shown in Figure 1. The marginal treatment effects generated by each method are shown in
Figure 2 through Figure 5. The MTE is evaluated at values at which the propensity score(P(z))
and unobservable factors (ud ) are equivalent (Heckman, Urzua and Vytlacil, 2006a; 2006b).
Heckman and Vytlacil (2005) emphasize the role of the unobservable characteristics in the
interpretation of the MTE: for smaller values of the unobservables (ud) (points closer to zero on
the x axis), the MTE is the expected benefit for individuals who are more likely to participate in
treatment and who would participate even if the mean scale utility (μd(Z) ) were small.
Conversely, for larger values of ud the mean scale utility (μd(Z)) would have to be much larger to
induce individuals’ participation in treatment and they are less likely to participate. The MTE
may also be interpreted as the mean gain for persons with observable characteristics (X) who
would be indifferent between acquiring legal status or not, and may be viewed as a willingness to
pay (WTP) measure if the outcomes are value outcomes (Heckman and Vytlacil, 2007a; 2007b).
The latter interpretation of the MTE is useful given the findings depicted in Figures 2
through 5 which seem to conflict with the positive sorting on the gains indicated by the average
treatment effect parameters. Figure 2, which is based on the parametric method, suggests that
the worker who became legalized (on account of having a low ud ) benefited less than the worker
who was not legalized (on account of having a high ud). Although this is difficult to reconcile
with the positive sorting on the gains indicated by the average treatment effect parameters, the
WTP interpretation of the MTE may offer reasonable explanation. The upward slope of Figure 2
would therefore suggest an increasing willingness to pay by workers who have larger
unobservables that usually would make them less eligible for participation in the program. The
increasing ud values may be indicative of idiosyncratic enhanced productivity, and a larger
willingness to pay for legal status in order to permit more options to earn better returns.
15
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