There is a considerable amount of disagreement regarding how to deal with young offenders. For the purpose of this exam,

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There is a considerable amount of disagreement regarding how to
deal with young offenders. For the purpose of this exam, young
offenders are those between 15-17 who are charged with a crime and
cannot be charged as an adult. Recidivism is high among young
offenders who commit petty crimes. On the one hand, some argue that
stiffer punishments will deter young offenders from recommitting a
crime, and therefore we should deal with this group harshly to
avoid repeat offenses. On the other hand, some argue that putting
youth in jail or corrections institutions isolates them from
society and reinforces criminal behavior that they learn from their
peers in the correction system. Thus, we should avoid jail and
harsh punishment when possible and attempt to rehabilitate the
young offenders.
There are a set of policies designed to rehabilitate young
offenders. These include counseling, meeting victims of their
crimes in person, educational programs and probation and
supervision. Those who advocate for harsher punishment refer to
these policies as `coddling’ the young offenders. They prefer the
standard approach of jail time or community service. When a case is
brought to court, the judge decides which course of action to
pursue: coddling or punishing. Judges make their decision given
their own beliefs about each program and the circumstances of the
case. For example, a judge my pursue a harsh penalty when a weapon
was involved in a crime, because this might be an indicator of type
of criminal involved in the offense.
Given that the treatment of young offenders is left to the
judges discretion, it is hard to make causal claims about which
method is better at reducing recidivism. Thus, to pursue the matter
further, the city of Vancouver conducted a randomized trial. All
youth cases that were brought before the court for judgment were
randomly assigned into treatment and control groups (punishment or
coddled).
In practice, judges sometimes did not comply with random
assignment. When a case comes before a judge, it is assigned a
number. This number was randomly generated to end with
a 0 or 1, indicating that the youth was to be put
into the control or treatment group. However, judges could assign
whatever punishment they saw fit given the circumstances of the
crime, since participation was voluntary. For the most part, judges
did follow the recommended assignment. Deviations could occur
because of a judge’s mistake, the circumstance of a crime, or the
judge’s own interaction with the youth, and so on.
The data for this question: Get data
The main relationship of interest is:
Ri=α+δPi+ηi(1)(1)Ri=α+δPi+ηi
That is, we’d like to know whether punishing young offenders
affects the rate of recidivism.
(a)
Estimate equation (1). Are those that are punished more likely
to re-offend? Is this relationship likely to be causal?
(b)
Since the judge might deviate from the ranodm assignment based
on circumstances of the crime, a CIA strategy might work.
Re-estimate (1) controlling for other characteristics of the case,
such as whether a gun was involved. Does this change your
conclusions from (a)? Speculate on why?
(c)
Assume that there is treatment heterogeneity. That is, each
youth might respond differently to being punished. Run an OLS
equation, with the same controls you used in part (b), but
replace P, actual punishment, with Z the assignment
that the judge was supposed to follow. Interpret your output, what
parameter does this reduced form regression yield?
(d)
Now estimate the first-stage, using the controls in part (b).
What was the compliance rate of the judges? Is the instrument
relevant?
(e)
Use your reduced form and first stage estimates to find the 2SLS
estimates of the impact of punishment on recidivism. Why is it
different from the coefficient in part (c)? Do you think that
pushishing youth is a good policy?