The elasticity of substitution as a proxy measure of economic integration

The Elasticity of Substitution as a Proxy Measure of Economic Integration GEORGE K. ZESTOS*

This study examines how the accession of Greece to the European Union affected the Greek economy. Transcendental production functions of agriculture, industry, and service sectors of Greece, Germany, and France were estimated and tested for structural stability. Based on two estimated parameters of sectoral production functions and the corresponding data on capital-to-labor ratios, sectoral elasticities of substitution were constructed as vectors of values, varying with time. It was found that the elasticities of the traded sectors, industry, and manufacturing converged. The elasticities of substitution of the nontraded sector service and the traded, but protected, sector of agriculture diverged. (JEL F15)

I. Introduction

Greece became an associate member of the European Union (EU) with the Athens agreement in 1962. As an associate member, Greece was allowed a transitional period to adjust its economy to the other EU economies. The Athens agreement dealt primarily with trade liberalization. Greece agreed to reduce trade barriers against EU countries and the EU countries reciprocated. Greece was also required to adopt the common external tariffs of the EU against non-EU countries. These tariffs were generally lower than the Greek ones. Greece became a full member of the EU in 1981. As a full member, the country had to adopt all EU legislation and the common EU policies. There is some statistical evidence that Greece became a closer trading partner to the EU and a more open economy during the period of associate membership. This research study looks at how the Greek economy has been affected by its association with the EU. There are few direct variables which are used to measure economic integration in the economics literature. For this research, an indirect variable measure of economic integration, the elasticity of substitution (~) between capital and labor, is used as a proxy measure of economic integration. 1 In this study, cr is calculated based on two estimated parameters of the constant-returns-to-scale, transcendental, sectoral production function and the sectoral time series data of the capital-to-labor ratios for Greece, Germany, and France. The sectors studied are agriculture, industry, and service. The elasticities of substitution of the corresponding sectors of the three countries are constructed and compared for convergence. Convergence in the elasticity of substitution means that firms in the three

"Christopher Newport University.The author is grateful to MicheleFratianni and Pravin Trivedi for their help. The author also thanks Gregory Zimonopoulosfor excellent research assistance. Direct measures of economicintegrationmainlyfocus on the convergence in the standards of living such as the per capita GDP. 43

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AEJ: MARCH 1996, VOL. 24, NO. 1

countries become equally sensitive to changes of the factor-price ratio. This researcher's position is that cr behaves as a leading indicator. This approach was adopted since convergence in the standards of living between Greece and the rest of the EU does not seem attainable in the near future. Two oil crises and the initial shock from the accession to the EU have disrupted the convergence process which was taking place in Greece during the 1960s and 1970s. 2 Firms receive signals from market conditions and are apt to act based on these signals. However, there is a time lag for the full effect of the firms' responses to market conditions. The elasticity of substitution, which captures the firms' responses, is used as a predictor proxy of convergence or divergence of the sectors of the three economies, For the estimation of the sectoral production functions, a time series data set was constructed, consisting of 27 annual observations on output (Y), capital (K), and labor (L). 3 The output and labor data are published in the Organization for Economic Cooperation and Development's (OECD) "National Accounts."4 The capital stock is estimated using the perpetual inventory method. These data appear in the OECD's "Flows and Stocks of Fixed Capital," published in several volumes.

II. The Transcendental Production Function and the Elasticity of Substitution The first step in obtaining estimates for the elasticity of substitution is to estimate the constant-returns-to-scale, transcendental production function. This production function is:

Y = Ae ZtK'~L 1-'~e~ke u,

(1)

where Y and K are output and net capital stock, respectively, in 1970 billion Greek drachmas (DRS), million German deutsche marks (DM), and million French francs (FF). Labor is measured in thousands of workers per year. The variable k is the capital-to-labor ratio and t is time in years. The parameters A, X, c~, and ~ are as follows: A is an efficiency parameter; X measures neutral technical change; o~ is the elasticity of the percapita output with respect to capital-to-labor ratio; and/z is the substitution parameter. The term e is the base of the natural logarithms and u is the regression error. 5 A formula for the elasticity of substitution is derived from (1). It utilizes the definition of the marginal rate of technical substitution of capital for labor:

MRTSKL -

MP K

k E a +1I.zk 1t '

2production functionsof manufacturing, a subsector of industry, were also estimated and utilized in this study. All the Greek production functions were reestimatedusing a new set of data which was constructed after the capital and labor data were adjustedfor the capacityutilizationof the two inputs based on the method of Panic [1978] and Taylor [1982], respectively. Thus, this set of data is referred to as the adjusted data set in contrast with the original data set. 3The data set consists of 28 observations for France and Germany. 4Data for Greek labor were provided by the Central Bank of Greece. 5This production function was introducedby Ferguson [1965].

ZESTOS: ECONOMIC INTEGRATION

45

where M P L and MPI,: are the marginal products of labor and capital, respectively. The elasticity of substitution between capital and labor is: 6 a (k)

: 1 -

/xk (a +/xk) 2 - a

(3)

The elasticity of substitution, therefore, depends on the capital-to-labor ratio k and the estimated parameters o~ and tz of the sectoral, transcendental production functions. The elasticity of substitution a is then constructed as a vector of values by utilizing the time series data on the capital-to-labor ratios and the estimated parameters c~ and # of the transcendental production function. For this reason, the transcendental production function of (1) is also referred to as variable elasticity of substitution (VES). The elasticity of substitution is often denoted by a,, where the subscript t refers to time. It is interesting to note that for /~ = 0, the VES production function collapses to Cobb-Douglas; a is consequently equal to unity. III. Estimations of the Transcendental or VES Production Functions

The estimated form of (1) is: In

Y L

K K : lnA+)~t+aln--+/z--+u. L L

(4)

Although Lovetl [1968, 1973] introduced this function in his research, he did not estimate this production function directly for fear of multicollinearity. Bairam [1987, 1988] recently estimated the VES production function directly for the former Soviet Union and Romania and found that it performs statistically better than the Cobb-Douglas production function. An estimated production function without econometric problems will yield reliable estimates of the coefficients, provided the choice of the production function is the correct specification and there are no structural breaks during the estimation period in the production function. IV. Greek Agricultural and Industrial VES Production Functions

To test for structural stability during the sample period, the Chow test was performed for two different periods: the oil crisis of 1973-74 and 1980-81, the year of the accession of Greece to the EU. The estimated regressions of agriculture and industry for the VES production function are reported below (Equation (5) and Table 1, respectively). Results of the Chow test indicate no structural break(s) on the agricultural sector but two breaks on the industrial sector. Y ln--L

K K 1.67-.02t+5.91n--+3.71-L L (.25) (.01) (.06) (1.9) R2--.98,

6The

derivation of a (k) of (3)

can

F=603,

be obtained from the author.

DW=2.2.

(5)

46

AEJ: MARCH 1996, VOL. 24, NO. 1 TABLE 1 Estimated Greek Industry VES Production Function

Production Function

lnA

X

a

lz

1961-87

1.92 (0.34)

0.002 (0.013)

1.81 (0.14)

-6.00 (1.05)

1961-73

-3.54 (2.10)

-0.3 (0.04)

-0.09 (0.83)

4.18 (2.03)

1974-80

36.0 (11.0)

0.02 (0.01)

15.2 (4.5)

-61.0 (19.0)

1981-87

-14.0 (5.3)

-0.03 (0.01)

-5.7 (2.5)

21.8 (8.4)

F

DW

R2

RSS

413.0

1.24

0.97

0.043

592.0

1 . 4 5 0.99

0.004

3.07

0.90

0.001

10.0 2.20

0.82

0.0005

19.0

1961-73 1974-80 197v~0" 1981-87"*

YES YES

Notes: RSS = residual sum squares; YES = a structural break between the periods shown on the top of the column; * = 1973 versus 1980; and ** = 1980 versus 1987. Numbers in parentheses are the standard errors of the regression coefficients. To reinforce the results of the Chow test, three other tests were performed: the Cusum test, the Cusum of squares test, and the moving Chow test [see Brown et al., 1975; Hendry, 1989]. These tests are based on the recursive least squares method of estimation. The results of these tests are supportive of the Chow test results. They differ from the Chow test because with these tests the researcher does not know the exact year of the expected structural break. Hence, these tests are designed to reveal the structural break. 7 Based on the estimated coefficients a and/z, the structural break(s) as revealed by the Chow test, and the sectoral capital-to-labor ratios data, the sectoral elasticities of substitution are calculated.

V. Comparison of the Sectoral Elasticities of Substitution The means and standard deviations of the differences in the sectoral elasticities of substitution of agriculture and service are reported in Table 2. Three subsamples were chosen based on the expected structural breaks in the Greek sectors. The mean and standard deviations in o of the three countries' agricultural and service sectors are presented pair-wise. 8

7The results of these tests are available from the author. sThe regression results of the Greek service and manufacturingsectors are not reported. The regression results of the four sectors are not reported for France and Germany.

47

ZESTOS: ECONOMIC INTEGRATION TABLE 2

Agriculture and Service Difference of Sectoral Elasticities of Substitution Agriculture

Service

G-D

G-F

D-F

G-D

G-F

D-F

1961-73

Mean SD

0.20 4.70

0.39 4.70

0.20 0.10

0.01 0.43

-1.47 0.24

-1.48 0.20

1974-80

Mean SD

0.08 0.26

-0.09 0.14

-0.17 0.20

0.24 0.00

-1.26 0.00

-1.50 0.00

1981-87

Mean SD

0.71 0.10

0.24 3.08

-0.47 5.46

0.62 0.17

-t .45 0.00

-2.07 0.20

Notes: G-D = Greek minus German; D-F = German minus French; G-F = Greek minus French; and SD = standard deviation. By observing the mean differences and standard deviations in a in each column, there is no evidence for convergence in the corresponding elasticities of the three countries. If there was convergence in a, the mean difference from subsample to subsample chronologically should have declined and eventually converged to zero. Similar results are shown in Figure I, where the corresponding agricultural and service elasticities of the three countries are presented together graphically. FIGURE I

Agriculture Elasticities of Substitution

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

o

t

-,

i

\1

6061 62 63 64 65 66 67 68 ~ 70 71 72737475767778798081 8283848586

48

AEJ: MARCH 1996, VOL. 24, NO. 1 FIGURE I (CONT.) Service Elasticities of Substitution 0.4 0.30.2 - %,,

0-

~ , , ,,,4"~

.o.1-

-Y,

,;/ -'/

-0.2 -

SIGMA

i

'b

-"-.

o,-if

-IA -.~ -1.2

~--- -

I

- -

I

I

I I

\

\

I .;

C'r. Adj. Cxxmaay

v

I

l

',,

~. ;

Ca. Org.

I--T -+" I

"..

i

. o . 6 - . ~ -o.r-L;

"

-*"--

....

i:

i/

-0,

I---

. I

~-.,._

//

Ir'~

;

I

1

I

I

I

i

t

i -7

i

I

i

t

I I,,

l

#

I

t

I

6061 6 2 6 3 6 4 6 5 6 6 6 7 6 8 6 9 7 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 8 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 YEAR

Notes: Gr. Org. = Greek original, based on Greek original data (unadjusted) on capital and labor; and Gr. Adj. = Greek adjusted, based on Greek data on capital

and labor adjusted for capacity utilization. There is a plausible explanation for this divergence. The elasticity of substitution captures a firm's behavior. It measures the firm's responsiveness to changes in the factorprice ratio. The business firm's responsiveness can be observed optimally under free competition. Under free competition, firms have an incentive to make the necessary adjustments and, thus, undergo structural changes to remain competitive. These changes involve the adoption of new technologies, as indicated by changes in the capital-to-labor ratios. The agricultural sectors of the three countries are protected by the EU. This protection allows farmers to employ the same production technologies despite the fact that the agricultural commodities are traded internationally. The elasticity of substitution of the service sectors diverged during the same time period. The reason for this is that many services are not traded and, consequently, are not subject to international competition. The elasticities of substitution of the industrial sectors and the manufacturing subsectors of the three economies converged as shown in Table 3. Here the absolute value of the mean differences and standard deviations of the elasticities of substitution decline over time. This indicates evidence of convergence. The same results are depicted in Figure II, where the industrial and manufacturing elasticities of substitution of the three countries are graphed together. The convergence of the elasticities of substitution of the industrial and manufacturing sectors is attributed to the openness of these sectors to intra-EU and international trade competition.

49

ZESTOS: ECONOMIC INTEGRATION TABLE 3

Industry and Manufacturing Difference in Elasticities of Substitution Industry

Manufacturing

G-D

G-F

D-F

G-D

G-F

D-F

1961-73

Mean SD

-0.86 0.45

-1.58 0.50

-0.72 0.34

1.13 0.42

-2.05 1.48

-3.18 1.62

1974-80

Mean SD

-0.30 0.10

-0.19 0.17

-0.72 0.17

0.06 0.14

-1,85 0.64

-1.91 1.62

1981-87

Mean SD

0.04 0.14

-0.09 0.17

-0.13 0.00

0.56 0.14

-0.30 0.03

-0.87 0.17

Notes: G-D = Greek minus German; D-F = German minus French; G-F = Greek minus French; and SD = standard deviation. F I G U R E II

Industry Elasticities of Substitution

0.81 0,6 O.7

0.5 0.4 - ~ , 0 . 3 - ~ ~ ~,,.. 0.2 - ~ " ' ~, 0.1 ~"~..,, _

I

-o.1-

~,

-o~.SIGMA

~_

-'-

-#"~

",I/

V

g

-0.4 4).541.64),741.8

-o.19 .....

-1.1 -1.2 -

-1.4-'~'~ "

I

I

~

I

I

I

I

I

~

I

I

I

i

I

I

I

I

I

C~0~.

Fruce 1

I

I

I

I

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I

I

"

8061 ~ ~ 6 4 6 5 ~ 6 T ~ ~ 70TI 72 73 74 75 78 7"/'T8Tg BO BI 82 B3 84 I~ BB B7

50

AEJ: MARCH 1996, VOL. 24, NO. 1 FIGURE II (CONT.) Manufacturing Elasticities of Substitution 8 mlu*m

7-

A B-

~

.... -

-

'

Fnme¢

$-

4-

SIGMA

3~,_

1-

O-

60

1~

63 64 ~

f~ 67 m lm To 7 1 7 2 73 74 75 76 77 "~q~79 Ki

I a211~4~11687

Notes: Gr. Org. = Greek original, based on Greek original data (unadjusted) on capital and labor; and Gr. Adj. = Greek adjusted, based on Greek data on capital and labor adjusted for capacity utilization.

VI. Conclusions on the Convergence or Divergence in the Elasticity of Substitution The results of this study support the hypothesis that the accession of Greece to the EU affected the elasticity of substitution of the industrial and manufacturing sectors of the Greek economy, converged to the elasticities of substitution of the corresponding sectors of France and Germany. No evidence of convergence of the elasticity of substitution is observed in the Greek service and agricultural sectors. The differential effects of the accession on the productive sectors of the economy are discussed below. The Greek industrial and manufacturing sectors are subject to trade competition from the EU and the rest of the world. Competition affects firms differently. In the highly competitive sectors of industry and manufacturing, firms search for new methods of production for competitive advantage. Continuous capital accumulation and supply shocks, such as the oil crisis, affected all these elasticities. In the primarily nontraded service sector, firms in a relatively noncompetitive environment adopt production techniques and hire factors of production independently of international and inter-EU competition. This behavior is the reason for the nonconvergence of the elasticities in the service sector. In the agricultural sector, despite the fact that Greek prices converged to EU prices, the elasticities of substitution did not converge. This is the result of protective policies by Greece and the EU in this sector. Another finding of this study is that the elasticities of substitution of the manufacturing sectors of all countries declined over time. This result is consistent with other studies that found declining a from time series data in the manufacturing sectors of Western and Eastern European countries [Ilkovitz, 1987; Bairam, 1987, 1988]. Declining ~r can have

ZESTOS: E C O N O M I C I N T E G R A T I O N

51

detrimental effects on the manufacturing sectors of these economies. A declining a means that manufacturing firms are less able to substitute factors of production and, thus, are unable to take full advantage of changes in factor prices. Such inflexibility and inability to make the necessary adjustments for changes in market conditions may have contributed to the stagnation of the industrial sectors of the EU economies and the economies of Eastern Europe. These findings are also supported by the fact that Greek industry and manufacturing sectors in the post-EU period experienced no growth, while the agriculture and service sectors remained unaffected across time periods. REFERENCES Bairam, E. "Variable Elasticity of Substitution, Technical Change and Industrial Growth: The Romanian Experience," Journal of Quantitative Economics, 4, 1, January 1988, pp. 123-31. . "Soviet Postwar Industrial Growth and Capital Labour Substitution," Economic Letters, 24, 1987, pp. 331-4. Bank of Greece. "Monthly Statistical Bulletin," several issues. Brown, R. L.; Durbin, J.; Evans, J. M. "Techniques for Testing the Constancy of Regression Relationships Over Time," Journal of Royal Statistical Society, B37, November 1975, pp. 149-92. Ferguson, C. "Capital-Labor Substitution and Technological Progress in the United States: Statistical Evidence From a Transcendental Production Function," mimeographed, 1965. Hendry, D. F. PC-Give, An Alternative Econometric Modelling System, Oxford, England: University of Oxford Press, 1989. Ilzkovitz, Fabienne. Economic Papers, Commission of the European Communities, Directorate-General for Economic and Financial Affairs, No. 57, September 1987. Lovell, C. A. Knox. "Estimation and Prediction with CES and VES Production Functions," Review of International Economics, 1973, pp. 676-92. . "Capacity Utilization and Production Function Estimation in Postwar American Manufacturing," Quarterly Journal of Economics, 82, 1968, pp. 219-39. Organization for Economic Coooperation and Development. Flows and Stocks of Fixed Capital, Paris, France: OECD, several issues. Panic, M. "Capacity Utilization in UK Manufacturing Industry," Discussion Paper No. 5, United Kingdom: National Economic Development Office, 1978. Taylor, J. "On Measuring the Utilization Rate of Employed Labour," Applied Economics, 14, 1982, pp. 591601.