413047-Underground-Commercial-Sex-Economy

direct estimation method applied to the survey data generates values of
below.
provided in the table
Table 3.4 Proxy
for Pimp Population Size
City
Atlanta 0.212
Dallas 0.207
Denver 0.054
Miami 0.410
San Diego 0.103
Seattle 0.105
DC 0.139
Kansas City N/A
A potential objection to the aforementioned proxy is that it does not take into account the distance
between UCSE participant’s home city and candidate city. Such an objection, if valid, would further argue
that the reason Seattle attracted few UCSE participants could be that Seattle is far away from the other
cities in the sample—and not that it is inherently unattractive. Such a sampling frame necessarily implies
that cities which are central (resp. distant) from the cities in the study would witness larger (resp.
smaller) cardinalities for , which, in turn would introduce a distance related bias into the above
proxy. The next proxy remedies this specific potential concern.
B. Pimp Population Size Proxy : Gravity Model based Estimation
Here we present the Gravity Model, a stochastic process that governs the inclination of pimps to work in
cities outside of their “home” city. In the limit (of large pimp populations and long timescales), the Gravity
Model yields a stationary distribution of the numbers of pimps across cities.
We follow the notational conventions of the previous section, restated briefly here:
is the set of UCSE participants, and
is the set of cities. Each UCSE participant
identifies a “home” city , as well as the set of cities, excluding , which they
“visited” in the course of their work history.
For the Gravity Model, we assume that each city
has some exogenously determined (and possibly
unobservable) characteristic that stands to attract each UCSE participant to it, leading them to
overcome the costs implied by the distances between their home at and .
Let be an indicator variable encoding whether UCSE participant decided to work in city
. We express via a logistic model
where is the “attraction force” between UCSE participant and city . Following the formal
structure of the gravitational law in Newtonian mechanics, we take the force of attraction to exhibit the
following proportionalities
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