Table 5.

Predictable Heterogeneity

A. Gini Decomposition
	NLS/66	NLSY/79	% Growth
Factual Economy: Predictable Heterogeneity and Uncertainty1	0.1803	0.2088	15.85%
Counterfactual: Predictable Fixing Schooling Choices as in Factual Economy Predictable Heterogeneity Only2	0.1591	0.1825	14.73%
B. The Theil Entropy Index T (Overall)
	NLS/66	NLSY/79	% Growth
Factual Economy: Predictable Heterogeneity and Uncertainty1	0.0502	0.0693	37.98%
Counterfactual: Fixing Schooling Choices as in Factual Economy Predictable Heterogeneity Only2	0.0390	0.0522	33.76%
Within Schooling Groups
	NLS/66	NLSY/79	% Change
Factual Economy: Predictable Heterogeneity and Uncertainty1	0.0491	0.0631	28.53%
Counterfactual: Fixing Schooling Choices as in Factual Economy Predictable Heterogeneity Only2	0.0378	0.0465	22.85%
Between Schooling Groups
	NLS/66	NLSY/79	% Change
Factual Economy: Predictable Heterogeneity and Uncertainty1	0.0011	0.0062	447.37%
Counterfactual: Fixing Schooling Choices as in Factual Economy Predictable Heterogeneity Only2	0.0011	0.0057	394.22%

¹

Let Y_k,s,t,i denote the earnings of an agent i, i = 1, …, n_k, at age t, t = 22, …, 36, in schooling level s, s = high school, college, and cohort k,k = NLS/1966, NLSY/1979. We model earnings Y_k,s,t,i as:

$$Y_{k,s,t,i}={\mu }_{s,k}\left({\mathit{X}}_k\right)+{\theta }_{1,k,i}{\alpha }_{1,k,s,t,i}+{\theta }_{2,k,i}{\alpha }_{2,k,s,t,i}+{\theta }_{3,k,i}{\alpha }_{3,k,s,t,i}+{\epsilon }_{k,s,t,i}.$$ (i)

The present value of earnings at schooling level s, Y_k,s,i, is $Y_{k,s,i}={\sum }_{t=1}^{T^{\ast }}\frac{Y_{k,s,t,i}}{{(1+\rho )}^{t-1}}$. The observed present value of earnings satisfies Y_k,i = S_k,iY_k,1,i + (1 − S_k,i) Y_k,0,i where S_k,i = 1 if agent i in cohort k graduates college, and S_k,i = 0 if the person graduates high school. Let C_k,i denote the direct costs for individual i in cohort k. The schooling choice is:

$$S_{k,i}=1\iff E(Y_{k,1,i}-Y_{k,0,i}-C_{k,i}\mid {\mathcal{I}}_k)\ge 0.$$ (ii)

This is the factual economy. In this row, we show the inequality measure in the subtitle.

²

We simulate the economy by replacing (i) with:

$$Y_{k,s,t,i}^h={\mu }_{s,k}\left({\mathit{X}}_k\right)+{\theta }_{1,k,i}{\alpha }_{1,k,s,t,i}+{\theta }_{2,k,i}{\alpha }_{2,k,s,t,i},$$

where $Y_{k,s,t,i}^h$ are the individual earnings when idiosyncratic uncertainty is completely shut down. The present value of earnings when only heterogeneity is accounted for is constructed in a similar manner: $Y_{k,s,i}^h={\sum }_{t=1}^{T^{\ast }}\frac{Y_{k,s,t,i}^h}{{(1+\rho )}^{t-1}}$. The schooling choices are as determined in (ii). In this row, we show the inequality measure for the concept given in the subtitle for the observed truncated present value of earnings $Y_{k,s,i}^h$ when we constrain schooling choices to be the same as in the economy that generates the first row.