Sub-Saharan Africa Working Paper Series, #10 Page 1 of 2

THE WORLD BANK GROUP

Regions: Sub-Saharan Africa

Africa Region Working Paper Series No. 10

Revisiting Growth and Convergence: Is Africa CatchingUp?

Charalambos G. Tsangarides

December 2000

Abstract

This paper draws on neoclassical and endogenous growththeories to investigate convergence and determinants of percapita growth rates in Africa and OECD countries. A paneldata, general method of moments estimator is employed,which eliminates the inconsistencies arising from omittedvariable and/or endogeneity bias that plague some of theempirical work in the literature. First, for both of the Africaand OECD samples the results indicate that (i) per capitaincomes converge to their steady state levels at rates inexcess of ten percent, in sharp contrast to the two to threepercent reported in the literature; and (ii) the Solow modelboth in its textbook and augmented form is not consistentwith the evidence presented and thus cannot account for theimportant features of cross-country income differences.Second, focusing on the Africa sample, we found evidencein support of the hypothesis that African economies withhigher savings rates, lower population growth rates, moreoutward-oriented policies, a faster pace of financialdevelopment, and a more democratic environment, havetended to grow faster; there is only tentative evidence thatgovernment consumption impinges negatively on growth.

Finding rates of convergence in excess of ten percent forboth African and OECD samples implies that countries arevery close to their steady states. On one hand, this suggeststhat variations in the per capita income levels acrosscountries can be explained primarily by differences in theirsteady state values, not the distance from their steady states.On the other hand, this result calls for more policy activism.Under the Solow framework with the identical production

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Sub-Saharan Africa Working Paper Series, #10 Page 2 of 2

functions setup, policies were directed to saving and laborforce growth rates. Allowing differences in the productionfunction the focus is now on the factors that may enter intothe individual country effects. Empirical work usingendogenous growth theory has extended the role of policiesto bring about improvements in the components oftechnology and efficiency in the economy. The results ofthis study point towards that direction: policies can not onlyaccelerate the pace of countries reaching their long runlevels of incomes, but most importantly, they can affect thelong run income levels.

Full text of paper. Tables are linked to from the paper, butalso available here: table I, table 2, table 3, table 4, table _5,table 6. (All files are in Adobe Acrobat format. RequiresAcrobat PDF viewer)

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1. Introduction

Following the seminal papers of Mankiw et al. (1992), and Barro (1991), there has been arevival of interest in the determinants of long-run economic growth, with the neoclassical Solowframework being the workhorse for empirical analysis of growth in industrial and developingcountries. In this framework, steady state growth in the levels depends on the exogenoustechnological progress and population growth; without technological progress, output per capitadoes not grow. Economic policies do not affect steady state growth, although they can affect thelevel of output or its growth rate when the economy is in transition from one state to the other.

An important feature of the neoclassical model that has been the central focus ofempirical work is the convergence property: output levels of countries with similar technologiesconverge to a given level in the steady state. On one hand, the Solow framework predicts atendency towards absolute convergence in per capita income if we assune that all countries sharethe same technology, and savings and population growth rates. On the other hand, in light of thefact that economies differ in various respects such as propensities to save, growth rates of thepopulation, and access to technology, this convergence may apply in conditional terms, that isconvergence to different levels of per capita income but to the same steady state growth rates. Inthe end, ceteris paribus, the Solow framework predicts that the lagging poor countries will tend tocatch up with the rich. The literature seems to have reached a broad consensus on the issue ofconvergence: the poor do catch up with the rich, at a rate of two to three percent per year.'

This study challenges the consensus. We argue that some estimates of the convergencerates and growth coefficients in the existing cross-country empirical work are unreliable becausethey fail to account for correlated individual effects and the endogeneity of explanatory variables.We construct a panel data, general method of moments estimator to examine rates of convergencefor African and OECD countries and investigate the determinants of per capita growth ratesdrawing on the neoclassical and the endogenous growth theories. Our findings are summarizedas follows. First, we estimate rates of convergence above 10 percent, which implies thatcountries are very close to their steady states. Thus, observed differences across per-capitaincomes between countries are primarily due to differences in the countries' steady states and notthe distance from the steady states. Second, various economic factors such as initial conditions,investment, population growth, human capital development, government consumption, openness,financial development, and the political environment, are found to contribute to economicgrowth. Finally, we observe that the Solow framework, both in its textbook and augmented form,is not consistent with the empirical evidence and therefore cannot account for the importantfeatures of cross-country income differences.

The rest of the paper is organized as follows. Section 2 presents the empirical model anddiscusses the two potential inconsistencies that may arise in the literature, namely the correlatedindividual effects and endogeneity of the explanatory variables, when inappropriate estimationmethods are used. We then present the general method of moments estimator, which corrects forboth inconsistencies. Section 3 summarizes the empirical results from testing the Solow modelsfor both the Africa and OECD samples. We employ our consistent generalized method ofmoments estimator, as well as three other estimators commonly used in the literature in order toidentify the magnitude of the inconsistencies resulting from their incorrect use. Section 4 extends

Mankiw et al. (1992), Barro (1991), Barro and Sala-i-Martin (1992), Sala-i-Martin (1994) are suchpapers. Rates of convergence of two (three) percent imply that a country spends 35 (23) years to cover halfof the distance between its initial position and its steady state.

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the model to incorporate endogenous growth theory considerations focusing only on the Africasample. Section 5 summarizes the main conclusions.

2. Theoretical Considerations

2.1 Model Specification

Following Mankiw et al. (1992) and consistent with the empirical literature on cross-country comparisons of economic growth we begin by assuming a Solow model with a Cobb-Douglas production function and labor-augmenting technological progress. Technology andpopulation growth rates as well as the saving rate, are constant and exogenous. Anapproximation of the behavior of a country's growth rate around the steady state is:

+f3X hWNn+g+8)+(a - j lns)

Iny-lnyo =(l-e At Ia (1)

_ lrp)h)+S In AO+gt-lnyo

An empirical counterpart of equation (1) for the i-th country in the t-th period considered in thisstudy is the dynamic equation with lagged dependent variable as a regressor, written as:

In yit = i70In yi t-r + 7 il( ni ,t + g +3 ) + 712 hi SO + i3 ln h1 , +UZq +us + vt + ±i't (2)

where Yi,, is per capita GDP in country i, period t; nit is the population growth rate; g is the rate oflabor augmenting technological change; 6 is the rate of depreciation; si,, and hi, are measures ofphysical and human capital accumulation, respectively; Zi, are other determinants of economicgrowth; ui is a country specific effect; v, is a time constant; and j,, is an overall error term.

The textbook and augmented Solow models are nested in equation (1). The elasticitiesfor the textbook and augmented Solow models may be obtained from equation (2). Further, theprediction that the elasticities sum to zero can be tested using the hypotheses Th + 72 = 0 and7), + 172 + 73 = 0 for the textbook and augmented Solow models, respectively. Finally, the speed

of convergence is obtained by l = hI +7)) and the implied physical and human capital sharest

a, and ,3, can be recovered from the estimated coefficients.

2.2 Estimation Issues

Empirical work on growth can potentially suffer from two sources of inconsistency:omitted variable bias, and endogeneity bias. First, omitted variable bias may arise when countryspecific effects which represent differences in tastes or technology, are wrongly assumed to beuncorrelated with the other regressors. It is shown that this assumption is violated due to thedynamic structure of the model. Second, there is a strong theoretical basis for a number of the

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explanatory variables to be endogenous, and failing to control for this will bias the results.2 Withthese in mind, we first describe how these biases affect cross section and panel data estimatorsand then present the generalized method of moment estimator which corrects for both of thebiases. To facilitate the discussion, rewrite equation (2) as:

hI yij, = yr In yi , + lWit + ui + VI + Ei t

where now Wi, is a vector of all determinants of economic growth, and yf - are parameters.

2.2.1 Cross-section Regressions

Pure cross section analyses give inconsistent results because they suffer from both theomitted variable and endogeneity biases. In particular, the first problem that arises in theseregressions is the country specific effect: OLS is consistent only under the assumption that theindividual country effect is assumed to be uncorrelated with the regressors.3 This assumption isclearly violated and the estimators are inconsistent, since, using (3) we can show that ui and Inyi. 1 -T

are correlated.

E[ui(In y,- )] = E [u, (In Y-2r + OWi,t-T +ui +Vt-T + • 0,since E[u ] •0

The second problem has to do with the endogeneity of a subset of the W variables. It issometimes difficult to justify why variables such as the rate of investment and the rate ofpopulation growth are not determined simultaneously with the rate of growth, and therefore,treating them as exogenous results in a bias. Despite the potential inconsistencies arising from itsuse, we apply this cross-section OLS estimation (CROSS) as one of the estimation methods toallow for comparison with results the literature and our GMM estimator.

2.2.2 Panel Data Estimators: Fixed and Random Effects

Combining cross-section and time-series data is useful for three main reasons. The use ofpanel data allows expanding the sample size, it is necessary when analyzing growth in Africabecause the growth performance of developing countries varies substantially over time, andfinally, it can improve upon the issues that cross-sectional data fail to address.

One issue that arises with the use of panel data is whether the individual effect isconsidered to be fixed or random. First, while random effects estimation addresses theendogeneity issue by instrumenting potentially endogenous variables, it also assumes that theindividual country effects are uncorrelated with the exogenous variables, an assumption, which isviolated, based on the arguments in Section 2.2.1. On the other hand, the fixed-effects methoddeals successfully with the correlated effects problem, yet it fails to account for potentialendogeneity of the regressors.4 Also, Nerlove (1996) shows that due to the dynamic character ofthe model, the parameter estimates under fixed effects estimation are inconsistent under a finitesample with the bias disappearing as t approaches infinity. In summary, both fixed and random

2 Caselli et al. (1996), and Durlauf and Quah (1998) discuss these issues in detail, so a brief summary willbe presented here.3Nerlove (1996) discusses the sign of the bias and describes estimators from other panel methods.4Islam (1995), and Knight, Loyaza, and Villanueva (1993) are examples of studies where only theindividual effects bias was addressed. Also, Barro and Sala-i-Martin (1995, Ch. 12), and Barro (1997) areexamples of studies where only the endogeneity bias was addressed.

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effects estimations address only one of the two biases, and thus give inconsistent estimates. Forcomparison with our GMM results and the rest of the literature we selected out of the panelmethods the fixed effects estimation (FIXED) and the pooled estimation (POOLED) where allcountries are restricted to have identical intercepts.5

2.2.3 A Consistent Panel Data Estimator: Generalized Method of Moments

We employ a panel data estimator that simultaneously addresses the issues ofendogeneity and omitted variable bias. The estimator is an application of the generalized methodof moments estimator (hereafter GMM) used by Caselli et al. (1996). The estimator isconstructed in two steps: first, we take first differences from the dynamic model in equation (3)which eliminates the individual effect u,; then, we instrument all the right-hand side variablesusing their lagged values. The first step eliminates the omitted variable bias, and we no longerneed to make any probabilistic assumptions on the country effect. The second step eliminates theinconsistency arising from potential endogeneity of the regressors.

The GMM estimator addresses consistently and efficiently both estimation problems, butthis consistency relies on the assumption that the lagged values of the regressors are validinstruments. Following Caselli et al. (1996) we make the following assumptions: (i) there is nof-order serial correlation, (ii) the variables measured at the beginning of the period in the vectorW, are predetermined, and (iii) the variables measured as an average of the 'r periods are notpredeternined for ei, but are predetermined for ei,t+r The implications of these assumptions canbe demonstrated by the following example: yi, o and the stock variables in Wio (those measured atthe beginning of the period) may be used as instruments for the equation Yi.2r - yR,I with yi,r -Yi,o and Wi, - Wi,o as regressors. Furthermore, in the equation Yi,T - Yi,2r we can use Yi,o the stockand flow variables in WiU0 and yi,r and the stock variables in WiT as instruments.6 The validity ofthe set of instruments is examined using the J-statistic specification test on the overidentifyingrestrictions and is discussed in the estimation section.

2.3 Data and Samples

Equation (1), which encompasses the textbook and augmented Solow modelspecifications is estimated with pooled and panel data. Annual data from the Summers andHeston data set is used, as made available by the Penn World Tables 5.6a, covering the period1960 to 1990. Two samples of countries is considered, OECD and Africa, in order to check forrobustness of our results when samples with different country characteristics are used. In order toallow comparisons with the literature, the first sample consists of the 22 OECD countries withpopulation greater than one million. The second sample consists of the 42 African countries, withthe sample size in each specification determined solely by data availability.

Switching from a single cross section to panel estimation is made possible by dividing thetotal period into shorter time spans. We focus on five-year time intervals (T = 5), so we obtain atotal of six panels: 1965, 1970, 1975, 1980, 1985, and 1990. For example, the saving andpopulation rates at t-T (say 1965) are non-overlapping averages over the five years preceding t

5 The Hausman test was run for all the estimated equations: the hypothesis that the individual effects areuncorrelated with inyit,_ is (strongly) rejected, so, E[u (0nyjt_-) ] X 0. This confirms empirically the use offixed effects (over random effects), so random effects estimation was not selected as one of the comparisonestimation methods in this paper.6 Caselli et al. (1996) describe in detail the construction of this estimator, and for the interest of brevity wewill not repeat the procedure here.

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(1960-1964). Finally, following previous studies (g+5) is set to 0.05.7 The Appendix includesthe list of countries in each of the samples, as well as variables definitions.

3. Results from the Solow Model

In order to see how our results differ from those in the literature because of differences inestimation methods, samples, and perhaps construction of variables, we first run the CROSS,POOLED, and FIXED estimators (which, as Section 2 discussed, are unreliable), and comparewith our GMM estimator. The results from testing the convergence hypothesis using the fourestimation techniques are shown in Tables 1-3. Depending on whether factors accounting fordifferences in the steady-state growth rates are included, conditional and unconditionalconvergence is tested in the textbook, and the augmented Solow model.

Approximating in a neighborhood of the steady states gives the textbook and augmentedmodels, respectively, both nested in equation (1).

nyi,, -iny, = (1-e a h){-(l-) n+g+35)+(ja frs)-InYi"_ +u2i+Ei,t (4)

-(a+# h}n+g+3)+ a h s0K) +

Iny j, - nyi, = (I - ) + ui + Ei l (5)

( hI a, rh) - In y,T

3.1 The Textbook Solow Model

Our investigation of unconditional convergence begins by reporting regressions of thechange in the log of income per capita without controlling for population growth, investment, andschool enrollment. Table I presents the results for both the Africa and OECD samples.

The results show that there is a clear tendency toward convergence in the OECD sample,with significant and negative coefficients on the initial level of income per capita, and highadjusted W2. For the Africa sample, evidence is found for unconditional convergence only withthe FIXED estimator while our GMM estimator gives non-significant results. Overall, theseresults agree with the conclusions in the literature: Mankiw et al. (1992), and Barro and Sala-i-Martin (1992) reject unconditional convergence for a diverse group of countries (includingdeveloped). However, for studies focusing on homogeneous country groups like the OECD andAfrican countries, factors such as technology, preferences, and natural resources that may accountfor discrepancies in the steady state growth rates are unlikely to be significant, and unconditionalconvergence is not rejected. In fact, Mankiw et al. (1992) and Savvides (1995) provide evidencein favor of unconditional convergence when they examine the OECD and African countries,respectively.

Adding to the list of regressors measures of the rates of investment and populationgrowth, we apply our GMM estimator first to an unrestricted and then a restricted version of (4).The first panel of Table 2 gives the results of the estimations in unrestricted form, while the

7Various researchers point out that variation of this figure does not alter the results significantly.

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second panel contains the results from the estimation after imposing the restriction that the sum ofthe coefficients of the investment and population growth is zero.8

In both samples the estimated coefficient on initial income is negative and highlysignificant, confirming the conditional convergence hypothesis. For the GMM estimator, thecoefficient on the investment rate is positive and highly significant. The estimated coefficientindicates that an increase in the investment to GDP ratio by one percent is associated with anincrease of 0.39 and 0.31 percent in the GDP growth rate for Africa and OECD respectively. Asalso predicted by the Solow model, the growth of population contributes negatively andsignificantly to the GDP growth rate: an increase in the annual growth rate of population by onepercentage point reduces GDP growth by 0.26 and 0.13 percent for Africa and OECD,respectively. Comparisons of the coefficient estimates between the Africa and OECD samplesconfirm the greater impact that physical capital accumulation and population growth have onAfrica's growth.

The rate of convergence A can be estimated from the coefficient on lagged output foreach of the estimation methods.9 Rows 6 and 11 of Table 2 report the rates of convergence forthe GMM and the other three estimation methods used in this paper, for both the Africa andOECD samples. The difference across estimation methods is striking. To identify the source ofthis difference we examine the results from the four estimation methods in Table 2. 1 0

First, our estimate of A is four times higher than the one estimated by CROSS andPOOLED methods, and two times higher than the one estimated by FIXED. Taking each of theinternediate estimates separately, we observe that the POOLED method (which essentiallyapplies least squares to a pooled regression of our panel) gives an estimate of A that is only0.0017 higher than the one found by the CROSS method; this suggests that our results are notdriven by the breaking up of the thirty year period into smaller panels. Next, the FIXED columnrepresents the estimation, which as argued in Section 2.2, treats correctly the correlated individualeffects but fails to account for the potential endogeneity in the explanatory variables. Theestimated rate of convergence is now higher than the one estimated by CROSS but still smallerthan the one estimated by GMM. The improvement over CROSS reflects the correct treatment ofthe correlated individual effect; the difference between FIXED and GMM measures the biasresulting from failing to account for endogeneity. Finally, these results show that while thecountry effect is important, the correction for endogeneity accounts for the majority of the bias.Specifically, out of the 0.068 difference between the CROSS and GMM methods, correcting forthe individual effect accounts for one-fifth while the correcting for endogeneity accounts for four-fifths of the difference."

8 The restricted version of the model was estimated for the cases where the Wald test failed to reject thehypothesis that the sum of the coefficients was zero. Henceforth, unless specifically stated, the analysis ofthe results will refer to either the restricted or the unrestricted model, depending on whether the Wald testfails to reject or rejects the relevant null hypothesis, respectively.9 Due to differences in time intervals and variable definitions in different studies, the estimated variablecoefficients are not directly comparable across studies. However, the convergence rate X can be used as anormalizing variable for comparisons with other work in the literature (see Tables 4a and 4b).10 Mankiw et al. (1992) estimate ) to be 0.0173 using cross sectional data, five times lower than our GMMestimate. The estimator using CROSS-method essentially reproduces the results of Mankiw et al. (1992):our CROSS Aestimate of 0.0217 is 0.0044 higher than the one by Mankiw et al.l l In general, estimates of the rate of convergence are not affected by the use of the restricted over theunrestricted model. This implies that the result of correcting for endogeneity and individual country effectsis robust to the model specification.

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Similar conclusions are drawn from the Africa sample results. The GMM estimate of theconvergence rate is 0.0418, which is eight and five times higher than the CROSS and POOLEDestimates, respectively, but smaller than the FIXED estimate. In the Africa case, correcting forthe individual effects accounts for a large part of the difference between the CROSS and GMM,and failing to account for endogeneity biases the convergence rate upwards.

The validity of the Solow model in both models may be tested by first, examining therestriction that the coefficients of In(s) and in(n+g+3) sum to zero, and second, estimating theimplied physical capital share, a, and observing how it compares to one-third (which is the shareof income paid to capital for most countries). For the OECD sample the Solow model is rejectedat the 0.05 level of significance; this is in contrast to results from Islam (1995), and the CROSS,POOLED, and FIXED estimates presented in this paper.'2 In contrast to the OECD results, themodel is not rejected in the Africa sample on the basis of the Wald test on the restriction, but theimplied physical capital share is 0.64, about twice the magnitude of the value of one-third.Overall, on the basis of both the specification tests of the Solow model on the Africa and OECDsamples, it is concluded that the Solow model is not adequate to describe the features of the cross-country income differences in either one of the samples.

Next, the validity of the moment restrictions in the GMM framework is checked byemploying the J-test; all the specification tests from estimating equation (4) are presented inTable 6.1 3The J-statistic and corresponding p-values reported in column 2 of Table 6 marginallyfail to reject the null hypothesis at the 0.05 level of significance. In light of these results, for boththe Africa and OECD samples, the moment conditions underlying our GMM estimator aresupported.

3.2 The Augmented Solow Model

Endogenous growth models have shown that the decision of individuals to invest inhuman capital enhances technological progress; this establishes a link between human capitalaccumulation and growth of per capita output. Human capital accumulation enhances economicgrowth because it is a direct input to research or because of positive extemalities.'4 Thus, policiesthat promote investment in hunan capital development are expected to contribute to per capitagrowth; Mankiw et al. (1992) show that this conclusion is consistent with the predictions of theclassical Solow model when the model is augmented to include human capital.

Table 3 presents results from estimating equation (5), adding the secondary schoolenrollment rate as a measure of human capital accumulation. Both restricted and unrestrictedversions of the model are examined. The coefficients on the initial income, population growth,and investment ratio remain significant for both the Africa and OECD samples. However, thehuman capital measure enters significantly only for the OECD sample. Similar studies in theliterature such as Barro (1991) estimate a positive and significant coefficient for the secondary

12 Islam (1995) performs the single cross-section, pooled regression, and fixed effects estimation methodsfor three samples of countries, among which the OECD. He fails to reject the Solow model for all fourestimates with respective p-values of 0.70, 0.90, and 0.90.13 The J-statistic can be used to test the validity of the over-identifying restrictions when there are moreinstruments than parameters to estimate. Under the null hypothesis that the over-identifying restrictions aresatisfied, the J-statistic multiplied by the number of regression observations is distributed as x2 with degreesof freedom equal to the number of over-identifying restrictions.'4 The relevant papers are by Lucas (1988), and Romer (1990).

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enrollment ratio (when examining a pool of both developed and developing countries), whileother studies, such as Romer (1989), find no significant effect for literacy rates.

This finding should not be interpreted as an indication of lack of importance of humancapital accumulation in African economic growth. The lack of significance may be attributed tocollinearity of the enrollment ratios with one of the other regressors or measurement problems.Another explanation is offered by Knight et al. (1993): they observe that enrollment ratios havetended to rise over time in developing countries while growth rates have stagnated, or in somecases fallen. Empirically, they obtain a negative (and significant) coefficient when the variablemeasuring human capital accumulation is allowed to change over time but when the temporalnature of this human capital variable is suppressed, it contributes positively to growth. 5

Inclusion of human capital raises the estimated rate of convergence for both samples.Starting with OECD, the estimated X with our GMM estimator is 0.1285, which is much higher inmagnitude than the one of Mankiw et al. (1992), and Islam (1995); comparisons of rates ofconvergence across some of the literature are summarized in Tables 4a and 4b. Next, using ourestimate from CROSS as a proxy for the estimate of Mankiw et al. (1992), we can estimate thecontribution of the omitted variable and endogeneity biases.'6 Once again, there is not much of adifference between the CROSS and the POOLED procedures, therefore, breaking up the period inpanels does not significantly affect the results. However, controlling for the omitted variable andendogeneity biases explains one-fifth and four-fifths, respectively, of the difference betweenCROSS and our GMM estimator; so the contributions of these biases remain roughly unchangedcompared to Section 3.1.

Similar conclusions are obtained for the Africa sample. The GMM estimate of theconvergence rate is 0.0501, which is about three times higher than the CROSS estimate,respectively, but (still) smaller than the FIXED estimate. The FIXED estimate of A corrects forthe individual effects and accounts for a large part of the difference between the CROSS andGMM, but fails to account for the endogeneity bias, and tends to bias the convergence rateupwards compared to GMM.

Testing the validity of the augmented model is equivalent to testing that the sum of thecoefficients on In(s), ln(n+g+35) and In(h) is equal to zero, and examining the magnitude of theestimated shares of physical and human capital, a and ,B, respectively. The bottom row of Table3 indicates that augmented Solow model is rejected for the OECD sample on the basis of theWald test on the restriction, while the model is rejected for the Africa sample on the basis of anunrealistic value for the physical capital share, and a negative value of the human capital share.

It is interesting to note that for both samples the results from the CROSS estimationindicate that the augmented Solow model is appropriate (for both Africa and OECD), and giverates of convergence in the two to three percent range, and physical capital shares in the range of30 to 40 percent (which are sufficiently close to the value of one-third). These results from theCROSS estimation method would mistakenly lead to a strong acceptance of the validity of theSolow model; however, based on the discussion in Section 2, OLS results are biased and shouldnot be trusted. Finally, just as in the case of the textbook version of the Solow model the tests of

15 For example, cross section estimation suppresses the temporal nature of the human capital variable.Indeed, as shown in Table 3, the Africa CROSS estimate gives a positive and highly significant coefficienton In(h), while all the other estimation methods which allow the variable to vary with time, giveinsignificant results.16 Mankiw et al. (1992) estimate i to be 0.0206 and our corresponding CROSS estimate is 0.0239.

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moment restrictions shown in Table 6 indicate that the moment conditions underlying our GMMestimator are robustly supported for both samples.

To reiterate, our results from Sections 2 and 3 indicate the importance of correcting forthe endogeneity and omitted variable biases. Failure to do so results in dramatic changes in theresults for both the Africa and OECD samples: the rates of convergence are four to five timeshigher for OECD and three times higher for Africa when both of these biases are eliminated.Using our GMM estimator we find that neither the textbook nor the augmented Solow model areconsistent with the data for both the OECD and Africa samples; this contradicts the results ofMankiw et al. (1992) and Islam (1995). As a result, the Solow framework is extended to allowfor a more general formulation based on the endogenous growth theory.

4. Results from the Endogenous Growth Theory

4.1 Theoretical Considerations

The obvious shortcoming of the neoclassical model is that long-run per capita growth isdetermined by the exogenous rate of technology. Work on endogenous growth theory hasintroduced alternative models that explain long-run growth, and provide a theory of technologicalprogress: growth is generated by factors other than exogenous technical change. By assumingaggregate production functions that exhibit non-decreasing returns to scale, endogenous growthmodels have provided mechanisms through which economic and social policies can affect long-run growth through their effects on human and physical capital accumulation. Recent cross-country empirical work on growth has been inspired by the neoclassical model extended toinclude government policies, human capital, and some measure of technology diffusion. Theremainder of this section reviews how macroeconomic policies and political variables influencegrowth.

Macroeconomic Stability

Researchers have identified a number of economic policies to be partially correlated withgrowth, and the role of these policies has been discussed at length in the literature.17 Briefly,macroeconomic policies affect economic growth directly through their effect on accumulation ofcapital, or indirectly through their impact on the efficiency with which the factors of productionare used. Macroeconomic stability is reflected in low and stable rate of inflation, sustainablebudget deficits and low consumption to GDP ratios, outward oriented trade policies, and soundfinancial development.

Appropriate monetary policy promotes a stable financial environment necessary foreconomic growth by maintaining a low inflation rate. High and variable rates of inflation areexpected to lower the monetary authorities' credibility and reduce the returns on private savings

1" Papers by Hadjimichael et al. (1995), Easterly et al. (1991), and Levine and Renelt (1992) who also listother relevant studies. In their paper, Levine and Renelt use Leamer's extreme bounds analysis on a largecross section of developed and developing countries, and conclude that the link between macroeconomicvariables and economic growth is quite fragile. However, the same conclusion has not been established inthe case of panel data studies. Further, some believe that the extreme bound test is too strong for anyvariable to pass it; Sala-i-Martin (1997) proposes that instead of analyzing the extreme bounds of thecoefficient estimates, one should analyze the entire distribution of the coefficient.

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and investment; thus high inflation rates are expected to decrease private investment anddomestic savings. Also, the effect of the size of the financial sector and financial policies on therate of economic growth has been examined in the literature since the seminal work of McKinnon(1973). Financial deepening lowers the cost of borrowing, increases the rate of domestic saving,and thus stimulates investment. In this study the ratio of M2 to GDP is used to test the effect offinancial development on growth.

The role of fiscal policy and the extent of government involvement in the economy havereceived a lot of attention in the growth literature. Keeping all else constant, higher budgetdeficits crowd out private investment as result of higher real interest rates. Also, governmentinvestment can be used as a proxy for government's involvement in capital accumulation, and anindicator of social infrastructure. This study uses government consumption ratio to GDP as ameasure of fiscal policy. This captures the concern of supply-side theories that highergovernment spending creates expectations of future tax liabilities and hence, distorts incentivesand lowers growth.

Finally, the proposition that more outward-oriented economies tend to grow faster hasbeen tested extensively in the literature, and the majority of the evidence tends to support thisproposition. A measure frequently used in the literature is the ratio of the sum of import andexports to GDP. However, this measure is subject to the endogeneity problem: the volume oftrade may be a consequence of the growth performance rather than a measure of how a country'sopenness contributes to its economic growth; said differently, the trade share may be jointlydetermined with economic growth rather than being an exogenous determinant of growth. In thisstudy we use the trade share growth rate as a measure of openness, which avoids the endogeneityproblem.

Economic Growth and Political Freedom

The impacts of political freedom on economic performance as well as the jointdetermination of political instability and economic growth have generated considerable interest inthe literature.'8 Some observers such as Friedman believe that the two freedoms are mutuallyreinforcing; in this view, increasing political rights promotes economic rights and thereforestimulates growth.'9 Empirically, Alesina et al. (1992), have found that political instabilityreduces growth, and Fosu (1992) constructs an index of political instability, which he shows to bea significant determinant of per capita income in sub-Saharan Africa. Further, Easterly andLevine (1997) examine the hypothesis that ethnic divisions influence economic growth. Theirrationale is that polarized societies have more difficulties agreeing on the provision of publicgoods such as infrastructure, education, and growth enhancing policies, simply becausepolarization impedes agreement between ethnic groups which engage in competitive rent-seeking.

This paper examines the hypothesis that political freedom is a significant determinant ofeconomic growth across Africa using the democracy data from PolitylIl which contains codedannual information on regime and authority characteristics for all countries covering the years1800-1998. The democracy variable measures the general openness of political institutions and itincludes considerations such as free and fair elections and decentralized political power.20

18 For example, Alesina et al. (1992), Knack and Keefer (1995).19 Barro (1997) has a chapter on The Interplay Between Economic and Political Development and arguesthat the connection between political and economic freedom is not always clear-cut.20 Refer to the Appendix for details on the construction of the index.

11

4.2 Estimating African Growth and Convergence

The results in Table 5 show the role of adding to the set of the "conventional" regressorsvarious political and policy-related variables as potential determinants of the long-run rate ofeconomic growth. Equation (2) is estimated applying our GMM estimator to a set of cross-country regressions. First, in accordance with the literature, we find that policy variables andpolitical environment matter for growth.2' Second, correcting for the endogeneity and individualeffect biases (by using the GMM estimator) changes the results concerning the speed ofconvergence: our estimated X for Africa is several times higher than the one to two percentreported in the literature. Finally, based on the Wald test results, for all specifications we rejectthe hypothesis that the sum of the coefficients of In(s), In(n+g+b) and ln(h) is zero. This isanother indication that the Solow model does not explain the features of African growth, andjustifies the need to extend the model to include endogenous theory considerations.

Columns 1-5 in Table 5 report GMM estimates for five different specifications of the22growth regressions. The first column of Table 5 adds to the augmented Solow formulation the

ratio of government to GDP and growth of openness. Both of these variables enter significantlywith the expected signs. Ceteris paribus, countries experienced faster growth rates (than others inthe sample) if their government consumption to GDP was lower, or their growth rate of trade toGDP was higher: a one percent increase in the average consumption to GDP ratio decreases thegrowth rate of per capita income by 0.71 percent, while a one percent increase in the annualgrowth rate of openness increases per capita income growth by 0.35 percent. Also, compared tothe augmented Solow model results, the coefficients for the "conventional" variables change onlyslightly in magnitude but still enter significantly, except for the human capital developmentvariable, which is still insignificant. Finally, the speed of convergence increases by roughly oneand a half percentage points reaching 6.4 percent, which is roughly four times higher than the oneestimated by the CROSS method.23 As discussed in Section 3, these differences in the estimatedrates of convergence indicate that the inconsistencies arising from the endogeneity and omittedvariable biases have strong qualitative and quantitative effects in the growth empirics.

The human capital variable, which was not significant in the first specification, isdropped in column 2. The magnitudes of the coefficients and the rate of convergence do notchange by much and the rate of convergence is slightly higher; it was decided henceforth to keepthe human capital variable out of the model. Then, the specification in column 3 investigates theimpact of the financial sector on growth. The size of the financial sector proxied by the ratio ofM2 to GDP contributes significantly to economic growth: a one percent increase in the M2 toGDP ratio raises the annual per capita GDP growth by 0.35 percent. However, the addition ofthis financial sector variable causes the population growth rate to become insignificant and, mostimportantly, the coefficient of initial income to increase dramatically; as a result, the rate ofconvergence rises to 11.6 percent.24

21 Some papers on determinants of African growth are: Easterly and Levine (1997), Ghura andHadjimichael (1996), Sachs and Warner (1997), and Savvides (1995).22 Table 6 shows the results for the specification tests for all the regressions reported in Table 5. The J-testfails to reject the validity of the overidentifying restrictions for specifications I through 5 of Table 5.23 All equations in Table 5 were estimated and the convergence rate was calculated using the CROSSmethod for comparison purposes to the GMM. The results are available from the author.24 Both the insignificance of the population variable, and the dramatic change in initial income are partlydue to the insignificance of the constant. Hence, we drop the constant for the remaining two specifications.

12

The democracy index is introduced in the last two columns of Table 5. After a briefspecification search the constant is eliminated, and we first examine the effect of the democracyindex on per capita income growth when it is added to the list of regressors of the model incolumn 3. This addition is successful, suggesting that a one percent increase in the democracyindex increases the rate of per capita growth by 0.64 percent. Also, the remaining explanatoryvariables remain significant with the exception of government consumption. This does not implythat government consumption does not affect growth. One explanation for that is that thegovernment consumption variable is sufficiently correlated with the democracy index that it losesits independent association with per capita growth in specification (4). Finally, excluding thegovernment consumption variable in the last specification, we get an estimated rate ofconvergence around 14 percent; all the explanatory variables are significant and with theexpected signs.

Overall, our results regarding the effect of policies on growth are standard. The negativesign on the initial income variable captures the idea of convergence, the positive effect ofinvestment captures the effect of savings on the steady state, the negative sign on populationgrowth captures the detrimental effect of overpopulation, government spending affects growthindirectly, the positive sign on openness underlines the effect of trade and interdependence, thepositive sign on money growth captures the effect of a healthy financial system, and finally, thepositive effect of the democracy index underlines the impact of a healthy political environment.

5. Summary and Conclusions

This paper investigates empirically the determinants of economic growth across theOECD countries and the developing countries of Africa over the period 1960-1990, with specialfocus on the issue of convergence. We have pointed out that cross-country empirical work whichfails to account for the country specific effects and endogeneity of the explanatory variablesyields inconsistent parameter estimates and rates of convergence, and we have demonstratedempirically the inconsistencies of some of those estimation methods. Our proposed panel datageneral method of moments estimator corrected for those inconsistencies that plague standardestimation techniques. Taking into account the country-specific effects, as well as potentialendogeneity produced strikingly higher rates of convergence than the ones reported in theliterature. From the theoretical viewpoint, these country-specific effects highlight the differencesin the aggregate production functions and by taking into account the country-specific effect wehave controlled for further sources of difference in the steady state levels of income.

We applied our consistent estimator to examine two formulations of the Solow model andto explore the differences between the samples for Africa and OECD. First, we concluded thatneither the textbook nor the augmented version of the Solow model is consistent with the data forboth Africa and OECD samples. Next, we found evidence that the conditional convergencehypothesis is supported for both Africa and OECD, with rates of convergence for the textbook(augmented) version of four (five) percent for Africa, and nine (thirteen) percent for OECD.These rates of convergence are several orders of magnitude higher than the two to three percentgenerally reported in the literature, although Caselli et al. (1996) do report rates of convergencearound ten percent for non-oil countries. Finally, differences in the rates of physical and humancapital development as well as population growth rates between the OECD and Africa sampleshighlighted the greater importance placed upon higher human and physical capital developmentas well as low population growth rates for the African countries.

13

Second, focusing on the Africa sample only, we presented results from extending theSolow formulation to include some policy and political variables in accordance with theendogenous growth theory. We found evidence in support of the hypothesis that Africaneconomies with higher savings rates, lower population growth rates, more outward-orientedpolicies, a faster pace of financial development, and a more democratic environment, have tendedto grow faster; there is only tentative evidence that government consumption impinges negativelyon growth. Further, the estimated rate of convergence reaches magnitudes of thirteen to fourteenpercent (which is slightly above the estimated OECD rate of convergence) indicating that onaverage, an African economy is expected to close half the distance between its initial and steadystate position in five years.

The theoretical implication of finding rates of convergence in excess of ten percent forboth African and OECD samples is that countries are very close to their steady states. First, thissuggests that variations in the per capita income levels across countries can be explainedprimarily by differences in their steady state values, not the distance from their steady states.Second, this result calls for more policy activism. Traditionally, and under the Solow frameworkwith the identical production functions setup, policies were directed to saving and labor forcegrowth rates. Allowing differences in the production function the focus is now on the factors thatmay enter into the individual country effects; empirical work using endogenous growth theoryhas extended the role of policies to bring about improvements in the components of technologyand efficiency in the economy. If we are primarily interested in convergence in the absoluteterms, namely that countries converge to the same levels of income, discovering that countries inthe world are converging at a faster rate than previously thought is of little interest if the points towhich they are converging remain different. The results of this study point towards that direction:policies can not only accelerate the pace of countries reaching their long run levels of incomes,but most importantly, they can affect the long run income levels.

A final note on Africa. In order to be successful any growth-oriented adjustment strategygetting Africa out of the "low-level equilibrium trap" needs to address a lot of challenges,including the demographic trap of population, growth, savings and poverty, the restoration peace,social and political stability, the improvement of institutions and performance, and theimprovement of human welfare. Each of these challenges involves interrelated and mutuallyreinforcing multiple factors interacting in a dynamic fashion.

The adjustment process is unlikely to be an easy one, given the declines in per capitaincomes registered during the past two decades, the existing imbalances, and the deep-rooteddevelopmental constraints that the African continent faces. The recent wave of political changeand democratization in some of leading performers in Africa together with some hopeful signs ofeconomic revival in several countries, generate some conservative optimism about the continent'sfuture. However, this optimism is moderated by the fact that these leading performers have justbegun to recover from civil wars and long periods of economic decline, and it will require solidgrowth at rates of East Asia in order to make up for the lost ground.

References

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Barro, R. (1991) "Economic Growth in a Cross Section of Countries", Quarterly Journal ofEconomics, 106 (2): 223-51.

(1997) Determinants of Economic Growth: A Cross-country Empirical Study, CambridgeMA: MIT Press.

Barro, R. and X. Sala-i-Martin (1992) "Convergence", Journal of Political Economy, 100 (2):223-51.

Barro, R. and X. Sala-i-Martin (1995) Economic Growth, New York: McGraw-Hill.

Caselli, F., G. Esquivel and F. Lefort (1996) "Reopening the Convergence Debate: A New Lookat Cross-country Growth Empirics", Journal of Economic Growth, 1 (3): 363-89.

Chamberlain, G. (1983) "Panel Data", in Z. Griliches and M. Intriligator (eds), Handbook ofEconometrics, Amsterdam: North-Holland.

Durlauf, S. and D. Quah (1998) "The New Empirics of Economic Growth", Working Paper 6422,Cambridge, MA: National Bureau of Economic Research.

Easterly, W., R. King, R. Levine and S. Rebelo (1991) "How Do National Policies Affect Long-Run Growth: A Research Agenda", Working Paper WPS 794, Washington, DC: World Bank.

Easterly, W. and R. Levine (1997) "Africa's Growth Tragedy: Policies and Ethnic Divisions",Quarterly Journal of Economics, 112 (4): 1203-50.

Fosu, A. (1993) "Effect of Export Instability on Economic Growth in Africa", Journal ofDevelopment Areas, 25 (2): 323-32.

Ghura, D. and M. Hadjimichael (1996) "Growth in Sub-Saharan Africa", International MonetaryFund Staff Papers, 43 (3): 605-34.

Greene, W. (1997) Econometric Analysis, New York: Macmillan Publishing.

Hadjimichael, M., D. Ghura, M. Muhleisen, R. Nord and M. Ucer (1995) Sub-Saharan Africa:Growth Savings and Investment, 1986-93, Occasional Paper 118, Washington, DC: InternationalMonetary Fund.

International Monetary Fund (1999) International Financial Statistics Yearbook 1999,Washington, DC: International Monetary Fund.

Islam, N. "Growth Empirics: A Panel Data Approach", Quarterly Journal of Economics, 110 (4):1127-70.

Knack, S. and P. Keefer (1995) "Institutions and Economic Performance: Cross-country TestsUsing Alternative Institutional Measures", Economics and Politics, 7 (3): 207-27.

Knight, M., N. Loyaza, and D. Villanueva (1993) "Testing the Neoclassical Theory of EconomicGrowth: A Panel Data Approach", International Monetary Fund Staff Papers, 40 (3): 5124 1.

Levine, R. and D. Renelt (1992) "A Sensitivity Analysis of Cross-country Growth Regressions",American Economic Review, 82 (4): 942-63.

Leamer, E. (1985) "Sensitivity Analyses Would Help", American Economic Review, 75 (3): 308-13.

Lucas, R. (1988) "On the Mechanics of Economic Development", Journal of MonetaryEconomics, 22 (2): 342.

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Mankiw, G., D. Romer and D. Weil (1992) "A Contribution to the Empirics of EconomicGrowth", The Quarterly Journal of Economics, 107 (2): 407-37.

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(1989) "Human Capital and Growth: Theory and Evidence" Working Paper 3173,Cambridge, MA: National Bureau of Economic Research.

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(1997) "I Just Ran Four Million Regressions", Working Paper 6252, Cambridge, MA:National Bureau of Economic Research.

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Appendix

Samples

AFRICA: Algeria, Benin, Botswana, Burkina Faso, Burundi, Cameroon, Central African Republic, Chad,Congo (former Zaire), Congo (Republic of), Egypt, Ethiopia, Gabon, Gambia, Ghana, Guinea, Ivory Coast,Kenya, Lesotho, Liberia, Madagascar, Malawi, Mali, Mauritania, Mauritius, Morocco, Mozambique, Niger,Nigeria, Rwanda, Senegal, Sierra Leone, Somalia, South Africa, Sudan, Swaziland, Tanzania, Togo,Tunisia, Zambia, Zimbabwe.

OECD: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy,Japan, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UnitedKingdom, United States of America.

Definition of variables and sources

Ln(y): Logarithm of real GDP per worker.Source: Penn World Table (Mark 5.6a).

Ln(yoJ: Logarithm of initial real GDP per worker.Source: Penn World Table (Mark 5.6a).

Ln(s): Logarithm of real investment as ratio to GDP (1985 international prices).Source: Penn World Table (Mark 5.6a).

Ln(n+g+t4: Logarithm of population annual growth rate plus 0.05.Source: Penn World Table (Mark 5.6a).

Ln(h): Logarithm of secondary education enrollment ratio.Source: World Bank, World Development Indicators.

Government: Logarithm of real government consumption as ratio to GDP (1985 international prices).Source: Penn World Table (Mark 5.6a).

Openness: Average annual rate of growth of openness where openness is the ratio of exports plusimports to GDP.Source: Penn World Table (Mark 5.6a).

M2: Ratio of M2 to GDP.Source: International Monetary Fund, International Financial Statistics.

Democracy: Index constructed additively (with scores 0-10) from the following four variables ofauthority characteristics: PARCOMP measuring the extent to which non-elites are able toaccess institutional structures for political expression, XRCOMP measuring the extent towhich executives are chosen through competitive elections, XROPEN measuring theopportunity for non-elites to attain executive office, and XCONST measuring theindependence of the chief executive.Source: Polity98 Project (data available from the Center for International Developmentand Conflict Management, University of Maryland).

TABLE 1: Unconditional Convergence in the Solow ModelSingle cross section and panel methods: Dependent variable is lnyt-lnyo

Sample: AFRICA OECDCROSS POOLED FIXED GMM CROSS POOLED FIXED GMM

Constant 0.6470 0.2015 * -0.0440 ** 5.1373 *** 1.1410 **' 0.0148 ***

(1.1011) (0.1183) (0.0199) (0.6314) (0.1106) (0.0048)ln(yo) -0.0427 -0.0206 -0.3030 **4 0.2105 -0.4660 ** -0.1052 * -0.1958 *** -0.2427 **

(0.1476) (0.0154) (0.0367) (0.2209) (0.0672) (0.0113) (0.0177) (0.0242)

R2 adjusted -0.03 0.00 0.27 0.69 0.40 0.58

ImpliedX 0.0015 0.0035 0.0602 *5* -0.0318 0.0209 ** 0.0185 * 0.0363 *** 0.0463 **

(0.0051) (0.0026) (0.0088) (0.0304) (0.0042) (0.0021) (0.0002) (0.0053)N 37 246 246 204 22 132 132 110

Notes:Three asterisks, two asterisks, and one asterisk denote statistical significance at the 0.01, 0.05, and 0.10 levels, respectively, with standard errorsin parentheses; for the convergence rate (A) the standard errors are estimated using the Delta Method.For the estimation methods: CROSS is the single cross-section, POOLED is the pooled regression, FIXED is the least squares dummy variablewith fixed effects, and GMM is the generalized method of moments.

TABLE 2: Conditional Convergence in the Solow ModelSingle cross section and panel methods: Dependent variable is lnyt-Inyo

Sample: AFRICA OECD

CROSS POOLED FIXED GMM CROSS POOLED FIXED GMM

Unrestricted

Constant 2.1520 1.1679 * -0.0177 ** 5.2607 * 1.1160 *** 0.0414 *(2.5227) (0.2274) (0.0081) (1.0927) (0.1764) (0.0050)

ln(yo) -0.1507 -0.0466 "** -0.3152 ** -0.2217 * -0.4850 *** -0.1141 *** -0.2056 *** -0.4161 ***

(0.1290) (0.0154) (0.0364) (0.0656) (0.0534) (0.0111) (0.0185) (0.0330)In(s) 0.4156 *** 0.0746 * 0.1462 *** 0.3857 *** 0.4844 0.1027 *** 0.1158 ** 0.3126

(0.1064) (0.0136) (0.0256) (0.0498) (0.1916) (0.0287) (0.0478) (0.0318)ln(n+g+8) -0.7584 -0.4491 * -0.4066 ** -0.2573 ** -0.8666 ** -0.1262 ** -0.1959 ** -0.1294 *

(1.1146) (0.1001) (0.1134) (0.1222) (0.3481) (0.0496) (0.0738) (0.0352)

R2 adjusted 0.26 0.14 0.40 0.81 0.46 0.61

Implied X 0.0054 0.0080 * 0.0631 *** 0.0418 * 0.0221 *** 0.0202 *** 0.0384 *** 0,0897 ***

(0.0051) (0.0027) (0.0088) (0.0141) (0.0035) (0.0021) (0.0039) (0.0094)

Restricted

Constant 1.4146 0.4254 *** -0.0174 ** 4.3894 * 1.0562 * 0.0307 *(0.9419) (0.1211) (0.0080) (0.5341) (0.1059) (0.0037)

ln(yo) -0.1457 -0.0494 *** -0.3444 * -0.2120 *** -0.4791 ** -0.1130 *** -0.1979 *** -0.3650 *

(0.1263) (0.0158) (0.0343) (0,0644) (0,0528) (0.0108) 0.0172 (0.0269)ln(s)-ln(n+g+o) 0.4080 * 0.0706 * 0.1587 *** 0.3769 *** 0.5829 * 0.1082 *** 0.1314 *** 0.2494 ***

(0.1023) (0.0139) (0.0253) (0.0488) (0.1578) (0.0256) (0.0457) (0.0266)

R2 adjusted 0.28 0.10 0.39 0.81 0.47 0.61

Implied a 0.7369 *** 0.5883 * 0.3154 * 0.6400 *** 0.5489 * 0.4891 *** 0.3992 *** 0.4059 *(0.0486) (0.0477) (0.0344) (0.0298) (0.0670) (0.0591) (0.0834) (0.0257)

ImpliedX 0.0052 0.0084 *** 0.0704 * 0.0397 *** 0.0217 *** 0.0200 *** 0.0367 *5* 0.0757 *(0.0049) (0.0028) (0.0073) (0.0136) (0.0034) (0.0020) (0.0036) (0.0071)

N 37 246 246 204 22 132 132 110

Wald test for restriction:p-value 0.75 0.00 0.03 0.26 0.37 0.67 0.27 0.00

Notes:Three asterisks, two asterisks, and one asterisk denote statistical significance at the 0.01, 0.05, and 0.10 levels, respectively, with standard errorsin parentheses; for the convergence rate (A), and the physical capital share (a) the standard errors are estimated using the Delta Method.For the estimation methods: CROSS is the single cross-section, POOLED is the pooled regression, FIXED is the least squares dummy variablewith fixed effects, and GMM is the generalized method of moments.

TABLE 3: Conditional Convergence in the Augmented Solow Model

Single cross section and panel methods: Dependent variable is Iny,-lny 0

Sample: AFRICA OECDCROSS POOLED FIXED GMM CROSS POOLED FIXED GMM

Unrestricted

Constant 2.7711 1.0998 *** -0.0228 4.5356 *** 1.1947 *** 0.0431 *(2.2275) (0.2675) (0.0184) (1.1306) (0.1865) (0.0041)

ln(yo) -0.3826 ** -0.0399 * -0.3458 ** -0.2734 * -0.5121 *** -0.0928 *** -0.2352 ** -0.5374 ***

(0.1339) (0.0221) (0.0443) (0.0681) (0.0535) (0.0172) (0.0362) (0.0176)

In(s) 0.2979 ** 0.0739 0.1464 *** 0.4540 0.4466 ** 0.1188 *** 0.0993 * 0.2987(0.1004) (0.0142) (0.0261) (0.0598) (0.1843) (0.0307) (0.0499) (0.0205)

ln(n+g±S) -0.5293 -0.4368 *** -0.4649 *** -0.3601 ** -0.6657 * -0.2065 * -0.2133 ** -0.0798 ***

(0.9831) (0.1065) (0.1228) (0.1077) (0.3535) (0.0573) (0.0830) (0.0088)ln(h) 0.3327 ** -0.0027 0.0162 0.0106 0.1722 -0.0463 * 0.0271 0.1286 *

(0.1020) (0.0134) (0.0146) (0.0487) (0.1037) (0.0236) (0.0370) (0.0140)

R2 adjusted 0.43 0.13 0.40 0.83 0.47 0.61

Implied X 0.0161 ** 0.0068 * 0.0707 *** 0.0532 *** 0.0239 *** 0.0162 *** 0.0447 *** 0.1285 ***

(0.0072) (0.0038) (0.0113) (0.0156) (0.0037) (0.0032) (0.0079) (0.0064)

Restricted

Constant 2.9818 *** 0.3632 * -0.0169 4.4299 0.9679 *** 0.0309 ***

(0.9517) (0.1724) (0.0151) (0.4981) (0.1443) (0.0028)In(ys) -0.3830 * -0.0411 * -0.3669 *** -0.2597 *** -0.5123 * -0.1022 *** -0.2449 *** -0.4081 ***

(0.1318) (0.0226) (0.0440) (0.0677) (0.0520) (0.0166) (0.0346) (0.0129)In(s)-In(n+g+o) 0.3006 ** 0.0696 ** 0.1599 *** 0.4489 *** 0.4551 ** 0.1315 *** 0.1088 ** 0.2066 *

(0.0954) (0.0145) (0.0258) (0.0593) (0.1607) (0.0303) (0.0488) (0.0169)In(h)-ln(n+g+o) 0.3312 ** -0.0034 0.0110 -0.0040 0.1771 * -0.0202 0.0450 0.0533 ***

(0.0995) (0.0138) (0.0147) (0.0422) (0.0899) (0.0193) (0.0315) (0.0108)

R2 adjusted 0.45 0.08 0.39 0.84 0.46 0.61

Implied x 0.2962 *** 0.6487 *** 0.2974 *c 0.6371 *** 0.3976 0.6158 *** 0.2728 *** 0.3094 ***

(0.0527) (0.0501) (0.0334) (0.0308) (0.0744) (0.0620) (0.0848) (0.0168)Implied 0.3264 *4* -0.0314 0.0205 -0.0056 0.1548 * -0.0943 0.1128 0.0797 ***

(0.0526) (0.1400) (0.0265) (0.0608) (0.0584) (0.1125) (0.0668) (0.0143)Implied 0.0161 ** 0.0070 * 0.0762 ** 0.0501 ** 0.0239 *** 0.0180 *** 0.0468 ** 0.0874 *

(0.0071) (0.0039) (0.0116) (0.0153) (0.0036) (0.0031) (0.0076) (0.0036)N 37 234 234 188 22 119 119 96

Wald test for restriction:p-value 0.92 0.00 0.01 0.39 0.92 0.06 0.36 0.00

Notes:Three asterisks, two asterisks, and one asterisk denote statistical significance at the 0.01, 0.05, and 0.10 levels, respectively, with standard errors inparentheses; for the convergence rate (A), and the physical and human capital shares (a and , ), the standard errors are estimated using the Delta NFor the estimation methods: CROSS is the single cross-section, POOLED is the pooled regression, FIXED is the least squares dummy variablewith fixed effects, and GMM is the generalized method of moments.

TABLE 4a: Comparisons with the Literature

Conditional Convergence in the Textbook Solow Model

Sample: OECD NON-OILMRW KLV CEL ISL GMM MRW KLV CEL ISL

onrestricted X 0.0173 0.1067 0.0897 0.0061 0.0626 0.1280 0.0507(0.0019) (0.0181) (0.0094) (0.0018) (0.0124) (0.0300) (0.0091)

Vald testp-value 0.9000 0.0000 0.3720 0.0110 0.7000

.estricted X 0.0926 0.0652 0.1350 0.0467(0.0157) (0.0121) (0.0550) (0.0088)

lethod Cross Fixed GMM Cross H1-matrix GMM Fixed'ountries 22 22 22 98 98 97 96r 22 110 110 98 490 382 480

TABLE 4b: Comparisons with the Literature

Conditional Convergence in the Aumnented Solow Model

Sample: OECD NON-OILMRW KLV CEL ISL GMM MRW KLV CEL ISL

Jnrestricted X 0.0203 0.0913 0.1285 0.0137 0.0391 0.0790 0.0375(0.0020) (0.0160) (0.0064) (0.0019) (0.0127) (0.0018) (0.0093)

Vald testp-value 0.4700 0.0000 0.4000 0.0000 0.4300

estricted X 0.0206 0.0142 0.0679(0.0020) (0.0019) (0.0206)

4ethod Cross Fixed GMM Cross fl-matrix GMM Fixed'ountries 22 22 22 98 98 97 79I 22 110 96 98 490 377 395

dotes:'olumns labeled MRW, KLV, CEL, ISL quote the results reported, respectively, in Mankiw et al. (1992); Knight et al. (1993); Caselli et al.1996); Islam (1995); the GMM column responds to results from this paper using the generalized method of moments estimate.he estimation methods: CROSS is the single cross-section, POOLED is the pooled regression, FIXED is the least squares dummy variable,ith fixed effects, Il-matrix is the approach originally proposed by Chamberlain (1984), and GMM is the generalized method of moments.

TABLE 5: African Economic Growth RegressionsDependent variable is lnyt-lnyo

Specification: (1) (2) (3) (4) (5)

Constant -0.0300 * 0.0000 0.0057(0.0165) (0.0067) (0.0064)

ln(yo) -0.3175 *** -0.3257 *** -0.5023 *** -0.5829 * -0.5634(0.0532) (0.0622) (0.0522) (0.0505) (0.0547)

In(s) 0.4025 *** 0.3885 *** 0.3600 *** 0.3052 *** 0.3254(0.0431) (0.0348) (0.031) (0.0320) (0.0374)

1n(n+g+5) -0.2353 ** -0.1905 * -0.1168 -0.1251 * -0.1449(0.0932) (0.1007) (0.0754) (0.0693) (0.0810)

ln(h) 0.0634(0.0426)

Government -0.0071 ** -0.0076 *** -0.0039 * -0.0021(0.0026) (0.0025) (0.0020) (0.0018)

Openness 0.0035 *** 0.0026 *** 0.0027 *** 0.0034 *** 0.0039(0.0007) (0.0007) (0.0006) (0.0005) (0.0006)

M2 0.0035 *** 0.0064 *** 0.0071(0.0012) (0.0017) (0. 0019)

Democracy Index 0.0063 *** 0.0057(0.0021) (0.0020)

lmpliedX 0.0637 *** 0.0657 *** 0.1163 *** 0.1457 *** 0.1381(0.013) (0.0154) (0.0175) (0.0202) (0.0209)

N 188 204 158 153 153

Wald test for restriction:p-value 0.02 0.03 0.00 0.00 0.01

Notes:Three asterisks, two asterisks, and one asterisk denote statistical significance at the 0.01, 0.05, and 0.10 levels,respectively, with standard errors in parentheses; for the convergence rate, the standard errors are estimatedusing the Delta Method.

TABLE 6: Specification Tests

Regressions from Tables (I)-(5) for AFRICA and OECD

Specification: Table 1 Table 2 Table 3 Table 5 (1) Table 5 (2) Table 5 (3) Table 5 (4) Table 5 (5)

OECD

Unrestricted x xRestricted

p-value 0.00 0.00

Implied a 0.41 *** 0.31 **Implied ,B 0.08 ***

J-Test 17.69 21.28 21.55p-value 0.00 0.05 0.16

Countries 22 22 22

N 110 110 96

AFRICA

Unrestricted x x x x xRestricted x x

p-value 0.26 0.39 0.02 0.03 0.00 0.00 0.01

Implied a 0.64 *** 0.64 ***Implied 3 -0.01

J-Test 14.76 20.66 20.26 29.30 32.36 25.67 29.90 26.25p-value 0.01 0.05 0.26 0.21 0.04 0.37 0.37 0.16

Countries 42 42 42 42 42 42 42 42

N 204 204 188 188 204 158 153 153

Notes:The columns correspond to the GMM regressions in Tables (1)-(5); the numbers in parentheses indicate the specificationsof Table 5.Three asterisks, two asterisks, and one asterisk denote statistical significance at the 0.01, 0.05, and 0.10 levels, respectively,with standard errors in parentheses; for the convergence rate ( X), and the physical and human capital shares (a and 1) thestandard errors are estimated using the Delta Method.