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

392 CARNEIRO, HANSEN, AND HECKMAN
0.35
Actual
Predicted
0.3
0.25
Dens ity(Utility)
0.2
0.15
0.1
0.05
0
0 2 4 6 8 10 12
Utility
All densities are estimated using a 100 point grid over the domain and a Gaussian kernel with bandwidth of 0.12.
Utility=
1
Σ a(1+0.03) a log(Y a,s )
FIGURE 1
DENSITY OF EX POST GROSS UTILITY
most of the variance in the utility outcome system (see Table 3a). The return to
college in terms of gross utility (gross utility differences) is given by
V 1,c + V 2,c − V 1,h − V 2,h = (¯δ 1,c + ¯δ 2,c − ¯δ 1,h − ¯δ 2,h ) + X ′ ( ¯β 1,c + ¯β 2,c − ¯β 1,h − ¯β 2,h )
+ (ᾱ
1,c ′ + ᾱ′ 2,c − ᾱ′ 1,h − ᾱ′ 2,h )θ +(¯ε 1,c + ¯ε 2,c − ¯ε 1,h − ¯ε 2,h )
Both factors raise returns (see the base of Table 3a). Although the second factor
explains much more of the variance in utility than the first factor, the first factor
explains more of the variance in returns than the second factor, although it
only explains 30% of the variance in returns. We infer that agents know θ (the
factors) based on the superior fit of a model that includes nonzero factor loadings
on both factors in the choice equation but not the innovations in outcomes (the
ε’s in the outcome equations) at the time they make their schooling decisions.
Our results indicate that the unpredictability in gross utility gains (i.e., differences)
of going to college is much larger than the unpredictability in utility levels.
Both factors have a negative impact on “costs” (the factor loadings are negative in
the “cost” or psychic return function). Therefore, both factors positively influence