Sources of Economic Growth: An Extensive Growth Accounting Exercise
Author: Mr. Abdelhak S Senhadji

Contributor Notes

Author’s E-mail Address: asenhadji@imf.org
Publication Date:
01 Jun 1999
ISBN:
9781451849974
Language:
English
Keywords:
WP; dummy variable; correlation coefficient; TFP level; time series; production function estimate; TFP analysis; TFP equation; TFP relative
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A growth accounting exercise is conducted for 88 countries for 1960-94 to examine the source of cross-country differences in total factor productivity (TFP) levels. Two differences distinguish this analysis from that of the related literature. First, the critical technology parameter—the share of physical capital in real output—is econometrically estimated and the usual assumption of identical technology across regions is relaxed. Second, while the few studies on the determinants of cross-country differences in TFP have focused on growth rates of real output this analysis is on levels. Recent theoretical as well as empirical arguments point to the level of TFP as the more relevant variable to explain.

Abstract

A growth accounting exercise is conducted for 88 countries for 1960-94 to examine the source of cross-country differences in total factor productivity (TFP) levels. Two differences distinguish this analysis from that of the related literature. First, the critical technology parameter—the share of physical capital in real output—is econometrically estimated and the usual assumption of identical technology across regions is relaxed. Second, while the few studies on the determinants of cross-country differences in TFP have focused on growth rates of real output this analysis is on levels. Recent theoretical as well as empirical arguments point to the level of TFP as the more relevant variable to explain.

I. INTRODUCTION

The heated debate on the sources of growth in the East Asian countries initiated by Young (1994) and then Krugman (1994) has spurred a growing literature on the subject. Both authors contend that the “Asian Miracle” is a myth because the engine driving the spectacular growth in the region (at least until recently) came essentially from capital accumulation instead of total factor productivity (TFP) growth. Why does the source of growth matter? The neoclassical growth model, with its main assumption of diminishing returns in physical, capital provides the answer. If this assumption is correct—and the large empirical growth literature tends to support it—capital accumulation cannot sustain long-term growth while TFP can. Thus, the source of growth is crucial for the long-term perspective of a country. The Krugman-Young analysis has been reexamined and extended to other countries.2

All these studies use the growth accounting framework, which is based on an aggregate production function expressed in growth rates. The results of the growth accounting exercise therefore depend on the specification of the production function. The bulk of the literature has adopted the Cobb-Douglas production function whose parameter, the share of the remuneration of physical capital in aggregate output, is typically set to a benchmark value of 1/3 suggested by the national income accounts of some industrial countries.3,4 This numerical specification is assumed to be the same across countries, which implies identical production technology for all countries. Although most authors provide some sensitivity analysis on the value of the share of physical capital, they do not address the issue of adequacy of the assumption of identical technologies across countries. If the data fail to support this assumption, and there is no compelling reasons to believe it does—on the contrary, one may think of many reasons why technologies differ across countries and regions—the comparison of the sources of growth across countries and regions may be flawed.

For the growth accounting exercise in this paper, the assumption of identical technologies across regions is relaxed. The 88 countries in the sample are divided into six regions. The production function is assumed to be identical across countries within regions but different among countries across regions. The estimates of the production function for each region are obtained either by averaging individual country estimates belonging to each region or through regional panel estimation.5

An argument often made in the literature against the estimation of production functions for determining the share of physical capital (the key parameter in the accounting exercise) is the problem of potential endogeneity of the explanatory variables, namely capital and labor inputs. The Fully-Modified estimator, which is used to estimate the production function of each country, corrects for this potential problem as well as for the likely autocorrelation of the error term.

The estimation of the production function also raises the issue of whether to estimate it in levels or in first differences. As is well known, the first difference operator removes all the long-run information in the data. One important insight from the cointegration literature is that we know much more about the long-run than the short-run relationship between macroeconomic variables. Consequently, differencing amounts to disregarding the most valuable part of information in the data.

In the context of production function estimation, this point is particularly relevant. It will be shown below that the growth rate of real GDP varies much more than does the growth rate of capital (both physical and human) and labor inputs; thus the link between GDP growth and input growth is likely to be very weak. Furthermore, the business cycle frequencies of the production process may be dominated by variations in capacity utilization factors which are difficult to measure, especially for developing countries. In light of the discussion above, the production function will be estimated in levels. Nonetheless, given that the Cobb-Douglas production function has traditionally been estimated in first-difference, the paper will also provide first-difference estimates for comparison.

This growth accounting exercise uses a different production function estimates for each region to break down the growth rate of real GDP into contributions from capital and labor for the 88 countries in the sample and six regional aggregates. The analysis of TFP covers the periods 1960–73, 1974–86,1987–94, and 1960–94 and the issue of robustness is examined through extensive sensitivity analysis.

Few studies have attempted to explain cross-country differences in TFP. The ones that have, focused on cross-country differences in growth rates of TFP, with the notable exception of Hall and Jones (1998), who show that a significant share of the cross-country variation in TFP level can be explained by “social infrastructure”.6 Three reasons describe why levels matter more than growth rates. First, growth rates are important only to the extent that they are a determining factor of levels. Second, recent contributions to the growth literature focus on levels instead of growth rates. For example, Easterly and others (1993) show that growth rates over decades are only weakly correlated, suggesting that cross-country differences in growth rates may essentially be transitory. Moreover, several recent models of technology transfer across countries imply convergence in growth rates as technology transfers prevent countries from drifting away from each other indefinitely. In these models, long-run differences in levels are the pertinent subject of analysis. And, third, the cointegration literature has clearly demonstrated the superiority of level equation versus first-difference equations when series are nonstationary. Formal unit-root tests show indeed that these variables cannot reject the unit-root hypothesis.

As in Hall and Jones (1998), this paper analyzes the determinants of cross-country differences in TFP levels, but with three important differences. First, Hall and Jones assume the same technology across-countries and regions by setting the share of physical capital to one-third for all countries, whereas this paper assumes different technologies for each of the six regions and estimates the technology parameter econometrically. Second, Hall and Jones focus on the institutions as the determining factor of cross-country differences in TFP levels. While institutions undoubtedly play a fundamental role in shaping the productive capacity of a country, it is a tour de force trying to quantify their effects, for good proxies for the quality of institutions do not exist. Third, while Hall and Jones use cross-section data to conduct their analysis, this paper uses panel data, which enriches the analysis by considering not only the cross-country differences in the TFP level but also the evolution of TFP for a given country.

The paper is organized as follows. Section II briefly reviews the growth accounting framework, discusses the estimation strategy of individual country and regional production functions, and analyses the estimation results. Section III uses the results from the previous section to conduct the growth accounting exercise for the 88 countries in the sample and for the six regions. Section IV examines the determinants of the TFP level, and the conclusions are reported in Section V.

II. COUNTRY AND PANEL ESTIMATES OF THE PRODUCTION FUNCTION PARAMETERS

A. Methodology and Data Sources

The production function parameters are central to the decomposition of output growth into contributions from physical capital, labor, and productivity. This section provides estimates of these parameters for the following production function:

Yt=AtKtα(LtHt)1−α(1)

where Yt is GDP in real terms, At is TFP, Kt is the stock of capital, Lt is total employment (or the labor force if employment is not available), Ht is an index of human capital, and thus LtHt is a skilled-adjusted measure of labor input. Taking logs and differentiating totally both sides of equation (1) yields:

y^t=a^t+αk^t+(1−α)(l^t+h^t)(2)

where the lowercase variables with a “hat” correspond to the growth rate of the uppercase variables described in equation (1).7 Equation (2) decomposes the growth rate of output into the growth of TFP, and a weighted average of the growth rates of physical capital and skill-augmented labor. Under constant returns to scale (assumed here), these weights are given by the shares of these two inputs in aggregate output.8

The remainder of this section briefly describes the series Kt, Lt, and Ht.9 The measure of capital, Kt, is based on a perpetual inventory estimation with a common geometric depreciation rate of 0.04. Generally, estimates of the physical capital stock are considered unreliable because of lack of information about the initial physical capital stock and the rate of depreciation. However, the World Bank data set used by Collins and Bosworth (1996) incorporates the results of previous studies of individual or small groups of countries in which the physical capital stock was estimated from investment data going back to 1950.10

The quantity of labor, Lt, is actual employment for the industrial countries. For developing countries, it is the International Labor Organization’s estimate of the economically active population. The index Ht was constructed following Barro and Lee’s (1994) methodology based on educational attainment. It is defined as follows:

Ht=∑j=17WjtPjt(3)

where Pj t represents the share of the population that completed the level of education j (where j varies from 1, corresponding to the share of the population with no schooling, to 7, corresponding to beyond secondary education) and Wj t represent aggregation weights based on the observed relative earnings of the different educational groups.11

B. Time Series Estimation of the Production Function

Traditionally, equation (1) is estimated in first difference of logs—that is, equation (2). As is well known, the first difference operator removes all the long-run information (by removing the low frequencies in the data) and emphasizes the short-run fluctuations in the data. An important insight offered by the cointegration literature is that we know much more about the long-run than we do about the short-run relationships among macroeconomic variables. Consequently, differencing amounts to disregarding the most valuable part of information in the data.

This point is particularly relevant for production function estimation. As shown below, the growth rate of GDP varies much more than the growth rate of the inputs Kt and Lt. Thus the link between GDP growth and input growth is likely to be very weak. Furthermore, the business cycle frequencies of the production process may be dominated by variations in capacity utilization issues that are difficult to measure, especially for developing countries. In light of these issues, the production function in this exercise will be estimated in levels, but for comparison purposes, the production function will also be estimated in first-difference form.

1. Time series estimation

The estimation of the production function in levels (equation 1) requires taking into account the potential nonstationarity of the data, which leads to the following two-step strategy:

  • First, test the three variables in the production function for the presence of a unit-root.

  • The second step depends on how many variables contain a unit-root. If at least two of the three variables contain a unit-root, a long-run relationship between output per capita, physical capital, and skill-augmented labor will exist only if the nonstationary variables are cointegrated. The case of only one nonstationary variable is problematic because it implies that no stable relationship exists between inputs and output (this case does not occur in the data set used here). The only case where classical inference is valid is the one where all three variables are (trend) stationary. To avoid spurious regressions, two residual-based tests of cointegration are performed for cases where some of the three variables contain a unit-root. The Phillips-Ouliaris’ (1990) cointegration test has non-cointegration as the null hypothesis while Shin’s (1994) cointegration test has cointegration as the null.

Unit-root test

The unit-root hypothesis is tested using the Augmented-Dickey-Fuller (ADF) test, which amounts to running the following set of regressions for each variable:

xt=μ+γt+ϕ0xt−1+∑i=1k−1ϕiΔyt−i+ξt,k=1,…,5(4)

Note that for k=l, there are no Δyt-1 terms on the right-hand side of equation (4). The lag length (k) in the ADF regression is selected using the Schwarz Criterion (SIC). Table 2 presents the results for the two variables entering the Cobb-Douglas production function—namely output and stock of physical capital expressed in terms of skill-augmented labor—for 66 countries.12 For GDP per capita, the unit-root hypothesis can be rejected at 5 percent or less only for two countries, Sierra Leone and Uruguay. For physical capital per capita, the unit-root hypothesis can be rejected at 5 percent or less for the following eight countries: India, Indonesia, Italy, Malaysia, Myanmar, Pakistan, Thailand, and Uruguay. Uruguay is the only country for which the unit root can be rejected for both variables. These results show that, in general, the unit-root hypothesis cannot be rejected at conventional significance levels. Thus, the estimation of the production function requires a cointegration framework.13

Table 1.

Regional estimates of the Share of Physical Capital per Capita (α)

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Note: The first two columns are averages over the regional country estimates (from Table 3a), while columns 3 and 4 are averages over the seven panel estimates for each region (from Tables 4a and 4b). The columns labeled with H and without H report panel estimates for the equations with and without human capital.
Table 2.

Augmented-Dickey-Fuller Test for a Unit-Root

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Note: Variables are as follows: real GDP divided by skill-augmented labor, Y/(L*H), and physical capital divided by skill-augmented labor, K/(L*H). These two variables are tested for the existence of a unit root using the Augmented-Dickey-Fuller (ADF) test. The optimal lag selected by the Schwarz criterion in the ADF regression is given by k. Critical values are a linear interpolation between the critical values for T=25 and T=50 (where T is the sample size) given in table B. 6, case 4, in Hamilton (1994). Significance levels equal or less than 5 percent are indicated by the symbol *.
Estimation results

This paper uses the Fully-Modified (FM) estimator developed by Phillips and Hansen (1990) and Hansen (1992) to estimate the production function. The FM estimator is an optimal single-equation method based on the use of OLS with semiparametric corrections for serial correlation and potential endogeneity of the right-hand variables. The FM estimator has the same asymptotic behavior as the full systems maximum likelihood estimators.14 The correction for potential endogeneity of the explanatory variables is an attractive property of the FM estimator since physical capital per capita and the index of human capital are likely to be endogenous.

The production function was estimated by both OLS and FM methods for 66 countries, 46 of which are developing countries. Since the literature has predominantly used the first-difference specification, this paper provides estimates of α (the share of physical capital in aggregate output) in both levels and first differences for comparison (see Table 3a). Table 3b summarizes the estimation results by giving the mean, median, standard deviation, minimum, and maximum of α by region for the FM method.

Table 3a.

Cobb-Douglas Production Function Estimates for 66 Countries

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Note: Table 3a provides OLS and Fully Modified (FM) estimates of the share of physical capital (α) for the following Cobb-Douglas production function: Yt=AtKtα(LtHt)1−α, where At is total factor productivity, Kt, is the stock of physical capital, Lt is the active population, and Ht is an index of human capital, both in levels and first difference for 66 countries. For following statistics are provided: the adjusted R2(R¯2), the Dubin-Watson statistic (D.W.), the Phillips-Ouliaris (P-O) and Shin’s (SH) cointegration tests. The 1%, 5%, and 10% critical values are -4.29, -3.5, and -3.22 for P-O, and 0.184, 0.121, and 0.097 for SH, respectively. The superscripts a, b, c indicate significance at 1, 5, and 10 %percent, respectively.
Table 3b.

Summary Statistics of Cobb-Douglas Production Function Estimates

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Note: Table 3b gives regional summary statistics for Table 3a which shows the OLS and Fully Modified (FM) estimates of the share of physical capital (α) for the following Cobb-Douglas production function: Yt=AtKtα(LtHt)1−α, where At is total factor productivity, Kt is the stock of physical capital, Lt is the active population, and Ht is an index of human capital, both in levels and first difference for 66 countries.

Estimates of α vary significantly across regions, both in levels and first differences. In levels, Sub-Saharan Africa has the lowest mean value (0.43) and industrial countries the highest (0.64). The mean value for the other regions are Middle East and North Africa (0.63), Latin America (0.63), East Asia (0.48), South Asia (0.56), and the whole sample (0.55). The results are quite different in first differences. East Asia has the lowest mean estimate (0.30), while Latin America shows the highest mean estimate (0.62). However, the mean estimate for industrial countries (0.58) and the whole sample (0.53) are relatively close to the corresponding estimates in levels. There is substantial cross-country variation: the share of capital estimates range from 0.13 to 1.00 in levels, and from 0.01 to 0.99 in first differences. The estimates of α are generally quite precise.

Even though estimates of α in first difference regressions are statistically significant, physical capital and (skill-augmented) labor account for only a modest share of the short-term variation in GDP per capita. This corroborates the earlier discussion about estimates in levels versus in first differences. The first difference operator eliminates low frequencies, and thus emphasizes short-term fluctuations in the data. As noted earlier, at the business cycle frequencies, the production process may be dominated by capacity utilization and other short-term factors that are not measurable (at least for the large sample used). This implies that level regressions, by combining both the short- and long-term information in the data, should yield more accurate estimates of α.

It is worth noting that the average estimate of the share of physical capital (0.55 in levels and 0.53 in first differences) is significantly higher than the usual values (ranging from 0.30 to 0.40) used in growth accounting exercises.

Finally, for the equations in levels, it remains to be verified whether coefficient estimates provide a meaningful economic relationship that is not the result of a spurious regression. This amounts to testing whether output and input variables are cointegrated. The cointegration tests used are the Phillips-Ouliaris (P-O) test, which has non-cointegration as the null hypothesis and Shin (SH) test, which has cointegration as the null. While P-O rejects the null of non-cointegration for only 26 countries (which is likely the result of the test’s low power in small samples), the SH test fails to reject the null of cointegration for all 66 countries. Thus, the combined evidence from both tests favors the hypothesis of cointegration.

2. Panel Estimation

In order to increase the sample size, it will be assumed that the share of physical capital differs across regions but is identical for countries from the same region. Hence, a panel for each region will be used to estimate α. Since the FM estimator does not apply to panel cointegration, only results for the first differences are reported.

The Cobb-Douglas production function was estimated both with and without human capital to show the effect of human capital on estimates of α. Equation (1) specifies the production function with human capital and equation Yt=AtKtα(LtHt)1−α specifies the production function without human capital. Robustness was also checked with respect to the estimation method by using seven different methods—pooled regression without fixed effects (pooled), generalized least squares (GLS), seemingly unrelated regressions (SUR), pooled regression with fixed effects, GLS with fixed effects, SUR with fixed effects, and GLS with random effects. Tables 4a and 4b, respectively, report results with and without human capital.

Table 4a.

Panel Estimates of the Cobb-Douglas Production Function (with Human Capital)

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Note: Table 4a provides different estimates of the share of physical capital (α) for the following Cobb-Douglas production function: Yt=AtKtα(LtHt)1−α, where At is total factor productivity, Kt is the stock of physical capital, Lt is the active population, and Ht is an index of human capital. The production function is estimated in first difference. Note that for the GLS equations, both the unweighted (first line) and weighted (second line) R¯2 are given.
Table 4b.

Panel Estimation of a Cobb-Douglas Production Function (with no Human Capital)

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Note: Table 4b provides different estimates of the share of physical capital (α) for the following Cobb-Douglas production function: Yt=AtKtαLt1−α, where At, is total factor productivity, Kt, is the stock of physical capital, and Lt is the active population. The production function is estimated in first difference. Note that for the GLS equations, both the unweighted (first line) and weighted (second line) R¯2 are given.

The mean over the seven estimation methods are 0.48 for Africa, 0.44 for East Asia, 0.28 for South Asia, 0.65 for Middle East, 0.72 for Latin America, 0.54 for the industrial countries, and 0.55 for the whole sample (world). Table 1 compares the regional panel estimates (third column) with the corresponding regional means of individual country estimates in levels (first column) and in first differences (second column):

Table 1 shows that estimates of α vary substantially across regions. However, they are remarkably stable across estimation methods, approximating 0.55 for the whole sample. Regional estimates are more varied across estimation methods, even though they generally do not differ significantly except for East and South Asia. Finally, comparison of with and without human capital (the last two columns) shows that discarding the human capital variable (H) from the production function does not significantly change the estimates of α.

It has often been argued in the literature that the share of physical capital (α) must be higher in developing than in developed countries since the marginal product of capital is higher in developing countries.15 However, α = (∂Y/∂K) (K/Y) is the product of the marginal product of capital (the term in parentheses) and the capital-output ratio. It is true that under decreasing returns to capital, the marginal product of capital is theoretically higher in developing countries. But by the same reasoning the capital-output ratio in developing countries is lower. Thus the product defining α can be either lower or higher for developing countries. This ambiguous result is reflected in Table 1, where some developing regions have higher while others have lower estimates of α than do industrial countries.

III. A COMPARATIVE ANALYSIS OF SOURCES OF GROWTH

In section II, we saw that under a constant-returns-to-scale Cobb-Douglas production function, the only parameter determining the contribution of physical capital and skill-augmented labor to growth of output is the share of physical capital, that is parameter α (see equation 2). Table 1 shows this parameter to vary significantly across countries, regions, and estimation methods. Thus, to be informative, a sources of growth exercise must take into account this variation of α. In this exercise, the decomposition of output has been carried out with five different values of α, reflecting the range shown in Table 1.

Tables 5a–5e report the decomposition of real output for five values of α. Tables 5a–5c report the decomposition for the values 0.2, 0.4, and 0.6, respectively. These values are assumed to be the same for all regions, which implies identical technologies across regions. Tables 5d and 5e relax this assumption by allowing α to differ across regions. The decomposition of output was computed for seven regions: East Asia, South Asia, Sub-Saharan Africa, Middle East and North Africa, Latin America, Industrial Countries, and the whole sample for the periods 1960–73, 1974–86, 1987–94 and 1960–94.

Table 5a.

Decomposition of the Growth Rate of Real GDP (α = 0.2)

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Note: Assume output follows a Cobb-Douglas production function: Yt=AtKtα(LtHt)1−α where Yt, is aggregate ouptut, At, is total factor productivity, Kt, is the stock of physical capital, Lt is the active population and H t is an index of human capital. Hence, dTFP=log(At/At-1), dkc=αlog(Kt/Kt-1), dlc=(1-α)log(Lt/Lt-1), dhc=(1-α)log(Ht/Ht-1), and dy=log(Yt/Yt-1). The statistics are computed by varying both the time and the regional cross-section dimensions (for example, the mean TFP for AFRICA is computed by taking the average over the countries in AFRICA of the individual African countries’ average over 1960-1994 period). The statistics ρL and ρD provide the autocorrelation coefficients of the corresponding variable in level and in first difference. The regions are: East Asia (EASIA), South Asia (SASIA), Sub-Saharan Africa (AFRICA), Middle East and North Africa (MENA), Latin America (LATAM), and Industrial Countries (INSUS).
Table 5b.

Decomposition of the Growth Rate of Real GDP (α = 0.4)

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Note: Assume output follows a Cobb-Douglas production function: Yt=AtKtα(LtHt)1−α where Yt, is aggregate ouptut, At, is total factor productivity, Kt, is the stock of physical capital, Lt is the active population and Ht is an index of human capital. Hence, dTFP=log(At/At-1), dkc=αlog(Kt/Kt-1), dlc=(1-α)log(Lt/Lt-1), dhc=(1-α)log(Ht/Ht-1), and dy=log(Yt/Yt-1). The statistics are computed by varying both the time and the regional cross-section dimensions (for example, the mean TFP for AFRICA is computed by taking the average over the countries in AFRICA of the individual African countries’ average over 1960-1994 period). The statistics ρL and ρD provide the autocorrelation coefficients of the corresponding variable in level and in first difference. The regions are: East Asia (EASIA), South Asia (SASIA), Sub-Saharan Africa (AFRICA), Middle East and North Africa (MENA), Latin America (LATAM), and Industrial Countries (INSUS).