Partially Identified Treatment Effects Under Imperfect Compliance: The Case of Domestic Violence

Abstract

The Minneapolis Domestic Violence Experiment (MDVE) is a randomized social experiment with imperfect compliance that has been extremely influential in how police officers respond to misdemeanor domestic violence. This article reexamines data from the MDVE, using recent literature on partial identification to find recidivism associated with a policy that arrests misdemeanor domestic violence suspects rather than not arresting them. Using partially identified bounds on the average treatment effect, I find that arresting rather than not arresting suspects can potentially reduce recidivism by more than two-and-a-half times the corresponding intent-to-treat estimate and more than two times the corresponding local average treatment effect, even when making minimal assumptions on counterfactuals.

KEY WORDS:

• Bound analysis
• Experiments
• Policing

Acknowledgments

I am grateful to the editor Hal Stern, an anonymous associate editor and two anonymous referees for comments and advice in the revision. I am also indebted to Marco Caliendo, Gordan Dahl, David Jaeger, Peter Kuhn, Charles F. Manski, Andrew Oswald, Adam Rosen, Joerg Stoye, Aleksey Tetenov, Christopher Taber, and seminar participants at the University of Bonn, Queen Mary University of London, the University of Edinburgh, the Institute for the Study of Labor (IZA), Rutgers University, New York Federal Reserve, and the University of Reading for comments and suggestions. All errors are my own.

Notes

According to Hirschel (2008), 23 states including the district of Columbia had some form of a mandatory arrest law by 2008, all covering felony domestic violence and many also covering misdemeanor domestic violence.

Iyenger (2009) provided evidence of reporting biases with the introduction of mandatory arrest policies following the MDVE.

This strategy for the MDVE data was adopted by Berk et al. (1988).

This strategy was adopted for the MDVE data by Angrist (2005).

Partial identification in randomized experiments with imperfect compliance was described in Manski (1990, 1996) and Balke and Pearl (1993, 1997); Kitagawa (2009) extended the partial identification treatment effects of Balke and Pearl (1993, 1997) for binary outcomes to continuous outcomes. Horowitz and Manski (2000) examined partial identification in randomized experiments when there are missing data on covariates and outcomes.

A recent review of related literature on partial identification going back to the 1930s is given in Tamer (2010). The first formal exposition of partial identification of treatment response is found in Robins (1989) and Manski (1990).

Applications of partial identification to examine crime and deterrence include Manski and Nagin (1998) and Manski and Pepper (2013). Applications in labor economics include Hotz, Mullin, and Sanders (1997) who estimated bounds on teen mother outcomes following teenage childbearing by the use of contaminated instruments; Manski and Pepper (2000) who estimated bounds on returns to schooling by using MIVs; and Blundell et al. (2007) who estimated bounds on wage inequality, which allow for nonrandom selection into work.

This approach is typical of partial identification in which progressively stronger identifying assumptions are made and a menu of outcomes (or bounds on outcomes) depending on the assumptions estimated. The approach allows one to select outcomes (or bounds on outcomes) based on identifying assumptions deemed most credible.

The arrest treatment involved arresting the suspects for short time periods, so among cases for which initial victim interviews were obtained, 43% of the suspects had been released within one day and 86% of the suspects had been released within 1 week.

Table 2 gives aggregate data for the nonarrest treatments (separation and advice) due to the focus of the literature on nonarrest versus arrest as a policy response to misdemeanor domestic violence.

The MDVE public use data files (Berk and Sherman 1993) provide data on assigned treatment, delivered treatment, and covariates for each subject but not on recidivism outcome (see also the discussion in Angrist 2005). An important consequence of the limitation on data availability was that it was not possible to take clustering into account when making inferences in the latter half of the article.

Nonarrest is a treatment in which it is equally likely that the suspect is either separated or advised by the police.

In the Roy model of occupation choice from labor economics, occupations are treatments and wages are outcomes. An individual knows the wage associated with different occupations and chooses the occupation with the highest wage.

In so far as the MDVE was carried out in specific neighborhoods for convenience of data collection, the MDVE data are representative of a population of domestic violence suspects who are found in neighborhoods similar to those of the Minneapolis precincts where the MDVE was implemented.

Regarding the construction of confidence interval associated with nonarrest, note that given the one-sided noncompliance, there are some practical problems in these estimation of confidence intervals; I make the simplifying assumption that mean recidivism associated with nonarrest among those assigned arrest and deviating to nonarrest is zero with a standard error of zero.

Adjusting for the width of the identified set ensures that when the underlying model is point identified or close to point identified, the size of the confidence interval is maintained. See details in Chernozhukov, Lee, and Rosen (2009).