1. Application 2: Minnesota Domestic Violence Experiment Methods of Economic Investigation Lecture 6

2. Why are we doing this?  Walk through an experiment Design Implementation Analysis Interpretation  Compare standard difference in means with “instrumental variables”  Angrist (2006) paper is a very good and easy to understand exposition to this (he’s talking to criminologists…)

3. Outline  Describe the Experiment  Discuss the Implementation  Discuss the initial estimates  Discuss the IV estimates

4. Minnesota Domestic Violence Experiment (MDVE)  Motivated over debate on the deterrence effects of police response to domestic violence  Social experiment to try to resolve debate: Officers don’t like to arrest (variety of reasons) Arrest may be very helpful

5. Experiment Set-up  Call the Police  police action  3 potential responses Separation for 8 hours Advice/mediation Arrest  Randomized which response when to which cases  Only use low-level assaults—not serious, life-threatening ones…

6. How did they randomize?  Pad of report forms for police officers  Color coded with random ordering of colors  For each new case, get a given response with probability 1/3 independent of previous action  Police need to implement…

7. What went wrong? Police Compliance  Sometimes arrested when were supposed to do something else Suspect attacked officer Victim demanded arrests Serious injury  Sometimes swapped advice for separation, etc.  Sometimes forgot pad

8. Nature of Compliance Problem Source: Angrist 2006 Perfect compliance implies these are 100

9. Where are we?  Experiment intended to randomly assign  Treatment delivered was affected by a behavioral component so it’s endogenous Treatment determined in part by unobserved features of the situation that’s correlated with the outcome  Example: Really bad guys assigned separation all got arrested Comparing actual treatment and control will overstate the efficacy of separation

10. Definition: Intent to Treat (ITT)  Define terms: Assigned to treatment: T =1 if assigned to be treated, 0 else Received treatment: R = 1 if treatment delivered, 0 else Ignore compliance and compare individuals on the initial random assignment ITT = E(Y | T=1) – E(Y | T=0)

11. Putting this in the IV Framework  Simplify a little: Two behaviors: Arrest or Coddle Can generalize this to multiple treatments  Outcome variable: Recidivism (Y i ) Outcome for those coddled : Y 1i Outcome for those not coddled (Arrest): Y 0i

12. Observed Recidivism Outcome  Both outcomes exist for everyone BUT we only observe one for any given person  Y i = Y 0i (1-R i )+Y 1i R i  Don’t know what an individual would have done, had they not received observed treatment Individuals who were not coddled Individuals who were coddled

13. What if we just compared differences on outcomes based on treatment? E(Y i |R i =1) – E(Y i | R i =0) = E(Y 1i |R i =1) – E(Y 0i | R i =0) = E(Y 1i - Y 0i |R i =1) –{E(Y 0i | R i =1) – E(Y 0i | R i =0)} TOT Interpretation: Difference between what happened and what would have happened if subjects had been treated Selection Effect > 0 because treatment delivered was not randomly assigned

14. Using Randomization as an Instrument  Consequence of non-compliance: relation between potential outcomes and delivered treatment causes bias in treatment effect  Compliance does NOT affect the initial random assignment Can use this to recover ITT effects

15. The Regression Framework  Suppose we just have a constant treatment effect Y 1i - Y 0i = α  Define the mean of the Y 0i = β + ε i where E(Y 0i )= β i  Outcomes: Y i = β + αR i + ε i  Restating the problem: R and ε are correlated

16. The Assigned Treatment  Random Assignment means T and ε are independent  How can we recover the true TE?  This should look familiar: it’s the Wald Estimator

17. How do we get this in real life?  First, a bit more notation. Define “potential” delivered treatment assignments so every individual as: R 0i and R 1i  Notice that one of these is just a hypothetical (since we only observe one actual delivered treatment) R = R 0i + T i (R 1i – R 0i )

18. Identifying Assumptions 1. Conditional Independence: Z i independent of {Y 0i, Y 1i, R 0i, R 1i } Often called “exclusion restriction” 2. Monotonicity: R 1i ≥ R 0i or vice versa for all individuals (i) WLOG: Assume R 1i ≥ R 0i In our case: assume that assignment to coddling makes coddling treatment delivered more likely

19. What do we look for in Real Life? Want to make sure that there is a relationship between assigned treatment and delivered treatment so test: Pr(Coddle-delivered i ) = b 0 + b 1 (Coddle Assigned i ) + B’(Other Stuff i ) + e i

20. What did Random Assignment Do?  Random assignment FORCED people to do something but would they have done treatment anyway? Some would not have but did because of RA: these are the “compliers” with R 1i ≥ R 0i Some will do it no matter what: These are the “always takers” R 1i = R 0i =1 Some will never do it no matter what: These are the “never takers” R 1i = R 0i =0

21. Local Average Treatment Effect  Identifying assumptions mean that we only have variation from 1 group: the compliers  Given identifying assumptions, the Wald estimator consistently identifies LATE LATE = E(Y 1i - Y 0i |R 1i >R 0i )  Intuition: Because treatment status of always and never takers is invariant to the assigned treatment: LATE uninformative about these

22. How to Estimate LATE  Generally we do this with 2-Staged Least squares We’ll talk about this in a couple weeks  Comparing results in Angrist (2006) ITT = 0.108 OLS (TOT + SB) = 0.070 IV (LATE) = 0.140

23. What did we learn today  Different kinds of treatment effects ITT, TOT, LATE  When experiments have problems with compliance, it’s useful have different groups (always-takers, never-takers, compliers)  If your experiment has lots of compliance issues AND you want to estimate LATE—you can use Instrumental Variables (though you don’t know the mechanics how yet!)

24. Next Time  Thinking about Omitted Variable Bias in a regression context: Regressions as a Conditional Expectation Function When can a regression be interpreted as a causal effect What do we do with “controls”