participate in the legalization program benefited the most from it - more so than the average
person and more so than their cohorts who were not legalized.
A comparison of the different estimation methods shows a striking difference between the
parametric and nonparametric methods in the magnitude of sorting gains from legalization. The
sorting gains are the difference between the ATET and ATE estimates - the average gains for the
worker who opts for treatment (legalization) versus the worker who randomly selects into
treatment. The parametric method reports the smallest sorting gain of the four estimation
methods: the average earnings gain for the legalized (treated) foreign worker was 0.0023,
implying that the average earnings gain to legalization was 0.23% greater than the average
earnings gain for the average foreign worker who randomly selected into legalization. The gains
for the nonparametric methods (polynomial, nonparametric I, and nonparametric II) range from
3.16% to 6.57%.
A comparison of the estimates reported within shows significant differences in the
magnitude of average returns to legalization for the treated (legalized) and untreated (non-
legalized) groups. The parametric method estimates are the exception in this respect: earnings
gains average 10% across the board irrespective of treatment status. The differentials are largest
for the nonparametric I method, followed by the nonparametric II and polynomial methods,
respectively. The average earnings gain for the untreated (ATEU) range between 15% and 18%,
and those for the treated (ATET) range between 24% and 26%. The ATEU are particularly
informative as they suggest the potential gains of a future legalization for workers, most of
whom would have entered the US after the SAWs program.
The relevant support for each marginal treatment effect (MTE) is given by the propensity
score frequencies for foreign workers who were treated (legalized) and untreated (not legalized)
14
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