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



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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


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Suspect attacked officer
Victim demanded arrests
Serious injury

Sometimes swapped advice for
separation, etc.

Sometimes forgot pad
Nature of Compliance Problem
Perfect compliance
implies these are 100
Source: Angrist 2006
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:
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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)

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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
Individuals who
were not coddled

Individuals who
were coddled
Don’t know what an individual would have
done, had they not received observed
treatment
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)}
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

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 Assumptions
1.
Conditional Independence: Zi
independent of {Y0i , Y1i , R0i , R1i}

2.
Often called “exclusion restriction”
Monotonicity: R1i ≥ R0i or vice versa for
all individuals (i)

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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?
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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

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We’ll talk about this in a couple weeks
Comparing results in Angrist (2006)
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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:
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Regressions as a Conditional Expectation
Function
When can a regression be interpreted as a
causal effect
What do we do with “controls”