Abstract
In this chapter, the author employs cross-national quantitative analysis to explore the relationship between modernization, globalization, democratization, and education inequality. She finds that non-democratic regimes, such as communist or authoritarian state capitalist regimes perform just as well or better than free-market democracy in predicting more equal education outcomes. Torpey-Saboe also finds that modernization is associated with lower education inequality and that the effect of globalization depends on factor abundance. Globalization is associated with higher education inequality for capital-abundant countries and lower education inequality for labor-abundant countries. Further implications of this result are explored and preliminary evidence is found for a relationship between the types of industry in a country and the gender gap in educational attainment. For example, countries with a larger clothing export industry also tend to have more equal educational attainment for women and men.
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Notes
- 1.
Capital stock is notoriously difficult to measure, particularly for developing countries. However, in the Cobb-Douglas production function: Y = AKαL1 − α, where A = Technology, K = Capital, L = Labor, and 0 < α < 1 to reflect diminishing marginal returns, GDP per worker is a function of the capital-labor ratio:
$$ y=\frac{Y}{L}=\frac{A{K}^{\alpha }{L}^{1-\alpha }}{L}=\frac{A{K}^{\alpha }}{L^{\alpha }}=A{\left(\frac{K}{L}\right)}^{\alpha }=A{k}^{\alpha } $$Although A and α differ from country to country, when I computed the capital-labor ratio using the World Bank’s measure of gross capital formation and compared this to GDP/worker, the measures were correlated at 0.96. Therefore, since data on GDP/worker was available for a much larger number of cases, this is the measure I have chosen to use.
- 2.
Failing to account for such auto-correlation or heteroskedasticity would cause the standard errors to be underestimated, possibly leading to overconfidence in the results of the model. Two methods for addressing these potential problems would be a random effects model or a fixed effects model. A fixed effects model is unbiased, but less efficient because it includes a dummy variable for each country, thus using up many degrees of freedom. The random effects model is more efficient but can lead to biased estimates if the country-level effect is correlated with any of the independent variables in the model. In order to test this, I ran both a random effects and a fixed effects model and performed a Hausman test to check for bias in the random effects model. The Hausman test indicated that the null hypothesis that the random effects estimator was consistent should be rejected: therefore, the fixed effects model, though less efficient, is preferred.
- 3.
The AIC and BIC are ways of measuring relative fit of models to a certain set of data. They are based on the likelihood theory of inference (Fisher 1925). Given a set of observed data, the likelihood function charts the relative likelihood of a particular model having produced the observed data. This likelihood changes with different parameter values (in the case of regression, with different coefficients for the independent variables). A maximum likelihood estimator chooses the parameter values that will maximize the value of the likelihood function. This maximum of the likelihood function can also be a useful number in comparing goodness of fit across models. While a higher maximum likelihood does indicate better model fit, the model selection process must also take into account the number of parameters to be estimated. This is because any model will have a higher likelihood just by adding more parameters. In the extreme example, a model that contained a parameter for every observation would be a perfect fit. AIC and BIC take this into account by adding penalties for each additional parameter. The formula for AIC is AIC = − 2 ln (L) + 2k, where L is the maximum of the likelihood function of the model and k is the number of parameters to be estimated. Thus, lower AIC indicates better model fit, and additional parameters are penalized in an additive form. BIC has an even more severe penalty for additional parameters. Its formula is BIC = − 2 ln (L) + k ∗ ln (n), where n is the sample size or number of observations.
- 4.
Sri Lanka also benefitted from the strong foundation laid by C.W.W. Kannangara, the first Minister of Education following independence, who pushed for a number of educational reforms, including free education and the expansion of secondary schools to rural areas.
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Appendix
Appendix
Full Regression Results
Regression Diagnostics
In order to further assess the robustness of my model, I run a number of post-estimation tests. To look for influential observations that could be skewing the results, I calculated the Cook’s Distance, or “Cook’s”. This measures how much parameter estimates of a model would change if a particular observation were to be dropped from the analysis. A general rule of thumb is that D values larger than 4/n are considered influential. Out of 700 observations, 40 of my observations had a value for D higher than 4/700 (approximately 0.0057). I also created added variable plots to examine which variables seemed particularly influenced by a few observations. The plots for trade openness, urban population, democracy, and the capital-labor ratio all looked fairly normal. It was only the plot for the labor-land ratio that stood out.
The United Arab Emirates, Qatar, and Kuwait all seem to be influencing the estimated relationship between education inequality and the land-labor ratio. The proper response to influential data would not be to drop the data points, since that would also cause bias, but rather to try other estimation techniques that are more robust to extreme values. One such technique is median regression. Rather than modeling the mean of y as a function of x, median regression models the median of y conditional on x. This means that it minimizes the least absolute deviations rather than the least squared errors. In other words, a median regression line is placed such that there is the same number of residuals above and below the regression line, and the magnitude of the residual does not matter, so outliers do not have the same power to pull the regression line toward themselves. Using quantile regression, it is possible to model not only the median but any quantile in order to see whether the parameter estimates are different for different quantiles. Table 5.13 shows the results of three models for different quantiles: the 25th percentile, the median, and the 75th percentile. The results are all fairly similar and consistent with my main model.
Next I checked the normality of the residuals in my main model. In a linear regression where errors are identically distributed, residuals in the middle of the domain will have higher variability than residuals for observations near the end points, since high leverage points will pull the regression line toward themselves. For this reason, studentized residuals are residuals adjusted for expected variability, depending if the observations fall in the middle of the domain or near one of the ends. The distribution of studentized residuals looked fairly normal.
Finally, I tested for heteroskedasticity, since this would be a violation of the assumption of constant variance for the errors. Scatter plots of the residuals versus the fitted values, the dependent variable, and the independent variables did not indicate any strong patterns.
Nevertheless, the Breusch-Pagan test for heteroskedasticity had a p-value of 0.000, indicating that the null hypothesis of constant variance could be rejected. Therefore, I re-ran the model with standard errors clustered by country, as seen in Table 5.14. All of the variables that were statistically significant in the original model remained so except for the percentage of the population living in urban areas.
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Torpey-Saboe, N. (2019). Education Inequality Around the World. In: Measuring Education Inequality in Developing Countries. Springer, Cham. https://doi.org/10.1007/978-3-319-90629-4_5
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DOI: https://doi.org/10.1007/978-3-319-90629-4_5
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