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# Application 2: Minnesota Domestic Violence Experiment - PowerPoint PPT Presentation

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”

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### Application 2: Minnesota Domestic Violence Experiment

Methods of Economic Investigation

Lecture 6

• 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…)

• Describe the Experiment

• Discuss the Implementation

• Discuss the initial estimates

• Discuss the IV estimates

• 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

• Call the Police  police action

• 3 potential responses

• Separation for 8 hours

• Arrest

• Randomized which response when to which cases

• Only use low-level assaults—not serious, life-threatening ones…

• 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…

• Sometimes arrested when were supposed to do something else

• Suspect attacked officer

• Victim demanded arrests

• Serious injury

• Sometimes swapped advice for separation, etc.

Perfect compliance implies these are 100

Source: Angrist 2006

• 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

• 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)

• 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

• 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

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)}

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

Using Randomization as an Instrument treatment?

• 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 treatment?

• 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 εare correlated

The treatment?Assigned Treatment

• Random Assignment means T and εare 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? treatment?

• 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 Assumptions treatment?

• Conditional Independence: Zi independent of {Y0i , Y1i , R0i , R1i}

• Often called “exclusion restriction”

• 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? treatment?

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? treatment?

• 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 treatment?

• 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 treatment?

• Generally we do this with 2-Staged Least squares

• Comparing results in Angrist (2006)

• ITT = 0.108

• OLS (TOT + SB) = 0.070

• IV (LATE) = 0.140

What did we learn today treatment?

• 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 treatment?

• 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”