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The Developing Economies, XLV-4 (December 2007): 391–436

DETERMINANTS OF SECTORAL COMPOSITION IN A SMALL OPEN ECONOMY: THEORETICAL AND QUANTITATIVE INVESTIGATIONS OF THE PHILIPPINES

THE Developing DEVE 2007 0012-1533 Journal Original XXX DETERMINANTS The DEVELOPING compilation Articles Authors Economies OF ©Ltd ECONOMIES 2007 SECTORAL Institute of COMPOSITION Developing Economies Blackwell Oxford, UK Publishing

Kazuhiro YUKI Faculty of Economics, Kyoto University, Japan

First version received February 2007; final version accepted June 2007 The Philippine economy since the 1980s has undergone shifts of production, employment, and consumption in the direction of the greater share of nontradable sectors, despite relatively stagnant economic growth. This paper examines sources of the sectoral shifts theoretically and quantitatively based on a dynamic model of a small open economy. The theoretical analysis identifies possible factors affecting the evolution of the sectoral composition: changes in sectoral total factor productivity (TFP), the tariff rate, and the terms of trade. Then, the relative importance of these factors is examined quantitatively by conducting simulations of the model calibrated to the Philippine economy. Keywords: Sectoral composition; Small open economy; Nontradable sector; The Philippines JEL classification: F41, O11, O53

I. INTRODUCTION Philippine economy since the 1980s has undergone shifts of production, employment, and consumption in the direction of the greater share of nontradable sectors. Figure 1 presents shares of real value added of tradable and nontradable sectors for the years 1980–2004.1 Although the share of nontradable sectors temporarily decreased during the economic crisis of the mid-1980s, it increased greatly over the 25 years—from 47.4% in 1980 to 54.7% in 2004—and the increase was particularly strong in the early 1980s and in the 1990s. The shift of employment

T

HE

The Developing Economies, XLV-4 (December 2007): 000–00

Valuable comments and suggestions from an anonymous referee are gratefully appreciated. Useful comments on earlier versions of the research were provided by participants of the research project, Macroeconomic Implications of Imperfect Markets in Developing Countries, at the IDE-JETRO. All remaining errors are the author’s own. 1 Out of nine major sectors of the National Income Accounts (NIA), agriculture, mining, and manufacturing are classified as tradable sectors, and the remaining sectors—construction, utilities, transportation and communications, trade, finance and dwellings, and other services—are classified as nontradable sectors. © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

doi: 10.1111/j.1746-1049.2007.00047.x

392

the developing economies Fig. 1. Shares of Real Value Added of Tradable and Nontradable Sectors in the Philippines, 1980–2004 (Base Year = 1985)

Source: National Income Accounts.

is even greater and the share of nontradable sectors rose from 36.8% in 1980 to 53.2% in 2004 (Figure 2). Finally, Figure 3 shows shares of nominal personal consumption expenditure on tradable and nontradable goods for the same period. The share of expenditure on nontradable goods increased from 36.0% in 1980 to 53.0% in 2004 and the increase was particularly large after the mid-1990s. How can these changes in sectoral composition be understood? It is well known that shares of production and employment of the agriculture sector fall and those of the service sector rise with per capita income growth (see Kongsamut, Rebelo, and Xie 1997, for the evidence based on cross-country and US time series data). There is also some evidence that shares of consumption expenditure follow the same pattern (see Kongsamut, Rebelo, and Xie 1997, for the evidence based on US time series data). In the case of the Philippine economy during the focused period, however, income growth seems not to be the only major factor affecting the sectoral shifts. Figure 4 shows that per capita real GDP declined sharply during the economic crisis of the mid-1980s and did not surpass the precrisis peak level until the year 2003.2 There must be other factors significantly affecting the development of the sectoral composition during this period. The purpose of this paper is to examine sources of the sectoral shifts theoretically and quantitatively. 2

Per capita GNI (GNP) follows the same pattern. Although the difference between GNI and GDP increased after 1996, GNI is greater than GDP only by 8.5% in 2004.

© 2007 The Author Journal compilation © 2007 Institute of Developing Economies

determinants of sectoral composition

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Fig. 2. Shares of Employment of Tradable and Nontradable Sectors in the Philippines, 1980–2004

Source: Labor Force Survey. See Appendix II for details.

Fig. 3. Shares of Nominal Personal Consumption Expenditure on Tradable and Nontradable Goods in the Philippines, 1980–2004

Source: See Appendix II.


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the developing economies Fig. 4. Per Capita Real GDP of the Philippines, 1980–2004

Source: National Income Accounts (GDP) and National Statistics Office (population, see Appendix II for details).

The model used is a small open economy populated by infinitely lived individuals. In the economy, there exist two production sectors, the tradable sector and the nontradable sector, that use physical capital and labor to produce final goods. 3 Investment in physical capital requires the purchase of both the domestic tradable good and the imported tradable good, which tries to capture the fact that imported capital goods are important in the Philippine economy, particularly from the mid-1990s. A representative infinitely lived consumer spends her income from labor and wealth on the consumption of the domestic tradable, the imported tradable, and the nontradable. Her utility function is such that the expenditure share on the nontradable good increases with income growth. 4 And, the government imposes tariffs on the imported tradable and consumes the revenue.5 Because of the specific utility function, the model does not have a balanced growth path where all variables are time invariant or grow at constant rates. However, a path does exist where exogenous variables, endogenous price variables, 3

4

5

Theoretical explorations of a small open economy composed of the two sectors include Brock (1988), Engel and Kletzer (1989), and Brock and Turnovsky (1994). Similar utility functions are used in Echevarria (1997), Kongsamut, Rebelo, and Xie (1997), and Caselli and Coleman (2001) in order to generate sectoral shifts associated with long-run economic growth. As for theoretical analyses of effects of tariff policy in a small open economy, see, for example, Brock and Turnovsky (1993) and Osang and Turnovsky (2000).



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and aggregate consumption are time invariant or grow constantly. Such a growth path is named a generalized balanced growth path (GBGP). On a GBGP, it is shown that shares of consumption expenditure, employment, and nominal output of the nontradable sector increase over time, as long as the total factor productivity (TFP) growth of at least one sector is positive. Although the productivity growth is the driving force of perpetual sectoral shifts, levels of several exogenous variables—the sectoral TFPs, the tariff rate, and the terms of trade—are shown to affect the sectoral composition on a GBGP. Finally, numerical simulations are carried out based on the developed model. Because economic agents are forward-looking, expectation formation on future paths of exogenous variables is important to results. In this paper, two contrasting cases are considered: the case where agents have precise knowledge about future paths of exogenous variables; and the case where they do not have any knowledge but long-run growth rates of nonstationary variables. The model is calibrated to the Philippine economy, and the relative importance of the factors identified in the theoretical analysis in the evolution of the sectoral composition for the years 1980– 2004 is investigated. There do not seem to exist simulation studies investigating sources of sectoral shifts in the “middle run,” except Coleman (2005), who studies the relationship between Japan’s shift of production from the manufacturing sector to the service sector (and growth slowdown) and a deterioration of the terms of trade (due to the advent of a large low-cost supplier of manufacturing goods, China) from the 1990s. Preceding simulation analyses of Southeast Asian economies include Go (1994) and Diao, Rattso, and Stokke (2005), both of which are based on the dynamic computational general equilibrium (CGE) models. Go (1994) investigates the effects of tariff reform and changes in the import commodity price and the world interest rate on key macroeconomic variables such as GNP, investment, and foreign debt of the Philippine economy in the 1970s, relying on the impulse-response analysis. Diao, Rattso, and Stokke (2005) examine the effects of trade policy on the TFP and GDP growth of the postwar Thai economy. Recently, numerical simulations based on dynamic general equilibrium models have been widely used in macroeconomics and related fields, and are accepted as complementary to nonstructural regressions. In the context of economic growth and development, Easterly (2005) points out that results of regression analyses, which try to detect factors common to many economies, are often not robust enough to variables included in regressions and estimation techniques. Furthermore, regarding the growth of developing economies, Rodrik (2005) stresses that the same factors could have very different effects on different economies or on an economy at different points in time, depending on their specific characteristics and surroundings. Developing economies are highly heterogeneous in terms of degrees of the incompleteness of various markets and economic, political, and social institutions © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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the developing economies

affecting economic activities. Thus, in order to understand the workings of a particular economy, taking into account the specificity would be important and numerical simulations are suitable for it. 6 Although this paper uses a relatively standard model as a benchmark, the model can be extended to reflect the specificity to improve its performance. This paper is organized as follows: Section II develops the model and Section III presents analytical results on a GBGP of the model. Based on the developed model and motivated by the theoretical results of the previous section, Section IV conducts numerical examinations and presents and interprets the results, and Section V concludes the paper. II. MODEL Consider a small open economy populated by homogeneous infinitely lived individuals. Time is discrete and the initial period is 0. A. Production There exist two production sectors, the tradable sector (sector T) and the nontradable sector (sector N). The production function of sector i (i = T,N ) is given by the following equation: Yi, t = ( Ai, t Li, t )α i Ki1,−t α i ,

0 < α i < 1, α T ≠ α N ,

(1)

where Li,t and Ki,t are labor and capital hired in the sector, respectively, and Ai,t is the TFP level of the sector, in period t. Because factor markets are competitive and factors move freely across the sectors, the following equations are obtained from first-order conditions of the profit maximization problem: rkt = PT, t (1 −

 α T ) ATα,Tt

KT,t   LT, t 

−α T

K  = PN ,t (1 − α N ) ANα ,Nt  N ,t   LN , t  K  wt = PT ,tα T ATα,Tt  T ,t   LT ,t 

−α N

,

(3)

1−α T

K  = PN ,tα N ANα ,Nt  N , t   LN , t  6

(2)

(4) 1−α N

,

See Yuki (2006) for more on this point.


(5)


397

where rkt and wt are rental rates of capital and labor, respectively, and PT,t and PN,t are prices of the tradable good (good T) and the nontradable good (good N), respectively, in period t. From (2), 1

KT , t  (1 − α T )PT , t  α T = AT , t   . LT , t rkt  

(6)

Substituting this equation into (4),  1 − αT  wt = PT , t α T AT , t  rkt  1 αT

1−α T αT

(7)

.

And, from (3) and (5), K N , t 1 − α N wt = . LN , t α N rkt

(8)

The above three equations show that KT,t/LT,t, wt, and KN,t /LN,t are expressed as functions of rkt. By substituting (8) and (7) into (3) and solving it for PN,t, the price of the nontradable good too is expressed as a function of rkt:

PN , t

[

1

]

α N αT  P (α T AT , t )α T (1 − α T )1−α T   α T −α N T , t = (rkt ) αT  . (α N AN , t )α N (1 − α N )1−α N  

[

]

(9)

Equations (6)–(9) show that the sectoral capital-labor ratios, wt, and PN, t are fixed once rkt is determined. B. Investment The dynamics of aggregate capital stock is governed by the following equation: Kt+1 = (1 − δ )Kt + It ,

0 < δ < 1,

K0 given,

(10)

where It is period t investment and δ is the depreciation rate of capital. The investment good is produced by using the domestically produced tradable (good T) and the imported tradable (good M) based on the following constant elasticity of substitution (CES) function: η−1

η−1

η

1 1 η−1 It = λη ( IDT , t ) η + (1 − λ ) η ( IDM , t ) η  ,  

0 ≤ λ < 1, η > 0,

(11)

where IDi,t (i = T,M ) is the input of good i and η is the elasticity of substitution between the inputs. Given It, IDi,t is chosen so as to minimize the production cost, © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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thus, from first-order conditions of the minimization problem, the following equation is obtained: −η

1 − λ IDT , t  PT , t  = . λ IDM , t  PM , t 

(12)

From the above two equations, the price of the investment good, PI,t, equals 1

1−η 1−η   PM , t   PI , t = PT , t λ + (1 − λ )    .  PT , t   

(13)

Because of the assumption of a small open economy, investment is determined so as to equate the rate of return from investment in physical capital with the world interest rate rt: rkt+1 PI , t+1 + (1 − δ ) = 1 + rt+1. PI , t PI , t

(14)

Note that the rate of return from investment reflects a change in the price of the investment good. By solving the above equation for rkt+1, rkt+1 = (1 + rt+1 ) PI , t − (1 − δ )PI , t+1.

(15)

The above equation and (13) show that rkt+1 is determined by exogenous price variables. Hence, sectoral capital-labor ratios, factor prices, and the nontradable price from period 1 are determined independent of consumption decisions and the market clearing condition of the nontradable good. C. Consumption The period utility function of a representative consumer is constant relative risk aversion (CRRA) regarding the consumption of the composite good, ct: c1− σ − 1 U (ct ) = t , σ > 0, 1 − σ1 1

(16)

where σ is the intertemporal elasticity of substitution. The composite good consumption is, in turn, Cobb-Douglas regarding the aggregate consumption of the two tradables, 7, and the sum of nontradable consumption, cN,t, and a constant, 8 > 0: ct = (7 )ω (cN , t + 8 )1−ω ,

0 < ω < 1.

(17)

The presence of 8 implies that, with an increase in income, consumption shifts toward the nontradable good. And, aggregate tradable consumption, 7, is CES © 2007 The Author Journal compilation © 2007 Institute of Developing Economies


399

with respect to the consumption of the domestically produced tradable (good T) and that of the imported tradable (good M):

[

1

θ −1

1

]

θ θ −1 θ −1

7 = γ θ cTθ, t + (1 − γ ) θ c Mθ, t

,

0 < γ < 1, θ > 0,

(18)

where θ is the elasticity of substitution between the goods. The determination of cT,t and cN,t: Given total expenditure on the tradables, cT,t and cM,t are chosen so as to maximize (18), hence from first-order conditions of the maximization problem, the following equation is derived: −θ

1− γ cT , t  PT , t  = . γ cM , t  PM , t 

(19)

If 9 is defined to be the minimum expenditure needed to purchase a unit of the aggregate tradable consumption, 7, 1

1−θ 1−θ  P   9 = PT , t γ + (1 − γ )  M , t   .  PT , t   

(20)

Then, cT,t and cM,t are expressed as: −θ

cT , t

P  = γ  T ,t  7,  9

cM , t

P  = (1 − γ ) M , t  7 .  9

(21) −θ

(22)

The determination of 7 and cN,t: Given total consumption expenditure, expt, 7 and cN,t are chosen so as to maximize (17), hence, from the first-order conditions of the maximization problem, the following equation is obtained: −1

ω (cN , t + 8 )  PN , t  =  . (1 − ω )7 9

(23)

By substituting the first-order conditions into (17) and solving it for expt, ω

 9  P  expt =    N , t   ω  1 − ω 

1−ω

ct − PN , t 8.

(24)

Let Pt be the expenditure required to increase ct by a unit (the marginal price of ct): ω

 9  P  Pt =    N , t   ω  1 − ω 

1−ω

.

(25) © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

400


Then, 7 and cN,t are expressed as: 7 =

ω Pc , 9 t t

(26)

cN , t =

1−ω Pc − 8. PN , t t t

(27)

Intertemporal utility maximization: An infinitely lived representative consumer chooses per capita composite-good consumption ct = Ct/Lt (Ct is the aggregate consumption of the composite good and Lt is aggregate labor supply), in order to maximize the discounted sum of period utilities weighted by Lt subject to the budget constraint: ∞

max{Ct}∑ β tU t =0

 Ct  L,  Lt  t

0 < β < 1,

(28)

s.t. PC t t − PN , t 8 Lt + Wt +1 = wt Lt + (1 + rt )Wt ,

W0 given,

(29)

where β is the discount factor on future utilities and Wt is aggregate wealth in period t. Note that, from (24) and (25), aggregate consumption expenditure equals PtCt − PN,t8Lt. From first-order conditions of the maximization problem, U′

P  Ct  C  = t (1 + rt+1 )βU ′ t+1 ,  Lt  Pt+1  Lt+1 

(30)

which, from (16), is expressed as: σ

Ct+1  Pt  L = (1 + rt+1 )β  t+1 . Ct P t + 1   Lt

(31)

The transversality condition is: lim T→ ∞

1 Πts+=Tt+1(1

+ rs )

Wt+T +1 = 0.

(32)

From (29) and (32), the intertemporal budget constraint is: ∞

∞

s=t

s=t

∑ Rt, s ( PC s s − PN , s 8 Ls ) = (1 + rt )Wt + ∑ Rt , s ws Ls , where

Rt, s =

1 Π vs =t+1(1

+ rv )

,

Rt, t = 1.


(33)

(34)


401

By substituting (31) into (33) and solving it for Ct, Ct =

Lt (1 + rt )Wt + ∑ ∞s=t Rt, s (ws Ls + PN , s 8 Ls ) ⋅ . Pσt ∑ ∞s=t β σ (s−t ) ( Ps Rt, s )1−σ Ls

(35)

Remember that all endogenous price variables are expressed as functions of rkt and rental prices of capital from period 1 are determined by the arbitrage condition (15). Hence, from the above equation and (31), Ct is expressed as a function of rk0. Once Ct is determined, CT,t, CM,t, and CN,t are determined by (21), (22), (26), (27), and Lt. D. Government The government imposes tariffs on imports of good M and consumes tax revenues. The governmental consumption CG,t is assumed not to affect consumers’ utilities or firms’ productivities. Let the tradable good produced abroad be a numeraire (thus, PT,t is the terms of trade) and let τt be the tariff rate on imports of the good. Then, the domestic price of good M is: PM , t = 1 + τ t .

(36)

The government’s budget constraint is: CG, t = τ t (CM , t + IDM , t ).

(37)

E. Market Equilibrium The market clearing condition of the nontradable good is: YN , t = CN , t .

(38)

By substituting PN,tYN,t = rktKN,t + wtLN,t and (27) into the above equation,   K N, t t t − PN , t 8 Lt . rkt LN, t + wt  LN , t = (1 − ω )PC

(39)

From first-order conditions of the profit maximization problem and market clearing conditions of factor markets,

α T Kt − K N , t α N KN,t = , 1 − α T Lt − LN , t 1 − α N LN , t ⇔ LN , t =

1 αT − α N

−1    KN,t  1 ( − ) K α α  − α N (1 − α T ) Lt .  T N t L  N,t   

(40)

(41)


402


By substituting the above equation and (8) into (39), 1 α rk K − (1 − α T ) wt Lt ] = (1 − ω )PC t t − PN , t 8 Lt , αT − α N [ T t t ⇔ Kt =

{

(42)

}

1 (α T − α N )[(1 − ω )PC t t − PN , t 8 Lt ] + (1 − α T )wt Lt . α T rkt

(43)

From results obtained in previous subsections, the right-hand side of the above equation can be expressed as a function of rk0. Hence, given K0, rk0 is determined by the above equation for t = 0 and Kt for t ≥ 1 is determined by the above equation of the corresponding period. Once rk0 and Kt are fixed, sectoral capital and labor are derived from (41) and factor market clearing conditions, and sectoral output is obtained from the production functions, (1). Finally, It is determined by (10), IDi,t (i = T,M) are obtained from (11) and (12), and CG,t is from (37). III. ANALYTICAL RESULTS A. Generalized Balanced Growth Path In the model without sectoral shift of consumption, namely, 8 = 0, once τt, PT,t, PM,t, and rt become time-invariant and other exogenous variables start to grow at constant rates, growth rates of endogenous variables become constant and thus the economy is on a balanced growth path. With 8 > 0, the model does not have such a balanced growth path (unless AT,t and AN,T remain constant), but it does have a path where τt, PT,t, PM,t, and rt are constant, the remaining exogenous variables, endogenous price variables, and Ct grow at constant rates, and asymptotic growth rates of all variables are constant. Henceforth, such growth path is called a generalized balanced growth path (GBGP). The (net) growth rate of labor on a GBGP is denoted gL ≥ 0 and that of sector i (i = T, N) TFP is denoted gAi ≥ 0. The next proposition presents conditions for the existence of a GBGP and GBGP growth rates of endogenous price variables and Ct. Proposition 1. Suppose that τt, PT,t, PM,t, and rt are constant, Lt grows at gL, and Ai,t grows at gAi (i = T, N ). Then, an economy is on a GBGP iff 1 + gAT = (1 + gP)1−σ [(1 + r)β]σ and [(1 + gAT )(1 + gL)]/(1 + r) < 1 hold, where 1 + gP ≡ [(1 + gAT )/(1 + gAN )](1−w )α N. On a GBGP, PI,t, 9 , and rkt are time-invariant, (PN,t+1/PN,t) = [(1 + gAT )/(1 + gAN )]α N ≡ 1 + gPN, Pt+1 / Pt = 1 + gP , wt+1 / wt = gAT , and Ct+1/Ct = [(1 + gAT )(1 + gL )]/(1 + gP ). Proof. In Appendix I. As noted above, with productivity growth at least in one sector, most of the remaining variables do not grow at constant rates on a GBGP. The next proposition shows how growth rates of several key sectoral variables change over time and converge to asymptotic rates. © 2007 The Author Journal compilation © 2007 Institute of Developing Economies


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Proposition 2. Suppose that an economy is on a GBGP. Then, (i) PTCT,t and PMCM,t (and thus CT,t, CM,t, and 6) grow at (1 + gAT )(1 + gL ) − 1, while, when gAT > 0 or gAN > 0, PN,tCN,t grows faster but slows down over time, and its growth rate converges to (1 + gAT )(1 + gL ) − 1. (ii) When gAT > 0 or gAN > 0, the growth rate of LN,t is greater than gL, while that of L T,t is lower, and both rates converge monotonically to gL. (iii) When gAT > 0 or gAN > 0, the growth rate of PN,tYN,t is greater than (1 + gAT )(1 + gL ) − 1, while that of PTYT,t (and thus YT,t ) is lower, and both rates converge monotonically to (1 + gAT )(1 + gL ) − 1. Proof. In Appendix I, where 1 + gP ≡ [(1 + gAT )/(1 + gAN )](1−w )α N . Because of 8 > 0, increased per capita income driven by productivity growth raises the consumption of the nontradable more than proportionately, and thus the share of consumption expenditure on the nontradable grows over time. Since the nontradable must be produced domestically and capital and labor are complementary in production, the share of employment of sector N increases accordingly. And the shift of employment implies the shift of nominal output, because labor is freely mobile between the sectors and sectoral shares of labor income in production are constant.7 B. Factors Affecting Sectoral Composition on a GBGP Although productivity growth is the driving force of perpetual sectoral shifts, changes in other exogenous variables do affect sectoral composition. In this subsection, the effects of changes in exogenous variables and growth rates of Lt, AT,t, and AN,t on sectoral composition of a GBGP economy are analyzed. The next proposition examines effects on the share of consumption expenditure on the nontradable good. Proposition 3. On a GBGP, when Wt > 0, ( PN , t CN, t )/( PC t t − PN , t 8 Lt ) is increasing in AN,t and Wt / Lt , and decreasing in gAT , gAN , and gL. If αT > αN, it is decreasing in PM (and thus τ) as well. Further, if per capita wealth Wt / Lt is small (large), it increases (decreases) with PT (the terms of trade) and AT,t, and, when αT < αN, decreases (increases) with PM. The effect of r is ambiguous. Proof. In Appendix I, where 1 + gP ≡ [(1 + gAT )/(1 + gAN )](1−w )α N . The expenditure share of the nontradable increases with per capita income and wealth measured in terms of the nontradable: It is increasing in wt / PN , t and Wt /( PN , t Lt ). wt / PN , t increases with sectoral productivities (see equation 5): directly 7

Further, as for the ratio of consumption quantity, CN, t /6 , from (26) and (27), as far as gPN ≤ 0 (gAT ≤ gAN ) holds, it increases over time (and, if gPN = 0, converges to [(1 − ω )/ω ]( 0 / PN ), while, if gPN > 0 (gAT > gAN ), the ratio converges to zero asymptotically, although it could increase temporarily (while cN,t is low and thus the effect of 8 is relatively large). Similarly, the ratio of output volume, YN ,t / YT ,t, increases over time if gAT ≤ gAN (and, if gAT = gAN , converges to a positive value), while, if gA T > gAN , the ratio could go up temporarily but converges to zero asymptotically. © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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with AN,t and indirectly with AT,t through a positive effect on K N , t / LN , t. Further, decreases in the price of the investment good (from lower PT or PM) and the world interest rate, and an increase in the price of the export good, PT, raise rk, K N , t / LN , t, and thus wt / PN , t (as for PT , the latter effect dominates). By contrast, Wt /( PN , t Lt ) > 0 increases with lower PN,t through an increase in AN,t or decreases in AT,t and PT. Further, decreases in PI (from lower PT or PM) and r lower rk and thus the relative price of the good of greater capital intensity, hence, when sector N is capital intensive relative to sector T, namely, αT > αN, PN,t decreases and Wt /( PN , t Lt ) increases, while the effects are opposite in direction when αT < αN. Thus, higher AN,t and Wt / Lt and lower PM (when αT > αN) increase the expenditure share, and when the effect through wt / PN , t dominates (is dominated), higher PT and AT,t and lower PM (when αT < αN) raise (lower) the share. Note that trade opening (a decrease in τ) lowers the domestic price of the import good, PM, and thus raises the share, unless αT < αN is satisfied and Wt / Lt > 0 is large.8 The next proposition, in turn, examines effects on the employment share of the nontradable sector. Proposition 4. On a GBGP, when Wt > 0, LN , t / Lt is increasing in AN,t and Wt / Lt > 0, and decreasing in gAT , gAN , and gL. Further, when Wt / Lt is small (large), the share increases (decreases) with PT (the terms of trade) and AT,t, and decreases (increases) with PM (and thus τ). The effect of r is ambiguous. Proof. In Appendix I, where 1 + gP ≡ [(1 + gAT )/(1 + gAN )](1−w )α N . Because sectoral shares of labor income are constant and labor is freely mobile between the sectors, the employment share of sector N equals the share of labor income generated in the sector and thus, is proportional to the ratio of PN,tYN,t = PN,tCN,t to wtLt. ( PN , t CN , t )/(wt Lt ) increases with Wt /(wt Lt ), and decreases with PN , t / wt (higher PN,t has a negative effect on per capita expenditure on the nontradable). From (7), (15), and (13), increases in PT and AT,t directly, and decreases in PM / PT and r indirectly 8

Effects of gAT , gAN , and gL can be explained as follows. Changes in the growth rates affect the expenditure share through consumption propensity. (Note that the expenditure share increases with per capita expenditure because of 8 > 0.) First, the acceleration of the growth rate of aggregate output, (1 + gAT )(1 + gL ) − 1, lowers present consumption expenditure, because a greater portion of Wt / Lt is allocated to future consumption. Second, higher (1 + gAT )(1 + gL ) − 1 raises future expenditure on the nontradable more than proportionately and thus has a negative effect on the present expenditure, while higher gPN (from higher gAT or lower gAN ) has a negative effect on future nontradable expenditure and thus increases the present expenditure (as for gAT , the former effect dominates). Hence, increases in the growth rates lower the present expenditure share. As for effects on the quantity ratio of nontradable consumption to aggregate tradable consumption, CN, t /6 , it can be shown that, when Wt > 0, the ratio increases with AN,t and Wt / Lt , and decreases with gAT , gAN , and gL. Effects of PT, PM, and AT,t are now ambiguous: their effects on the ratio are decomposed into the effect through the expenditure share and the one through the price ratio 9 / PN , t , and the two effects are opposite in sign.



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through their effects on rk, raise wt and thus lowers Wt /(wt Lt ) > 0, while their effects on wt / PN , t are opposite in sign, as is explained in the paragraph following Proposition 3. Thus, effects of changes in prices and productivities are as presented in the proposition. The following corollary is straightforward from the proposition. Corollary 1. Qualitative effects of changes in exogenous variables on ( PN , t YN , t )/( PT YT , t + PN , t YN , t ) are same as those on LN , t / Lt . Proof. From (1), (4), and (5), PN , t YN , t α N LN , t = PT YT , t + PN , t YN , t α T LT , t + α N LN , t =

αN

−1

L  α T  LN , t  − (α T − α N )  t 

,

(44)

where 1 + gP ≡ [(1 + gAT )/(1 + gAN )](1−w )α N . (45)

The above corollary implies that the qualitative effects on the share of the nontradable sector in real value-added too is the same (except gAN ) as those on the employment share, as long as the economy is on a GBGP in the base period. This is because PT is constant and PN,t grows constantly at rate gPN on a GBGP. Finally, the next proposition presents the effects on YN , t /YT , t , which is useful in interpreting results of quantitative examinations in the next section. Proposition 5. On a GBGP with Wt > 0, YN , t /YT , t is increasing in AN,t and Wt / L t , and decreasing in gAT , gAN , and gL. Further, when αT > ( ( ( αN, the effect of the tariff rate on the expenditure share is always negative.



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Fig. 7. PT,t (Terms of Trade) of the Philippines, 1980–2004

Source: See Appendix II.

How have these exogenous variables changed over time in the Philippine economy? Figures 5–7 present the evolution of the sectoral TFPs, the effective protection rate, 10 and the terms of trade, respectively, for the years 1980–2004. Both sectoral TFPs fell sharply during the economic crisis of the mid-1980s and recovered in the late 1980s. After that, the tradable TFP started almost persistent growth from the mid-1990s, while the nontradable TFP remained stagnant. The effective protection rate fell until the year 1985, remained relatively stable in the late 1980s, and started to fall almost continuously after the year 1992. The terms of trade improved significantly in the mid-1980s, stayed relatively high until the mid-1990s, then fell sharply and remained low. All of the variables exhibited large changes during the period, suggesting the possible importance of these variables in the evolution of the sectoral composition. IV. QUANTITATIVE EXAMINATIONS Based on the model presented in Section II, this section examines how important each of the factors identified in the previous section is in explaining the changing 10

The effective protection rate rather than the nominal tariff rate is presented, because the former is used in quantitative examinations of the next section. The model does not consider intermediate goods, hence the use of the effective protection rate would be more appropriate. © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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sectoral composition of the Philippine economy for the years 1980–2004. Because economic agents are forward-looking in the model, expectations on future paths of exogenous variables are important to results. Two contrasting cases are considered regarding the expectation formation. One case is where agents have precise knowledge about future paths of exogenous variables. Paths of stationary exogenous variables after the year 2004 are extrapolated based on AR(1) regressions of log-transformed variables (as for the interest rate, the original variable), and those of nonstationary variables are extrapolated based on AR(1) regressions of their growth rates, using data for the years 1980– 2004.11 It was found that all the variables except labor and the tariff rate become close enough to long-run values in the year 2040, thus it is assumed that the economy reaches a GBGP in that year. The construction of the model’s exogenous variables is explained in Appendix II. The other case is where agents do not have any knowledge about future paths of exogenous variables except long-run growth rates of nonstationary variables. In each period, they make decisions expecting that future stationary exogenous variables remain constant at present levels and future nonstationary variables grow at GBGP rates. That is, they always suppose that the economy reaches a GBGP in the next period, and thus changes in levels of the stationary variables and in growth rates of the nonstationary variables are completely unexpected. A. Calibration 1. Parameters Most of the model’s parameters are set based on data or empirical works. The remaining parameters are determined so that the evolution of the model’s sectoral composition match those of data as close as possible. Shares of labor in sectoral production functions, αi (i = T, N ): Felipe and Sipin (2004) calculate factor shares of the Philippine economy for the years 1980–2002 and find that the average share of labor income is 0.687.12 In terms of the model, from (1), (4), and (5), the average labor income share equals: wt Lt  α T PT , t YT , t + α N PN , t YN , t    (46) E = E  PT , t YT , t + PN , t YN , t   wt Lt + rkt Kt    PT, t YT, t PN, t YN, t     = αT E   + α N E  PT , t YT , t + PN , t YN , t . P Y + P Y T , t T , t N , t N , t     (47) 11 12

The future path of the number of workers, Lt, is extrapolated in a different manner. See Appendix II. Following Gollin (2002), they take into account the fact that a large portion of labor income in a developing country is recorded as operating surplus (total profits) of private unincorporated enterprises and make adjustments accordingly.



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Further, from (40),

αT αN K  K  E T ,t = E N, t . 1 − α T  LT , t  1 − α N  LN , t 

(48)

In the above equations, E[wt Lt /(wt Lt + rkt Kt )] = 0.687 from Felipe and Sipin (2004), and values of the remaining variables are calculated from data (for the years 1980–2002). By solving the equations, αT = 0.7570 and αN = 0.6196. Depreciation rate of physical capital, δ: Cororaton and Cuenca (2001) estimates the average value for the years 1980–98, so their estimate, δ = 0.1011, is used. Parameters of the CES function for the investment good, λ and η: From (12), PT , t IDT , t λ  PT , t  = PM , t IDM , t 1 − λ  PM , t 

1−η

,

P   P ID   λ  + (1 − η) ln  T , t  . ⇔ ln  T , t T , t  = ln   1 − λ   PM , t   PM , t IDM , t 

(49)

(50)

From a regression based on the above equation, the parameters are set at λ = 0.7253 and η = 2.7895. Parameters of the CES utility function for the tradables, γ and θ : From (19),  P C  P   γ  + (1 − θ ) ln  T , t  . ln  T , t T , t  = ln 1 − γ   PM , t CM , t   PM , t 

(51)

The parameters are set at γ = 0.9079 and θ = 2.8437 from a regression based on the equation. GBGP growth rates of labor and sectoral TFPs, gL, gAT , and gAN: The estimation of a future path of labor is explained in Appendix II. Its GBGP growth rate is set at the growth rate in the year 2040, in which, as mentioned earlier, the model is assumed to reach a GBGP. The value is gL = 0.00542. GBGP growth rates of sectoral TFPs are set in the manner as explained at the beginning of this section, and gAT = 0.00996 and gAN = 0. Parameter of the CRRA period-utility function, σ , and the discount factor on future utilities, β: From Proposition 1, for the existence of a GBGP, 1 + gAT = (1 + gP )1−σ [(1 + r )β ]σ must be satisfied between the two parameters. σ is set at 0.1 because the model matches data better with this value. Parameters of the function for composite good consumption ct, (17), ω and 8: These parameters are set so that changes in the model’s sectoral composition become as close as possible to those of data. Unfortunately, there do not seem to exist parameter values that match the sectoral composition of total consumption expenditure (the sum of private and governmental expenditure) and of employment and real value added simultaneously satisfactorily. In this paper, results when the © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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parameters are set focusing on the latter two variables are presented. Results are qualitatively similar when they are set focusing on total consumption expenditure. The parameters are set at ω = 0.065 and 8 = 121 for the model where changes in exogenous variables are unexpected, and at ω = 0.148 and 8 = 38 for the perfect foresight model. 2. Initial conditions and other adjustments The construction of initial aggregate capital K0 is intricate and thus explained in Appendix II. Initial aggregate wealth W0 is constructed as follows. Assume that initial physical capital is totally possessed by domestic residents and the arbitrage condition (equation [14]) holds in period −1. Then, initial aggregate wealth equals: W0 = B0 + PI ,−1K0 = B0 +

rk0 + (1 − δ )PI ,0 K0 , 1 + r0

(52)

where B0 is initial net foreign asset. B0 is set based on data from the IMF International Financial Statistics (IMF-IFS), r0 and K0 are calculated as explained in Appendix II, and PI,0 and rk0 are determined within the model. Finally, several adjustments are made regarding movements of exogenous variables. First, in order to take into account sluggishness of economic decisions in the actual economy, exogenous variables (except labor and the effective protection rate) are adjusted by taking weighted averages of the actual series and the series lagged by a year (with the weight on the actual series equals 2/3). Second, the model is found to be extremely sensitive to changes in the world interest rate rt, hence its volatility is significantly reduced by taking a weighted average of the actual series and the long-run value (with the weight on the actual series equals 0.02). Further, the perfect foresight model is found to be sensitive to changes in the rental price of capital rkt, thus a similar adjustment is made (the weight on the actual values equals 0.2). B. Results of the Model with Unexpected Shocks In this subsection, simulation results of the model with unexpected shocks are presented. Figure 8 displays shares of total consumption expenditure (the sum of private and government consumption expenditure), employment, and real value added (the base year is 1985, following data) of the nontradable sector of the model and the actual economy. As mentioned in the previous subsection, since values of parameters ω and 8 are set focusing on the evolution of the sectoral composition of employment and real value added, the model’s share of total consumption expenditure is well above the data. Although the model reproduces the trend of an increasing expenditure share on the nontradable, the magnitude of the change is much smaller than the data and a counterfactual large drop and recovery of the share occurs during the period of the economic crisis and recovery in the mid- to late © 2007 The Author Journal compilation © 2007 Institute of Developing Economies


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Fig. 8. Shares of the Nontradable Sector: The Model with Unexpected Shocks vs. Data

Source: See Appendix II for the data series. © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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1980s. Changes in shares of employment and real value added are more consistent with data. As for the employment share, the model is successful in reproducing the slow growth in the early 1990s and 2000s, the moderate growth in the early 1980s, and the rapid growth of the late 1990s, although the timings are slightly different. The major failure occurs again in the mid- to late 1980s in which a counterfactual drop and recovery of the share is observed. Finally, as for the real value-added share, the model is successful in reproducing in the rapid growth in the early 1980s and the stagnant growth in the 2000s. It is less successful in matching the evolution in the 1990s, when the growth of the model’s share is similar to that of the employment share, while slow but persistent growth is observed in the data. Again, a large drop and recovery in the mid- to late 1980s is the main failure. Now, the calibrated model is used to examine the relative importance of changes in exogenous variables in explaining the development of sectoral composition. The method of examination is to compare the evolution of the model without variations of an focused variable with that of the calibrated model. As for sectoral TFPs and PM,T (and thus τt), clear trends are observed during the examined period, hence, in analyzing the importance of each of the variables, a counterfactual experiment is conducted by setting its value at the 1980 level. As for PT,t, a clear trend is not observed and thus its value is set at the long-run level in conducting the experiment. Figure 9 presents results of the simulation where AT,t is set at the 1980 level. The expenditure share is higher than the baseline economy all the time, although the difference decreases from the late 1990s. As for the employment share, the difference is negligible until the year 1997, after which the share of the hypothetical economy consistently exceeds that of the baseline economy and the difference is large in the early 2000s. Excluding in the mid-1980s, the real value-added share is higher than the baseline economy. Because of the assumed expectation formation, the results can be interpreted relatively easily based on analytical results on a GBGP in Section III. According to the propositions in the previous section, the expenditure share and the employment share are increasing in per capita wealth and, when per capita wealth is small (large), increasing (decreasing) in AT,t. In the actual economy, the tradable TFP fell sharply between the years 1983 and 1985, recovered in the late 1980s, started persistent growth in the mid-1990s, and surpassed the 1980 level in 1997 (see Figure 5 at the end of the previous section). Per capita wealth of the hypothetical economy (when AT,t remains at the 1980 level) was found to be consistently higher than the baseline economy after the year 1986. Hence, the result on the employment share indicates that the (direct) effect of AT,t on the share is negative. By contrast, the diminishing difference in the expenditure share between the two economies after the year 1997 suggests that the effect of AT,t is positive. Finally, the real value-added share is increasing in the output volume ratio YN , t /YT , t multiplied by the price ratio PN / PT of the base year (1985). Because the effect of AT,t on YN , t /YT , t is analytically © 2007 The Author Journal compilation © 2007 Institute of Developing Economies


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Fig. 9. Shares of the Nontradable Sector of the Model with Unexpected Shocks: AT at the 1980 Level


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ambiguous, the result on the share is difficult to interpret. What is certain is that the effect of AT,t on the price ratio is positive, since PN,t increases with AT,t, according to Lemma 1 (ii) of Appendix I. Figure 10 presents results of the simulation where AN,t is set at the 1980 level. The expenditure share and the employment share are consistently higher than the baseline economy, while the real value-added share is lower in the early 1980s and higher during most of the remaining period. Note that the expenditure share is very stable in the mid- to late 1980s. According to the propositions in Section III, the expenditure share, the employment share, and YN , t /YT , t are increasing in per capita wealth and AN,t. In the actual economy, the nontradable TFP fell greatly between the years 1984 and 1985 and remained much lower than the 1980 level (see Figure 5). And per capita wealth is found to be lower when AN,t is fixed at the 1980 level. Thus, the results on the first two shares suggest that the effect of the higher nontradable TFP dominates that of the lower per capita wealth in the hypothetical economy. As for the real value-added share, because PN,t decreases with AN,t (Lemma 1 [ii] of Appendix I) and AN,1985 is much lower than AN,1980 (see Figure 5), PN , 1985 / PT , 1985 is much lower in the hypothetical economy. This explains the reason why the share is lower than the baseline economy in the early 1980s. Figure 11 shows results of the simulation where PM,t (and thus τt) is set at the 1980 level. The shares are consistently lower than the baseline economy. The effect on the expenditure share is greater in magnitude than the other shares, particularly from the early 1990s. The propositions in Section III show that the expenditure share, the employment share, and YN , t /YT , t are increasing in per capita wealth and, when per capita wealth is small (large), decreasing (increasing) in PM,t (actually, the expenditure share always decreases with PM,t because αT > αN holds.). The difference in per capita wealth is very small between the two economies. Hence, the results on the first two shares indicate that the (direct) effect of PM,t on the shares are negative. As for the real value-added share, the effect on PN,1985 needs to be taken into account. According to Lemma 1 (ii) of Appendix I, PN,t increases with PM,t when αT > αN. Thus, the effect of the lower YN , t /YT , t seems to dominate that of the higher base-year price ratio in the hypothetical economy. Finally, Figure 12 presents results of the simulation where PT,t is constant at the long-run level. The shares are higher than the baseline economy from the mid-1980s to the mid-1990s and lower during the rest of the period. The expenditure share, the employment share, and YN , t /YT , t are increasing (decreasing) in PT,t, when per capita wealth is small (large), according to the propositions in Section III. In the actual economy, PT,t was relatively higher from the late 1980s to the mid-1990s and lower in the rest of the period, particularly from the year 1998 (see Figure 7). Hence, the results on the first two shares suggest that the effect of PT,t on the shares are negative. As for the result on the real value-added share, because PT,1985 is very close to the long-run level, it is determined by the effect of PT,t on YN , t /YT , t , which is again negative. © 2007 The Author Journal compilation © 2007 Institute of Developing Economies


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Fig. 10. Shares of the Nontradable Sector of the Model with Unexpected Shocks: AN at the 1980 Level


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Fig. 11. Shares of the Nontradable Sector of the Model with Unexpected Shocks: PM at the 1980 Level



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Fig. 12. Shares of the Nontradable Sector of the Model with Unexpected Shocks: Constant PT


418


To sum up, when shocks to exogenous variables are completely unexpected, the effect of the nontradable TFP on the shares are positive, whereas effects of PM,t (and thus the tariff rate) and the terms of trade are negative. The effect of the tradable TFP on the expenditure share seems to be positive, while its effect on the other shares are negative. The relative importance of each exogenous variable can be summarized as follows. In general, the nontradable TFP has the greatest impact on the shares, particularly on the expenditure share, although, from the late 1990s, the terms of trade has a larger effect on the employment share and both the terms of trade and the tradable TFP have greater impacts on the real value-added share. As for the expenditure share, the variables other than the nontradable TFP are similar in importance, except in the mid-1980s when the tradable TFP was more important and from the late 1990s when the effect of the terms of trade was greater. On the employment share, the terms of trade has the second greatest effect, followed by the tradable TFP especially from the late 1990s, and the tariff rate has the smallest effect. Finally, on the real value-added share, the tradable TFP has a slightly greater effect than the terms of trade, and the effect of the tariff rate is smallest. C. Results of the Perfect Foresight Model In this subsection, simulation results of the perfect foresight model are presented. Figure 13 displays shares of total consumption expenditure, employment, and real value added of the nontradable sector of the model and the actual economy. As mentioned in Section IV-A, since values of parameters ω and 8 are set focusing on the evolution of the sectoral composition of employment and real value added, the share of total consumption expenditure of the model is well above the data. As in the model with unexpected shocks (see Figure 8), the magnitude of an increase in the share over the examined period is much smaller than the data. The major difference from the case of unexpected shocks is a very smooth change of the expenditure share. As for the employment share and the real value-added share, their volatilities are much greater than the data and the model with unexpected shocks. In general, the perfect foresight model is less successful in replicating changes in the shares of the actual economy. Although it reproduces the stagnant growth of the shares in the early 2000s and the slow growth in the early 1980s, it fails greatly in the mid- to late 1980s and in the early 1990s. In both periods, counterfactual large increases and then drops of the shares are observed. Now, the calibrated model is used to examine the relative importance of changes in exogenous variables in explaining the development of sectoral composition. Figure 14 shows results of the simulation where AT,t is set at the 1980 level. In contrast to the model with unexpected shocks (see Figure 9), both the expenditure share and the employment share are lower than the baseline economy except in the early 2000s. The real value-added share is lower than the baseline case in the midto late 1980s and in most of the early 1990s, which is again contrasting to the case © 2007 The Author Journal compilation © 2007 Institute of Developing Economies


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Fig. 13. Shares of the Nontradable Sector: The Perfect Foresight Model vs. Data

Source: See Appendix II for the data series. © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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Fig. 14. Shares of the Nontradable Sector of the Perfect Foresight Model: AT at the 1980 Level



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of unexpected shocks where the share is almost consistently higher than the baseline case. These results suggest that (direct) effects of AT,t on the shares, including the expenditure share, are now negative and stronger. The effect on the expenditure share is much smaller in magnitude than the effects on the other shares, while, in the case of unexpected shocks, the effects on the expenditure share and the employment share are not very different in magnitude. In general, changes in the sectoral TFP affect the shares more significantly than the model with unexpected shocks. In particular, the difference in the effects on the employment share is striking. Figure 15 presents results of the simulation where AN,t is set at the 1980 level. In contrast to the previous experiment, effects on the shares are qualitatively similar to the model with unexpected shocks (see Figure 10). The expenditure share and the employment share are consistently higher than the baseline economy, while the real value-added share is lower than the baseline economy in the early 1980s and in the early 2000s and higher during most of the remaining period. Quantitatively, the effect on the expenditure share is much greater than the other shares. In particular, the effect on the real value-added share is very small and almost negligible after the 1990s. Effects on the shares are smaller in magnitude than the model with unexpected shocks. Figure 16 displays results of the simulation where PM,t (and thus τt) is set at the 1980 level. As with the previous experiment, effects on the shares are qualitatively similar to the model with unexpected shocks (see Figure 11). The shares are consistently lower than the baseline economy, and the effect on the expenditure share is greater in magnitude than the effects on the other shares. Compared to the case of unexpected shocks, the effects of the tariff rate are much greater, particularly in the early 1980s when the effects are quantitatively negligible in the former experiment. Finally, Figure 17 presents results of the simulation where PT,t is constant at the long-run level. As for the employment share and the real value-added share, effects are qualitatively similar to the model with unexpected shocks (see Figure 12). The shares are higher than the baseline economy from the mid-1980s to the mid-1990s and lower during the remaining period. The effect on the consumption expenditure share too is not very different from the case of unexpected shocks qualitatively, although now the share is almost consistently lower than the baseline economy. Quantitatively, as in the case of unexpected shocks, effects on the employment share and the real value-added share are much greater than the effect on the expenditure share. Effects on the former two shares are particularly large after the year 1997, which is also same as the former experiment. To summarize, effects of the exogenous variables on the shares are qualitatively same as the case of unexpected shocks, except the effect of the tradable TFP on the expenditure share, which is now negative. The relative importance of each exogenous variable is different for each of the shares. As for the consumption expenditure share, the nontradable TFP has the © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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Fig. 15. Shares of the Nontradable Sector of the Perfect Foresight Model: AN at the 1980 Level



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Fig. 16. Shares of the Nontradable Sector of the Perfect Foresight Model: PM at the 1980 Level


424

the developing economies Fig. 17. Shares of the Nontradable Sector of the Perfect Foresight Model: Constant PT



425

greatest effect, followed by the tariff rate and the tradable TFP, and the terms of trade has the smallest effect. Regarding the employment share, the tradable TFP had the greatest effect until the early 1990s and the terms of trade had the largest effect from the late 1990s, then the nontradable TFP follows, and the tariff rate is least important. Finally, on the real value-added share, the tradable TFP has the greatest effect, followed by the terms of trade and then the tariff rate, and the nontradable TFP has the smallest effect. Compared to the model with unexpected shocks, the relative importance of the tradable TFP and the tariff rate increases, while that of the nontradable TFP decreases. V. CONCLUSIONS The Philippine economy since the 1980s has experienced shifts of real value added, employment, and nominal consumption expenditure in the direction of the greater share of nontradable sectors, despite relatively stagnant economic growth. This paper has examined sources of the sectoral shifts theoretically and quantitatively based on a dynamic model of a small open economy. The theoretical analysis has identified possible factors affecting the evolution of the sectoral composition: changes in sectoral TFPs, the tariff rate, and the terms of trade. Then, the relative importance of these factors has been examined quantitatively by conducting simulations of the model calibrated to the Philippine economy. Main results of the quantitative examination can be summarized as follows: (1) The model with unexpected shocks is more successful than the perfect foresight model in matching the evolution of shares of employment and real value added of the nontradable sector. (2) Effects of the exogenous variables on the shares are qualitatively the same in both models, except the effect of the tradable TFP on the expenditure share. The nontradable TFP affects the shares positively, while the tradable TFP (except on the expenditure share), the tariff rate, and the terms of trade have negative effects. The effect of the tradable TFP on the expenditure share is positive (negative) in the model with unexpected shocks (the perfect foresight model). The qualitative effect of the terms of trade on the employment and real value-added shares is consistent with the result of Coleman (2005) on the Japanese economy from the 1990s. (3) The relative importance of the exogenous variables is different depending on the shares and in the two models and is thus difficult to summarize generally. What is clear is that the relative importance of the terms of trade is much higher from the late 1990s, and that of the tradable (nontradable) TFP and the tariff rate is much more (less) important in the perfect foresight model.13 Based on the results of the quantitative examination, the evolution of the sectoral composition of the Philippine economy may be understood in the following manner. 13

The result suggests that the effectiveness of the tariff reform depends greatly on its effect on the expectation formation of economic agents on a future path of the policy. © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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Increases in the shares in the early 1980s seem to be related to decreases in the terms of trade and the tariff rate. A sharp decline of the real value-added share and the stagnant growth of the other shares in the mid-1980s appear to be connected to a large drop in the nontradable TFP and the improvement of the terms of trade, while the recovery of the nontradable TFP may have contributed to increases in the employment and real value-added shares in the late 1980s. The development of the early 1990s is difficult to interpret, because the employment share declined slightly, while the other shares increased. In the late 1990s, all of the shares increased greatly, which may be connected to the declining tariff rate and the deterioration of the terms of trade. And in the early 2000s, the growth of employment and the real value-added shares were stagnant, while the expenditure share continued to grow strongly, which seems to be related to the strong growth of the tradable TFP. The present model is relatively simple in structure, hence analytical results are obtained regarding the sectoral composition on a GBGP, and simulation results can be interpreted relatively easily based on the analytical findings. However, it is not very successful in matching data, particularly when shocks are perfectly expected. The improvement of the model’s performance is left for future work. Possible modifications include introducing adjustment costs of investment, frictions in intersectoral factor mobility, and credit constraints that affect intertemporal resource allocations, although they make solving the model numerically a much harder task. An important issue to address in modifying the model is how to choose a particular modification: developing economies might deviate from standard models in many aspects and thus various modifications would be possible. In order to choose an appropriate model, attention should be paid not only to the model’s performance but also to empirical support for the model’s structure by microeconomic studies. REFERENCES Brock, Philip L. 1988. “Investment, the Current Account, and the Relative Price of Nontraded Goods in a Small Open Economy.” Journal of International Economics 24, nos. 3–4: 235–53. Brock, Philip L., and Stephen J. Turnovsky. 1993. “The Growth and Welfare Consequences of Differential Tariffs.” International Economic Review 34, no. 4: 765–94. ———. 1994. “The Dependent-Economy Model with Both Traded and Nontraded Capital Goods.” Review of International Economics 2, no. 3: 306–25. Caselli, Francesco, and Wilbur John Coleman II. 2001. “The U.S. Structural Transformation and Regional Convergence: A Reinterpretation.” Journal of Political Economy 109, no. 3: 584–616. Coleman, Wilbur John II. 2005. “Terms-of-Trade, Structural Transformation, and Japan’s Growth Slowdown.” Durham, N.C.: Duke University. http://www.econ.duke.edu/ ~staff/ wrkshop_papers/2005-Fall/Coleman.pdf. Cororaton, Caesar B. 2004. “Philippines.” In Total Factor Productivity Growth: Survey Report, ed. Asian Productivity Organization. Tokyo: Asian Productivity Organization. © 2007 The Author Journal compilation © 2007 Institute of Developing Economies


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Cororaton, Caesar B., and Janet S. Cuenca. 2001. “Estimates of Total Factor Productivity in the Philippines.” PIDS Discussion Paper no. 2001–02. Makati: Philippine Institute for Development Studies. Diao, Xinshen; Jorn Rattso; and Hildegunn Ekroll Stokke. 2005. “International Spillovers, Productivity Growth and Openness in Thailand: An Intertemporal General Equilibrium Analysis.” Journal of Development Economics 76, no. 2: 429–50. Easterly, William. 2005. “National Policies and Economic Growth: A Reappraisal.” In Handbook of Economic Growth. Vol. 1A, ed. Philippe Aghion and Steven N. Durlauf. Amsterdam: Elsevier. Echevarria, Cristina. 1997. “Changes in Sectoral Composition Associated with Economic Growth.” International Economic Review 38, no. 2: 431–52. Engel, Charles, and Kenneth Kletzer. 1989. “Saving and Investment in an Open Economy with Non-traded Goods.” International Economic Review 30, no. 4: 735–52. Felipe, Jesus, and Grace C. Sipin. 2004. “Competitiveness, Income Distribution, and Growth in the Philippines: What Does the Long-Run Evidence Show?” ERD Working Paper no. 53. Manila: Asian Development Bank. Go, Delfin S. 1994. “External Shocks, Adjustment Policies and Investment in a Developing Economy: Illustrations from a Forward-Looking CGE Model of the Philippines.” Journal of Development Economics 44, no. 2: 229–61. Gollin, Douglas. 2002. “Getting Income Shares Right.” Journal of Political Economy 110, no. 2: 458–74. Greenwood, Jeremy; Zvi Hercowitz; and Per Krusell. 1997. “Long-Run Implications of InvestmentSpecific Technological Change.” American Economic Review 87, no. 3: 342–62. Hooley, Richard W. 1968. “Long-Term Growth of the Philippine Economy, 1902–1961.” Philippine Economic Journal 7, no. 1: 1–24. Kongsamut, Piyabha; Sergio Rebelo; and Danyang Xie. 1997. “Beyond Balanced Growth.” NBER Working Paper no. 6159. Cambridge, Mass.: National Bureau of Economic Research. Osang, Thomas, and Stephen J. Turnovsky. 2000. “Differential Tariffs, Growth, and Welfare in a Small Open Economy.” Journal of Development Economics 62, no. 2: 315–42. Rodrik, Dani. 2005. “Growth Strategies.” In Handbook of Economic Growth. Vol. 1A, ed. Philippe Aghion and Steven N. Durlauf. Amsterdam: Elsevier. Tan, Elizabeth S. 1994. “Trade Policy Reforms in the 1990s: Effects of E.O. 470 and the Import Liberalization Program.” PIDS Research Paper no. 94–11. Makati: Philippine Institute for Development Studies. Yuki, Kazuhiro. 2006. “Keizai seisaku to tojokoku no keizai seicho / keizai hatten” [Economic policy and economic growth and development of low income nations]. In Hatten tojOkoku no makuro keizai bunseki josetsu [Introduction to macroeconomic analysis of developing countries], ed. So Umezaki. Chiba: Institute of Developing Economies, JETRO.

APPENDIX I PROOFS OF PROPOSITIONS A. Proofs of Propositions 1 and 2 Proof of Proposition 1: From (13), PI,t is time-invariant. Then, from the arbitrage condition (14), rkt is constant as well. So, from (2), ( KT, t+1 / LT, t+1 )/( KT, t / LT, t ) = 1 + gAT . Because [α T /(1 − α T )]( KT, t / LT, t ) = [α N /(1 − α N )]( K N, t / LN, t ) (equation [40]) © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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always holds, ( KT , t+1 / LT , t+1 )/( KT , t / LT , t ) = ( K N , t+1 / LN , t+1 )/( K N , t / LN , t ), and thus, from (3), ( PN , t+1 / PN , t ) = [(1 + gAT )/(1 + gAN )]α N . Then, from (25), ( Pt+1 / Pt ) = ( PN , t+1 / PN , t )1−ω = [(1 + gAT )/(1 + gAN )](1−ω )α N . And, from (8) and ( KT , t+1 / LT , t+1 )/( KT , t / LT , t ) = 1 + gAT , wt+1 / wt = 1 + gAT . The constancy of 9 is from (20). Now the conditions for the existence of a GBGP and the growth rate of Ct are derived. Because wt Lt grows at (1 + gAT )(1 + gL ) − 1 on a GBGP, from the budget constraint (29), aggregate consumption expenditure PtCt − PN,t8Lt and Wt must grow at the same rate asymptotically. Since (1 + gAT )(1 + gL ) ≥ (1 + gPN )(1 + gL ) (the GBGP growth rate of PN,t8Lt), the asymptotic growth rate of PtCt must be (1 + gAT )(1 + gL ) − 1. From (31), ( Pt+1 / Pt )(Ct+1 / Ct ) = (1 + gP )1−σ [(1 + r )β ]σ (1 + gL ). Hence, 1 + gAT = (1 + gP )1−σ [(1 + r )β ]σ must hold. And, from (28) and (16), for the discounted sum of period utilities to be finite, β[(Ct+1 / Ct )/( Lt+1 / Lt )]1−(1/σ ) (1 + gL ) < 1 must be true. Since (Ct+1 / Ct )/( Lt+1 / Lt ) = (1 + gP )−σ [(1 + r )β ]σ , the condition is expressed as:

β {(1 + gP )−σ [(1 + r )β ]σ }

1−

⇔

1 σ

(1 + gL ) < 1,

(1 + gAT )(1 + gL ) < 1. (From 1 + gAT = (1 + gP )1−σ [(1 + r )β ]σ ) 1+ r

(53) (54)

Finally, the sufficiency of these conditions for the existence of a GBGP is proved. When 1 + gAT = (1 + gP )1−σ [(1 + r )β ]σ is satisfied, the asymptotic growth rate of PC t t − PN , t 8 Lt is (1 + gAT )(1 + gL ) − 1, as seen above. Then, from (29), Wt grows at the same rate asymptotically, so does Kt from (43). Because ( KT , t+1 / LT , t+1 )/( KT , t / LT , t ) = 1 + gAT and ( Kt+1 / Kt ) = (1 + gAT )(1 + gL ) asymptotically, from (41), the asymptotic growth rate of LN,t (and thus LT,t ) is gL. Then, from (40), sectoral physical capital grows at the same rate as Kt asymptotically. The constancy of asymptotic growth rates of remaining variables can be proved straightforwardly. Finally, from [(1 + gAT )(1 + gL )]/(1 + r ) < 1, the transversality condition (32) is satisfied. Proof of Proposition 2: (i) From (26), 6 grows at the same rate as PtCt, which grows at (1 + gAT )(1 + gL ) − 1 from Proposition 1. Then, growth rates of CT,t and CM,t are obtained from (21) and (22), respectively. From Proposition 1, PtCt grows faster than PN,t Lt when gAT > gPN , which is true iff gAT > 0 or gAN > 0, thus, from (27), the growth rate of PN,tCN, t is greater than (1 + gAT )(1 + gL ) − 1. Since PN , t CN , t / PC t t converges to 1 – ω monotonically, the growth rate of PN,tCN,t approaches monotonically to (1 + gAT )(1 + gL ) − 1. (ii) When gAT > 0 or gAN > 0, from (i), the growth rate of PN,tCN,t converges monotonically to (1 + gAT )(1 + gL ) − 1 from above. Thus, when αT > ( ( 0, by using Lemma 1 (ii), the consumption share is affected negatively by PT, AT,t, gAT , gL, and positively by AN,t. Further, when αT > ( 0, the consumption share is increasing in AN,t and Wt / Lt , and decreasing in gAT , gAN , and gL. The effect of PM is unambiguously negative when αT > αN. Further, as far as Wt / Lt is not large enough that the second effect dominates the first one, the share is increasing in PT and AT,t , and, when αT < αN, decreasing in PM. The effect of r is ambiguous because the first effect and the third one have opposite signs, where 1 + gP ≡ [(1 + gAT )/(1 + gAN )](1−w )α N . Proof of Proposition 4: From (1) and (5), LN , t α N PN , t YN , t = Lt wt Lt =

(68)

α N PN , t CN , t , (from equation [38]) wt Lt

P PC   = α N (1 − ω ) t t − N, t 8 . (from equation [27]) w L w t t t  

(69) (70)

From (60) of Lemma 2,   (1 + gAT )(1 + gL )   PN , t 8 PC Wt  t t . = 1 + 1 −  (1 + r ) wt Lt + wt 1+r (1 + gPN )(1 + gL )  wt Lt   1−  1+r  (71) © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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By using the above equation, (1 − ω )

(1 + gAT )(1 + gL )  Wt   (1 + r ) wt Lt  1 − + 1 r    (1 + gAT )(1 + gL )   1−  PN , t  1+r 8. − 1 − (1 − ω ) (1 + gPN )(1 + gL )  wt   1− 1+r  

P  PC t t − N , t 8 = (1 − ω )1 + wt Lt wt 

(72)

From Lemma 1 (iii), the effect through the first term (when Wt > 0) is such that LN , t / Lt is affected positively by PM and Wt / Lt , and negatively by PT, AT,t, gAT and gL, while the effect of r is ambiguous. As for the effect through the second term, from (67), Lemma 1 (iv), and gAT ≥ gPN , (Proposition 1), LN, t / Lt is affected positively by AT,t, AN,t, and PT / PM , and negatively by gAT , gAN , and gL, while the effect of r is ambiguous again. Thus, LN , t / Lt is increasing in AN,t and Wt / Lt > 0, and decreasing in gAT , gAN , and gL. Further, as far as Wt / Lt is not large enough that the first effect dominates the second one, the share is increasing in PT and AT,t, and decreasing in PM, where 1 + gP ≡ [(1 + gAT )/(1 + gAN )](1−w )α N . Proof of Proposition 5: From (1), YN , t = YT , t

 ANα ,Nt LN , t 

KN,t    LN , t 

 ATα,Tt LT , t 

KT , t    LT , t 

Aα N L = Nα,Tt N , t AT , t LT , t A  =  N,t   AT , t 

1−α N

 KN,t  L   N,t 

αN

LN , t LT , t

(73)

1−α T

α T −α N

1−α T

 α T  α N  −1  1 − α  1 − α   T N  

(from equation [40]) (74)

−1 1−α N  1−η 1−η  1 − α T   αT 1 − α N   PM     r + δ λ + (1 − λ ) P     α N 1 − αT  T      

α T −α N αT

, (75)

where the last equation is obtained by substituting (59). From the above equation and Proposition 4, when Wt > 0, YN , t /YT , t is increasing in AN,t and Wt / Lt , and decreasing in gAT , gAN , and gL. Further, when αT > αN and Wt / Lt is not large enough that the effect on LN , t / LT , t through the first term of (72) in the proof of Proposition 4 dominates the one through the second term, the ratio is increasing in PT and decreasing in PM, where 1 + gP ≡ [(1 + gAT )/(1 + gAN )](1−w )α N . © 2007 The Author Journal compilation © 2007 Institute of Developing Economies


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APPENDIX II DATA A. Exogenous Variables of the Model This subsection explains the construction of the model’s exogenous variables (or their sources) for quantitative examinations. Aggregate labor, Lt: As for the series up to the year 2004, it is computed as the sum of sectoral employment, which is obtained from Employment by Major Industry Group of the Labor Force survey. Note that the data until 1999 are based on the 1980 census population projection, while the data from 2000 are based on the 1995 census population projection, and thus the two series are not mutually consistent. Hence, the latter series are adjusted based on data of the two series for the overlapping period of 1999Q4–2000Q3. The series after 2004 is estimated as follows. First, a future path of the working-age population is estimated by regressing it on a constant, year, and year-squared, using data for the years 1980–2050 from the World Population Prospects (the 2002 revision) by the United Nations. Then, future employment is calculated by multiplying the estimated working-age population by the average employment ratio for the years 1980–2004. Sectoral total factor productivity, Ai,t (i = T,N): They are obtained by substituting sectoral value added, labor, and capital series into the production function, (1), where the parameters of the function are set as explained in Section IV-A-1. The derivation of the sectoral capital series are described in detail later in this subsection and the data source of sectoral value added is noted in the next subsection. Effective protection rate (EPR), τt, and the domestic price of the import good, PM,t: EPRs for the years 1990–2004 are sectoral weighted average values calculated by the Philippine Tariff Commission. They do not compute EPRs for earlier years using the same procedure, hence alternative sources must be consulted. Tan (1994) calculates sectoral and sectoral average EPRs for the years 1983, 1985, 1986, 1988, and 1989/90–95. Unfortunately, her estimation procedure seems to be different from the one used by the tariff commission: her estimates of EPRs do not coincide with the commission’s estimates for the years 1990–95. Hence, EPRs for the years 1983, 1985, 1986, 1988, and 1989 are calculated based on the Tan’s sectoral EPRs by utilizing the information from the two data sources for the overlapping years. For the years 1980 and 1985, sectoral EPRs are calculated by the tariff commission based on a different procedure from the post-1990 series. Hence, EPRs for 1980 and 1985 are calculated by adjusting the commission’s estimates accordingly. For years when data are not available, EPRs are computed assuming that they are averages of values for adjacent years. And, PM,t = 1 + τt from (36). The terms of trade, PT,t: PT,t is computed as the ratio of the implicit price deflator of the tradable good (see footnote 1 for the classification) to that of total merchandise © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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import from the National Income Accounts (NIA). The price deflator of the tradable good rather than that of total merchandise export is used, because a nonnegligible portion of goods classified as tradable are actually traded little with foreign economies and the model fits data better with the use of the tradable price. World real interest rate, rt: The quarterly 3-month US dollar deposit rate (London offer) series from the IMF-IFS is converted to yearly real series using the implicit price deflator of total merchandise import from NIA and the Peso/US dollar nominal exchange rate. B. Sectoral and Aggregate Capital Stock Sectoral physical capital is obtained by the perpetual inventory method based on sectoral investment and initial sectoral capital stock whose derivations are explained next. Sectoral investment: Sectoral investment series are not available in the NIA. Cororaton and Cuenca (2001) calculate sectoral values for the years 1980–98 by allocating the gross domestic capital formation of NIA to each sector based on sectoral data of the gross addition to fixed capital of the Annual Survey of Establishments (ASE ). One problem with their estimates is that the breeding stocks and orchard development of NIA is not taken into account in calculating investment in the agriculture sector. Further, as for the agriculture sector, sectoral gross domestic capital formation is available in NIA from 1981. Hence, in the present paper, the NIA series is used for agricultural investment (the 1980 value is estimated based on a regression of total agricultural investment on the breeding stocks and orchard development using data of later years), and sectoral investment series of nonagricultural sectors are estimated by allocating the gross domestic capital formation of nonagricultural sectors of NIA to each sector based on sectoral gross addition to fixed capital of ASE. Sectoral investment series from 1998 are calculated in the same manner using the 2002 and 2003 Annual Survey of Philippine Business and Industry (ASPBI, formerly ASE) for the years 2001and 2003, and the 2000 Census of Philippine Business and Industry (CPBI) for 1999. For the years 2000 and 2002, survey data of sectoral investment are not available, hence sectoral values are estimated using average sectoral shares of investment for the post-1995 period. Initial (the year 1980) aggregate and sectoral capital stock: The aggregate capital stock is estimated using the perpetual inventory method, that is, as the sum of past gross capital formation net of depreciations. Cororaton (2004) estimates aggregate capital stock using this method, but there are two problems in his calculation. First, he uses the depreciation rate of 5%, which is too low in comparison to the estimated value of 10.11% by Cororaton and Cuenca (2001) based on the ASE data for the years 1980–98. Second, in calculating initial (the year 1966) capital stock, he assumes straight-line depreciation, while, for the calculation of capital stock for later years, he assumes declining-balance depreciation, which is not consistent. In © 2007 The Author Journal compilation © 2007 Institute of Developing Economies


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this paper, initial aggregate stock in 1980 is calculated assuming declining-balance depreciation. As for the depreciation rate, using the 10.11% estimate by Cororaton and Cuenca (2001) may not be appropriate for earlier years, because the composition of investment has changed over time in the direction of the increased proportion of durable equipment investment. Greenwood, Hercowitz, and Krusell (1997) find that the (economic) depreciation rate is 5.6% for structures and is 15.12% for equipment in the US economy for the years 1954–90. Hence, the latter value is applied for investment in durable equipment and the former value is applied for the rest of aggregate investment. The investment series are available from 1946 in NIA, and it is found that only 0.45% of equipment installed in 1946 is still in use in 1980, which is negligible considering the fact that it is 0.0018% of equipment invested over the years 1946–80 and used in 1980, while 14.93% of structures built in 1946 is still in use in 1980. Thus, investment in structures before 1946 must be taken into account. The stock of structures in 1946 is estimated assuming that the economy is in steady state in 1946, the steady state growth rate is 3%, which is the average GNP growth rate for the years 1902–38 estimated by Hooley (1968), and 20% of the accumulated stock is lost due to the World War II. The investment value of 1947 is used in the calculation because the value in 1946 is much lower than subsequent years probably due to the war. Sectoral capital stock in 1980 is calculated by allocating aggregate capital stock to each sector proportional to the average investment share of the sector in 1980 and 1981. Aggregate and sectoral capital stock from the year 1981: Sectoral capital stock from 1981 is calculated using the derived sectoral investment series and sectoral depreciation rates estimated by Cororaton and Cuenca (2001). Aggregate capital stock is obtained as the sum of capital stock of each sector. C. Other Variables In this subsection, the construction of variables (or their sources) used for drawing figures, setting parameters values of the model (Section IV-A-1), or evaluating results of quantitative examinations is explained. Sectoral labor, Li,t (i = T,N): See the explanation on aggregate labor above. GDP and sectoral value added, nominal and real: They are from Gross Domestic Product by Industrial Origin at Current and Constant Prices (in million pesos at 1985 prices) of NIA. Nominal investment and consumption expenditures on the imported good: For years 1980–90, adjusted series of imports of machinery and equipment and imports of total consumer goods in Imports by End Use of the 1990 and 1992 Philippine Statistical Yearbooks are used. These variables are FOB values and measured in US dollars, hence, to be consistent with NIA, they are converted to CIF values measured in pesos. These series are not available from 1991, but series of imports of capital goods and imports of consumer goods are found in Imports by Major Commodity © 2007 The Author Journal compilation © 2007 Institute of Developing Economies

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Group of the Foreign Trade Statistics of the Philippines. Comparisons of these series with the corresponding series in Imports by End Use for overlapping years 1985–90 indicate that the capital good imports in the Foreign Trade Statistics are much greater and seem to include imported machineries for intermediate use. Thus, the latter series are adjusted accordingly. In particular, from 1992, NIA contain data on exports of finished electrical machineries, which grew rapidly in the 1990s, hence the series is subtracted from imports of capital goods. Nominal consumption (personal and total) expenditures on the tradables and the nontradable: Personal Consumption Expenditure by Purpose of NIA contains data on expenditures on major categories of goods. Expenditures on beverages, tobacco, clothing and footwear, and household furnishings are classified as the expenditure on (domestic or imported) tradables, while those on fuel, light and water, household operations, transportation/communication, and miscellaneous are classified as the expenditure on the nontradable. Further, the expenditure on food is separated into food consumed at home (categorized as the tradable) and food consumed outside home (the nontradable) based on data from Total Family Expenditure by Major Expenditure Group in the Philippine Statistical Yearbook. Expenditures on miscellaneous are classified as nontradable because they include expenditures on services such as medical care, recreation, and education. As for government consumption, the compensation of employees is classified as the nontradable, while the rest of governmental consumption is allocated to the tradables and the nontradable in the same proportion as personal consumption expenditure. Then, total tradable consumption expenditure is separated into the expenditure on the domestic tradable and the one on the imported tradable using the consumption expenditure on the imported good derived above. Nominal investment expenditures on the tradables and the nontradable: NIA contain data on investment expenditures on construction, durable equipment, and breeding stocks and orchard development. The expenditure on construction is categorized as the nontradable, while the remaining ones are considered tradable. Total tradable investment expenditure is separated into the expenditure on the domestic tradable and the one on the imported tradable using the expenditure on the imported good derived above. Population: Mid-year (July 1) population estimates by the National Statistics Office, which are based on the census of population, are used.
