413047-Underground-Commercial-Sex-Economy

using interview data for the relative size of the underground commercial sex economy and proxies for the
other cash categories. Unfortunately, during initial pilot interviews, we determined that pimps would not
be able to express the relative size of different markets across cities or over time. Since this posed a
serious problem, we sought instead to estimate the relative size based on the available interview data. The
total amount of underground commercial sex market revenue is the product of average income per sex
worker, multiplied by the number of sex workers. The interview data provided ample information to
estimate the average income per sex worker. The problem, then, is to estimate the relative size of the sex
worker population.
To do so, we employed the conceptual approach of a gravity model, popularized in social science by
(among other applications) migration and trade decisions. Isaac Newton discovered that gravity exists
between any two objects and the attraction between those objects could be expressed based on the size of
each object and the distance between them. The larger the object, the stronger the pull. The closer they
are, the stronger the pull. This approach has been brought to the social science field and applied to a wide
variety of issues, including migration and trade. The intuition behind using this method for our purposes
is as follows: Suppose there are three objects on a table and you know each object’s location. Also, suppose
that you are told the strength of the gravitational pull between those objects. Based on the pull’s strength
between these three locations, you can determine the size of each object.
We adapted this logic and, instead of objects on a table, we considered cities in the United States. Instead
of measuring the gravitational pull between the cities, we measured the “pull” on pimps. Consider three
cities: Kansas City, Dallas, and Atlanta. A pimp who works in Kansas City is deciding whether to also work
in Dallas or Atlanta. His decision will be influenced by the distance to the potential new city and the size
of its market. Likewise, pimps in Dallas and Atlanta are deciding whether to work in the other cities. With
a large enough number of pimps, we can observe what portion of pimps from each city decided to go to
each of the other cities and, because we know how far apart the cities are, we can infer the “pull” of each
city.
We used a logistic regression to estimate the propensity to travel of each pimp (the mass of the pimp), the
effect of distance on pimps’ decision to travel, and the residual appeal of each city. This appeal of each city
is a latent variable that leads to sex worker migration decisions. Then we can infer the relative number of
sex workers who choose to work in a given city based on the residual appeal estimated in the logistic
regression. Note that this gives information only on the relative number of sex workers. With the relative
number of workers and the average income per worker, we were able to construct a proxy for the size of
the underground commercial sex economy.
Our initial method proposed using a single proxy for the relative size of the underground drug and
weapons markets, as well as for other uses of cash. However, in reading the literature for potential
proxies, we developed a list of multiple appropriate proxies. When looking at these proxies, we realized
that they had very different implications for the patterns of underground activity over time and across
place. Therefore, we sought instead to aggregate proxies using a simple regression.
Over the course of the study, we collected a variety of proxies by using city-specific data from a number of
national-level data collection efforts. In total, we had seven drug proxies (including number of drug users
reported in the National Survey of Drug Use and Health [NSDUH]; number of youth encountering drugs
reported in the Youth Risk Behavior Surveillance System [YRBSS]; and number of drug-related visits to
the emergency department reported in the Drug Abuse Warning Network [DAWN]), three proxies for
guns (including number of students carrying a gun reported in the YRBSS; weapons seized by the Bureau
of Alcohol, Tobacco, and Firearms [ATF]; and the fraction of suicides committed with firearms reported
in National Vital Statistics data [NVSS]), and three proxies for “other” (including construction-related
employment and food service employment).
However, these proxies are in completely different units. To aggregate across proxies, we must convert
them to comparable units. For each proxy, we divided each city and year by the value for Miami in 2003
(since this was the observation with the most data available). For example, one drug proxy was the
percent of high school students offered, sold, or given drugs at school, weighted by the population of the
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