Abstract
This paper explores the linkage between school quality, educational attainment and the wage gap. In a model of statistical discrimination based on both the quality and quantity of schooling, we show that lower-quality education can, on average, lead to lower human capital accumulation if agents anticipate future labor market discrimination. Because blacks in general have less access to good-quality schools compared to whites, this link provides a novel explanation for the differences in black–white educational attainment and the resulting wage gap.
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Notes
Because much of the literature on the black–white wage gap focuses on male income (to separate racial discrimination from gender-based discrimination), we refer to black and white males throughout the paper. However, as will be evident from the discussion below, the modeling framework is applicable more widely to any two groups of individuals that fit into the general story.
To eliminate concerns of units of measurement, suppose that all measurements are in terms of cost equivalence to some numeraire good, say, money.
This point addresses AC77’s critique of Phelps (1972) that assumes differences in both the mean and variance of innate ability between Blacks and Whites.
To solve this problem, we refer to the following Leibniz rule for differentiating an integral. For a well-defined function \(f(z, s_i)\), if \({\mathcal {I}}(s_i) = \int _{a(s_i)}^{b(s_i)}f(z, s_i){\mathrm{d}}z\), then
$$\begin{aligned} {\frac{{\mathrm{d}}{\mathcal {I}}}{{\mathrm{d}}s_i}} = \int _{a(s_i)}^{b(s_i)} {\frac{\partial \,f(z, s_i)}{\partial \,s_i}}{\mathrm{d}}z + f(b(s_i), s_i) {\frac{{\mathrm{d}}b}{{\mathrm{d}}s_i}} - f(a(s_i), s_i) {\frac{{\mathrm{d}}a}{{\mathrm{d}}s_i}} \end{aligned}$$Letting \(f(z, s_i) = [(1 - \gamma (\phi )){\bar{y}} + \gamma (\phi )s_i]{\mathrm{e}}^{-\theta (z-s)}\), \(a(s_i) = s + s_i\) and \(b(s_i) = \infty\),
$$\begin{aligned} {\frac{{\mathrm{d}}{\mathcal {I}}}{{\mathrm{d}}s_i}}&= \int _{s+s_i}^{\infty } \gamma (\phi ){\mathrm{e}}^{-\theta (z-s)}{\mathrm{d}}z - [(1 - \gamma (\phi )){\bar{y}} + \gamma (\phi )s_i]{\mathrm{e}}^{-\theta s_i} \\&= -\left. {\frac{\gamma (\phi )}{\theta }}{\mathrm{e}}^{-\theta (z-s)}\right| _{s+s_i}^{\infty } - [(1 - \gamma (\phi )){\bar{y}} + \gamma (\phi )s_i]{\mathrm{e}}^{-\theta s_i} \\&= {\mathrm{e}}^{-\theta s_i}\left( {\frac{\gamma (\phi )}{\theta }} - [(1 - \gamma (\phi )){\bar{y}} + \gamma (\phi )s_i]\right) \end{aligned}$$Setting equal to zero yields the interior solution (3) to the problem.
The MB is the discounted PV of increase in lifetime wages from an additional year of schooling, whereas the marginal cost is a one period opportunity cost in the form of forgone wages.
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Ramamurthy, S., Sedgley, N. A Note on School Quality, Educational Attainment and the Wage Gap. Eastern Econ J 45, 415–421 (2019). https://doi.org/10.1057/s41302-018-00132-1
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DOI: https://doi.org/10.1057/s41302-018-00132-1