Journal of Quantitative Criminology

, Volume 23, Issue 2, pp 151–178 | Cite as

Is the Magic Still There? The Use of the Heckman Two-Step Correction for Selection Bias in Criminology

  • Shawn Bushway
  • Brian D. Johnson
  • Lee Ann Slocum
Original Paper


Issues of selection bias pervade criminological research. Despite their ubiquity, considerable confusion surrounds various approaches for addressing sample selection. The most common approach for dealing with selection bias in criminology remains Heckman’s [(1976) Ann Econ Social Measure 5:475–492] two-step correction. This technique has often been misapplied in criminological research. This paper highlights some common problems with its application, including its use with dichotomous dependent variables, difficulties with calculating the hazard rate, misestimated standard error estimates, and collinearity between the correction term and other regressors in the substantive model of interest. We also discuss the fundamental importance of exclusion restrictions, or theoretically determined variables that affect selection but not the substantive problem of interest. Standard statistical software can readily address some of these common errors, but the real problem with selection bias is substantive, not technical. Any correction for selection bias requires that the researcher understand the source and magnitude of the bias. To illustrate this, we apply a diagnostic technique by Stolzenberg and Relles [(1997) Am Sociol Rev 62:494–507] to help develop intuition about selection bias in the context of criminal sentencing research. Our investigation suggests that while Heckman’s two-step correction can be an appropriate technique for addressing this bias, it is not a magic solution to the problem. Thoughtful consideration is therefore needed before employing this common but overused technique.


Sample selection Selection bias Heckman correction Two-step estimator 



The authors would like to thank Justin McCrary, Wayne Osgood, Anne Piehl, Jeff Smith and seminar participants at the Economics and Crime summer workshop for helpful comments. We would also like to thank Gary Sweeten for research assistance and useful discussions. Most of the research for the paper was completed while Bushway was a professor at the University of Maryland. The paper is dedicated to the memory of our friend, mentor, and former colleague Douglas A. Smith. Doug helped us to understand the relevant selection issues, and encouraged us to pursue the paper in its formative stages. He is sorely missed.


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Shawn Bushway
    • 1
  • Brian D. Johnson
    • 2
  • Lee Ann Slocum
    • 2
  1. 1.School of Criminal JusticeState University of New York at AlbanyAlbanyUSA
  2. 2.Department of Criminology and Criminal JusticeUniversity of MarylandCollege ParkUSA

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