Truncation Bias

In the case of truncation, which is the widespread phenomenon plaguing the majority of all elds of empirical research, the observed data distri- bution function is truncated and related to participants' covariates only, rendering Heckman's seminal and known correction procedure not imple- mentable. Thus, for the correction of endogenous selectivity bias propa- gated by truncation we introduce a new methodology that recovers the unobserved part of the data distribution function, using only its observed truncated part. The correlation patterns among the non-participants' co- variates (which are all functions of the recovered non-participants' density function) are recovered as well. The rationale underlying the ability to recover the unobserved complete density function from the observed trun- cated density function relies on the fact that the latter is obtained by conditioning the former on the selection rule. Consequently, the param- eters set which characterizes the truncated density function contains all the parameters characterizing the unobserved non-truncated density func- tion. Thus, it is possible to characterize the unobserved non-participants' density function in terms of the parameters estimated using the truncated data soley. Once this unobserved part is recovered one can estimate the selection rule equation for the hazard rate calculation as if the full sample consisting of both participants and non-participants is observable. Monte- Carlo simulations attest to the high accuracy of the estimates and above conventional p n consistency.