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

EFFECTS OF UNCERTAINTY ON COLLEGE CHOICE 401
0.9
1
High School*
College**
0.8
0.7
Density(Returns)
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.5 0 0.5 1 1.5 2 2.5
Returns
*f((PV c /PV h )-1|Choice=High School)
**f((PV c
/PV h
)-1|Choice=College)
PV
1
h = Σ a (1+0.03) a Y h,a
All densities are estimated using a 100 point grid over the domain and a Gaussian kernel with bandwidth of 0.12.
FIGURE 7
DENSITY OF EX POST RELATIVE GROSS EARNINGS DIFFERENCES (COLLEGE–HIGH SCHOOL)
knowledge of (¯ε 1,c , ¯ε 2,c , ¯ε 1,h , ¯ε 2,h ), keeping their average expected earnings the
same, very few of them would change their schooling decision. Uncertainty in
gains to schooling is substantial but knowledge of this uncertainty has a very small
effect on the choice of schooling because the variance of gains is so much smaller
than the variance of psychic costs or benefits, and it is the latter that drives most
of the heterogeneity in schooling decisions. In addition, there is uncertainty about
the level of both college and high school earnings. See the variances reported for
each in Table 9. The uncertainty in the return comes from both sources although
the literature emphasizes the uncertainty in college earnings. When conducting
this experiment, we make sure that the average expected earnings are the same
because a mean preserving reduction in the uncertainty faced by the agents in
terms of utility is not the same as a mean preserving change in uncertainty in terms
of levels of earnings (see Appendix D). 34 In particular, a change in the variance of
(¯ε 1,c , ¯ε 2,c , ¯ε 1,h , ¯ε 2,h ) would not change the expected utility in each schooling level
34 See the numbers posted at the website.