Truncation Bias

33 Pages Posted: 31 May 2016

See all articles by Nir Billfeld

Nir Billfeld

University of Haifa

Moshe Kim

University of Haifa - Department of Economics

Date Written: May 28, 2016


In the case of truncation, which is the widespread phenomenon plaguing the majority of all fields of empirical research, the observed data distribution function is truncated and related to participants' covariates only, rendering Heckman's seminal and known correction procedure not implementable. Thus, for the correction of selectivity bias propagated 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' covariates (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 truncated density function relies on the fact that the latter is obtained by conditioning the former on the selection rule. 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 √(n) consistency.

Keywords: Selectivity bias correction, Truncated Probit

Suggested Citation

Billfeld, Nir and Kim, Moshe, Truncation Bias (May 28, 2016). Available at SSRN: or

Nir Billfeld

University of Haifa ( email )

Mount Carmel
Haifa, 31905

Moshe Kim (Contact Author)

University of Haifa - Department of Economics ( email )

Haifa 31905
(972) 4 8240115 (Phone)
(972)4-8240059 (Fax)

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