augmented solow model essay, 1300 words

The augmented Solow model and the African

growth debate*

Anke E. Hoeffler

Centre for the Study of African Economies, University of Oxford

I. Introduction

Within the empirical growth literature considerable attention has been paid to

the slow growth performance of Sub-Saharan Africa. Among others Barro

(1991, 1997), Levine and Renelt (1992) and Sala-i-Martin (1997a, 1997b) find

that the coefficient on a dummy variable for African countries is negative and

significant in a number of different specifications. The significance of the

coefficient on the Africa dummy is interpreted as evidence that some

regularities are missing from the model, i.e. that these growth models cannot

fully account for Africa’s low growth performance. The aim of this paper is to

re-examine this standard result in the literature.

None of these studies control for unobserved country specific effects nor

for the endogeneity of the regressors. We note that for a dynamic panel data

model ordinary least squares (OLS) levels as well as within groups estimation

are likely to provide biased estimates. We suggest a recently developed system

generalized method of moments (GMM) estimator as our preferred estimation

method for panel growth regressions, which we find confirmed by our results.

Using these preferred estimation results we suggest a ‘two step’ procedure

to examine Africa’s growth performance. We use the preferred coefficient

estimates of the augmented Solow model obtained by system GMM estimation

as the ‘step one’ regression results and calculate the residuals. In the ‘step two

regression’ we regress these residuals on the Africa dummy. We estimate this

‘step two regression’ by OLS. These ‘step two regression’ results describe

*I would like to thank my DPhil supervisors Stephen Bond and Paul Collier for their support. Stephen O’Connell provided helpful written comments and the paper benefited from a presentation at the African Economic Research Consortium (AERC) conference 26th-27th March 1999 in Harvard, MA.

OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 64, 2 (2002) 0305-9049

135 � Blackwell Publishers Ltd, 2002. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA.

whether the Africa dummy can account for some of the variation in countries’

growth performance that is not explained by the augmented Solow model.

The paper is structured in the following way. Section II provides a brief

discussion of the (augmented) Solow model. In Section III we discuss

different estimation methods for growth regressions and present some results

in Section IV. Section V concentrates on the examination of Africa’s growth

performance. The last section concludes.

II. The Solow Model

In the Solow model growth in output per worker depends on initial output per

worker, yð0Þ, the initial level of technology, Að0Þ, the rate of technological progress, g, the savings rate, s, the growth rate of the workforce, n; the depreciation rate, d; the share of capital in output, a, and the rate of convergence to the steady state, k.1 Thus, the model predicts that a high saving rate will affect growth in output per worker positively, whereas high labour

force growth (corrected by the rate of technological progress and the rate of

depreciation) will have a negative effect on growth in output per worker. The

basic model is

ln y tð Þ � ln y 0ð Þ ¼ �ð1 � e�ktÞ ln yð0Þ þ ð1 � e�ktÞ ln Að0Þ þ gt

þ ð1 � e�ktÞ a

1 � a lnðsÞ � ð1 � e�ktÞ

a 1 � a

lnðn þ g þ dÞ

ð1Þ where yðtÞ denotes the logarithm of output per worker in period t.

In the augmented version of the Solow model investment in human capital

is an additional determinant of growth in output per worker

ln yðtÞ � ln yð0Þ ¼ �ð1 � e�wtÞ ln yð0Þ þ ð1 � e�wtÞ ln Að0Þ þ gt

þ ð1 � e�wtÞ a

1 � a � b lnðskÞ

þ ð1 � e�wtÞ b

1 � a � b lnðshÞ

� ð1 � e�wtÞ a þ b

1 � a � b lnðn þ g þ dÞ ð2Þ

where sk and sh denote the proportion of output invested in physical and human capital, respectively and w denotes the rate of convergence to the steady state.

We refer to equation (1) as the textbook Solow model and to equation (2)

as the augmented Solow model. Equations (1) and (2) have for example been

used as the framework for empirical analysis by Mankiw, Romer and Weil

1 For a detailed discussion of the Solow model please refer for example to Mankiw, Romer and

Weil (1992) and Barro and Sala-i-Martin (1997) chapter 1.

136 Bulletin

� Blackwell Publishers 2002

(1992) (henceforth MRW), Islam (1995) and Caselli, Esquivel and Lefort

(1996) (henceforth CEL). We will follow these studies and base our empirical

analysis on the same equations.

III. Methodology

Single Cross-Section Regressions

Typically the empirics of long run economic growth have been analyzed in a

cross section regression framework using average data for long periods of 25

or 30 years. MRW follow this approach, but other examples are the studies by

Barro (1991), Levine and Renelt (1992) and Sala-i-Martin (1997a, 1997b).

Their analysis is based on a regression of the following form

gi ¼ a þ byi þ cxi þ ui ð3Þ

where gi denotes the growth rate of real GDP per worker averaged over a 25 or 30 year period, yi is the initial level of real GDP per worker, ui represents an error term and i ¼ 1; . . . ; N denotes a country index. For empirical tests of the Solow model the regression includes two additional regressors, the

investment rate and population growth. However, most empirical studies are

based on more general models and include a range of other socio-economic

variables. These variables are either initial values or average values over the

time period. For the discussion of the econometric methodology it does not

make any difference whether we think of the (augmented) Solow model or

more general models and for expositional purposes we will concentrate here

on a single regressor, xi. We will not use single cross-country regressions for the analysis of the

Solow model for a number of reasons. First, reducing the time series to a single

(average) observation means that not all available information is used. Second,

it is very likely that single cross-section regressions suffer from omitted

variable bias. Third, one or more of the regressors may be endogenous. Since

single cross-section growth regressions potentially suffer from these problems

we will instead use a dynamic panel data approach. Previous papers have used

a dynamic panel data approach to address the omitted variable and/or

endogeneity issues, most notably Islam (1995) and CEL. Within the dynamic

panel data framework we concentrate on two estimators, the Arellano and

Bond (1991) first differenced generalized method of moments (DIF-GMM)

estimator and the Blundell and Bond (1998) system generalized method of

moments (SYS-GMM) estimator. Both GMM estimators address the bias

problems encountered in single cross-section regressions, because in a

dynamic panel data model we will be able to account for unobserved country

specific effects and allow for the endogeneity of one or more of the regressors.

137The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

Single cross-section growth regressions are likely to suffer from omitted

variable bias, because for example they do not allow for any difference in the

initial level of technology, Að0Þ, across countries. Thus, the error term, ui, in the single cross-country regression (3) is likely to contain unobserved country

specific effects due to the difference in initial levels of technology, Að0Þ. These unobserved country specific effects are likely to be correlated with

some of the observed regressors and in particular any permanent unobserved

influences will necessarily be correlated with the initial GDP level. Thus, the

OLS estimation of (3) is very likely to suffer from an omitted variable bias.

However, accounting for unobserved country specific effects is not possible in

the single cross-section model.

Dynamic Panel Data Analysis

An alternative approach is to exploit the time series data for each country and

consider repeated observations for shorter periods, instead of averaging over

the entire period of 25 or 30 years. This provides a panel data set for the study

of economic growth. In a panel data model we can then explicitly account for

permanent unobserved country specific effects, gi. This provides a panel data model of the form

gi;t ¼ a þ byi;t�1 þ cxit þ gi þ vit ð4Þ where t denotes points in time t ¼ 2; . . . ; T. For example git may reflect the average growth rate over a series of five year periods, with yi;t�1 being the level of income per worker at the beginning of each of these periods, and xit being measured either at the beginning of each period, or as an average over

each of the five year periods.

Since the relevant five year growth rate in (4) is the logarithmic difference

in GDP per worker, we have the following dynamic panel data model

yit � yi;t�1 ¼ a þ byi;t�1 þ cxit þ gi þ vit ð5Þ or equivalently

yit ¼ a þ b�yi;t�1 þ cxit þ gi þ vit ð6Þ where b� ¼ ðb þ 1Þ. It is important to note that the typical panel in the study of economic growth then has a small number of time series periods, i.e. T is

small. Asymptotic results discussed below focus on the case where the

number of countries N becomes large for fixed T.

OLS Levels Estimation and Within Groups Estimation

As Hsiao (1986) shows, omitting unobserved time invariant country effects

in a dynamic panel data model will cause OLS levels estimates to be biased

138 Bulletin

� Blackwell Publishers 2002

and inconsistent. The lagged dependent variable, yi;t�1, is positively correlated with the permanent effects, gi. As a result the OLS levels estimate of the coefficient bb�b� in the typical growth regression is likely to be biased upward.

2

An alternative estimation technique which takes account of the unobserved

country specific effects is the within groups estimator. For this method model

(6) is transformed by subtracting out the time series means of each variable for

each country. In this transformation process the country specific effects are

eliminated, because the country specific effects gi are invariant over time. The transformed model is then estimated by OLS.

3 However, as shown by Nickell

(1981), using the within groups estimator will also provide biased and

inconsistent estimates in a dynamic panel model with fixed T. In contrast to

the OLS levels estimation, the within groups estimate of the coefficient b� is likely to be biased downward. Consequently, the estimate bb�b� obtained from OLS levels can be regarded as an approximate upper bound on this coefficient,

and the estimate obtained from within groups estimation can be regarded as an

approximate lower bound.

General Method of Moments Estimation

In addition to these inconsistency problems one or more regressors in (6) may

be correlated with gi and/or vit. Both problems can be addressed by using a first differenced GMM estimator (Hansen (1982)). In order to obtain a

consistent estimate of b� as N�!1 for fixed T we take first differences of (6) which eliminates the country specific effects gi

4

ðyit � yi;t�1Þ ¼ b�ðyi;t�1 � yi;t�2Þ þ cðxit � xi;t�1Þ þ ðvit � vi;t�1Þ: ð7Þ Since the differenced lagged dependent variable and the differenced error term

are correlated OLS estimation of (7) will not produce a consistent estimate of

b�, even if the regressor, xi;t, is strictly exogenous. Thus, valid instruments have to be found for Dyi;t�1 ¼ ðyi;t�1 � yi;t�2Þ. Assuming that the errors are independent across countries and serially uncorrelated

EðvitvisÞ ¼ 0 for s 6¼ t and that the initial conditions satisfy

Eðyi1vitÞ ¼ 0 for t 2

2 See Hsiao (1986, pp 76–78). The sign of this bias can be derived unambiguously in cases where

there are no xit variables, or where all the variables xit are strictly exogenous with respect to (gi þ mit).

3 For further details see for example Hsiao (1986). 4 See Anderson and Hsiao (1982).

139The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

then values of yit lagged two periods or more are valid instruments in the first differenced growth equation, since yit�2 and earlier values are generally correlated with Dyi;t�1, but not with Dvit. According to these assumptions yi;t�1 is predetermined with respect to vit, i.e. shocks to GDP in one time period are not correlated with initial GDP of this time period.

If the regressor xit is strictly exogenous

EðxitvisÞ ¼ 0 for all s; t then all the past, present and future values of xit are valid instruments in each of the differenced equations, even if the xit are correlated with gi. However, there are a number of reasons to believe that some of the regressors in

empirical growth models, e.g. investment, may not be strictly exogenous.

There may be a feedback mechanism where past shocks to GDP are correlated

with current investment. Maintaining the assumption that current shocks to

GDP are uncorrelated with current investment, this means that

EðxitvisÞ 6¼ 0 for s<t and

EðxitvisÞ ¼ 0 for s t: Following Arellano and Bond (1991) we can then use values of the

predetermined xit lagged one period or more as valid instruments in the first differenced growth equation.

It is also straightforward to treat for example investment as an endogenous

variable. This means that we are allowing for correlation between current

investment and current shocks to GDP, as well as feedback from past shocks

to GDP, i.e.

EðxitvisÞ 6¼ 0 for s � t and

EðxitvisÞ ¼ 0 for s > t only. In this case, valid instruments in the differenced equations are values of the

endogenous xit lagged two periods or more. However, as Blundell and Bond (1998) show, estimators relying on lagged

levels as instruments for current differences are likely to perform poorly when

the series are close to a random walk. In this case the available instruments are

only weakly correlated with the endogenous variables, and the GMM

estimator is likely to suffer from serious finite sample bias, as well as

imprecision. Instead they suggest to estimate a system combining two sets of

equations. One set of equations are the differenced equations (7)

ðyit � yi;t�1Þ ¼ b�ðyi;t�1 � yi;t�2Þ þ cðxit � xi;t�1Þ þ ðvit � vi;t�1Þ

140 Bulletin

� Blackwell Publishers 2002

for which we use suitably lagged levels of yit and xit as instruments, as discussed for the first differenced GMM estimation. The other set of equations

in the system are the levels equations (6)

yit ¼ a þ b�yi;t�1 þ cxit þ gi þ vit:

Provided the xit regressor satisfies

EðDxitgiÞ ¼ 0 ð8Þ

and the initial conditions satisfy the restriction

EðDyi2giÞ ¼ 0 ð9Þ

we can use Dyi;t�1 and Dxit as instruments in the levels equations. 5 Estimators

of this type were proposed by Arellano and Bover (1995). Assumption (8)

allows the level of xit to be correlated with the unobserved country specific effects, gi, but requires the changes in xit to be uncorrelated with gi. This is clearly weaker than requiring the levels of xit to be uncorrelated with gi. Given (8), assumption (9) will be satisfied provided the process (6) has been

generating the yit series for a sufficiently long time – this is a kind of stationarity restriction. Alternatively, Blundell and Bond (1999) show that

sufficient conditions for (9) and (8) are for the series xit and yit to have time- invariant means.

As an empirical matter, the validity of these additional instruments can be

tested using standard Sargan tests of overidentifying restrictions, or using

Difference Sargan tests comparing first differenced GMM and system GMM

results (cf. Arellano and Bond (1991)). Exploiting the additional restrictions

(9) and (8) means that the system GMM estimator is more efficient than the

differenced GMM estimator, provided these restrictions are valid. Blundell

and Bond (1998) show that the efficiency gain can be dramatic when the series

are close to being random walks, and that the differenced GMM estimator can

also have large finite sample biases in these cases. In a model with no x variables, the differenced GMM estimate of the coefficient b� is found to be biased downward in small samples when the instruments are weak. More

generally, Blundell and Bond (2000) show that if the instruments available are

weak, the differenced GMM estimator will be biased towards the within

groups estimator.

We now turn to a brief discussion of the unobserved country specific

effects, gi. One important question is whether we have to account for these unobserved country specific effects.

5Dxit can be used if xit is strictly exogenous or predetermined with respect to vit. This should be replaced by Dxi;t�1 if xit is endogenous. The use of further lags beyond Dyi;t�1 and Dxit can be shown to be redundant, given the moment conditions E(yi;t�sDvitÞ ¼ 0 for s 2 and E(xi;t�1DvitÞ ¼ 0 for s 1 (or s 2 if xit is endogenous) that are exploited in the first differenced equations in the system.

141The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

If the unobserved country specific effects are not significant, equation (6)

becomes

yi;t ¼ a þ b�yi;t�1 þ cxit þ vit ð10Þ

and we could estimate (10) by instrumenting the endogenous regressors in the

following way. Assuming as before that the errors are serially uncorrelated

and that xit are endogenous, values of xit lagged one period or more are valid instruments for xit in the levels equations. (Since yi;t�1 are predetermined there is no need to instrument for them in the levels equations.) We refer to

this estimation method as IV levels.

In Section IV we compare the results estimating (10) by IV levels and

estimating (6) by system GMM. (10) is a restricted version of (6), because

according to model (10) all countries have the same intercept term, whereas

(6) allows the intercept to vary across countries. Thus, the comparison of the

IV levels and the system GMM results will allow us to examine whether

significant country specific effects are present. As in the case of OLS levels,

we would expect the IV levels estimate of b� to be biased upwards in the presence of significant country specific effects.

The Treatment of Time Invariant Country Characteristics

We now turn to a discussion of the inclusion of time invariant country

characteristics, such as geographic location, in these growth regressions. If we

include measured time invariant country characteristics, wi, in our analysis, the growth equation (6) becomes

yit ¼ a þ b�yi;t�1 þ cxit þ dwi þ gi þ vit: ð11Þ

Since the measured country characteristics wi may be correlated with the unobserved country specific effects and/or the error term vit we estimate the model in the following two step procedure. First, we estimate (11) without

including the measured country specific characteristics, wi

yit ¼ a þ b�yi;t�1 þ cxit þ g�i þ vit ð12Þ

where g�i ¼ dwi þ gi. 6 Using the Blundell and Bond (1998) system GMM

estimator allows us to obtain consistent estimates of the b� and c coefficients, whatever the correlation between wi and the error components. We then use these consistent estimates bb�b� and bcc to estimate the residuals of equation (12).

6 When we estimate (12), we allow both yi;t�1 and xit to be correlated with g

� i , so there is no

‘omitted variable bias’ resulting from the omission of wi.

142 Bulletin

� Blackwell Publishers 2002

In the second step we regress these residuals on the measured country

characteristics, wi 7

ðyit � baa � bb�b�yi;t�1 � bccxitÞ ¼ dwi þ ðgi þ vitÞ: ð13Þ The advantage of this two step procedure is that we obtain consistent estimates

of the b� and c coefficients. Alternatively, one could estimate equation (11) by system GMM. However, these coefficient estimates are only consistent if the

measured country characteristics, wi, are all uncorrelated with the unobserved country effects, gi. If this strong assumption is not correct this procedure would not only give biased and inconsistent estimates of the d but also for the b� and c coefficients.

OLS levels estimates of (13) will generate consistent estimates of d if and only if all wi characteristics are uncorrelated with gi. Since this is a very strong restriction we cannot attach much causal significance to the coefficient

estimate of bdd. However, the results will indicate whether observed country characteristics are correlated with variations in the unobserved country

specific effects. Due to the presence of the unobserved country specific effects,

we also expect the error term ðgi þ vitÞ of equation (13) to exhibit positive serial correlation.

IV. Testing the Augmented Solow model

Data and Sample

One important question when testing the Solow model is whether to use per

capita or per worker variables. According to the Solow model it seems more

appropriate to use per worker GDP and the growth of the workforce, because

the model is based on a production function and not every person contributes

to production. We would expect the results of growth regressions to be

sensitive to the very different dependency ratios across countries. In Sub-

Saharan African countries for example the population growth rate has been

higher than the growth of the workforce on average.

MRW use per worker variables, whereas Islam (1995) and CEL use per

capita values. We have run all regressions in per worker as well as per capita

terms. The results do not seem to be sensitive to the choice of per worker or

per capita values. 8 This somewhat surprising result may be due to the data

quality. Real GDP per capita and real GDP per worker data were obtained

from the Penn World Table Mark 5.6 (PWT 5.6). Workforce in PWT 5.6 is

defined as the working age population, i.e. the population aged 15–65.

7 Battese and Coelli (1995) and Blanchlower, Oswald and Sanfey (1996) apply a similar two-step

procedure. 8 Results for per worker values are available upon request.

143The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

Censuses are taken about every 10 years in most countries. Annual population

data are obtained by interpolation and workforce data is calculated from these

data. Workforce data are probably measured with considerable measurement

error. Since the results seem to be robust to the choice of data we decided to

concentrate on the per capita variables in order to make our results comparable

to two other panel data studies by Islam (1995) and CEL.

In the Solow model per capita income growth depends on the initial level

of per capita GDP, average savings and the average population growth rate

(adjusted for the depreciation rate and the rate of technological progress). In

the augmented version of the model a measure of schooling is added to the

textbook version.

Real GDP per capita, yit, data was obtained from PWT 5.6. RGDPCH is the preferred measure of real per capita GDP, because it is adjusted for

purchasing power parity and it is based on a chain index. Quinquennial real

per capita GDP data is used, starting in 1960, 1965, . . . and ending in 1990. Following MRW, Islam (1995) and CEL we proxy the saving rate by the

aggregate investment to GDP ratio. The data was obtained from PWT 5.6. The

time series were averaged over 1960–64, 1965–69, . . ., 1985–89.9

Population data was obtained from a World Bank source, World Data,

available on CD-ROM. It is superior to the population data reported by PWT

5.6, because there are discontinuous for a number of countries in the PWT 5.6

data series around 1970. Only for Taiwan, which is not available from the

World Bank, was PWT 5.6 population data used. Average population growth

rates were computed as the difference between the natural logarithms of total

population at the end and beginning of each period and dividing this

difference by the number of years. In this study the average population growth

rates for 1960–64, 1965–69, . . ., 1985–89 were computed.10

Like Islam (1995), MRW and CEL, technological progress and the

depreciation rate were assumed to be constant across countries and that they

sum to 0.05. The natural logarithm of the sum of population growth and 0.05

was calculated for lnðn þ g þ dÞ. Instead of proxying human capital investment using school enrolment rates

like MRW, we include a measure of the level of human capital in our

regressions. 11 Gemmell (1996) shows that proxying the level of human capital

by using school enrolment rates is problematic, because it conflates the level

and accumulation effects of human capital and leads to misinterpretations of

9 Islam (1995) averages over 1960–65, 1965–70, . . . . However, averaging over these overlapping

periods did not alter our results. 10 Again, the results remain unchanged when the average rates from 1960–65, 1965–70, . . .,

1985–90 are used. Calculating the compound growth rates also did not alter the results. 11 Please refer to MRW (p 418) for a discussion of including the level of human capital versus the

investment in human capital in the Solow model.

144 Bulletin

� Blackwell Publishers 2002

the role of the labour force growth. To avoid these problems we proxy the

level of human capital by the average years of schooling. Data collected by

Barro and Lee (1996) provides the average years of total schooling for the

population aged 15 and older. The data is provided quinquennially, starting in

1960, 1965, . . . and ending in 1990. For this study schooling data at the beginning of each five year period was used.

We do not include a proxy for the initial level of technology. In cross-

country regressions it is implicitly assumed that both the level of initial

technology and the rate of technological progress are common to all

countries. Panel data studies, such as Islam (1995) and CEL, implicitly

assume that the rate of technological progress is common to all countries,

but allow for unobserved differences in the initial level of technology. Whilst

this is a weaker restriction than that required for cross-country regressions

to yield consistent parameter estimates, we are aware that it may still be

unduly restrictive. Studies of the diffusion of new technology suggest that

diffusion is likely to be costly, and take a considerable period of time. 12 This

is indeed an important motivation for allowing initial levels of technology to

differ across countries. However, if the diffusion of new technology is not

costless and instantaneous, we may want to go further and allow for

different rates of technological progress in different countries. Nevertheless,

in the absence of reliable data on rates of technological progress, we

maintain the standard assumption of a common rate of technical change in

this study. 13

Data is available for 85 countries. 14 However, data is not available for all

countries for all of the six periods, thus, making the panel unbalanced.

Results

The Textbook Solow Model

All reported results in this section are based on the textbook Solow model as

shown by equation (1). The econometrics package used is DPD98 for Gauss

12 For example, Karshenas and Stoneman (1995) find that there are often several decades between

the first application of a new technology, and it achieving a 90 percent market penetration. 13 Freeman(1994) discusses some of the difficulties in measuring technological change.

14 The sample consists of : 22 Sub-Saharan African countries (Benin, Botswana, Cameroon,

Central African Republic, Ghana, Kenya, Liberia, Malawi, Mali, Mauritius, Mozambique, Niger, Rwanda, Senegal, Sierra Leone, Sudan, Tanzania, Togo, Uganda, Zaire, Zambia, Zimbabwe) and 63 other countries (Algeria, Egypt, South Africa, Tunisia, Canada, Costa Rica, Dominican Republic, El Salvador, Guatemala, Haiti, Honduras, Jamaica, Mexico, Nicaragua, Panama, Trinidad and Tobago, USA, Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Paraguay, Peru, Uruguay, Venezuela, Bangladesh, Burma, Hong Kong, India, Israel, Japan, Jordan, Korea Republic, Malaysia, Myanmar, Nepal, Pakistan, Philippines, Singapore, Sri Lanka, Syria, Thailand, Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK, Australia, New Zealand, Papua New Guinea).

145The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

(Arellano and Bond (1998)). All reported standard errors are corrected for

heteroskedasticity. We report the one-step parameter estimates for the GMM

estimations. For the special case of spherical disturbances, the one-step and

two-step estimators are asymptotically equivalent for the differenced GMM

estimator (Arellano and Bond, 1991). In this case the two-step estimator is

more efficient. For system GMM the two-step estimator is always more

efficient than the one-step estimator. However, Monte Carlo studies show that

the efficiency gain is small and that the two-step estimator converges only

slowly to its asymptotic distribution. In finite samples, the asymptotic standard

errors associated with the two-step GMM estimators can be seriously biased

downwards (Blundell and Bond 1998). We therefore prefer to report the one-

step estimates.

All regressions include time dummies which we found to be jointly

significant in every regression. In order to conserve space the coefficients on

the time dummies are not reported in the tables.

The left hand side variable is the change in the logarithm of real per capita

GDP. First, an OLS levels regression was run. All variables are significant at

the one percent level and have the expected sign. The negative coefficient on

initial GDP as in most published growth regressions is interpreted as

conditional convergence while investment is positive and population growth is

negative as suggested by the Solow model. The implied speed of convergence,

k, is less than one percent per annum. The results are shown in the first column of Table 1.

Second a within groups estimator was used, the results are shown in the

second column of Table 1. Comparing the estimated coefficients of the OLS

levels regression and the within groups estimation, we see that the OLS

levels regression provides a higher estimate for the coefficient on the

lagged dependent variable than the within groups estimation. These

estimates provide the approximate upper and lower bounds for the

following regressions. Since the coefficient on the lagged dependent

variable is lower than the one obtained by OLS levels, the implied speed of

convergence based on the results of the within groups estimation is much

higher than the estimate obtained from OLS levels, it is about five percent

per annum.

Column 3 presents the results using the Arellano and Bond (1991) first

differenced GMM estimator. We assume that initial GDP is predetermined and

investment is endogenous. We assume that current population growth is

exogenous, in the sense of being uncorrelated with shocks to GDP per capita

in both the current and preceding five year periods, i.e.

Eððn þ g þ dÞit; ðvit � vi;t�1ÞÞ ¼ 0

146 Bulletin

� Blackwell Publishers 2002

This allows the use of both current and lagged levels of population growth as

instruments in the first differenced equations. 15

All coefficients are statistically significant, although investment is only

significant at the eight percent level. The main problem with these results is

that the coefficient on the lagged dependent variable is very close to the within

groups estimate. Simulation results reported in Blundell and Bond (1998)

show that the first differenced GMM estimator may be subject to a large

downward finite-sample bias in autoregressive models. 16 It may be that the

presence of explanatory variables other than the lagged dependent variable,

and more particularly the inclusion of current or lagged values of these

regressors in the instrument set, will improve the behaviour of the first

differenced GMM estimator in particular applications. However, in our case

the first differenced GMM estimate seems to be downward biased, because it

is very close to the within groups estimate which is expected to be seriously

biased downwards in a panel with six or fewer time periods (Nickell (1981)).

TABLE 1

Textbook Solow Model

(1) (2) (3) (4) (5) (6)

OLS WG DIF-GMM SYS-GMM

DIF-GMM

extra instr. IV Levels

ln(yt)1) )0.038 )0.230 )0.212 )0.139 )0.156 )0.025 (0.012) (0.046) (0.084) (0.041) (0.056) (0.013)

ln(investm.) 0.107 0.183 0.152 0.249 0.197 0.082

(0.014) (0.031) (0.062) (0.041) (0.047) (0.017)

ln(n + g + d) )0.165 )0.347 )0.326 )0.411 )0.345 )0.156 (0.056) (0.106) (0.127) (0.150) (0.100) (0.059)

k 0.008 0.052 0.048 0.030 0.034 0.005 (0.002) (0.007) (0.013) (0.007) (0.011) (0.003)

m1 0.00 0.00 0.00 0.00 0.00 0.00

m2 0.13 0.82 0.91 0.96 0.96 0.15

SarganTest 0.05 0.25 0.15 0.08

Diff. Sargan 0.99 0.82

Note: Standard errors in parentheses. The figures reported for the tests for first and second order correlation (m1 and m2, respectively) as well as for the Sargan tests are the p-values of the null hypothesis, valid specification. n = 489, 85 countries.

15 This assumption is weaker than strict exogeneity, since it allows for feedback from earlier GDP

shocks onto current population growth. We assess the sensitivity of our results to alternative as- sumptions about investment and population growth. These alternative treatments are available upon request.

16 For example, with T ¼ 4 and N ¼ 100 and a true value of a ¼ 0:9, the distribution of the first

differenced GMM estimator has a mean of 0.23 (with a standard deviation of 0.83) in Table 2(a) of Blundell and Bond (1998).

147The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

Since the coefficient estimates obtained from first differenced GMM

estimation are close to the ones obtained from within groups estimation the

estimated speed of convergence is also similar to the one estimated by within

groups. The Sargan test only accepts the validity of the instrumental variable

set at the five percent level.

We suggest the use of the Blundell and Bond (1998) system GMM

estimator as an alternative to the Arellano and Bond (1991) first differenced

GMM estimator. Again treating investment as endogenous and population

growth as exogenous in the sense described above, the system GMM results

are presented in column 4 of Table 1. The coefficient on the lagged dependent

variable falls between the ‘upper and lower bounds’, and the estimated speed

of convergence is about two percent per annum. Since additional moment

restrictions are used we expect the system GMM estimation to be more

efficient; all standard errors apart from that for population growth are smaller

than the standard errors obtained from the first differenced GMM estimation.

All regressors are statistically significant at the one percent level. For the

system GMM estimates the Sargan test does not reject the validity of the

instruments, and the Difference Sargan test does not reject the validity of

the additional instruments used compared to first differenced GMM.

Thus, system GMM is our preferred estimator for the Solow model for two

reasons. The estimate of the coefficient on the lagged dependent variable is

not obviously biased, i.e. it lies well above the within groups estimate and well

TABLE 2

Augmented Solow Model

(1) (2) (3) (4) (5)

OLS WG DIF-GMM SYS-GMM IV Levels

ln(GDPt)1) )0.048 )0.231 )0.183 )0.151 )0.041 (0.014) (0.046) (0.067) (0.053) (0.014)

ln(investm.) 0.100 0.184 0.192 0.249 0.071

(0.014) (0.030) (0.056) (0.039) (0.017)

ln(n + g + d) )0.170 )0.335 )0.310 )0.419 )0.163 (0.056) (0.116) (0.136) (0.144) (0.058)

ln(schooling) 0.019 )0.015 )0.036 0.011 0.030 (0.013) (0.036) (0.045) (0.037) (0.013)

w 0.010 0.053 0.041 0.033 0.008 (0.003) (0.007) (0.011) (0.009) (0.003)

m1 0.00 0.00 0.00 0.00 0.00

m2 0.13 0.82 0.94 0.94 0.16

SarganTest 0.16 0.44 0.05

Diff. Sargan 0.96

Note: Standard errors in parentheses. The figures reported for the tests for first and second order correlation (m1 and m2, respectively) as well as for the Sargan tests are the p-values of the null hypothesis, valid specification. n = 489, 85 countries.

148 Bulletin

� Blackwell Publishers 2002

below the OLS levels estimate, and the estimates of the coefficients are more

precise than the ones obtained from first differenced GMM. The additional

instruments used by the system GMM estimator appear to be both valid and

highly informative in this context.

We suspect that the poor performance of the first differenced GMM

estimator is due to the weakness of the instrument set used. Blundell and Bond

(1998) argue that the first differenced GMM estimator is likely to perform

poorly when the series are close to random walks. Lagged levels are then

weak instruments for current differences. We consider strengthening the

instrument set used by the basic first differenced GMM estimator by including

a measure of human capital.

The endogenous growth model as discussed by Romer (1990) provides a

theoretical basis for this choice of additional instruments. In his endogenous

growth model human capital is a key input in the research sector which

generates new designs and these in turn generate new investment opportun-

ities. Based on this assumption we add lagged values of the average years of

schooling to the basic instrumental variable set.

The results using this augmented instrumental variable set are shown in

column 5. The Difference Sargan test does not reject the validity of the

schooling variable as additional instruments. Notice that, compared to the

basic first differenced GMM results, all three coefficients move towards our

preferred system GMM estimates. Most importantly, the coefficient on the

lagged dependent variable now lies well above the corresponding within

groups estimate, and is not significantly different from the system GMM

estimate. 17 Investment, which was only significant at the eight percent level in

the basic differenced GMM results, becomes significant at the one percent

level when we include our schooling measure as an additional instrument. As

we will show in the next section when testing the augmented Solow model,

including the average years of schooling as a regressor turns out to be

insignificant in most regressions. However, although schooling is insignificant

as a regressor, including it in the instrument set appears to strengthen the

instrument set significantly.

In column 6 we present the results from the IV levels estimation. The

results are similar to OLS levels, and in particular the coefficient on initial

income is significantly higher than the system GMM estimate. 18

Both IV

levels and OLS levels estimates of this coefficient would be biased upwards

17 When conducting a Hausman test the test statistic is 0.93�N(0,1), thus the coefficient estimates

obtained from system GMM and the first differenced GMM estimation including extra instruments are not significantly different at conventional levels.

18 Using a Hausman test we find that the test statistic is 2.01 �N(0,1). Thus, it rejects the extra

moment conditions used by the levels estimator, compared to the system GMM estimator. In other words it rejects the null hypothesis that there are no unobserved country specific effects. Note that this is consistent with the Sargan test for the IV levels estimator.

149The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

by unobserved country specific effects. Thus, we interpret this as evidence for

the presence of significant unobserved country specific effects which requires

estimation techniques which correctly account for these effects. According to

the Sargan test, the validity of the instruments can only be accepted at the

eight percent level for the IV levels estimator.

Our preferred method of estimation, using the Blundell and Bond (1998)

system estimator, only provides consistent estimates if there is no serial

correlation in the shocks, vit. Thus, we test for second order serial correlation in the first differenced residuals.

19 The hypothesis of no second order serial

correlation in the first differenced residuals is not rejected for any of the GMM

estimations.

However, for the OLS level estimation as well as for the IV levels

estimation we find strong evidence of positive first order serial correlation in

the levels residuals, and weaker evidence of higher order serial correlation. We

interpret this as further evidence that the error term contains unobserved

country specific effects, which causes the levels residuals to be serially

correlated.

The Augmented Solow Model

In this section we present the results obtained from testing the augmented

Solow model as described in equation (2). The dependent variable is the

change in the logarithm of real per capita GDP. It is regressed on the logarithm

of initial GDP, the investment to GDP ratio, the population growth rate and the

average years of schooling measured at the beginning of the period. Thus, we

treat schooling as predetermined.

First, an OLS levels regression was run, the results are reported in column

1 of Table 2. As before for the textbook Solow model, the coefficients on all

variables are statistically significant and of the expected sign. However, the

schooling measure is only significant at the 10 percent level. The estimated

speed of convergence, w, is about one percent. Second, a within groups estimator was used, the results are shown in the

second column of Table 2. Schooling is no longer significant. As before the

OLS levels regression provides the approximate upper bound and the within

groups estimation provides the approximate lower bound for the coefficient on

the lagged dependent variable for the following regressions.

Column 3 presents the results using the Arellano and Bond (1991) first

differenced GMM estimator, assuming that initial GDP and schooling are

predetermined, that investment is endogenous and population growth is

19 Please refer to Arellano and Bond (1991). They present a discussion of the test statistic for serial

correlation which we report in the tables, it is asymptotically normally distributed. For the OLS levels estimates the serial correlation test tests whether the level of the error terms are uncorrelated, whereas for the GMM estimates, they test whether the first differences of the error terms are uncorrelated.

150 Bulletin

� Blackwell Publishers 2002

exogenous. Here the estimate of the coefficient on the lagged dependent

variable falls between the OLS levels and within groups estimates, although it

is not significantly different from the within groups estimate. Schooling is

again not statistically significant.

Using the system GMM estimator the estimate of the coefficient of the

lagged dependent variable falls between the ‘upper and lower bounds’. The

results are reported in column 4. Schooling is the only variable that is not

significant. Again the coefficient estimates are generally more precise than the

differenced GMM estimates, and neither the Sargan test nor the Difference

Sargan test reject the validity of the additional instruments used.

In the last column of Table 2 we present the IV levels estimates. 20 The

coefficient on the lagged dependent variable is again close to the OLS levels

estimate, and higher than the corresponding system GMM estimate. 21 This is

consistent with an upward bias, caused by not taking the unobserved country

specific effects into account. Like in the OLS levels results we detect

significant first order serial correlation in the levels residuals, which we

interpret as further evidence for the presence of unobserved country specific

effects. The Sargan test also rejects the validity of the levels IV instrument set

at the five percent level.

The coefficient on initial GDP is significantly negative in all five

regressions, confirming the so-called ‘conditional convergence’ hypothesis, a

standard result in cross-country growth regressions. Investment is highly

significant in all five regressions, even though investment is treated as

endogenous in the differenced and system GMM results, as well as in the IV

levels estimation. The coefficient on population growth is significantly

negative in all regressions. Schooling is statistically significant only in the

OLS levels regression and in the IV levels results; it is not statistically

significant in any of the results that control for unobserved country specific

effects. However, a number of studies have found that the partial correlation

between schooling and growth is not robust. 22

The Sargan test of

overidentifying restrictions does not reject the instrument set used in the

first differenced GMM and system GMM results. Moreover, the Difference

Sargan test does not reject the use of the additional instruments in the system

GMM estimation in comparison to the differenced GMM estimation. Again

the system GMM estimator gives our preferred results. However, it is

noticeable that the differences between the first differenced GMM results and

20 Notice that in the IV levels results reported here, we have used a reduced number of instruments,

rather than all the available lags. However, we found that this increased the power of the Sargan test to detect misspecification, but had very little impact on the estimated coefficients.

21 When conducting a Hausman test the test statistic is 1.57�N(0,1), thus the coefficient estimates

obtained from system GMM and IV levels estimation are not significantly different at the 10 percent level.

22 See for example Pritchett (2001).

151The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

the system GMM results are smaller here than they were for the textbook

Solow model. Although schooling is not significant once we control for

unobserved country specific effects, adding schooling to the instrument set

used by the first differenced GMM estimator seems to strengthen the

instrument set significantly. Indeed it was this observation that led us to

consider using schooling as an additional instrument when estimating the

textbook Solow model.

V. Can the augmented Solow model account for Africa’s low growth performance?

A number of growth studies, for example Barro (1991, 1997), Levine and

Renelt (1992) and Sala-i-Martin (1997a, 1997b), examine whether certain

regions experienced significantly different growth rates from the rest of the

world. These studies include regional dummies in their single cross-country

growth regressions, which take a value of one if the country is located in the

particular region and zero otherwise. In a Barro growth regression, a

significant coefficient on a regional dummy means that this region’s growth

performance on average was significantly different from the rest of the

World’s during the sample period, after accounting for the effects of the

included regressors. Thus, a significant coefficient on a regional dummy

indicates that some regularities are missing from the model to explain the

difference in regional growth, i.e. these regressions are not able to explain why

these regions’ growth rates have been different. Common findings are that

countries in Sub-Saharan Africa and Latin America experienced on average

lower growth rates, while East Asian countries experienced higher growth

rates. However, in this paper we want to concentrate on the analysis of

Africa’s growth experience.

Africa’s low growth performance and possible explanations have attracted

considerable attention in the literature. 23 There are two major studies in which

the Africa dummy is not significant. In Easterly’s and Levine’s (1997, 1998)

core growth regression the Africa dummy is negative and significant, however

adding the average growth rate of the country’s neighbours (weighted by their

GDP) makes the Africa dummy insignificant. Furthermore, the study finds that

neighbourhood spillovers magnify the effects from bad policies, such as high

23 One potentially important question is whether the conventionally used empirical growth models

are really adequate to explain Africa’s growth, or whether Africa is just too different from other regions and thus Africa specific models should be analyzed. Savvides (1995), Ojo and Oshikoya (1995) as well as Hadijmichael et al. (1995) use commonly used specifications of growth models in order to examine Africa’s growth performance. Rather than using a global sample they only include African countries in their studies. Their analyses show that the commonly found results, for example conditional convergence and a strong positive effect of investment on growth, hold for this reduced sample. We interpret this as evidence that there is no need to concentrate on an Africa specific model.

152 Bulletin

� Blackwell Publishers 2002

government deficits, repressed financial markets, distorted exchange rates and

political instability. However, why these neighbourhood spillovers matter is

not clear. The study suggests that since adaptation of technology to a local

environment is risky, a foreign direct investor may find it easier to invest in a

neighbouring country if the investment was successful in the first country. A

neighbours’ success may also have demonstration effects and reputation

effects. However, trade does not appear to be the channel for spillover effects.

Using trade weights Easterly and Levine found the spillover variable to be

insignificant. Although the Africa dummy is insignificant in their study we

remain sceptical as to how far the inclusion of a neighbourhood spillover

effect really explains Africa’s growth performance, because a neighbourhood

variable is very similar to the concept of a regional dummy, i.e. for each

African country, the neighbours will be other slow growing African countries.

Sachs and Warner (1997) pursue a different approach in their examination

of the African growth performance. They specify essentially a neo-classical

model and add their openness to international trade measure and a number of

geographical variables, such as a landlocked dummy and a tropical climate

dummy. The model is a single cross-country growth regression and the

estimation method is OLS. An Africa dummy is added to the core model and

found to be insignificant. Thus, Sachs and Warner suggest that poor policies,

most importantly lack of openness to international trade, as well as

geographical factors such as tropical climate and being landlocked are the

key variables in explaining Africa’s poor growth performance. However, we

will show that once we allow for unobserved country specific effects in

estimation, the Africa dummy is found to be insignificant even in a basic

augmented Solow growth model.

Before turning to our regression results we present some descriptive

statistics for our panel data set by region. As can be seen from Table 3 Sub-

Saharan Africa (SSA) experienced comparatively low growth rates per annum

(0.56%).

Turning to the explanatory variables we see that the average initial income

per capita for Sub-Saharan African countries was very low, only about 37

percent of the average initial income per capita. Thus, according to the

conditional convergence hypothesis African countries should have experi-

enced higher than average growth rates, ceteris paribus. However, on average

Sub-Saharan African countries invested less of their GDP (9.75%) than the

average country (17.08%), they had higher population growth (2.78%) than

the average country (2.07%) and much lower initial schooling (1.27 years)

than the average country (3.47 years). These differences should account for

some of Africa’s low growth performance.

We now turn to our regression results. First, we include a dummy variable

for African economies in the augmented Solow model. The dummy takes the

153The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

value of one if the country is located in Sub-Saharan Africa, and zero

otherwise. We first estimate this model by OLS levels, the results are

presented in the first column of Table 4.

The coefficient on the Africa dummy is significant and negative. This

confirms the commonly found result in the literature when unobserved country

specific effects and endogeneity are not accounted for, i.e. the Solow growth

model appears to be unable to account for the growth experience of African

economies.

Note however that we find significant positive autocorrelation in the

residuals from the OLS regression. This is consistent with the presence of

unobserved country specific effects which are not accounted for in the OLS

regression.

TABLE 4

Africa’s Low Growth Performance

(1) (2) (3)

OLS SYS-GMM Step 2

ln yt)1 )0.058 )0.151 (0.013) (0.053)

ln (inv) 0.095 0.249

(0.015) (0.039)

ln (n + g + d) )0.178 )0.419 (0.055) (0.144)

ln (schooling) 0.017 0.011

(0.012) (0.037)

SSA )0.049 )0.023 (0.025) (0.035)

m1 3.46 )4.37 4.81 m2 1.39 )0.08 4.15

Note: Standard errors in parentheses. The figures reported for the tests for first and second order correlation (m1 and m2, respectively) as well as for the Sargan tests are the p-values of the null hypothesis, valid specification. n = 489, 85 countries

TABLE 3

Descriptive Statistics

Sample OECD non-OECD SSA

per capita GDP growth* 1.93 2.93 1.57 0.56

real GDP per capita (US$)** 2550 5592 1487 835

investment to GDP ratio* 17.08 26.01 13.78 9.75

population growth* 2.07 0.77 2.55 2.78

initial total years of schooling** 3.47 6.56 2.39 1.27

number of countries 85 22 63 22

Notes: * indicates annual averages given in percent, ** measured for the earliest available year, for most countries in 1960

154 Bulletin

� Blackwell Publishers 2002

Since the OLS estimates suffer from fixed effects and endogeneity biases

we now use our preferred ‘two step estimation’ procedure to estimate the

coefficient on the Africa dummy. We use the consistent coefficient estimates

from system GMM estimation of the augmented Solow model to calculate the

residuals of this growth regression. For convenience we repeat the system

GMM coefficient estimates in Table 4, column 2. 24 Notice that the effects of

investment and population growth are found to be substantially higher in these

system GMM results. We then regress these residuals on the Africa dummy,

the results are presented in column 3. We find that the coefficient on the Africa

dummy is insignificant.

Thus, the Africa dummy is not required to account for the variations in

growth rates once we control for the presence of unobserved country specific

effects in estimating the model. This suggests that the augmented Solow

model can account for the difference in the growth performance experienced

by the African countries. Given our preferred coefficient estimates, the low

investment ratios and high population growth rates of the African countries

are sufficient to explain their slow growth of income per capita.

VI. Conclusion

In this paper we addressed the question whether Africa’s growth performance

can be accounted for in the framework of the augmented Solow model. First,

we presented a detailed methodological examination of empirical growth

models with unobserved country specific effects and a small number of time

periods. Based on the knowledge of the likely direction of the bias in OLS as

well as within groups estimation in dynamic panel data we established

approximate upper and lower bounds for the estimated coefficient on the

lagged dependent variable in growth regressions. Using first differenced

GMM estimation we found that the estimated coefficient on the lagged

dependent variable appeared to be biased downward. We suggest that the first

differenced GMM estimator is likely to perform poorly when the series are

persistent and the number of time series observations is small, because past

levels of the series provide weak instruments for the variables in first

differences. However, a system GMM estimator (using not only lagged levels

of the series as instruments in the first differenced equation, but also lagged

differences of the series as instruments in the levels equation) was shown to be

the preferred method, since it produced more precise and more reasonable

coefficient estimates than the estimates obtained from differenced GMM. The

additional instruments used by the system GMM estimator were not rejected,

and were found to be highly informative in these empirical growth models.

24 These are the same estimates as in Table 4.2, column 4.

155The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

We then applied our preferred method of estimation to the question

whether the augmented Solow model can account for Africa’s growth

experience. The commonly found result in the literature, that basic growth

models are unable to account for Africa’s low growth performance, was

only supported by our OLS levels estimation. However, when we account

for unobserved country specific effects and endogeneity using our ‘two step

regression’ procedure, we cannot confirm this result. In the ‘first step’ of

our estimation procedure, we use the preferred system GMM coefficient

estimates of the augmented Solow model in order to calculate the residuals.

In the ‘step two regression’ we investigate whether the Africa dummy can

account for some of the variation in these growth regression residuals. We

find that the coefficient on the Africa dummy is insignificant. This suggests

that the augmented Solow model can fully account for Sub-Saharan

Africa’s low growth performance provided we account for unobserved

country specific effects and for the endogeneity of investment in

estimation.

These results indicate that there is no systematic unobserved difference

between African and non-African countries. Hence, rather than concentrating

research efforts on the analysis of a spurious Africa dummy, it may be more

worthwhile to focus on the continent’s low investment ratios and high

population growth rates, which we found to be sufficient to explain Africa’s

low growth rates.

Descriptive statistics indicate that Africa is the region with the highest

population growth rate. As a result there is nearly one dependent per

potential worker aged between 15 and 64, most of them young. This

population structure severely limits African countries’ potential to increase

their saving rates. A number of studies suggest that one of the key

determinant of population growth is female education (e.g. World Bank

2000). However, in Africa women’s education increased only very little over

the past decades. In addition, comprehensive economic policy reforms have

to take place in order to increase domestic as well as foreign investment.

Collier and Gunning (1999) discuss a typology of possible causes of slow

African growth. They conclude that although geographic characteristics

adversely affect Africa’s economic performance poor policies are mainly to

blame for Africa’s growth tragedy. It is thus not destiny which determined

Africa’s growth during the past 30 years but policy failures. Unless policies

are changed to provide the right incentives for an increase in investment and

a reduction in population growth African income growth rates will remain

low and the poorest region will be unable to catch up with the rest of the

world.

Final Manuscript received September 2001.

156 Bulletin

� Blackwell Publishers 2002

References

Anderson, T. W. and Hsiao, C. (1982). Formulation and Estimation of Dynamic Models

Using Panel Data, Journal of Econometrics, Vol. 18, pp. 47–82.

Arellano, M. and Bond, S. (1998). Dynamic Panel Data Estimation Using DPD98 for

GAUSS: A Guide for Users, Institute for Fiscal Studies, London, Working Paper No 88/15.

Arellano, M. and Bond, S. (1991). Some Tests of Specification for Panel Data: Monte Carlo

Evidence and an Application to Employment Equations, Review of Economic Studies, Vol.

58, pp. 277–97.

Arellano, M. and Bover, O. (1995). Another Look at the Instrumental Variable Estimation of

Error-Components Models, Journal of Econometrics, Vol. 68, pp. 29–52.

Barro, R. J. (1991) Economic Growth in a Cross Section of Countries, The Quarterly Journal

of Economics, Vol. 106, pp. 407–43.

Barro, R. J. (1997). Determinants of Economic Growth (MIT Press, Cambridge, MA).

Barro, R. J. and Lee, J. W. (1996). International Measures of Schooling Years and Schooling

Quality, American Economic Review, Papers and Proceedings, Vol. 86, pp. 218–23.

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

Battese, G. E. and Coelli, T. J. (1995). A Model for Technical Inefficiency Effects in a

Stochastic Frontier Production Function for Panel Data. Empirical Economics, Vol. 20,

pp. 325–32.

Blanchflower, D. G., Oswald, A. J. and Sanfey P. (1996). Wages, Profits, and Rent-Sharing.

The Quarterly Journal of Economics, Vol 111, pp. 227–51.

Blundell, R. and Bond, S. (1998). Initial Conditions and Moment Restrictions in Dynamic

Panel Data Models, Journal of Econometrics, Vol. 87, pp. 115–43.

Blundell, R. and Bond, S. (2000). GMM Estimation with Persistent Panel Data: An Appli-

cation to Production Functions, Econometric Reviews Vol. 19, pp. 321–40.

Caselli, F., Esquivel, G. and Lefort, F.(1996). Reopening the Convergence Debate: A New

Look at Cross-Country Growth Empirics, Journal of Economic Growth, Vol. 1, pp. 363–89.

Collier, P. and Gunning, J. W. (1999). Why Has Africa Grown Slowly? Journal of Economic

Perspectives, Vol 13, pp. 3–22.

Easterly, W. and Levine, R. (1997). Africa’s Growth Tragedy: Politics and Ethnic Divisions,

The Quarterly Journal of Economics, Vol. 112, pp. 1203–50.

Easterly, W. and Levine, R. (1998). Troubles with the Neighbours: Africa’s Problem, Africa’s

Opportunity, Journal of African Economies, Vol. 7, pp. 120–42.

Freeman, C. (1994). The Economics of Technical Change, Cambridge Journal of Economics,

Vol. 18, pp. 463–514.

Gemmell, N. (1996). Evaluating the Impacts of Human Capital Stocks and Accumulation on

Economic Growth: Some New Evidence, Bulletin, Vol. 58, pp. 9–28.

Hadjimichael, M. T., Dhaneshwar, G. Mühleisen, M. Nord, R. and Ucer M. E. (1995). Sub-

Saharan Africa: Growth, Savings, and Investment (1986–93, IMF Occasional Paper No

118, January 1995, Washington.

Hansen, L.P. (1982). Large Sample Properties of Generalised Method of Moment Estimators,

Econometrica, Vol. 50, pp. 1029–54.

Hsiao, C. (1986). Analysis of Panel Data (Cambridge University Press, Cambridge, MA).

Islam, N. (1995). Growth Empirics: A Panel Data Approach. The Quarterly Journal of

Economics, Vol. 110, pp. 1127–70.

Kershenas, M. and Stoneman, P. (1995). Technological Diffusion, in Stoneman, P. (ed):

Handbook of the Economics of Innovation and Technological Change, Blackwell, Oxford

pp. 265–97.

157The augmented Solow model and the African growth debate

� Blackwell Publishers 2002

Levine, R. and Renelt, D. (1992). A Sensitivity Analysis of Cross-Country Growth

Regressions, American Economic Review, Vol. 82, pp. 942–63.

Mankiw, G. N., Romer, D. and Weil D. N. (1992). A Contribution to the Empirics of

Economic Growth, The Quarterly Journal of Economics, Vol. 107, pp. 407–37.

Nickell, S. (1981). Biases in Dynamic Models with Fixed Effects, Econometrica, Vol. 49,

pp. 1417–26.

Ojo, O. and Oshikoya, T. (1995). Determinants of Long-Term Growth: Some African Results,

Journal of African Economies, Vol. 4, pp. 163–91.

Pritchett, L. (2001). Where Has All the Education Gone? World Bank Economic Review,

Vol. 15, pp. 367–91.

Romer, P. M. (1990). Human Capital and Growth: Theory and Evidence, Carnegie-Rochester

Conference Series on Public Policy, Vol. 32, pp. 251–86.

Sachs, J. D. and Warner, A. M. (1997). Sources of Slow Growth in African Economies,

Journal of African Economies, Vol. 6, pp. 335–76.

Sala-i-Martin, X. (1997a). I Just Ran Four Million Regressions, Columbia University, mimeo.

Sala-i-Martin, X. (1997b). I Just Ran Two Million Regressions, American Economic Review,

Vol. 87, pp. 178–83.

Savvides, A. (1995). Economic Growth in Africa, World Development, Vol. 23, pp. 449–58.

The World Bank (2000). Can Africa Claim the 21st Century? Washington D.C.: The World

Bank.

158 Bulletin

� Blackwell Publishers 2002