Nonrandom sample selection may render estimated treatment effects biased even if assignment of treatment is purely random. Lee (2009, Review of Economic Studies, 76: 1071–1102) proposes an estimator for treatment-effect bounds that limit the possible range of the treatment effect. In this approach, the lower and upper bound correspond to extreme assumptions about the missing information that are consistent with the observed data. In contrast to conventional parametric approaches to correcting for sample-selection bias, Lee's bounds estimator rests on very few assumptions. I introduce the new command leebounds, which implements the estimator in Stata. The command allows for several options, such as tightening bounds by using covariates.
AhnH., and PowellJ. L.1993. Semiparametric estimation of censored selection models with a nonparametric selection mechanism. Journal of Econometrics58: 3–29.
2.
AugurzkyB., BauerT. K., ReichertA. R., SchmidtC. M., and TauchmannH.2012. Does money burn fat? Evidence from a randomized experiment. Ruhr Economic Papers No. 368. http://hdl.handle.net/10419/67304.
3.
BalkeA., and PearlJ.1997. Bounds on treatment effects from studies with imperfect compliance. Journal of the American Statistical Association92: 1171–1176.
CawleyJ., and PriceJ. A.2013. A case study of a workplace wellness program that offers financial incentives for weight loss. Journal of Health Economics32: 794–803.
6.
GrasdalA.2001. The performance of sample selection estimators to control for attrition bias. Health Economics10: 385–398.
7.
HeckmanJ. J.1976. The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models. Annals of Economic and Social Measurement5: 475–492.
8.
HeckmanJ. J.1979. Sample selection bias as a specification error. Econometrica47: 153–161.
9.
HorowitzJ. L., and ManskiC. F.2000. Nonparametric analysis of randomized experiments with missing covariate and outcome data. Journal of the American Statistical Association95: 77–84.
10.
IchimuraH., and LeeL.-F.1991. Semiparametric least squares estimation of multiple index models: Single equation estimation. In Nonparametric and Semiparametric Methods in Econometrics and Statistics, ed. BarnettW. A., PowellJ., and TauchenG., 3–49. Cambridge: Cambridge University Press.
11.
ImbensG. W., and ManskiC. F.2004. Confidence intervals for partially identified parameters. Econometrica72: 1845–1857.
12.
LeeD. S.2009. Training, wages, and sample selection: Estimating sharp bounds on treatment effects. Review of Economic Studies76: 1071–1102.
13.
ManskiC. F.1990. Nonparametric bounds on treatment effects. American Economic Review80: 319–323.
14.
ManskiC. F.1994. The selection problem. In Advances in Econometrics, Sixth World Congress, ed. SimsC., vol. 1, 143–170. Cambridge: Cambridge University Press.
15.
ManskiC. F.1995. Identification Problems in the Social Sciences.Cambridge, MA: Harvard University Press.
ManskiC. F., and PepperJ. V.2000. Monotone instrumental variables: With an application to the returns to schooling. Econometrica68: 997–1010.
18.
PalmerT. M., RamsahaiR. R., DidelezV., and SheehanN. A.2011. Nonparametric bounds for the causal effect in a binary instrumental-variable model. Stata Journal11: 345–367.
19.
PuhaniP. A.2000. The Heckman correction for sample selection and its critique. Journal of Economic Surveys14: 53–68.
