application 2: minnesota domestic violence experiment methods of economic investigation lecture 6
TRANSCRIPT
Application 2: Minnesota
Domestic Violence Experiment
Methods of Economic Investigation
Lecture 6
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…)
Outline Describe the Experiment
Discuss the Implementation
Discuss the initial estimates
Discuss the IV estimates
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
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…
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…
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
Nature of Compliance Problem
Source: Angrist 2006
Perfect compliance implies these are 100
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
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)
Putting this in the IV Framework Simplify a little:
Two behaviors: Arrest or Coddle Can generalize this to multiple treatments
Outcome variable: Recidivism (Yi) Outcome for those coddled : Y1i
Outcome for those not coddled (Arrest): Y0i
Observed Recidivism Outcome Both outcomes exist for everyone BUT we
only observe one for any given person
Yi = Y0i(1-Ri)+Y1iRi
Don’t know what an individual would have done, had they not received observed treatment
Individuals who were not coddled
Individuals who were coddled
What if we just compared differences on outcomes based on treatment?E(Yi |Ri=1) – E(Yi | Ri=0) =
E(Y1i |Ri=1) – E(Y0i | Ri=0) =
E(Y1i - Y0i |Ri=1) –{E(Y0i | Ri=1) – E(Y0i | Ri=0)}
TOTInterpretation: Difference between what happened and what would have happened if subjects had been treated
Selection Effect > 0 because treatment delivered was not randomly assigned
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
The Regression Framework Suppose we just have a constant treatment
effect Y1i - Y0i = α
Define the mean of the Y0i = β + εi where E(Y0i)= βi
Outcomes: Yi = β + αR i + εi
Restating the problem: R and ε are correlated
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
How do we get this in real life? First, a bit more notation. Define
“potential” delivered treatment assignments so every individual as: R0i and R1i
Notice that one of these is just a hypothetical (since we only observe one actual delivered treatment)
R = R0i + Ti (R1i – R0i )
Identifying Assumptions1. Conditional Independence: Zi
independent of {Y0i , Y1i , R0i , R1i} Often called “exclusion restriction”
2. Monotonicity: R1i ≥ R0i or vice versa for all individuals (i)
WLOG: Assume R1i ≥ R0i In our case: assume that assignment to
coddling makes coddling treatment delivered more likely
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-deliveredi) = b0 + b1(Coddle Assignedi) + B’(Other Stuffi) + ei
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 R1i ≥ R0i Some will do it no matter what: These are the
“always takers” R1i = R0i =1 Some will never do it no matter what: These
are the “never takers” R1i = R0i =0
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(Y1i - Y0i |R1i>R0i)
Intuition: Because treatment status of always and never takers is invariant to the assigned treatment: LATE uninformative about these
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
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!)
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”