Estimating Distributions of Counterfactuals with an Application ... - UCL

398 CARNEIRO, HANSEN, AND HECKMAN
TABLE 5
FACTUAL AND COUNTERFACTUAL RETURNS FOR PERSONS WHO GO TO HIGH
SCHOOL OR COLLEGE
Gross Return High School 1 College 2
College vs. high school (relative) + −0.0180 0.0126
Std. error 0.1590 0.0178
Net returns
College vs. high school (relative) ++ −0.2398 0.3161
Std. error 0.2502 0.3178
College vs. high school (relative) +++ −0.4227 0.1892
Std. error 0.5770 0.0144
1 + E((V c /V h ) − 1 | choice = high school).
2 + E((V c /V h ) − 1 | choice = college).
1 ++ E((V c /V h − ln P)/(V h + ln P) | choice = high school).
2 ++ E((V c /V h − ln P)/(V h + ln P) | choice = college).
1 +++ E((V c /V h − ln P)/(V h ) | choice = high school).
2 +++ E((V c /V h − ln P)/(V h ) | choice = college).
NOTE: We make the distinction between the second and third line in
this table because in our framework we cannot separate nonmonetary
costs from nonmonetary benefits of going to college, so we allocate
ln P both ways.
for psychic returns in analyzing schooling choices. Among high school graduates,
95.90% do not regret not going to college (measured in utils), but 85.26%
regret the decision financially. The marginal treatment effect has the same general
shape when present values of earnings are used instead of gross utility (see
Figure 8).
Table 8 shows the probability of being in decile i of the college potential discounted
earnings distribution conditional on being in decile j of the high school
potential earnings distribution. (These are gross earnings.) It shows that neither
an independence assumption across counterfactual outcomes, which is the Veil
of Ignorance assumption used in applied welfare theory, (see, e.g., Sen, 1973)
or in aggregate income inequality decompositions (DiNardo et al., 1996), nor a
perfect ranking assumption, which is sometimes used to construct counterfactual
joint distributions of outcomes (see, e.g., Heckman et al., 1997 or Athey and
Imbens, 2002) are satisfied in the data. There is a strong positive dependence
between potential outcomes in each counterfactual state, but there is no perfect
dependence. There are substantial nonzero elements outside the diagonal.
We get similar results for utility (discounted log earnings). See Table A13 at our
website.
We have already shown that there is a large dispersion in the distribution of
utilities, utility returns, earnings, and earnings returns to college. However, this
dispersion can be due to heterogeneity that is known at the time the agent makes
schooling decisions, or it can be due to heterogeneity that is not predictable by the
agent at that time. Figure 9 plots the densities of the unforecastable component
of college gross utilities at the time college decisions are made for fixed X values,