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Barro and Sala-i-Martin (1995) observe economic growth of several countries over time. A comparison of growth rates of per capita income (GDP) in 24 countries between the years 1965 and 1985 shows that the growth rates vary greatly from country to country. Some countries experience negative growth during the specified period, as low as -0.9% per capita (these countries include Mozambique, Nicaragua and several countries of Sub-Saharan Africa). In contrast, other countries in East Asia experience growth rates over +4.5%. Barro and Sala-i-Martin investigate a series of potential determining factors of these growth differences empirically. In contrast to hypotheses derived from the model, they estimate a negative impact of women’s education on growth.

The countries’ data were divided into 2 decades for the regression analysis: The first decade from 1965-1974 contains 87 countries. The second decade from 1975-1985 contains 97 countries.

The endogenous variable, the growth rate of real per capita income (GDP), is measured as the average rate for both decades (two endogenous variables: average growth rate 1965- 1974, average growth rate 1975-1985). This is how the panel data set is transformed to apply a cross country regression.

The following exogenous variables are taken into consideration as growth determinants:

• The natural logarithm of GDP per capita of the base year (represented in the regression table as log(GDP). The exogenous log(GDP) variable for the 1965-1974 growth rates as endogenous variable is the initial observation of the year 1965 of each country. The exogenous variable log(GDP) for the 1975-1985 growth rates as endogenous variable is the initial observation of the year 1975 of each country. This verifies Solow’s convergence thesis, which states that poor countries (with a limited level of per capita income) grow faster than wealthy countries. According to Solow’s growth model, it is expected that log(GDP) will have a negative correlation coefficient. Barro and Sala-i-Martin (1995) use the natural logarithm of GDP per capita in order to capture proportional rather than absolute differences in the distribution of GDP levels among countries.

• Human capital, measured on the basis of the proxy variables education and health. Life expectancy proxies health (log (life expectancy)).

Education is divided in male education and female education; The educational variables contain the number of years in primary school (years of schooling until 10 years of age), the number of years in secondary school and the number of years in higher education (male primary education, female primary education, male secondary

education, female secondary education, male higher education, female higher education).

According to the theory of Knowles et al. (2002), one can expect that human capital positively impacts growth and that women’s education has a larger impact on growth than men’s education due to higher marginal returns).5

• The ratio of education expenditures to GDP (G-educ/Y) is supposed to indicate education quality, since years of schooling only reflect the quantity of education received. This ratio is expected to impact growth positively, as according to Klasen (1999), for example, the quality of the labour force is growth stimulating.

• The ratio of government expenditures to GDP (G-cons./Y).

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depreciation among other factors makes it difficult to measure the level of physical capital and its evolution and definitions of physical capital vary widely across countries. Because the measured level education and health implicitly reflects a country’s

This ratio is expected to impact growth negatively as it is assumed – by Abu-Ghaida and Klasen (2002) for example, that income taxation in order to finance government consumption distorts household decisions.

• The relationship between investments and GDP (I/Y).

• The spread of the black market for foreign currencies as a proxy variable for market distortions (log(1+black-market premium)).

• Changes in terms of trade (growth rate terms of trade).

• Fertility rates (log(FERT)).

• The countries political instability (political instability).

The ordinary least squares method (OLS) searches for a linear estimator that best fits the empirical values by minimising the sum of residual squares:

∑

=

_ˆ

min

minQ

ε

The OLS-estimation yields a linear estimation with minimum possible variance. The OLS- estimates represent a change in the endogenous variable when a separate exogenous variable is increased, while all other exogenous variables remain constant. The estimated coefficients are not biased, consistent and efficient if the specification is correct and various assumptions of the regression model are satisfied6.

The random-effects-model is better at avoiding an omitted variable bias because unobserved exogenous variables that vary from country to country but remain constant over time are captured by an additional residual.

Another problem is that several exogenous variables, like for example those who contain information about education, risk to be correlated with one another (multicollinearity).

(

)

Cov (5.2)

with i, j = different variables

With multicollinearity, interpreting a regression coefficient is difficult, as the coefficient indicates how much the endogenous variable changes when one single exogenous variable is increased while all other exogenous variables stay constant hypothetically. If the

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classical assumptions for regression analysis with OLS are for example: the error is a random variable with a mean of zero conditional on the explanatory variables; the independent variables are error-free; the predictors are linearly independent, the errors are uncorrelated, the variance of the error is constant across observations.

exogenous variables correlate with one another, it is impossible to increase one exogenous variable while keeping the other exogenous variables constant. Consequently, it is impossible to find out which determinants causes changes in the dependent variable.

Furthermore, the variables risk following a time trend (non-stationarity). A trend correction with the help of deterministic or stochastic filters brings stationary time series data, in which all influences that come from the time trend are captured by the residual. However, this can lead to autocorrelation, which means that the residuals correlate with one another.

(

)

Cov

ε

ε

with i, j = different time periods

In this case, the estimates are on average not distorted and still consistent, but no longer efficient. Therefore, irregular residuals must be tested for their random character. This can be done with the help of autoregressive models (AR-models) that measure the interdependencies between the observations of a time series and adapt the OLS-estimator in a way that efficient parameters are obtained. When applying an AR-process, it is assumed that a series of observations yt is dependent upon its own past values. An AR-coefficient

shows to what extent the values of a time series depend on their past values.

Barro and Sala-i-Martin limit time series variations by dividing the measured time period into only two decades (1965-1975, 1975-1985). Table 1 in the appendix shows the first part of the regression results.

The results of the first column were estimated with the SUR-method (Seemingly Unrelated Regression) without taking into account potential correlation problems. This means that several equations could actually be estimated separately, yet they are estimated together (simultaneously). The SUR-method allows for the restriction that the coefficients of the two estimation equations representing both decades are identical. The information in the data is used efficiently by taking into account a possible correlation of the two residuals. The AR(1)7- correlation coefficient of the residuals is relatively small, at 0.21 (the coefficient measures the serial correlation of the second decade residual upon the first decade residual).

Now one must avoid that the exogenous variables are correlated with the residuals due to an endogenous relationship between growth and its determinants.

(

)

Cov

ε

This would lead to biased and inconsistent estimators. Therefore, an instrumental variable estimation is performed. The results are shown in column 2 of Table 1 in the appendix. An instrument that controls for endogeneity must be highly correlated with the exogenous variables and not at all with the endogenous variable. Investments in education in the 1950s can, for instance, serve as instrumental variable for the education level of 1965, because these investments directly impact the later level of education, but they can not be influenced by economic growth from 1965 on. This is why Barro and Sala-i-Martin use previous period observations (lagged variables) of exogenous variables as instruments.

Now I discuss the instrumental variable (IV) regression results in the second column. The variable log(GDP) represents per capita income of the years 1965 and 1975 (representing the first and second decade). Earlier values are used as instruments so that the income convergence rate is not overestimated.8 The correlation coefficient for log(GDP) (–0,026) accounts for the conditional convergence hypothesis: The negative coefficient shows that poor countries grow more strongly than wealthy countries and, therefore, the income levels of countries will equal over time given the hypothetical constancy of other growth factors. This means that only countries with the same characteristics in terms of education, health, government expenditure, etc., will converge in income.

The graph in figure 5 shows a simple plot of the variables income growth and income level.

If the income level was the only variable affecting income growth, there would be a positive relationship between the two variables. Hence, wealthy countries would grow faster than poor countries, which would disprove the absolute growth convergence hypothesis. Yet, when one takes into account other growth determinants, the coefficient for log(GDP) becomes negative. This means that, when given the same national structure, poor countries grow more strongly than wealthy countries (conditional convergence of income).

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Figure 5: Per capita growth rate 1965-85 against (nat. log) real per capita GDP 1965

Source: Barro and Sala-i-Martin (1995)

The coefficients of male secondary schooling and male higher education are 0.0164 and 0.050, respectively. The values in parenthesis are standard errors. The coefficient 0.0164 means that, with respect to the first decade, a rise in male secondary schooling by the extent of the standard deviation (0.68 years) increases the growth rate by 1.1 percentage points per year. This shows the following algebraric deduction:

011152 , 0 68 , 0 * 0164 , 0 68 , 0

secondaryeducation∗ = =

male

growth

δ

δ

Source: own calculation

The growth effect of an additional year of male higher education is larger than the growth effect of an additional year of male secondary schooling.

The coefficients of female secondary schooling and female higher education are, at –0.009 and –0.079, negative. The coefficient of female secondary schooling is insignificant and the coefficient of female higher education is only marginally significant, but a F-test of common significance shows a p-value of 0.007, according to Barro et al. (not shown in the table). Therefore, the coefficients of both female education variables are unequal to zero at a significance level of 1%.

The growth reducing effects of female education contradict the theoretical findings. Barro and Sala-i-Martin (1995) reason that this result emerges due to the high income level in wealthy countries. High gender differences in education can be seen as signs of economic underdevelopment and, therewith, as signs of high potential for income growth (convergence mechanism). Most wealthy countries with high income levels and low growth potential have smaller gender-specific differences in education. According to Barro and Sala-i-Martin (1995), this could be the reason why a growth regression (including growth rates instead of levels of GDP as endogenous variables) results in a negative impact of female human capital on growth.

The coefficient of government expenditures on education in relation to GDP (G-educ./Y), which represents a country’s quality of education, is also important to note. The coefficient is significantly positive, at 0.23. A country’s quality of education, therefore, promotes growth.

In column 4, primary education of men and women were added as additional exogenous variables. The variables are neither separately nor jointly significant. This closely relates to the fact that secondary and higher education produce higher growth rates than primary school. The additional variable primary schooling does not significantly change the coefficients of secondary and higher education.

The regression results in column 8 of table 2 in the appendix contain the growth effects of fertility rates. The coefficient is significantly negative. Hence, population size negatively impacts growth, which is consistent with the theory discussed by Solow (1956). The additional variable fertility does not change the coefficients of secondary and higher education significantly.

Column 20 of table 3 in the appendix shows the regression results for an estimation including dummy variables for the regions Latin America, East Asia, and Sub-Saharan Africa. Under- average growth was measured for many Latin American and African countries, and above- average growth was measured for East Asia. It could be that growth in these countries cannot be adequately described by the exogenous variables discussed above. Consequently, omitted exogenous variables would bias the estimation results.

The dummy variable regressors are significantly negative for Latin America, negative but not significant for Sub-Saharan Africa, and positive but not significant for East Asia. This means that the previous exogenous variables describe economic growth for Sub-Saharan Africa and East Asia quite well, yet they do not adequately describe Latin America’s weak growth

performance. Barro and Sala-i-Martin assume that essential aspects of Latin American politics during the 1970s and 1980s, such as corruption and a lax economic policy, are not adequately taken into account by the exogenous variables included in the regression.

Furthermore, the introduction of regional dummy variables changes several of the aforementioned regression results. What is most interesting is that the impact of female secondary schooling on growth becomes significantly positive. At the beginning of the time period measured, education was relatively uniformly distributed among women and men in Latin America compared to the other regions, and it grew little throughout the measured time period. Hence, in the regression without dummy variables, unobserved growth determinants in Latin America down biased the female education coefficients.

To conclude, the discussed regression results cannot fully describe the macroeconomic impact of women’s education, employment and income. The mostly significant negative impact of female education on growth raises questions about how data was gathered and measured, which I discuss in the next section. Nevertheless, Barro and Sala-i-Martin’s empirical results do present several important findings. The growth of a country is determined by a series of variables. One can observe that fast and slow growing countries differ mainly in terms of government consumption, as well as in terms of expenditures on education and investments.

Furthermore, the economists show that female education has a significantly negative impact on fertility and a significantly positive impact on health (regression results not shown here); these results strengthen the notion that women’s education generates growth also indirectly by affecting fertility and health. Because indirect effects are not considered in the growth regression discussed above, one can assume that the effects of female education on growth are significantly underestimated. The empirical estimates of Klasen (2002) presented in the next but one section deal with this problem.