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

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## Abstract

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.

## Keywords

Predicting recidivism Estimating treatment effects Survival analysis Instrumental variables## Notes

### Acknowledgments

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.

## References

- Abbring J, van den Berg G (2005) Social experiments and instrumental variables with duration outcomes
*.*Tinbergen Institute discussion paper 2005-047/3Google Scholar - 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
- 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
- Angrist J (2006) Instrumental variable methods in criminological work: what, why and how. J Exp Criminol 1–22Google Scholar
- Angrist J, Evans W (1998) Children and their parents’ labor supply: evidence from exogenous variation in labor supply. Am Econ Rev 450–477Google Scholar
- 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
- Angrist J, Lavy V (1999) Using Maimonides’ rule. Quart J Econom 114(2):533–575CrossRefGoogle Scholar
- Angrist J, Pischke J (2009) Mostly harmless econometrics: an Empiricist’s companion. Princeton University Press, PrincetonGoogle Scholar
- Baum C (2009) An introduction to stata programming. StataCorp, College StationGoogle Scholar
- 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
- Bloom H (1984) Accounting for no-shows in experimental evaluation designs. Eval Rev 8(2):225–246CrossRefGoogle Scholar
- 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
- Bowden R, Turkington D (1984) Instrumental variables. Cambridge University Press, CambridgeGoogle Scholar
- Bushway S, Smith J (2007) Sentencing using statistical statement rules: what we don’t know can hurt us. J Quant Criminol 377–387Google Scholar
- Cameron A, Trivedi P (2005) Microeconometrics: methods and applications. Cambridge University Press, CambridgeGoogle Scholar
- Cameron A, Trivedi P (2009) Microeconometrics using stata. Cambridge University Press, CambridgeGoogle Scholar
- Cleves M, Gould W, Gutierrez R, Marchenko Y (2008) An introduction to survival analysis using stata, 2nd edn. Stata Press, College StationGoogle Scholar
- Davidson R, MacKinnon J (1993) Estimation and inference in econometrics. Oxford University Press, OxfordGoogle Scholar
- 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
- 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
- Gottfredson S, Moriarty L (2006) Statistical risk assessment: old problems and new applications. Crime Delinq 52(1):178–200CrossRefGoogle Scholar
- Greene W (2008) Econometric analysis, 6th edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
- Hahn J, Hausman J (2003) Weak instruments: diagnosis and cures in empirical econometrics. Am Econ Rev 93(2):118–125CrossRefGoogle Scholar
- 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
- Heckman J (1979) Sample selection bias as a specification error. Econometrica 47(1):153–161CrossRefGoogle Scholar
- Heckman J, Leamer E (2007) Handbook of econometrics, vol 6B. North-Holland Press, AmsterdamGoogle Scholar
- Heckman J, Singer B (1984) The identifiability of the proportional hazard model. Rev Econ Stud 231–241Google Scholar
- 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
- Hughs J (2008) Results-based management in federal probation and pretrial services. Fed Probat 4–14Google Scholar
- Imbens G (2009) Better LATE than nothing: some comments on Deaton (2009) and Heckman and Urzua (2009), unpublished paper downloaded from http://www.economics.harvard.edu/faculty/imbens/files/bltn_09apr10.pdf on Dec 2, 2009
- Imbens G, Angrist J (1994) Identification and estimation of local average treatment effects. Econometrica 62(2):467–475CrossRefGoogle Scholar
- Kalbfleisch J, Prentice R (1980) The statistical analysis of failure time data. John Wiley, New YorkGoogle Scholar
- Kilmer B (2008) Does parolee drug testing influence employment and education outcomes? Evidence from randomized experiment with noncompliance. J Quant Criminol 93–123Google Scholar
- Kling J (2006) Incarceration length, employment and earnings. Am Econ Rev 96(3):863–876CrossRefGoogle Scholar
- Lancaster T (1990) The econometric analysis of transition data. Cambridge University Press, CambridgeGoogle Scholar
- Lee M (2005) Micro-econometrics for policy, program and treatment effects. Oxford University Press, OxfordCrossRefGoogle Scholar
- Lee D, Lemieux T (2009) Regression discontinuity designs in economics. Retrieved Jul 27, 2009, from NBER Working Paper Series: http://www.nber.org/papers/w14723
- Lipsey M, Petrie C, Weisburd D, Gottfredson D (2006) Improving evaluations of anti-crime programs. J Exp CriminolGoogle Scholar
- Manski C (2007) Identification for prediction and decision. Harvard University Press, CambridgeGoogle Scholar
- Moffitt R (1999) Commentrary: models of treatment effects when responses are heterogeneous. Proc Natl Acad Sci USA Sol 96:6575–6576CrossRefGoogle Scholar
- Morgan S, Winship C (2007) Counterfactuals and causal inferences: methods and principals for social research. Cambridge University Press, CambridgeGoogle Scholar
- 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
- Rhodes W (2009a) Estimating treatment effects: a primer for evaluators. Cambridge, unpublished manuscript available from the authorGoogle Scholar
- Rhodes W (2009b) Predicting criminal recidivism: a research note (under review)Google Scholar
- 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
- Rhodes W, Jalbert S, Flygare C (2009) Regression discontinuity design: a review and illustration (submitted for publication)Google Scholar
- Rosenbaum P (2002) Observational studies, 2nd edn. Springer, New YorkGoogle Scholar
- 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
- 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
- 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
- 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