Microfoundations of Earnings Differences

Abstract

This paper examines how human capital-based approaches explain the distribution of earnings. It assesses traditional, quasi-experimental, and new micro-based structural models, the latter of which gets at population heterogeneity by estimating individual-specific earnings function parameters. The paper finds one’s ability to learn and one’s ability to retain knowledge are most influential in explaining earnings variations. Marketable skills actually acquired in school depend on these two types of ability. However, schools may also implement ability-enhancing interventions which can play a role in improving learning outcomes. Policy initiatives that improve these abilities would be a possible strategy to increase earnings and lower earnings disparity.

Appendix 1

Optimally producing human capital to maximize lifetime earnings entails equating the marginal costs and marginal benefits of human capital creation in each year of one’s life. This process yields a nonlinear (in the parameters) earnings function (Polachek et al. 2015)

$$ \begin{array}{*{20}l} {Y_{t} } {\quad = W^{{\frac{1}{{\left( {1 - b} \right)}}}} \left[ {\left\{ {\left( {\frac{1}{\delta } + \left( {E^{1 - b} - \frac{1}{\delta }} \right)e^{{\delta \left( {b - 1} \right)t^{*} }} } \right)^{{\frac{1}{{\left( {1 - b} \right)}}}} - \left( {\frac{1}{\delta }\left[ {\frac{b}{r + \delta }} \right]^{{\frac{b}{{\left( {1 - b} \right)}}}} } \right)e^{{\delta \left( {t^{*} - t} \right)}} } \right\}} \right.} \hfill \\ {\quad + \left\{ {\frac{1}{{\delta \left[ {\left. {\frac{b}{r + \delta }} \right]} \right.^{{\frac{b}{{\left( {1 - b} \right)}}}} \left( {1 - \frac{b\delta }{r + \delta }} \right)}}} \right\} + \left\{ {\left[ {\frac{b}{r + \delta }} \right]^{{\frac{1}{{\left( {1 - b} \right)}}}} \frac{1}{{\left( {1 - b} \right)}}e^{{\left( {r + \delta } \right)\left( {t - N} \right)}} } \right\}} \hfill \\ {\left. {\quad - \left\{ {0.5\left[ {\frac{b}{r + \delta }} \right]^{{\frac{1}{{\left( {1 - b} \right)}}}} \left( {\frac{1}{{\left( {1 - b} \right)}}} \right)\left( {\frac{b}{{\left( {1 - b} \right)}}} \right)e^{{2\left( {r + \delta } \right)\left( {t - N} \right)}} } \right\}} \right] + \epsilon_{t} } \hfill \\ \end{array} $$

(9)

where $W = \beta R^{1 - b}$, $E = \frac{{E_{0} }}{{\beta^{{\left( {\frac{1}{1 - b}} \right)}} }},$ t* is the age at which the individual graduates from school, N is the anticipated retirement age which PDT take to be 65, and E₀ is the human capital stock when training begins. To identify each parameter $b_{i} ,\beta_{i} ,E_{{0_{i} }} ,r_{i} ,\delta_{i} \,{\text{and}}\,R$, PDT adopt a two-step process. First, they estimate (9) separately for approximately 1700 individuals in the NLSY79 to obtain b, W, E, d, and r for each individual. Their dependent variable is each of 1700 individual’s weekly earnings adjusted to 1982–1984 dollars. The independent variable is each individual’s age (t). Years of completed school for each individual are denoted as t^* and remain constant throughout each person’s life because PDT’s sample omits intermittently schooled individuals.

Second, to identify $\beta_{i}$, $E_{{0_{i} }}$, and the population-wide R, PDT first specify $\beta_{i}$ to equal $\beta e_{i}$, where β is the population average and $e_{i}$ is the individual deviation. Second, they rewrite the W = βR^1–b coefficient in (9) for individual i as $W_{i} = R^{{1 - b_{i} }} \beta e_{i}$. They then take the logarithm which yields $\text{ln}\,W_{i} = \left( {1 - b_{i} } \right)\text{ln}\,R + { \ln }\beta + { \ln }\,e_{i}$ which they then estimate using each individual’s values for $\widehat{W}_{l} \,{\text{and}}\,\hat{b}_{l}$ obtained from estimating (9) above. They obtain β_i by taking the antilog_e of the sum of the latter two terms ${ \ln }\beta + { \ln }\,e_{i}$ in the above equation. Utilizing $b_{i}$ and β_i values along with the coefficient $\widehat{E}_{l} = {{E_{{0_{i} }} } \mathord{\left/ {\vphantom {{E_{{0_{i} }} } {\beta_{i}^{{1/1 - b_{i} }} }}} \right. \kern-0pt} {\beta_{i}^{{1/1 - b_{i} }} }}$ obtained from estimating (9) yields individual-specific $E_{{0_{i} }}$. The population-wide rental rate is the coefficient of $\left( {1 - b_{i} } \right)$.