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Similarly, let s1
be the share of visitors victimized by
residents, and s2 the share of visitors
victimized by visitors. Then
the crime rate is s1 +s2 +(s1 +s2)V
P ; the diluted crime rate is (s1 +s2)wP +(s1
+s2)wV where wP
and wV are the share of visitors plus residents
made up by residents and visitors, respectively;
and the
probability of a resident’s being a crime victim
is s1 +s2. If residents do not victimize
visitors (s1 = 0),
then P = V and (s2 + s2) is smaller than s1. The
probability of a resident’s being victimized is
s1
without visitors, and it rises to s1 + s2 with
visitors. The diluted crime rate is s1 without
visitors and
falls to (s1 +s2 +s2)/2 with visitors. Thus in
this case the diluted crime rate falls while the
probability
of a resident’s being victimized rises.
In this study we are interested in the costs in
the host county associated with a change in
crime
from whatever source. We are therefore
interested in the total effect of casinos on
crime, and thus use
the undiluted crime rate based on equation (3).
C. Timing: Separating Casino Effects from Other
Effects
The version of equation (3) that we estimated is
Cit = a + ßiXi + ?tTt + dLit + ?Ait + eit (4)
where Cit is the crime rate (offenses per
100,000 people) of county i in year t, a is a
constant, and
ßi is the vector of estimated coefficients on
the county-level fixed effects that control for
unobserved
characteristics across counties. The time fixed
effect, Tt, controls for national crime rate
trends. Our
base specification of Lit is a vector of the
casino opening dummy variables that includes 2
leads and
casinos (coefficient d) and reported in section
IV. For example, we estimated the long-run
effect of a casino on
larcenies to be 615, which was roughly 60 times
larger than the effect of one million national
park visitors. This
means that if the crime consequences of casino
visitors and national park visitors were
identical, a casino would
have to attract over 59 million visitors
annually to account for 615 additional
larcenies. Las Vegas, the single
largest casino gambling destination in the
United States, attracted 30.3 million visitors
in 1994.
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