Sources of Economic Growth: An Extensive Growth Accounting Exercise
Author: Mr. Abdelhak S Senhadji
Publication Date:
01 Jan 2000
eISBN:
9781451974584
Language:
English
Keywords:
SP; TFP growth performance; TFP level; production function estimate; Cobb-Douglas production function; TFP performance; Total factor productivity; Human capital; Growth accounting; Production growth; East Asia; Middle East; Sub-Saharan Africa; South Asia; North Africa
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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 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. [JEL E25, O47]

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 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. [JEL E25, O47]

Heated debate initiated by Young (1995) and then Krugman (1994) on the sources of growth in East Asian countries 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) was fueled essentially by 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.1

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, which typically sets its parameter, the share of the remuneration of physical capital in aggregate output, to a benchmark value of one-third as suggested by the national income accounts of some industrial countries.2,3 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 the same region but different among countries across regions. The estimates of the production function for each region are obtained by averaging individual country estimates belonging to each region.

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, by differencing, we disregard 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 that 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 estimate 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. Those studies that have made the attempt focused on cross-country differences in growth rates of TFP, with the notable exception of Hall and Jones (1999), who show that a significant share of the cross-country variation in TFP level can be explained by “social infrastructure.”4 Three factors explain 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 (1999), 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, but 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 difficult to quantify their effects because 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.

This paper aims to:

  • estimate individual country production functions using econometric techniques that take into account the endogeneity of production inputs and the nonstationarity in the data;

  • using the production function estimates, relax the assumption of identical technologies across regions and conduct a growth accounting exercise for 88 countries for 1960–94; and

  • analyze the determinants of cross-country differences in TFP levels. Section I briefly reviews the growth accounting framework, discusses the estimation strategy of individual country production functions, and analyses the estimation results. Section II uses the results from Section I to conduct the growth accounting exercise for 88 countries grouped into six regions. Section III examines the determinants of the TFP level. Section IV reports the conclusions.

I. Country and Panel Estimates of the Production Function Parameters

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 gross domestic product in real terms, At is total factor productivity, Kt is the real capital stock, 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).5 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.6

The remainder of this section briefly describes the series Yt, Kt, Lt, and Ht.7 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 1950.8 Both Yt and Kt are in local currency, 1987 constant prices. In order for the TFP levels to be comparable across countries, the data on Yt and Kt were converted into 1987 international prices, using the purchasing power parities for 1987. For industrial countries, the quantity of labor, Lt, is actual employment. For developing countries, Lt 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. Ht is defined as follows:

Ht=∑j=17WjtPjt,(3)

where Pjt, 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). Wjt, represents aggregation weights based on the observed relative earnings of the different educational groups.9 The data are available for 88 countries and cover 1960–94. Countries included in the sample and the regional groupings are given in the Appendix.

Time Series Estimation of the Production Function

As argued in the introduction, there are compelling reasons for estimating the production function in levels (equation 1). To take into account the potential nonstationarity in the data, the following two-step estimation strategy has been adopted:

  • First, test the two variables (real output per capita and the stock of physical capital per capita) in the production function for the presence of a unit root.

  • The second step depends on how many variables contain a unit root. If both variables contain a unit root, a long-run relationship between output per capita and physical capital per capita will exist only if they are cointegrated. The case of only one non-stationary 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 both variables are (trend) stationary. Two residual-based tests of cointegration are performed. 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:

yt=μ+γt+φ0yt−1+∑i=1k−1φiΔyt−i+ξt,k=1,…,5(4)

Note that for k = 1, 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 (SC). Table 1 presents the results for the two variables entering the Cobb-Douglas production function—namely output and stock of physical capital, both expressed in terms of skill-augmented labor—for 66 countries.10 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.11

Table 1.

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 to 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.12 The correction for potential endogeneity of the explanatory variables is an attractive property of the FM estimator since physical capital per capita is likely to be endogenous.

The production function was estimated 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 2A).13 Table 2B summarizes the estimation results by giving the mean, median, standard deviation, minimum, and maximum of α by region for the FM method.

Table 2A.

Cobb-Douglas Production Function Estimates for 66 Countries

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Note: Table 2A 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. The following statistics are provided: the adjusted R2 (R2), the Phillips-Ouliaris (P-O) and Shin’s (SH) cointegration tests. The 1, 5, and 10 percent critical values are -4.29, -3.5, and -3.22 for P-O, and 0.184, 0.121, and 0.097 for SH, respectively.
Table 2B.

Summary Statistics of Cobb-Douglas Production Function Estimates

Statistics by Region

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Note: Table 2B gives regional summary statistics for Table 2A, which shows the 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 have the highest (0.64). The mean value for the other regions are Middle East and North Africa (0.63), Latin America (0.52), East Asia (0.48), South Asia (0.56), and the entire 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 entire 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 two estimation methods yield regional estimates that do not differ significantly, except for East and South Asia. The whole sample average is remarkably stable across estimation methods (around 0.55). 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 (of 0.33 and 0.40) used in growth accounting exercises. The estimates of α are generally quite precise.

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.14 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.

Even though estimates of α in first-difference regressions are statistically significant, physical capital normalized by skill-augmented labor accounts for only a modest share of the short-term variation in GDP per capita, corroborating 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.

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 per capita and capital per capita are cointegrated. The cointegration tests used are the Phillips-Ouliaris (P-O) test, which has non-cointegration as the null hypothesis and the Shin (SH) test, which has cointegration as the null. While P-0 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.

II. A Comparative Analysis of Sources of Growth

Section I showed 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). Tables 2A and 2B show 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 other words, a sensitivity analysis is warranted. But even without carrying out a detailed sensitivity analysis, it is easy to analytically show the relationship between TFP growth, which is the key element in this analysis, and the share of physical capital (α). From equation (2), we have:

a^t=y^t−αk^t−(1−α)(l^t+h^t).(5)

Taking the first partial derivative of TFP growth (ât) with respect to α yields

∂a^t/∂α=−k^t+(l^t+h^t).(6)

Equation (6) implies:

∂a^t/∂α{≥0<0⇔{k^t≤(l^t+h^t)k^t>(l^t+h^t).(7)

An increase in the share of capital will decrease (increase) TFP growth if the growth rate of capital stock is larger (smaller) than the growth rate of skill-augmented labor. Since in most countries, capital grows much faster than labor, the second inequality holds in equation (7). That is, countries with higher capital shares will tend to have lower TFP growth (for similar growth rates of capital and skill-augmented labor). This result is helpful in interpreting Tables 3A and 3B.

Table 3A.

Decomposition of the Growth Rate of Real GDP

(Mean α from level equations)

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Note: Assume output follows a Cobb-Douglas production function:Yt=AtKtα(LtHt)1−α,where Yt is aggregate output, 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 = log(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 sub-Saharan Africa is computed by taking the average over the countries in sub-Saharan Africa of the individual African countries’ average over the 1960–1994 period). The statistics ρL and ρD provide the autocorrelation coefficients of the corresponding variable in level and in first difference.
Table 3B.

Decomposition of the Growth Rate of Real GDP

(Mean α from first difference equations)

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Note: Assume output follows a Cobb-Douglas production function:Yt=AtKtα(LtHt)1−α,where Yt is aggregate output, 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 = log(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 sub-Saharan Africa is computed by taking the average over the countries in sub-Saharan Africa of the individual African countries’ average over the 1960–1994 period). The statistics ρL and ρD provide the autocorrelation coefficients of the corresponding variable in level and in first difference.