PROPOSED IMMIGRATION POLICY REFORM & FARM LABOR MARKET OUTCOMES

■ Average Treatment Effect (ATE). This is the expected gain from participating in a
program for a randomly chosen individual (Heckman, Tobias and Vytlacil, 2001),
calculated as the differences in expected outcomes before and after treatment:
αATE =E(∆)=E(Y1)-E(Y0)                                                   (4)

■ Average Treatment Effect on the Treated (ATET). This is the average gain from
treatment for those who select into the treatment (Heckman, Tobias and Vytlacil, 2001):
a_ATET = E (∆∖D = 1 )= E(Y_l∖D = 1 )-E (Y₀∖D = 1 )                            (5)

■ Average Treatment Effect on the Untreated (ATEU). This is the effect for non-
participants which may be useful for future policy decisions on extending treatment to
groups that were excluded from treatment (Caliendo, 2006):

αATEU =E(∆∖D=0)=E(Y1∖D=0)-E(Y0 ∖D=0)                           (6)

Marginal Treatment Effect (MTE). ¹ This is the expected effect of treatment conditional
on observed (X) and unobserved (Ud) characteristics of participants (Heckman and
Vytlacil, 2005).² One interpretation is that it is the mean gain for an individual with
characteristics X and unobservables Ud such that he is indifferent between treatment or

not given a set of Z values, z, where Φ(α ^,z)=u_d. It is defined as:

MTE(X,Ud)≡E(∆∖X=x,Ud=ud)=E(Y1-Y0∖X=x,Ud_i=ud)

=E(γ∖X =x,U_di =u_d)=X(β₁-β₀)+E[u_1i-u_0i ∖U_di =u_d]

The challenge posed by selection bias is evident from the ATET which shows a
hypothetical outcome in the absence of treatment for those individuals who received treatment
(Caliendo, 2006). With non-experimental data, this outcome is not equivalent to the outcome of
non-participants:

E (Yo∣ D = 1)≠ E (Yo∣ D = 0)                                                       (8)

Selection bias may arise since participants and non-participants may be deliberately selected
groups with different outcomes, even in the absence of treatment, due to observable and
unobservable factors that may determine participation (Caliendo, 2006):

E(Y1 |D=1)-E(Y0 |D=0)=E(Y1-Y0 |D=1)+[E(Y0 |D=1)-E(Y0 |D=0)]       (9)

^k                V                ^{j k}                            V                            ^j

ATET            Selection bias

¹ Bjorklund and Moffitt (1987) are credited with introducing this concept to the literature.

² The unobserved characteristics are introduced into the model by the decision rule described by equation (1).

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