TY - JOUR
T1 - Treatment effects in sample selection models and their nonparametric estimation
AU - Lee, Myoung Jae
PY - 2012/4
Y1 - 2012/4
N2 - In a sample-selection model with the 'selection' variable Q and the 'outcome' variable Y *, Y * is observed only when Q=1. For a treatment D affecting both Q and Y *, three effects are of interest: 'participation' (i.e., the selection) effect of D on Q, 'visible performance' (i.e., the observed outcome) effect of D on Y≡QY *, and 'invisible performance' (i.e., the latent outcome) effect of D on Y *. This paper shows the conditions under which the three effects are identified, respectively, by the three corresponding mean differences of Q, Y, and Y|Q=1 (i.e., Y *|Q= 1) across the control (D=0) and treatment (D=1) groups. Our nonparametric estimators for those effects adopt a two-sample framework and have several advantages over the usual matching methods. First, there is no need to select the number of matched observations. Second, the asymptotic distribution is easily obtained. Third, over-sampling the control/treatment group is allowed. Fourth, there is a built-in mechanism that takes into account the 'non-overlapping support problem', which the usual matching deals with by choosing a 'caliper'. Fifth, a sensitivity analysis to gauge the presence of unobserved confounders is available. A simulation study is conducted to compare the proposed methods with matching methods, and a real data illustration is provided.
AB - In a sample-selection model with the 'selection' variable Q and the 'outcome' variable Y *, Y * is observed only when Q=1. For a treatment D affecting both Q and Y *, three effects are of interest: 'participation' (i.e., the selection) effect of D on Q, 'visible performance' (i.e., the observed outcome) effect of D on Y≡QY *, and 'invisible performance' (i.e., the latent outcome) effect of D on Y *. This paper shows the conditions under which the three effects are identified, respectively, by the three corresponding mean differences of Q, Y, and Y|Q=1 (i.e., Y *|Q= 1) across the control (D=0) and treatment (D=1) groups. Our nonparametric estimators for those effects adopt a two-sample framework and have several advantages over the usual matching methods. First, there is no need to select the number of matched observations. Second, the asymptotic distribution is easily obtained. Third, over-sampling the control/treatment group is allowed. Fourth, there is a built-in mechanism that takes into account the 'non-overlapping support problem', which the usual matching deals with by choosing a 'caliper'. Fifth, a sensitivity analysis to gauge the presence of unobserved confounders is available. A simulation study is conducted to compare the proposed methods with matching methods, and a real data illustration is provided.
KW - Matching
KW - Sample selection
KW - Sensitivity analysis
KW - Treatment effect
KW - U-statistic
UR - http://www.scopus.com/inward/record.url?scp=84863176226&partnerID=8YFLogxK
U2 - 10.1016/j.jeconom.2011.09.018
DO - 10.1016/j.jeconom.2011.09.018
M3 - Article
SN - 0304-4076
VL - 167
SP - 317
EP - 329
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -