Comparative Research Of The Bias Of Matching And Difference-in-Difference Matching Under Sample Selection Theory

Matching and Difference-in-Difference Matching are two widespread methods to correct selection bias by using some pre-treatment outcomesand covariates in policy area.In this paper,comparative research of the bias of Matching and Difference-in-Difference Matching under sample selection theory.The self-selection model is constructed by a model of earning dynamics equation and entry into a Job training program(JTP)to study the selection bias and its impact mechanism when Matching and Difference-in-Difference Matching are used to evaluate treatment effects in the case of non-random allocation.The model introduces non-parametric functions of covariates to capture the effects of covariates and increases the dimension of the interaction between individuals and time.Finally,I asses their performances using Monte Carlo simulations of the model calibrated with realistic parameter values.I find that Matching and Difference-in-Difference Matching biases are negative under the limited information,that is,it underestimates the treatment effect of the program.But the performance of the Matching is still performs better than Difference-in-Difference Matching;What's more,the deviations of Matching and Difference-in-difference Matching can be positive or negative under the complete information.When the distance is far from the time relative to self-selection in the JTP,both of selection bias are negative and gradually approach zero,and the estimators of Matching can be consistent.It is an unbiased estimator,that is,the performance of the Matching is superior to the Difference-in-Difference Matching;When approaching the time relative to self-selection in the JTP,both of selection bias are positive.At this time,the estimator of Difference-in-Difference Matching can be consistent.It is an unbiased estimator,namely,Monte Carlo simulation show that Difference-in-difference Matching performs better than Matching.