

+

.05294

*

*

number of household members

income ( $ / ~ r )

F o r two v e h i c l e h o u s e h o l d s T y p i c a l u t i l i z a t i o n of e a c h v e h i c l e ( r Z t ) = 3331

+

household membes+ .04686

151.1

+

*

number of

income ( $ / y r )

The p a r a m e t e r s i n t h e s e e q u a t i o n s were e s t i m a t e d by o r d i n a r y l e a s t s q u a r e s u s i n g a v e r a g e u t i l i z a t i o n s d e r i v e d from a l l a v a i l a b l e p e r i o d s i n t h e household sample.

(LOO') z 10'

(010.) EIU'

(ZTO?

zzo

tzro') 11ro.

(LOO') CI0.

(OIO.! '1 I 0

. --.

1SVIN

nnn ZdX -IdX

(BZO'! CLZ (ZIO*) 910'

tr~o.) EIU'

I

01

portfolio.

The PIT0 parameter e s t i m a t e s a r e c o s x e c t l ~s3gned b u t

generally not very significant s t a t i s t i c a l l y ,

Also, 2t appears

households' v a l u a t i o n of o p e r a t i n g c o s t s is r e a s o n a b l y s t a b l e Q v e r time p r o v i d i n g t h e energy shock p e r i o d i s e l i m i n a t e d . is supported by t h e long-run

ThTs s t a b i l i t y

and s h o r t - r u n o p e r a t i n g c o s t / ; u t i l i z a t i o n

e l a s t i c i t i e s ( c a l c u l a t e d a t t h e p o p u l a t i o n mean) a s indicated i n Table 13. Dynamic Aspects The dynamic a s p e c t s i n c l u d e , a s s p e c i f i e d by t h e d e r i v a t i o n s i n Chapter 3 , t h e lagged u t i l i z a t i o n of t h e same v e h i c l e s i n t h e v e h i c l e p o r t f o l i o ( i . e . t h o s e v e h i c l e s owned i n p r e v i o u s time p e r i o d s ] and t h e lagged u t i l i z a t i o n of s i m i l a r make v e h i c l i e s i n t h e p o r t f o l i o .

The para-

meter e s t i m a t e s f o r t h e s e v a r i a b l e s (XI, X2, XP1, X . 2 ) a r e a l l of p l a u s i b l e s i g n and g e n e r a l l y s t a t i s t i c a l l y s l g n i f i c a n t .

Also, i t

should be p o i n t e d out t h a t t h e s e parameter e s t i m a t e s appear t o be q u i t e unstable, a s i n d i c a t e d by t h e i r magnitudes. I n comparing i n t e r t e m p o r a l and r e s t r i c t e d models, t h e same q u a l i t a t i v e c o n c l u s i o n found i n p r e v i o u s l y p r e s e n t e d e s t i m a t i o n s a p p l i e s here.

That i s t o s a y , t h a t a l t h o u g h t h e d i s t i n g u i s h i n g v a r i a b l e s X 2 and

XP2 r e s u l t i n s t a t i s t i c a l l y s i g n i f i c a n t parameter e s t i m a t e s , t h e e f f e c t t h a t t h e i n c l u s i o n of such v a r i a b l e s h a s on t h e remaining parameter e s t i m a t e s i s n o t g r e a t . T r i p Generaion V a r i a b l e s The t r i p g e n e r a t i o n v a r i a b l e s included i n t h e two-vehicle household u t i l i z a t i o n models where t h e same a s t h o s e s p e c i f i e d i n t h e one-vehicle

Table 13.

E l a s t i c i t y with respect t o Ope r n t i r ~ g

U t i l i z a t i o n E l a s t i c i t i e s (Standard E r r o r s i n P a r e n t h e s e s ] : Two-Vehicle Hotlseholds

I Period 1

-.102

R e s t r i c t e d Model

Intertemporal Model Period 2

-.004

Period 3

Periods 1.3

-.I27 (.116)

-.071 (.056)

I

I 1 1 1 Periods -.059 (.052)

Period 1

-.(.130) 105

Perlod 2

-.(.L36) 008

_

-

Period 1

PerLods 113

A11 Yeriodnl

-.I32 (.117)

-.0/14 (.056)

-.Dl9

-.--

---

(.05l)

-- .-.

1 I

- .--- 1

household c a s e ; income (IO), u r b a n l o c a t i o n (URB), n o r t h e a s t (NEAST), age of h o u s e h o l d head (HAGE), (NWORK)

.

residence i n the

and number of w o r k e r s

The income p a r a m e t e r e s t i m a t e s were p r o p e r l y s i g n e d and r e l a -

t i v e l y s t a b l e over t i m e a s i n d i c a t e d i n Table 12. a l s o r e f l e c t e d i n t h e long-run

This s t a b i l i t y i s

and s h o r t - r u n ~ n c o m e / u t i l i z a t i o n

e l a s t i c i t i e s p r e s e n t e d i n T a b l e 3. The URB p a r a m e t e r e s t i m a t e s were found t o be s t a t i s t i c a l l y i n s i g n i f i c a n t , which i s somewhat s u r p r i s i n g g i v e n t h e a c c e p t a b l y s i g n i f i c a n t r e s u l t s found i n t h e one-vehicle

household case.

Also, t h e other

l o c a t i o n s p e c i f i c v a r i a b l e (NEAST) produced i n s i g n i f i c a n t p a r a m e t e r e s t i m a t e s as was t h e c a s e w i t h s i n g l e v e h i c l e h o u s e h o l d s . The l i f e s t y l e v a r i a b l e , t h e head of t h e h o u s e h o l d ' s age (HAGE) and t h e number of w o r k e r s (NWORK) parameter e s t i m a t e s .

,

produced g e n e r a l l y p r o p e r l y s i g n e d

The one n o t i c e a b l e e x c e p t i o n i s t h e NWDRK p a r a -

m e t e r e s t i m a t e i n P e r i o d 2 which i s n e g a t i v e l y s i g n e d b u t n o t w2th a h i g h d e g r e e of s t a t i s t i c a l s i g n i f i c a n c e .

T h i s can be e x p l a i n e d , t o some

e x t e n t , by t h e f u e l s u p p l y c o n s t r a i n t s t h a t impacted u t i l i z a t i o n d u r i n g t h e second p e r i o d .

A s a f i n a l p o i n t , b o t h t h e HAGE and NWORK p a r a m e t e r

e s t i m a t e s a p p e a r t o b e u n s t a b l e o v e r t i m e , a s i n d i c a t e d by t h e i r corresponding parameter magnitudes. The f i n a l v a r i a b l e i n c l u d e d i n t h e two-vehicle household u t i l i z a t i o n model i s a dummy v a r i a b l e ( N W ) i n d i c a t i n g i f t h e v e h i c l e i s t h e newer ( i n t e r m s of v i n t a g e ) of t h e two v e h i c l e s c o m p r i s i n g t h e household's v e h i c l e p o r t f o l i o .

The h y p o t h e s i s h e r e i s t h a t newer

v e h i c l e s w i l l o f f e r s u p e r i o r r e l i a b i l i t y and comfort t h e r e b y making them

g e n e r a l l y more d e s i r a b l e t o u s e , were found t o have a v e r y

I n d e e d , t h e NEWV parameter e s t i m a t e s i n f l u e n c e on t h e d e t e r m l n a t i o n af

u t i l i z a t i o n , a s i n d i c a t e d by tlie magnitude of t h e parameter e s t i m a t e . Moreover, t h e s e e s t i m a t e s were found t o be v e r y h i g h l y s t a t i s t i c a l l y s i g n i f i c a n t and r e a s o n a b l y s t a b l e over time. Structural Stability

A number of Chow t e s t s were conducted t o t e s t f o r t h e s t r u c t u r a l s t a b i l i t y of t h e u t i l i z a t i o n equations over time.

As t h e P-statistics

i n d i c a t e ( s e e Table 1 2 ) , t h e h y p o t h e s i s of s t r u c t u r a l s t a b i l i t y can b e r e j e c t e d a t h i g h c o n f i d e n c e l e v e l s when a l l t h r e e p e r i o d s a r e c o n s i d e r e d . When t h e t u r b u l e n t e n e r g y shock p e r i o d (Period 2 ) i s excluded from cons i d e r a t i o n , i t i s found t h a t t h e s t r u c t u r a l s t a b i l i t y h y p o t h e s i s can

s t i l l be r e j e c t e d w i t h h i g h c o n f i d e n c e ( i , e . g r e a t e r t h a n 99%).

These

r e s u l t s i n d i c a t e t h a t t h e u t i l i z a t i o n e q u a t i o n s tend t o be u n s t a b l e o v e r t i m e , w h i l e t h e c o r r e s p o n d i n g two-vehicle household t y p e choi'ce models i n d i c a t e d r e l a t i v e s t r u c t u r a l s t a b i l i t y ( s e e S e c t i o n 5 . 3 ) . 5.6

Level Choice Models The l e v e l c h o i c e models s p e c i f y t h e p r o b a b i l i t y t h a t a household

w i l l choose t o own one o r two v e h i c l e s .

The g e n e r a l f o n n of t h e l e v e l

c h o i c e models i s t h a t i n d i c a t e d e a r l i e r by Equation ( 1 9 ) .

The a c t u a l

v a r i a b l e s i n c l u d e d i n e s t i m a t i o n a r e p r e s e n t e d i n Table 14 a l o n g w i t h t h e i r c o r r e s p o n d i n g summary s t a t i s t i c s , e s t i m a t e s a r e provided i n Table 15.

The r e s u l t i n g parameter

Before procedding w i t h a d i s c u s s i o n

of t h e s e e s t i m a t i o n r e s u l t s , i t should be p o i n t e d o u t t h a t t h e s t a n d a r d e r r o r s r e p o r t e d i n Table 15 a r e n o t c o r r e c t e d f o r t h e f a c t t h a t an

Table 1 4 . V a r i a b l e s Used i n t h e = Leve 1 Choice Mode 1s PRD la PRD 2b Mean Mean

PRD 3'

URB

.7291

.7257

.7273

LSUM

10.540

10.077

11.159

683

711

726

Variable Number of household members (Defined f o r 2 v e h i c l e a l t . only) Number of household workers (Defined f o r 2 v e h i c l e a l t . only) Income ( $ / r ) (Defined For 2 v e h i c l e a l t . only) j1 i f urban l o c a t i o n , Urban d m y 0 o t h e r w i s e ) (Defined f o r 2 v e h i c l e a l t . only) Log sum from t y p e c h o i c e models

Mean

Choice dummy ( 1 i f 2 v e h i c l e a l t . , 0 otherwise) Number of o b s e r v a t i o n s

--

% e r i o d 1 i s t y p e c h o i c e a s of December 1978, w i t h u t i l i z a t i o n from J a n . 1979 t o June 1979.The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $0.72 p e r g a l l o n . b ~ e r i o d2 i s t y p e c h o i c e a s of J u n e 1979, w i t h u t i l i z a t i o n from J u n e 1979 t o Dec. 1980. The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $0.96 p e r g a l l o n . (=Period 3 i s t y p e c h o i c e a s of December 1979, w i t h u t i l i z a t i o n from J a n . 1980 t o J u n e 1980. The mean f u e l p r i c e i n t h i s six-month p e r i o d i s $1.17 p e r g a l l o n .

e s t i m a t e d v a l u e of t h e logsum

@ b l c h i s t h e n a t u r a l l o g a r i - t h m of t h e

denominator

of t h e l o g i t t y p e c h o i c e model) was used a s opposed t o t h e

true value.

Amemiya (1976) h a s shown t h a t t h e u s e of e s t i m a t e d logsums

r e s u l t s i n s t a n d a r d e r r o r s t h a t a r e b i a s e d downward ( a c t u a l p a r a m e t e r estimates are not affected). i n Table , l 5 should be

A s such, t h e standard e r r o r s r e p o r t e d

viewed as a lower bound.

I n s t r u c t u r i n g t h e f o l l o w i n g d i s c u s s i o n , v a r i a b l e s Tncluded i n t h e l e v e l c h o i c e model s p e c i f i c a t i o n a r e c l a s s i f i e d i n t o two c a t e g o r i e s ; 1 ) s o c i o e c o n o m i c v a r i a b l e s and 2 ) t h e v e h i c l e t y p e logsum v a r i a b l e s . Socioeconomic

Variables

I n a l l , f o u r s o c i o e c o n o m i c v a r i a b l e s were i n c l u d e d i n t h e model s p e c i f i c a t i o n ; 1 ) t h e number of household members (NMEM),

2 ) number

of h o u s e h o l d w o r k e r s (NWORK), 3) household income (10) and 4) an u r b a n l o c a t i o n v a r i a b l e (URB) ,

S i n c e p a r a m e t e r e s t i m a t e s of s u c h v a r i a b l e s

can o n l y b e a t t a i n e d f o r one of t h e two a l t e r n a t i v e s ( i . e . t h e y d o n o t vary across a l t e r n a t i v e s ) , t h e two-vehicle

a l l of t h e s e v a r i a b l e s w e r e d e f i n e d o n l y f o r

alternative.

The number of household members i s i n l c u d e d a s an e x p l a n a t o r y v a r i a b l e s i n c e i t i s h y p o t h e s i z e d t h a t l a r g e r h o u s e h o l d s w i l l b e more l i k e l y t o own two v e h i c l e s as opposed t o one.

A s t h e e s t i m a t e s of

T a b l e 15 i n d i c a t e , NMEM p a r a m e t e r e s t i m a t e s a r e p r o p e r l y s i g n e d ( i . e . t h e l a r g e r t h e h o u s e h o l d , t h e g r e a t e r t h e p r o b a b i l i t y of owning two v e h i c l e s ) and s t a t i s t i c a l l y s i g n i f i c a n t .

I n t e r m s of p a r a m e t e r mag-

n i t u d e s , t h e r e a p p e a r s t o be a s l i g h t d e c l i n e i n t h e i m p o r t a n c e t h a t NMEM h a s on t h e p r o b a b i l i t y of s e l e c t i n g two v e h i c l e s .

Table 15.

L e v e l Choice Model P a r a m e t e r E s t i m a t e s ( S t a n d a r d E r r o r s i n Parentheses) I n L e r t e m p o r a l Model

I

R e s t r i c t e d Model

Variable

Period 1

Period 2

I'eriod 3

Perlods 163

A l l Periods

Period 1

NHM

.372 (.080)

.I87 (.075)

.247 (.071)

.I11 (.052)

.I45 (.043)

.379 (.O82)

.SO8 (.141)

.581 (.135)

.618 (.128)

.593 (.093)

.559 (.U76)

.356E-04 (.1008-04)

.731E-05 (.811E-05)

.199E-04 (.758E-05)

.254E-04 (.597E-05)

-.515 (.227)

-.453 c.214)

-.565 (.206)

.622 (.074)

871 (.094)

-2.34 (.327)

-1.95 (.304)

1-473.4

-492.8

1-305.6

-331.5

NUOIIK -

I0

Period 3

Periods I63

A l l Perio,lg

(.1175)

.293 (074)

.344 (.055)

(.044)

.482 (.142)

.5hl (.I%)

.511 (.133)

.4R2 (.007)

,472 (.l170)

.198E-04 (.48E-05)

.319E-04 (.1008-04)

.924E-05 (.H04E-05)

.142E-04 (.778E-05)

.170E-04 (.611E-05)

.12hh-0b (./,RE-(15)

-.557 (.150)

-.500 (.122)

-.487 (.232)

-.417 (.215)

-.503 (.212)

-.478 (.155)

-.447 (.12h)

.389 (.046)

.402 (.034)

.531 (.036)

,798 (.088)

.qI3 (.Ills)

.578 (.064)

.650 (.050)

.767

-1.86 (.283)

-2.14 (.212)

-2.17 (.174)

-2.47 (.31h)

-2.03 3 3

-2.13 (.297)

-2.29 (.223)

-2.23 ( .1 RO)

-501.2

-976.6

-1469

-473.4

-492.8

-;03.2

-976.6

-1469

-369.5

-691.6

-293.9

-321.8

-349.9

-646.2

-

--

Pcrlod 2

.302

-

URB

ISllH

ALTI

LOR I l k e l l h o o d a t Zero

.

-

Log l . l k e l l l ~ o o d nl C 19 79 Ford t... " , A ..,-r,.un.nr -cru.nuu*i ' 1972 Old C u t l a s s : r u ~ rJ A E ' ' 1979 Old

vrolet

.

vrolet

.

1

.a08

.797t-7h7

1.99

1.62

1.67

1.73

1.75

2.06

897

.922

1.17

.991

.976

,959

2.16

1.85

2.01

1.98

1.99

1.22

1.57

1.31

1.29

2'23

1.90

2.05

2.04

2.05

i.289

-.295

-1.70

-1.22

-1.06

-1.30

-1.33

-.466

-.315

-.253

-.337

-.343

-1.73

-1.24

-1.09

-1.33

-1.35

-.326

-.459

-.647

-. 495

-.278

-.393

-.598

-.424

-.410

-.278

-.393

-.598

-.424

-.410

-.649

-.628

I

--

I-

1

loyoca r o l l n : ContpacL 12 Ford

. , .....

a1ze

.968

I--

~

1.

1

.752

1 -.376 -.271 -.237 I

IY

I

A I I ~ ~ r l IPeJJod o d ~

I

1

c cosrs

(;ri...n..u. . 1972 Old c l l ~ l t ~ s sV:I I I 1979 n l d Cut I,,",,:

I l l t e r t e m > o r n l Model P e r 3 r o d 11

-1

"

.

P l o d 2

--

Corolla: -

W

Single-Vehicle Households

-~

1

I-' I-'

Type Choice E l a s t i c i t i e s :

--

-.479

-- -----

l l c s t r i c t e d Model l'erlod 3 Periods 113

l'erilld 2

.757

1.63 . .

.927

All PcrjwJr

--

-.

.995

.851

1.74

1.82

1.20

1.04

-

1.74

-- -- -.-.

-

.

.002

- -

--

-.

--

079. -

-

91L'-

179

.-

LSL'-

COB'EO'T-

-A-

L05'-

065'-

775.-

675'-

175'-

9'15'-

059'-

C59'-

779.-

679'-

900'-

ILL'-

-- -- . --

ELI'-

ZLL'-

-

--

..

559'.

L59.-

0SY'-

89L'-

----- 7-. 6 8 ' -

159'-

O7E'-

LUZV-

LEE'-

507.'-

-668'-

70.1-

09L'-

59L'-

--

[LC.-. ..--

9LL'-

199'-

---

7.59'-- 259'-

671'-

---

..

106'E6C'-- .-. - --.. -.

260'.-

571'-

70L '-

508'-

--

068'-

691'-

.-

L5Y'-

-

555'-

E06'-

675'255'-

55L'-

--

0SL'-

SLL'159'059'-

-.

--

CUS

.-

005'-,

559'-

919'-

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959'-

919'-

O9L'-

051. ' -

0ZC'-

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L0E'-

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96L'-

E69'-

865'-

'106'-

910.-

9H5'-

900'-

E0L'269'-

-

-

616'-

559'-

-Z05'768'-

TIC.-

197.-

-.-

709.-

70R.-

OLE'-

505'-

SIC'-

651'-

960'-

LOE '-

-

001. ' - -

0FZ'-

557'- --

--

-.

EZ7'--

-

-

6E.I

ZL9'-

259'-

YE9'-

15E.-

0SE'-

9ZE ' -

OZC 'OE9'-

979'-

ZZE.-

91E.-

609'-

765'-

595'E6Z'8'15'-

992'-

299'-

321s [[ll:l:fiRl![3ll> zSI J L I'I"~"I'IO -- .. .. ---GLGt JZlS 1 I n . l :!ist?[31>3 Z1,.JIT'IO"JSP10 7,161 JZISPlH :FpClll:J:) '151'.PJI'd 6LhC SZlSprW :?JTl>AVH LSE'---.Pl. o d 2161 -~ J W C ~ I U ~ :I n ~[rnion L6Z'e1odn.t 6 ~ 6 1 3.wi luon :a33anoq3 :aro.malin 6 l 6 1 3~~7uO:,~?i~~5iC5

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0-.0 ~ ' ZZE '-

61E'-

--.. -

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65E'c79.-

09H'-

6ZLe-

LE.1

6 1 '1

OZ'I

OZ'I

9Z'I

c6Z'-

8OZ'-

1'12.-

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11.1

91.1

51.1

9E6'

076'

92'1

52'1

90'1

10'1

558'

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LZ'I

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60'1

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918'

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3~onlaon: n l InJo:) e 3 ~ ~ ~ 6L61 n.t

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~3odo.l.ZL6T p"x,,~-:T3~

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101 '-

~ l -OJ ..A. ~--1-1 :.ZL61 .-. - - .l.)- --

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S.I.SO:l

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07.1 ZZ.1

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C75.115'Z9Z'-

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LZ'I

92'1

E65'-

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E9Z'LEE'-

-

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90'1

90'1

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655'hRZ'-

609'-

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6ZE'159'-

0CO'-

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I

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Z19'-

765'91E'---~ 7.62'-

11.1

01.1

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296 '

1p ~ 1 - a

POT-'~~

RWDNI

e l a s t i c i t i e s must be e q u a l i n magnitude (but o p p o s i t e i n s i g n ) t o t h e income e l a s t i c i t y .

I n p r e l i m i n a r y e s t i m a t i o n s , i t was found t h a t such

a r e s t r i c t i o n , which i s n o t i m p l a u s i b l e , was n e c e s s a r y t o o b t a i n r e a s o n a b l e e s t i m a t i o n r e s u l t s t h a t c o n t r o l l e d f o r income d i f f e r e n c e s among households. Turning now t o t h e s i n g l e - v e h i c l e household e l a s t i c i t y e s t i m a t e s p r e s e n t e d i n Table 1 6 , i t i s i n t e r e s t i n g t o n o t e t h a t t h e e a r l i e r f i n d i n g s of i n c r e a s i n g consumer's v a l u a t i o n s of o p e r a t i n g c o s t s and d e c r e a s i n g v a l u a t i o n s of c a p i t a l c o s t s ( s e e S e c t i o n 5 . 2 ) , over t i m e , a r e r e f l e c t e d i n these type choice e l a s t i c i t i e s .

Also n o t i c e t h a t t h e

i-ncome and c a p i t a l c o s t e l a s t i c i t i e s a r e much l a r g e r f o r new v e h i c l e s than f o r old vehicles.

T h i s emphasizes t h e importance of p r i c i n g i n

t h e s a l e of new v e h i c l e s .

Tn terms of o p e r a t i n g c o s t e l a s t i c i t i e s ,

i t a p p e a r s a s though o l d e r v e h i c l e s of t h e same c l a s s (e.g.

a r e more e l a s t i c than t h e i r newer v e h i c l e c o u n t e r p a r t s .

compacts)

As a f i n a l

p o i n t , a l t h o u g h t h e income and c a p i t a l c o s t e l a s t i c i t i e s of f o r e i g n and domestic producers a r e s i m i l a r , t h e domestic o f f e r i n g s a r e more sensitive t o

changes i n o p e r a t i n g c o s t s :

This r e f l e c t s a g e n e r a l

need f o r improved o p e r a t i n g c o s t performance among domestic manufacturers.

More on t h i s m a t t e r w i l l be s a i d i n S e c t i o n 5.7.3. For t h e c a s e of two-vehicle

households ( s e e Table 1 7 ) , i t i s

f i r s t i m p o r t a n t t o n o t e t h a t f o r a l l t h r e e e l a s t i c i t i e s (income, c a p i t a l c o s t s , and o p e r a t i n g c o s t s ) ,

'

two-vehicle households have

much l e s s v a r i a n c e a c r o s s v e h i c l e t y p e s t h a n do s i n g l e - v e h i c l e household.

It i s s p e c u l a t e d t h a t t h i s i s s o due t o t h e f l e x i b i l i t y t h a t

i s a f f o r d e d by

t h e ownership of an a d d i t i o n a l v e h i c l e , which l e a d s 115

,

t o more u n i f o r m r e s p o n s e s a c r o s s v e h i c l e t y p e s w i t h r e s p e c t t o c h a n g e s i n v e h i c l e c o s t s and income.

A l s o , I n comparing one- and t w o - v e h i c l e

household r e s p o n s i v e n e s s , T a b l e s 1 6 and 17 i n d i c a t e t h a t income and c a p i t a l c o s t e l a s t i c i t i e s a r e s i m i l a r f o r old v e h i c l e s , b u t two-vehicle h o u s e h o l d s a r e much l e s s e l a s t i c w i t h r e g a r d t o income and c a p i t a l c o s t e l a s t i c i t i e s f o r new v e h i c l e s .

T h i s i s p r o b a b l y due i n l a r g e p a r t t o

t h e g e n e r a l l y h i g h e r incomes of t h e two-vehicle h o u s e h o l d p o p u l a t i o n . F i n a l l y , i t i s o b s e r v e d t h a t t h e o p e r a t i n g c o s t s e n s i t i v i t i e s of twov e h i c l e households have i n c r e a s e d , over time, a t h i g h e r r a t e s t h a n t h e s i n g l e - v e h i c l e household o p e r a t i n g c o s t s e n s i t i v i t i e s .

Again, t h i s

p r o b a b l y r e f l e c t s t h e a d d i t i o n a l f l e x i b i l i t y of t h e two-vehicle

house-

h o l d i n t h a t t h e y a r e more l i k e l y t o e n t e r t h e m a r k e t and s e e k v e h i c l e s t h a t a r e more a p p r o p r i a t e i n t h e f a c e of t h e p r e v a i l i n g c o s t s and economic

climate.

5.7.2.

Household R e s p o n s i v e n e s s by V e h i c l e Make

With t h e g e n e r a l r e s p o n s i v e n e s s t o v a r i o u s v e h i c l e t y p e s d i s c u s s e d a b o v e , i t i s i n t e r e s t i n g t o d i r e c t a t t e n t i o n t o t h e r e s p o n s i v e n e s s of owners of s p e c i f i c makes of v e h i c l e s .

T h i s i s done by e s t i m a t i n g

e l a s t i c i t i e s , a s b e f o r e , b u t e n u m e r a t i n g o n l y o v e r t h a t p o r t i o n of t h e p o p u l a t i o n owning v e h i c l e s of a s p e c i f i e d make.

I n a l l , households

of s e v e n v e h i c l e makes ( F o r d , C h e v r o l e t , a l l f o r e i g n makes, C h r y s l e r , American M o t o r s , O l d s m o b i l e , and Toyota) were c o n s i d e r e d .

The e l a s t i -

c i t i e s were c a l c u l a t e d o n l y from t h e i n t e r t e m p o r a l t y p e c h o i c e model (since t h e e a r l i e r e s t i m a t e s i n T a b l e s 16 and 17 r e v e a l e d l i t t l e d i f f e r e n c e between t h e r e s t r i c t e d and i n t e r t e m p o r a l models) 116

and o n l y f o r

t h e p e r i o d s b e f o r e and a f t e r t h e e n e r g y shock. The r e s u l t i n g e l a s t i c i ' t y e s t i r a a t e s f o r s i n g g d - v e h i c l e househ o l d s are p r e s e n t e d i n T a b l e 1 8 .

F o r income e l a s t i c i t i e s , F o r d , AMC and

Toyota owners have t h e h i g h e s t e l a s t i c i t i e s f o l l o w e d by C h r y s l e r , C h e v r o l e t , O l d s m o b i l e , a n d f o r e i g n v e h i c l e owners.

The AMC owners had

t h e i n t e r e s t i n g e f f e c t of s l i g h t l y i n c r e a s i n g income e l a s t i c i t i e s f o r o l d c a r s and g r e a t l y d e c r e a s i n g e l a s t i c i t i e s f o r new c a r s , o v e r t i m e . It i s p o s s i b l e t h a t t h i s i r r e g u l a r e f f e c t w a s caused by d i f f e r e n t house-

h o l d s , w i t h d i f f e r e n t s o c i o e c o n o m i c c o n d i t i o n s , owning AMC v e h i c l e s i n t h e two t i m e p e r i o d s . The c a p i t a l c o s t elasticities r e f l e c t t h e same p a t t e r n w i t h F o r d , AMC and T o y o t a owners b e i n g t h e most e l a s t i c f o l l o w e d by C h r y s l e r , C h e v r o l e t , O l d s m o b i l e , and f o r e i g n v e h i c l e owners.

The AMC

owners a g a i n d e m o n s t r a t e u n u s u a l i n s t a b i l i t y o v e r t i m e as t h e y become much l e s s e l a s t i c w i t h r e s p e c t t o

capital costs.

For o p e r a t i n g c o s t

e l a s t i c i t i e s , t h e same r a n k of makes r e s u l t e d , w i t h h o u s e h o l d s becoming more e l a s t i c o v e r t i m e a s opposed t o t h e c a p i t a l c o s t c a s e , i n which t h e y became less e l a s t i c .

I n t e r m s of a b s o l u t e v a l u e s , b e f o r e t h e

e n e r g y s h o c k , o p e r a t i n g c o s t and c a p i t a l c o s t s e l a s t i c i t i e s were a b o u t e q u a l f o r o l d e r v e h i c l e s , and c a p i t a l c o s t e l a s t i c i t i e s w e r e g r e a t e r t h a n o p e r a t i n g c o s t e l e a s t i c i t i e s f o r new v e h i c l e s .

After t h e shock,

o p e r a t i n g c o s t e l a s t i c i t i e s exceed c a p i t a l c o s t e l a s t i c i t i e s f o r o l d e r v e h i c l e s b u t c a p i t a l c o s t e l a s t i c i t i e s s t i l l dominate o p e r a t i n g c o s t e l a s t i c i t l e s f o r newer c a r s .

T h i s s u g g e s t s t h a t even though

fuel

e f f i c i e n c y h a s become more i m p o r t a n t , t h e v e h i c l e c o s t i s s t i l l t h e critical factor.

T h i s f i n d i n g u n d e r s c o r e s t h e i m p o r t a n c e of new v e h i c l e 117

Table 18.

Type Choice E l a s t i c i t i e s by Make: Single-Vehicle Households ( I n t e r t e m p o r a l Model)

Ford

-

Income

Chev-rolet PRDl

PRD3

'72 Vega

.658

.931

'72 C o r o l l a

.738

1.01

'79 C h e v r o l e t

1.92

1.82

'79 C o r o l l a

2.03

1.90

' 72

Maverick

'79 Granada

.923

1.27

2.21

2.23

'72 Cutlass

1.19

1.67

'79 C u t l a s s

2.28

2.29

C a p i t a l Costs '72 Vega '72 C o r o l l a '79 C h e v r o l e t '79 C o r o l l a '72 Maverick ' 7 9 Granada '72 C u t l a s s '79 C u t l a s s

Operating

caste

'72 Vega

-.383

'72 C o r o l l a

-.I99

'79 Chevrolet

-.327

'79 C o r o l l a

-.326

' 7 2 Maverick

-.502

'79 Granada

-.497

'72 C r ~ t l a s s

-.679

'79 Cutlass

-.496

Foreign

Chrysler

rZMC

Oldsmobile

Toyota

p r i c i n g even when c o n s i d e r a b l e changes i n t h e v a l u a t i o n s of o t h e r v e h i c l e a t t r i b u t e s have o c c u r r e d . The e l a s t i c i t y e s t i m a t e s f o r two v e h i c l e households a r e given i n Table 19.

The o r d e r of t h e makes, b y magnitude of t h e income e l a s -

t i c i t y , i s s u b s t a n t i a l l y d i f f e r e n t t h a n t h a t o r d e r found i n t h e s i n g l e v e h i c l e case.

S p e c i f i c a l l y , Oldsmobile owners a r e t h e most e l a s t i c ,

followed by C h e v r o l e t , C h r y s l e r , A M C , Ford, f o r e i g n makes, and f i n a l l y Toyota owners.

The d i f f e r e n c e s i n t h e s e o r d e r i n g s a s opposed t o t h o s e

i n t h e s i n g l e v e h i c l e household c a s e , may be t h e r e s u l t of a number of f a c t o r s i n c l u d i n g t h e f a c t t h a t t h e "other" v e h i c l e owned i n t h e v e h i c l e p o r t f o l i o (which may o r may n o t be of t h e same make) can have a c o n s i d e r a b l e impact on e l a s t i c i t y e s t i m a t e s . For b o t h o p e r a t i n g c o s t and c a p i t a l c o s t e l a s t i c i t i e s , t h e o r d e r of t h e v e h i c l e makes based on t h e a b s o l u t e v a l u e s of t h e i r e l a s t c i t i e s

i s e s s e n t i a l l y t h e same as t h a t found i n t h e income e l a s t i c i t y c a s e d i s c u s s e d above.

Also, i n c o n t r a s t t o t h e s i n g l e v e h i c l e household c a s e ,

t h e a b s o l u t e v a l u e of t h e c a p i t a l c o s t e l a s t i c i t y i s g r e a t e r t h a n t h a t of t h e o p e r a t i n g c o s t e l a s t i c i t y b e f o r e t h e energy

shock, b u t t h e

o p p o s i t v e i s t r u e f o r a l l v e h i c l e t y p e s (old and new) a f t e r t h e energy shock.

T h e r e f o r e , i n t h e c a s e of t h e two v e h i c l e households, t h e sen-

s i t i v i t y t o t h e f u e l e f f i c i e n c y of new v e h i c l e s now outweights t h e sensitivity t o capital costs.

The f a c t t h a t t h i s i s n o t t h e c a s e i n

t h e s i n g l e v e h i c l e household may b e t h e r e s u l t of t h e d i f f e r i n g income l e v e l s of t h e two p o p u l a t i o n s .

Table 19.

Type Choice E l a s t i c i t i e s by Make :

Two-Vehicle Households

(Intertemporal M d e l )

Ford

Chevrolet

Foreign

Chrysler

AMC

Oldsmobile

Toyota

PRDl

PRD3

PRDl

PRD3

PRDl

PRD3

PRDl

PRD3

PRDl

PRD3

PRDl

P R K

' 7 2 Vega

.575

.886

,467

.637

.596

.907

.770

.902

.819

1.68

.454

.599

'72 C o r o l l a

.606

.917

.487

.659

.624

.938

.819

.934

.899

1.73

.491

.628

' 7 9 Chevette

.902

1.09

.699

.775

.919

1.12

1.33

1.12

1.75

2.03

.724

.714

'79 Corolla

.941

1.12

.726

.795

.956

1.14

1.39

1.15

1.85

2.07

.764

.737

'72 Maverick

.631

.980

.512

.715

.657

1.02

.874

1.02

.979

1.85

.511

.671

' 7 9 Granada

.984

1.23

,766

.887

1.01

1.28

1.48

1.28

1.98

2.27

.809

.821

'72 C u t l a s s

.717

1.14

.570

.823

.735

1.17

1.01

1.17

1.17

2.08

.585

,775

Income

'79 C u t l a s s C a p i t a l Costs "72 Vega '72 C o r o l l a '79 Chevette '79 C o r o l l a '72 Maverick ' 7 9 Granada '72 Cutlass '79 Cutlass

O p e r a t i n g Cos ' 7 2 Vega '72 C r o l l a '79 C h e v e t t e '79 C o r o l l a '72 Maverick '79 Granada '72 C u t l a s s '79 C u t l a s s

RD1

PRD3

1.39

5.7.3

Responsiveness t o M a n u f a c t u r e r O f f e r i n g s

To a s s e s s t h e r e l a t l ' v e c o m p e t i t i v e n s s of v e h i c l e m a n u f a c t u r e r s a s of t h e s p r i n g of 1980, t h e c a p i t a l c o s t , o e p r a t i n g c o s t , and income e l a s t i c i t i e s were c a l c u l a t e d f o r t h e m a n u f a c t u r e r s ' 1980 model y e a r vehicle offerings.

The e l a s t i c i t l ' e s were e s t i m a t e d u s i n g t h e e n t l r e one-

and two-vehicle p o p u l a t i o n s , and t h e t y p e c h o i c e parameter e s t i m a t e s of t h e Period 3 ( i . e .

s p r i n g of 1980) i n t e r t e m p o r a l model.

The r e s u l t i n g

e l a s t i c i t i e s f o r s i n g l e - v e h i c l e households a r e p r e s e n t e d i n Table 20, and t h e e s t i m a t e s f o r two-vehicle households a r e given i n Table 21. I n i n t e r p r e t i n g t h e s i n g l e - v e h i c l e household r e s u l t s , i t i s f i r s t n o t i c e d t h a t l u x u r y makes have model o f f e r i n g s t h a t a r e v e r y s e n s i t i v e t o c a p i t a l c o s t s and income.

Examples of t h i s i n c l u d e C a d i l l a c , L i n c o l n ,

BMW, J a g u a r , Mercedes, and Volvo.

It i s s p e c u l a t e d t h a t h i g h s e n s i t i v i t i e s

r e f l e c t t h e f a c t t h a t such v e h l c l e s a r e n o t economically a c c e s s i b l e t o a l a r g e p o r t i o n of t h e s i n g l e - v e h i c l e household p o p u l a t i o n .

Another

i m p o r t a n t f i n d i n g i s t h a t t h e s e n s i t i v i t y of domestic v e h i c l e s t o o p e r a t i n g c o s t s tend o t be g r e a t e r t h a n t h a t of t h e i r f o r e i g n c o u n t e r parts.

T h i s i s r e f l e c t e d i n t h e f a c t t h a t , a l t h o u g h many domestic

v e h i c l e models have o p e r a t i n g c o s t e l a s t i c i t i e s w i t h an a b s o l u t e v a l u e g r e a t e r t h a n u n i t y , o n l y one f o r e i g n model i s i n such a c a t e g o r y ( t h e Jaguar XJ6).

T h i s r e f l e c t s t h e p o t e n t i a l of domestic m a n u f a c t u r e r s t o

b e n e f i t from t h e improved f u e l a s of t h e s p r i n g of 1980. fuel

e f f i c i e n c y of t h e i r v e h i c l e o f f e r i n g s ,

Of c o u r s e any improvement d i r e c t e d towards

e f f i c i e n c y must be made w i t h t h e demand s e n s i t i v i t i e s t o c a p i t a l

c o s t s and income i n mind.

T a b l e 20.

Type Choice E l a s t i c i t i e s by 1980 Model Year O f f e r i n g s : S i n g l e - V e h i c l e Households ( I n t e r t e m p o r a l Model) E l a s t i c i t y with Respect t o

Make and Model

Capital Costs

Operating Costs

I n come

American Motors Concord

-1.42

-. 785

2.22

Pacer

-1.59

-1.01

2.63

Spirit

-1.39

-.785

2.19

Bui c k Century Electra Le S a b r e Regal Riviera Sky l a r k Skyhawk Cadillac D e Ville

Eldorado Seville Fleetwood Chevr o l e t Cheve t t e Corvette Impala Malibu Monte C a r l o Mon z a Camaro Citation (Continued n e x t page)

Table 20 (Continued) E l a s t i c i t y w i t h Respect t o

Make and Model

Capital Costs

Operating Costs

Income

Chrysler Cordoba Le Baron Newport New Yorker Dodge Aspen Colt Omni Diplomat S t . Regis Ford

Fairmont Fiesta Granada LTD Mustang Thunderbird Pinto Escort

Lincoln Mark V I Versailles Mercury Bobcat

-1.28

-.597

1.88

Cougar

-1.54

-1.22

2.79

Monar ch

-1.67

-1.01

2.70

Zephyr

-1.59

-.910

2.51

Capri

-1.77

-. 860

2.65

(Continued n e x t page)

T a b l e 20 (Continued) E l a s t i c i t y w i t h Respect t o Capital Costs

Operating Costs

Cut lass

-1.69

-,906

Delta

-1.94

Omega

-1.78

Starfi r e

-1.62

-. 859 -. 749 -. 719

Toronado

-3.14

-1.06

Make and Model

I n come

Oldsmobile

Ninety-Eight Plymouth Arrow Fury Horizon Volare Champ Pontiac Firebird Grand P r i x Pheonix Sunbird Foreign Audi Fox BMW 3 2 0 i

Datsun 200 SX Datsun 210 Datsun 2802 Datsun 510 Datsun 810 F i a t XI9 Honda C T V I C Honda CVCC (Continued n e x t page)

2.61 2,82 2.55 2.35 4.24

T a b l e 20 (Continued) E l a s t i c i t y with Respect t o Capital Costs

Operating Costs

Honda Accord

-2.01

-.638

2.66

J a g u a r XJ6

-5.14

-1.11

-6 .'31

Mazda GLC

-1.47

-.577

Mazda RX7

-3.09

-.946

Mercedes 280

-6.10

-. 927

7.07

MG MGB

-2.06

-1.07

3.15

Peugeot 504

-2.49

-.746

3.26

P o r s c h e 924

-4.30

-.706

5.03

R e n a u l t Le Car

-1.34

-.665

2.01

Subaru DL

-1.42

Subaru Wagon

-1.21

Subaru GF

-1.53

Toyota Corona

-1.85

-.954

2.82

Toyota C e l i c a

-2.02

-.954

3.00

Toyota C o r o l l a

-1.60

-.558

2.16

Toyota C r e s s i d a

-2.37

-. 9 5 1

3.34

Triumph TR7

-2.10

-. 688

2.80

VW Dasher

-2.08

-.748

2.84

VW R a b b i t

-1.70

-. 690

2.41

VW D i e s e l Rab.

-1.76

-.422

2.19

VW S c i r r o c c o

-2.17

-.688

2.87

Volvo 260 S

-3.03

-. 898

3.95

Make and Model

-.618 -. 642

-.617

Income

2.06 4.06

2.05 1.85 2.15

The two-vehicle

household t y p e c h o i c e e l a s t i c i t i e s (see T a b l e

21) r e v e a l p a t t e r n s s i m i l a r t o t h o s e found i n t h e s i n g l e - v e h i c l e household c a s e .

F i r s t , t h e c a p i t a l c o s t and income e l a s t i c i t i e s of

l u x u r y v e h i c l e s ( e . g. C a d i l l a c , L i n c o l n , Mercedes , and s o on) a r e h i g h r e l a t i v e t o o t h e r v e h i c l e c l a r s e s , b u t n o t n e a r l y a s h i g h a s t h e y were i n t h e s i n g l e - v e h i c l e household c a s e .

T h i s i s p r o b a b l y due t o t h e

h i g h e r two-vehicle household incomes and t h e g r e a t e r v e h i c l e ownership f l e x i b i l i t y a f f o r d e d t o two-vehicle households.

I n t e r m s of o p e r a t i n g

c o s t e l a s t i c i t i e s , s i n g l e - and two-vehicle households have e l a s t i c i t i e s of s i m i l a r magnitude, w i t h t h e two-vehicle household h a v i n g n o t i c e a b l y less v a r i a n c e i n e l a s t i c i t i e s a c r o s s v e h i c l e makes and models.

This

f i n d i n g s u p p o r t s t h e r e s u l t s p r e s e n t e d i n t h e p r e c e d i n g two s e c t i o n s o f t h i s chapter.

F i n a l l y , t h e two-vehicle households d e m o n s t r a t e t h e same

h i g h e r o p e r a t i n g c o s t s e n s i t i v i t y t o d o m e s t i c o f f e r i n g s , as opposed t o f o r e i g n o f f e r i n g s , a l t h o u g h t h e d i f f e r e n c e s between t h e s e s e n s i t i v i t i e s d o n o t a p p e a r t o be a s h i g h a s t h e y were i n t h e s i n g l e - v e h i c l e household case.

5.8

Model S p e c i f i c a t i o n T e s t s

A number of s p e c i f i c a t i o n t e s t s were conducted t o e v a l u a t e t h e v a l i d i t y of t h e m u l t i n o m i a l l o g i t (MNL) s t r u c t u r e used i n t h e e s t i m a t i o n of t h e v e h i c l e t y p e c h o i c e models.

S p e c i f i c a l l y , t e s t s a r e made t o a s s e s s

t h e r e a s o n a b l e n e s s of t h e l i m i t a t i o n s t h a t t h e MNL model imposes on t h e s u b s t i t u t a b i l i t y of t h e t y p e c h o i c e a l t e r n a t i v e s .

T h i s MNL l i m i t a t i o n ,

of c o u r s e , i s t h e w i d e l y known "independence of i r r e l e v a n t a l t e r n a t i v e s " (IIA)

property.

Table 2 1 .

Type Choice E l a s t i c i t i e s by 1980 Model Year O f f e r i n g s : Two-Vehicle Households (Intertempor a1

Make and Model

Capital Costs

Model) Operating Costs

American Motors Concord Pacer Spirit Bui ck Century Electr a Le Sabre Regal Rivier a Skylark Skyhawk Cadillac De'Ville Eld orado Seville Fleetw ood Chevrolet Cheve t t e Corvette Impala Malibu Monte C a r l o Monza Camar o Citation (Table contihued n e x t page)

Income

T a b l e 2 1 (Continued) Capital Costs

Operating Costs

-. 753

Cougar

-. 616 -.704

Mon ar c h

-.748

-.940

Zephyr

-. 722

-. 892

Make and Model Chr y s l e r Cordoba Le Baron Newp o r t New Y o r k e r Dodge Aspen Colt Omni Diplomat S t . Regis F ord Fairmont Fiesta Granada LTD Mustang Thunderbird Pinto Escort Lincoln Mark V I Versailles

M e r c u ry Bobcat

-1.04

(Table continued n e x t page)

Income

T a b l e 2 1 (Cont$nue.d)l Capital Costs

Operating Costs

-7.81

-. 871

Cutlass

-.754

Delta

-. 842

-. 892

Omega

-.787

-. 821

Starfire

- .731

-.808

Toronado

-1.25

Ninety-Eight

-1.00

-. 962 -. 997

A r r ow

-.730

-.761

Fury

-.716

-,969

Horizon

-.765

Make and Model Capri Oldsmobile

-.871

Plymouth

-.795

-. 664 -. 707

-.916

Audi Fox

-. 8 7 1

-. 822

BMW 3 2 0 i

-1.41

Datsun 200SX

-.824

-.789 -.822

Datsun 210

-.705

- .707

Datsun 2802

-1.24

-. 9 1 1

Datsum 510

-.757

Datsun 810 F i a t X19

-.812 -. 802

Honda C i v i c

-.707

Volare Champ

-.713

'Pontiac Firebird Grand P r i x Pheonix Sunbird Foreign

-.809 -. 873 -. 773 -.763

(Tab l e c o n t i n u e d n e x t page)

Table 2 1 (Continued) Make and Model

Capital Costs

Operating Costs

I n come

J a g u a r XJ6

-. 866 - 1.93

-. 7 5 3 -. 772 -. 986

2.89

Mazda GLC

-.681

-.745

1.39

Mazda

-1.23

-.9 1 1

2.10

Honda CVCC

-.743

Honda Accord

RX7

M e r c e d e s 280

-2.25

MG MGB

-. 882

Peugeot 504

-1.03

P o r s c h e 924

-. 898 -.969

1.45 1.60

3.13

1.81

-1.64

-.820 -.800

2.42

R e n a u l t Le Car

-.637

-.785

1.38

S u b a r u DL

-. 764

1.39

S u b a r u Wagon

-.667 -.5 9 1

-.775

1.32

S u b a r u GF

-.702

-. 743

1.43

T o y o t a Corona

-. 8 1 1

-.916

1.68

Toyota C e l i c a

-.870

-.915

1.74

Toyota C o r o l l a

-. 726

-.736

1.42

Toyota Cressida

- .987

-. 914

1.86

Triumph TR7

-. 896

-.795

1.65

VW D a s h e r

-.889

-.822 -.796

1.67 1.51

-.674

1.42

-. 794 -. 889

1.67

VW Diesel R a b b i t

-. 7 6 0 -. 7 7 9

VW S c i r r o c c o

- .918

V o l v o 260 S

-1.21

VW R a b b i t

1.81

2.06

I n t h e c a s e of v e h i c l e t y p e c h o i c e modeling, t h e r e a r e some i n t u i t i v e reasons f o r suspecting possible I I A v i o l a t i o n s .

For example,

u s i n g t h e MNL s t r u c t u r e , an i n c r e a s e i n t h e c a p i t a l c o s t of a Ford E s c o r t w i l l n e c e s s a r i l y r e s u l t i n t h e household's p r o b a b i l i t y of s e l e c t i n g any o t h e r v e h i c l e t y p e t o i n c r e a s e by t h e same p e r c e n t a g e .

It may b e more r e a l i s t i c t o e x p e c t t h e h o u s e h o l d l s p r o b a b i l i t y of s e l e c t i n g o t h e r compact c a r s t o i n c r e a s e more t h a n t h e i r p r o b a b i l i t y of s e l e c t i n g a l a r g e l u x u r y c a r (e.g.

Cadillac).

This t y p e of p o s s i b l e

I I A v i o l a t i o n l e d Berkovec and Rust (1981) t o e s t i m a t e a n e s t e d l o g i t s t r u c t u r e i n which households f i r s t s e l e c t t h e c l a s s of v e h i c l e t o own and t h e n t h e t y p e of v e h i c l e w i t h i n a g i v e n c l a s s ( s e e Chapter 2 f o r a f u r t h e r d i s c u s s i o n of t h i s e f f o r t ) .

Their empirical r e s u l t s

seem t o p o i n t towards r e j e c t i o n of t h e I I A p r i n c i p l e and an MNL t y p e choice s p e c i f i c a t i o n .

More r e c e n t l y , Booz, Allen 6r Hamilton (1983)

a t t e m p t e d t o e s t i m a t e a n e s t e d s t r u c t u r e s i m i l a r t o t h e Berkovec and Rust model, b u t t h e i d e a was abandoned when i m p l a u s i b l e e m p i r i c a l r e s u l t s were o b t a i n e d . I n p o i n t of f a c t , a number of s t a t i s t i c a l t e s t s a r e a v a i l a b l e t o e v a l u a t e t h e v a l i d i t y of an MNL s t r u c t u r e .

These t e s t s i n c l u d e t h o s e

of McFadden, T r a i n and Tye (1977), Horowitz (1981), Hausman and McFadden (1981), and Small and Hsiao (1982).

The r e c e n t work of Small

and Hsiao h a s i n d i c a t e d t h a t b o t h t h e McFadden-Train-Tye

and Horowitz

t e s t s a r e a s y m p t o t i c a l l y b i a s e d , and t h a t t h e Hausman and McFadden t e s t can be e x c e e d i n g l y d i f f i c u l t t o u s e i n c e r t a i n a p p l i c a t i o n s . S u b s e q u e n t l y , t h e t e s t s conducted i n t h i s work u s e t h e a s y m p t o t i c a l l y

u n b i a s e d l i k e l i h o o d r a t i o t e s t developed by Small and Hsiao. The Small-Hsiao t e s t p r o c e d u r e i s r e l a t i v e l y e a s y t o conduct. F i r s t , t h e h o u s e h o l d sample i s randomly d i v i d e d i n t o two e q u a l s i z e s , A

N

and N ~ and , model parameter e s t i m a t e s a r e o b t a i n e d f o r each of t h e s e

samples, v e c t o r s

;i

and

i:. A weighted

average of t h e s e p a r a m e t e r s

i s o b t a i n e d from:

Then, a r e s t r i c t e d c h o i c e s e t , D , i s c r e a t e d a s a sub-sample from t h e f u l l c h o i c e s e t , and t h e household sample N~ i s reduced t o i n c l u d e o n l y t h o s e h o u s e h o l d s which a c t u a l l y choose a l t e r n a t i v e s t h a t l i e i n D . models a r e e s t i m a t e d w i t h t h e reduced N

B

Two

household sample u s i n g t h e

c h o i c e s e t D a s i f i t were t h e e n t i r e choice s e t .

One model i s e s t i m a t e d A

by c o n s t r a i n i n g t h e parameter v e c t o r t o be e q u a l t o t h e OABvector d e f i n e d 0 above. *B

el.

The second model e s t i m a t e s t h e u n c o n s t r a i n e d parameter v e c t o r

The r e s u l t i n g l o g - l i k e l i h o o d s can be used t o e v a l u a t e t h e s u i t a b i l i t y

of t h e MNL model by c r e a . t i n g

a

Chi-square s t a t i s t i c w i t h t h e number of

d e g r e e s of freedom e q u a l t o t h e number of p a r a m e t e r s i n t h e v e c t o r s €I 0

iB 1'

and

This s t a t i s t i c i s :

The Small-Hsiao t e s t should a l s o be e s t i m a t e d by i n t e r c h a n g i n g t h e r o l e s of t h e N

A

and N

B

sub-samples

( i . e . reduce t h e N

A

household

sample t o t h o s e h o u s e h o l d s whose chosen a l t e r n a t i v e s l i e i n D , and proceed)

.

Using t h e same n o t a t i o n , Equation (45) i s r e w r i t t e n a s : 132

and t h e Chi-square

s t a t i s t i c i s now:

T e s t s of t h e m u l t i n o m i a l l o g i t t y p e c h o i c e s t r u c t u r e were conducted w i t h t h e s i n g l e - and two-vehicle household i n t e r t e m p o r a l model specifications.

The r e s u l t s of t h e s e t e s t s a r e p r e s e n t e d i n T a b l e 2 2 ,

and t h e i r i n t e r p r e t a t i o n i s p r e s e n t e d below. I n a l l , t h r e e d i s t i n c t Small-Hsiao s p e c i f i c a t i o n t e s t s were undert a k e n i n t h e c a s e of s i n g l e - v e h i c l e households.

The primary d i s t i n c t i o n

of t h e s e t e s t s i s t h e method by which t h e r e s t r i c t e d c h o i c e s e t , D , i s determined.

I n t h e f i r s t i n s t a n c e , t h e r e s t r i c t e d choice s e t

c o n s i s t s of f i v e a l t e r n a t i v e s t h a t were s e l e c t e d at random from t h e o r i g i n a l t e n a l t e r n a t i v e choice s e t s .

T h i s random c h o i c e s e t s h o u l d

g i v e some i n d i c a t i o n i f i n f a c t an I I A problem e x i s t s .

The t e s t

r e s t u l s i n d i c a t e ( s e e T a b l e 22) t h a t t h e n u l l h y p o t h e s i s of an MNL s t r u c t u r e cannot b e r e j e c t e d a t r e a s o n a b l e con£i d e n c e l e v e l s ( o n l y a t t h e 29 o r 35 p e r c e n t c o n f i d e n c e l e v e l s ) . I n t h e second t e s t , t h e r e s t r i c t e d c h o i c e s e t c o n s i s t s of o n l y U.S. made c a r s (one d e g r e e of freedom i s l o s t s i n c e t h e FORN p a r a m e t e r e s t i m a t e cannot b e d e t e r m i n e d ) .

The b e l i e f h e r e i s t h a t U.S.

c a r s may

be viewed a s grouped, and t h e r e f o r e s h a r e u n o b s e r v a b l e s i n v i o l o a t i o n of l o g i t assumptions.

Again, t h e n u l l h y p o t h e s i s of an MNL s t r u c t u r e

cannot b e r e j e c t e d a t r e a s o n a b l e c o n f i c e n c e l e v e l s ( o n l y at t h e 2 o r 10 p e r c e n t c o n f i d e n c e l e v e l s ) . 133

Table 22.

T e s t of t h e Multinomlal L o g l t Type Choice S p e c i f i c a t i o n

2

(X

Statistic)

I n t e r t e m p o r a l Model

S i n g l e V e h i c l e 'Households a Random Alternatives

'

U.S. b Cars

Large C Cars

Two V e h i c l e Household Rand om ~lternatives~

Small-Hsiao Statistic Small-Hsiao on i n t e r c h a n g e d subsamples

13.22

8.4

15.76

5.8

Degrees of Freedom

16

15

16

14

a

F i v e a l t e r n a t i v e s a r e s e l e c t e d a t random from t h e o r i g i n a l t e n a l t e r n a t i v e choice s e t .

b

Only American made v e h i c l e s comprise t h e r e s t r i c t e d c h o i c e s e t .

C

Only automobiles w i t h curb w e i g h t s exceeding 3500 l b s comprise t h e r e s t r i c t e d choice s e t .

In t h e f i n a l c a s e , t h e r e s t r i c t e d choice s e t c o n s i s t s o n l y of t h o s e automobiles w i t h curb w e i g h t s exceeding 3500 l b s ( i . e . large cars).

T h i s i s done based on t h e s u s p i c i o n t h a t c a r s

c l a s s a r e viewed as grouped.

of t h e same

T h i s , of c o u r s e , i s t h e premise of t h e

Eerkovec and Rust (1981) v e h i c l e c l a s s model.

Again i t i s found

t h a t t h e n u l l h y p o t h e s i s of an MNL s t r u c t u r e cannot be r e j e c t e d a t a c c e p t a b l e c o n f i d e n c e l e v e l s ( o n l y a t t h e 76 and 53 p e r c e n t c o n f i d e n c e levels). For two v e h i c l e h o u s e h o l d s , t h e Small-Hsiao t e s t was conducted only f o r a random r e s t r i c t e d c h o i c e s e t .

With f i v e a l t e r n a t i v e s

s e l e c t e d a t random from t h e o r i g i n a l t e n , i t i s found t h a t t h e MNL s p e c i f i c a t i o n can o n l y be r e j e c t e d w i t h 2 o r 3 p e r c e n t confidence. I n summary, t h e r e does n o t appear t o be any s t a t i s t i c a l j u s t i f i c a t i o n f o r b e l i e v i n g t h a t t h e s i n g l e - and two-vehicle household t y p e choice models e s t i m a t e d i n t h i s work a r e m i s s p e c i f i e d .

Indeed, t h e

MNL v e h i c l e t y p e c h o i c e s p e c i f i c a t i o n seems t o be q u i t e s a t i s f a c t o r y .

CHAPTER 6 ,

SUMNARY AND CONCLUSLONS

The o b j e c t i v e of t h i s work was t o a s s e s s t h e demand f o r motor v e h i c l e s i n t h e U.S.

To a c h i e v e t h i s , t h e a n a l y s i s w a s under-

t a k e n a t t h e household l e v e l , and f u l l e x p l l c i t c o n s i d e r a t i o n was g i v e n t o t h e i n t e r r e l a t i o n s h i p s between t h e h o u s e h o l d ' s c h o i c e s of q u a n t i t y of v e h i c l e s t o own, t y p e s of v e h i c l e s t o own ( d e f i n e d by make, model, and v i n t a g e ) and t h e e x t e n t t o which t h e s e v e h i c l e t y p e s a r e u t i l i z e d (measured i n v e h i c l e m i l e s t r a v e l e d ) .

Moreover, t h e dynamic a s p e c t s

of t h e h o u s e h o l d ' s v e h i c l e ownership and u t i l i z a t i o n d e c i s i o n were accounted f o r by viewing dynamics a s t h e e v o l u a t i o n of household t a s t e s . Based on fundamentally d i f f e r e n t economic t h e o r i e s r e l a t i n g t o t h e manner i n which households a d d r e s s t h e i n t e r t e m p o r a l n a t u r e of t h e i r v e h i c l e ownership problem, two dynamic econometric models of v e h i c l e owners h i p and u t i l i z a t i o n were d e r i v e d . The d e r i v e d models were e s t i m a t e d w i t h a n a t i o n a l household sample i n which a l l r e l e v a n t v e h i c l e ownership i n f o r m a t i o n was a v a i l a b l e f o r t h e same households f o r a two-and-one-half 1977 t o June 1980.

y e a r p e r i o d , December

The r e s u l t i n g model e s t i m a t i o n s i n d i c a t e t h e

following :

1.

Domestic m a n u f a c t u r e r s e n j o y an i n h e r e n t p r e f e r e n c e i n t h e h o u s e h o l d ' s v e h i c l e t y p e s e l e c t i o n p r o c e s s a s opposed t o t h e i r foreign counterparts,

2.

Householdsr v a l u a t i o n s of o p e r a t i n g c o s t s i n t h e determinat i o n of t h e t y p e of v e h i c l e t o own h a s i n c r e a s e d over t h e 1978 t o 1980 t i m e p e r i o d .

Correspondingly, t h e r a t e a t which

f u t u r e operating c o s t s a r e discounted has declined, i n d i c a t i n g l e s s myopic b e h a v i o r a n d / o r an e x p e c t a t i o n of f u t u r e i n c r e a s e s i n f u e l p r i c e s .

3.

The e l a s t i c i t i e s of o p e r a t i n g c o s t s and income w i t h r e s p e c t t o household v e h i c l e u t i l i z a t i o n (VMT) a r e q u i t e

small.

T h i s i s an i m p o r t a n t p o i n t t o keep i n mind i n t h e

f o r m u l a t i o n of n a t i o n a l e n e r g y p o l i c i e s .

4.

A s e x p e c t e d , t h e p r o c e s s t h r o u g h which v e h i c l e u t i l i z a t i o n i s d e t e r m i n e d was s t r o n g l y impacted by t h e s u p p l y r e s t r i c -

t i o n s of t h e e n e r g y s h o c k p e r i o d ( J u n e 1979 t o December 1 9 7 9 ) .

5.

A s t r o n g r e l a t i o n s h i p was found t o e x i s t between t h e c h o i c e of t h e number and t y p e s of v e h i c l e s t o own.

This relation-

s h i p i s an i m p o r t a n t concern t h a t s h o u l d b e a d d r e s s e d i n any v e h i c l e demand s t u d y .

6.

Domestic m a n u f a c t u r e r s c o u l d b e n e f i t s i g n i f i c a n t l y by i m p r o v i n g t h e f u e l e f f i c i e n c i e s of t h e i r model o f f e r i n g s .

7.

Household income i s a d r i v i n g f o r c e i n t h e d e t e r m i n a t i o n of b o t h t h e q u a n t i t y and t h e t y p e s of v e h i c l e s t o own. T h i s u n d e r s c o r e s t h e i m p o r t a n t r o l e t h a t macroeconomics p l a y i n t h e v i a b i l i t y of t h e a u t o m o b i l e i n d u s t r y .

I n summary, t h e r e s u l t s of t h i s s t u d y s u g g e s t t h a t v e h i c l e demand c o n d i t i o n s f a v o r t h e s u r v i v a l of t h e d o m e s t i c a u t o m o b i l e industry.

T h i s i s r e f l e c t e d i n t h e i n h e r e n t p r e f e r e n c e o f consumers

t o w a r d s GM and Ford p r o d u c t s , and t o a l e s s e r e x t e n t C h r y s l e r and AMC p r o d u c t s , as opposed t o f o r e i g n made v e h i c l e s .

However, t o e x p l o i t

t h i s p r e f e r e n c e , d o m e s t i c m a n u f a c t u r e r s must be a b l e t o o f f e r r e a s o n a b l y c o m p e t i t i v e v e h i c l e models, b o t h i n terms of performance and c a p i t a l costs.

Whether o r n o t t h i s can b e achieved i s a n i m p o r t a n t s u p p l y

o r i e n t e d q u e s t i o n that s h o u l d be a d d r e s s e d i n f u t u r e r e s e a r c h .

Appendix A .

D e r i v a t i o n of t h e R e s t r i c t e d Dynamic U t i l i z a t i o n E q u a t i o n

The f o l l o w i n g p r o c e d u r e i s u s e d t o e l i m i n a t e t h e u n m e a s u r a b l e s t a t e v a r i a b l e from t h e r e s t r i c t e d dynamic u t i l i z a t i o n e q u a t i o n .

Recall that the

u t i l i z a t i o n e q u a t i o n i s of t h e Sorm:

By d e f i n i t i o n ,

To b e g i n , r e c a l l from t h e t e x t t h a t

Now, c o n s i d e r an a p p r o x i m a t i o n of e q u a t i o n ( 3 a ) ,

A l s o , from e q u a t i o n s ( 2 a ) and (4.a) :

D i f f e r e n c i n g e q u a t i o n ( l a ) (and u s i n g a p p r o x i m a t i o n s a s i n e q u a t i o n ( 4 a ) ) , and s u b s t i t u t i n g e q u a t i o n ( 5 a ) , y i e l d s

2(xit

-

-

xit-1

= 2Bi(hit

- ni(Jlt+

Jit-l)

-hit-l)

-

ai6i

+ 2ai(sit - + -Sit-l (Sit 139

'it-1 ) )

+ 2Bi (Ait -

(6 a )

'it-1 )

X

where :

-

-

i t - It

= I

'it a n d h i t - l

t-1

-

Write equation ( l a ) a s

-aiSiSit

=

S i ~ i + GiBiXit

-Sixit.

(7 a )

S u b s t i t u t i n g e q u a t i o n (7a) i n t o e q u a t i o n ( 6 a ) and u s i n g t h e d e f i n i t i o n of J given i n t h e t e x t ( e q u a t i o n ( 8 ) )

2(xit

-

x

) = -Si(xit

it-1

+6iBi

, yields

+ Xit-l) + 2Bi(hit

(hit

+ a1. ( ( a x i t +

(axit-l

2SiTi

+

CX'

1 1).

it-1

will S i n c e t h e c h o i c e of o n l y one v e h i c l e i s b e i n g p e r m i t t e d x' it be z e r o .

Solving f o r x

i n t e r v a l t ) gives

where

it

( t h e u t i l i z a t i o n of t h e chosen v e h i c l e i i n time

it

and :

and t h e p a r a m e t e r s a

i'

a , c , a r e not recoverable.

Equation (9a) i s now an e s t i m a b l e dynamic e q u a t i o n of v e h i c l e utilization,

s i n c e t h e unmeasurable s t a t e v a r i a b l e h a s been removed.

A l l remaining v a r i a b l e s a r e r e a d i l y measurable.

Appendix B.

D e r i v a t i o n of ' t h e I n t e r t e m p o r a l Dynamic U t i l i z a t i o n E q u a t i o n

The e l i m i n a t i o n of t h e unmeasurable s t a t e and c o s t a t e v a r i a b l e s from t h e i n t e r t e m p o r a l dynamic u t i l i z a t i o n e q u a t i o n i s accomplished a s f o l l o w s , with a l l variables defined a s i n the text: The problem f s p l a c e d i n d i s c r e t e t i m e by u s i n g a p p r o x i m a t i o n s of t h e form:

-

and s i m i l a r l y f o r

, Sit,

hit

subscript i are deleted.

.

To s i m p l i f y n o t a t i o n

The dynamic i n t e r t e m p o r a l u t i l i z a t i o n i s ( a s from

the t e x t ) :

where: h

t

-

= (I

t

Ct)

.

Also, t h e f o l l o w i n g approximations a r e made :

A$t

=

*t+l

- Qt

As t = st + l - s t St+l- St

1 l(Ast+l

+

Ast)

I

*t+l - $

= T(A~t+l+ Ailt)

I n a d d i t i o n , from t h e t e x t :

where J

t

=

ax

t

+

cx'. t

t h e b a r s and t h e