Journal of Quantitative Criminology

, Volume 26, Issue 3, pp 391–413 | Cite as

Estimating Treatment Effects and Predicting Recidivism for Community Supervision Using Survival Analysis with Instrumental Variables

  • William RhodesEmail author
Original Paper


Criminal justice researchers often seek to predict criminal recidivism and to estimate treatment effects for community corrections programs. Although random assignment provides a desirable avenue to estimating treatment effects, often estimation must be based on observational data from operating corrections programs. Using observational data raises the risk of selection bias. In the community corrections contexts, researchers can sometimes use judges as instrumental variables. However, the use of instrumental variable estimation is complicated for nonlinear models, and when studying criminal recidivism, researchers often choose to use survival models, which are nonlinear given right-hand-censoring or competing events. This paper discusses a procedure for estimating survival models with judges as instruments. It discusses strengths and weaknesses of this approach and demonstrates some of the estimation properties with a computer simulation. Although this paper’s focus is narrow, its implications are broad. A conclusion argues that instrumental variable estimation is valuable for a broad range of topics both within and outside of criminal justice.


Predicting recidivism Estimating treatment effects Survival analysis Instrumental variables 



The author thanks Gerry Gaes, Stephen Kennedy, Jacob Klerman, Fatih Unlu, members of the Abt Associates Journal Authors Support Group, and three JQC reviewers for their comments.


  1. Abbring J, van den Berg G (2005) Social experiments and instrumental variables with duration outcomes. Tinbergen Institute discussion paper 2005-047/3Google Scholar
  2. Angrist J (1998) Estimating the labor force impact of voluntary military service using social security data on military applications. Econometrica 66(2):249–288CrossRefGoogle Scholar
  3. Angrist J (2001) Estimation of limited dependent variable models with dummy endogenous regressors: simple strategies for empirical practices. Am Stat Assoc J Bus Econ Stat 19(1):2–28CrossRefGoogle Scholar
  4. Angrist J (2006) Instrumental variable methods in criminological work: what, why and how. J Exp Criminol 1–22Google Scholar
  5. Angrist J, Evans W (1998) Children and their parents’ labor supply: evidence from exogenous variation in labor supply. Am Econ Rev 450–477Google Scholar
  6. Angrist J, Krueger A (1999) Empirical strategies in labor economics. In: Ashenfelder O, Card D (eds) Handbook of labor economics. Elsvier, Amsterdam, pp 1277–1366Google Scholar
  7. Angrist J, Lavy V (1999) Using Maimonides’ rule. Quart J Econom 114(2):533–575CrossRefGoogle Scholar
  8. Angrist J, Pischke J (2009) Mostly harmless econometrics: an Empiricist’s companion. Princeton University Press, PrincetonGoogle Scholar
  9. Baum C (2009) An introduction to stata programming. StataCorp, College StationGoogle Scholar
  10. Berk R, de Leeuw J (1999) An evaluation of California’s inmate classification system using generalized regression discontinuity design. J Am Stat Assoc 94(448):1045–1052CrossRefGoogle Scholar
  11. Bloom H (1984) Accounting for no-shows in experimental evaluation designs. Eval Rev 8(2):225–246CrossRefGoogle Scholar
  12. Bogue B, Campbell M, Carey M, Calwson D, Faust K, Forio K et al (2004) Implementing evidence-based practices in community corrections: the principles of effective intervention. National Institute of Corrections, Washington, DCGoogle Scholar
  13. Bowden R, Turkington D (1984) Instrumental variables. Cambridge University Press, CambridgeGoogle Scholar
  14. Bushway S, Smith J (2007) Sentencing using statistical statement rules: what we don’t know can hurt us. J Quant Criminol 377–387Google Scholar
  15. Cameron A, Trivedi P (2005) Microeconometrics: methods and applications. Cambridge University Press, CambridgeGoogle Scholar
  16. Cameron A, Trivedi P (2009) Microeconometrics using stata. Cambridge University Press, CambridgeGoogle Scholar
  17. Cleves M, Gould W, Gutierrez R, Marchenko Y (2008) An introduction to survival analysis using stata, 2nd edn. Stata Press, College StationGoogle Scholar
  18. Davidson R, MacKinnon J (1993) Estimation and inference in econometrics. Oxford University Press, OxfordGoogle Scholar
  19. Farrington D, Welsh B (2005) Randomized experiments in criminology: what we have learned in the last two decades. J Exp Criminol 1(1):9–38CrossRefGoogle Scholar
  20. Gennetian L, Morris P, Bos J, Bloom H (2005) Constructing instrumental variables from experimental data to explore how treatment produces effects. In: Bloom H (ed) Learning more from experiments: evolving analytic approaches. Russell Sage Foundation, New YorkGoogle Scholar
  21. Gottfredson S, Moriarty L (2006) Statistical risk assessment: old problems and new applications. Crime Delinq 52(1):178–200CrossRefGoogle Scholar
  22. Greene W (2008) Econometric analysis, 6th edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
  23. Hahn J, Hausman J (2003) Weak instruments: diagnosis and cures in empirical econometrics. Am Econ Rev 93(2):118–125CrossRefGoogle Scholar
  24. Hahn J, Todd P, van der Klaauw W (2001) Identification and estimation of treatment effects with a regression- discontinuity design. Econometrica 69(1):201–209CrossRefGoogle Scholar
  25. Heckman J (1979) Sample selection bias as a specification error. Econometrica 47(1):153–161CrossRefGoogle Scholar
  26. Heckman J, Leamer E (2007) Handbook of econometrics, vol 6B. North-Holland Press, AmsterdamGoogle Scholar
  27. Heckman J, Singer B (1984) The identifiability of the proportional hazard model. Rev Econ Stud 231–241Google Scholar
  28. Heckman J, Vytlacil E (2007) Econometric evaluation of social programs, Part I. In: Heckman J, Leamer E (eds) Handbook of econometrics, vol 6B. North Holland Press, AmsterdamGoogle Scholar
  29. Hughs J (2008) Results-based management in federal probation and pretrial services. Fed Probat 4–14Google Scholar
  30. Imbens G (2009) Better LATE than nothing: some comments on Deaton (2009) and Heckman and Urzua (2009), unpublished paper downloaded from on Dec 2, 2009
  31. Imbens G, Angrist J (1994) Identification and estimation of local average treatment effects. Econometrica 62(2):467–475CrossRefGoogle Scholar
  32. Kalbfleisch J, Prentice R (1980) The statistical analysis of failure time data. John Wiley, New YorkGoogle Scholar
  33. Kilmer B (2008) Does parolee drug testing influence employment and education outcomes? Evidence from randomized experiment with noncompliance. J Quant Criminol 93–123Google Scholar
  34. Kling J (2006) Incarceration length, employment and earnings. Am Econ Rev 96(3):863–876CrossRefGoogle Scholar
  35. Lancaster T (1990) The econometric analysis of transition data. Cambridge University Press, CambridgeGoogle Scholar
  36. Lee M (2005) Micro-econometrics for policy, program and treatment effects. Oxford University Press, OxfordCrossRefGoogle Scholar
  37. Lee D, Lemieux T (2009) Regression discontinuity designs in economics. Retrieved Jul 27, 2009, from NBER Working Paper Series:
  38. Lipsey M, Petrie C, Weisburd D, Gottfredson D (2006) Improving evaluations of anti-crime programs. J Exp CriminolGoogle Scholar
  39. Manski C (2007) Identification for prediction and decision. Harvard University Press, CambridgeGoogle Scholar
  40. Moffitt R (1999) Commentrary: models of treatment effects when responses are heterogeneous. Proc Natl Acad Sci USA Sol 96:6575–6576CrossRefGoogle Scholar
  41. Morgan S, Winship C (2007) Counterfactuals and causal inferences: methods and principals for social research. Cambridge University Press, CambridgeGoogle Scholar
  42. Rhodes W (1985) The adequacy of statically derived prediction instruments in the face of sample selectivity: criminal justice as an example. Eval Rev 9(3):369–382CrossRefGoogle Scholar
  43. Rhodes W (2009a) Estimating treatment effects: a primer for evaluators. Cambridge, unpublished manuscript available from the authorGoogle Scholar
  44. Rhodes W (2009b) Predicting criminal recidivism: a research note (under review)Google Scholar
  45. Rhodes W, Pelissier B, Gaes G, Saylor B, Camp S, Wallace S (2001) Alternative solutions to the problem of selection bias in an analysis of federal residential drug treatment programs. Eval Rev 331–369Google Scholar
  46. Rhodes W, Jalbert S, Flygare C (2009) Regression discontinuity design: a review and illustration (submitted for publication)Google Scholar
  47. Rosenbaum P (2002) Observational studies, 2nd edn. Springer, New YorkGoogle Scholar
  48. Smith H (1997) Matching with multiple controls to estimate treatment effects in observational studies. In: Raftery A (ed) Sociological methodology, vol 27. Blackwell, Boston, pp 325–354Google Scholar
  49. Stock J, Wright J, Yogo M (2002) A survey of weak instruments and weak identification in generalized method of moments. J Bus Econ Stud 518–529Google Scholar
  50. Truitt L, Rhodes W, Seeherman A, Carrigan K, Finn P (1999) Process and impact evaluation of the Escambia County, Florida, and Jackson County, Missouri drug courts. National Institute of Justice, Washington, DCGoogle Scholar
  51. United States Government Accounting Office (2009) Program evaluation: a variety of rigorous methods can help identify effective interventions. United States Government Accounting Office, Washington, DCGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Abt Associates Inc.CambridgeUSA

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