PROPOSED IMMIGRATION POLICY REFORM & FARM LABOR MARKET OUTCOMES

based on observable characteristics (x), and the participation decision for a program may be
defined as:

Y₁ = g₁(x)+ u₁ = β₁'X_i + u₁   (treated/p articipant group)

Y₀ = g₀(x)+ u₀ = β₀'X_i + u₀ (untreated /nonpartic ipant group)

D^* = α'Z_i + ε                (decision to participat e in treatment)

where D = 1 if D^* ≥ 0; D = 0 otherwise

In this setup,g1 (x) , g₀(x) represent the relationship between the observable characteristics and
the potential outcomes and u₁,u₀ ,ε , Z and x are unobserved and observed random variables,
respectively. The errors are assumed to be independent of x and Z. Ceteris paribus, the
treatment or causal effect is defined as shown by equation (4.2), and is the difference between
the potential outcomes:

∆i =Y1i-Y0i        i = 1,..., N                                                               (2)

This effect is not directly estimable as it is impossible to simultaneously observe an individual in
both states. The observed outcome is actually:

Yi = DiY1i +(1-Di)Y0i                                                               (3)

where the unobservable portion of the effect is referred to as the counterfactual outcome. (For
those individuals receiving treatment Y₀ is the counterfactual outcome; for those who do not, Y₁
is the counterfactual outcome.) The treatment effect of each person is independent of the
treatment of other individuals, implying that an individual’s potential outcomes are affected by
his participation decision only and not the decisions of other individuals (Wooldridge, 2002;
Caliendo, 2006).

Gains from treatment are typically defined as population averages. Some relevant
parameters include:

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