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413047-Underground-Commercial-Sex-Economy

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1.2.1. Linear Proxy<br />

We say that a variable is a linear proxy for if it is proportional to . In other words, we require that<br />

there exists some such that for some real number which is invariant over<br />

time and place. Note that we do not need to know what is. In other words, is a linear proxy if it (a)<br />

sufficiently captures the ratio of cash exchanged for sex in a given city across two distinct time intervals<br />

and :<br />

and (b) sufficiently captures the ratio of cash exchanged for sex in a given time interval<br />

two distinct cities and :<br />

across<br />

Modification to the Methodology Originally Proposed<br />

The methodology described in our original project proposal sought to estimate the relative sizes of cities’ commercial<br />

sex markets based on direct reports from pimps who worked in both cities. We had hoped to elicit Likert-scale<br />

responses such as<br />

“If the market in Atlanta is a 10, then the market in Kansas City is a 2.”<br />

Unfortunately, the subjects (pimps) interviewed were unable to provide information of this form. Subjects were,<br />

however, able to provide very specific information about their average weekly gross cash intake. In order to scale this<br />

gross cash intake data up to a linear proxy for S, we needed to construct a linear proxy for the number of pimps that<br />

worked in each city in a given time interval.<br />

The revised approach we took was to define the proxy<br />

as a product<br />

where is the mean weekly gross cash intake per pimp (by city and time) and is a<br />

linear proxy for pimp population size<br />

by city.<br />

Example<br />

Suppose we knew that “At any given time, the number of pimps working in Atlanta<br />

versus the number of<br />

pimps working in Kansas City is in a 1.5:1.2 ratio,” and we knew that “Pimps in Atlanta report a mean<br />

gross cash intake of $3,000 a week for 2012, while pimps in Kansas City reported $2,000 a week for 2012.”<br />

Then taken together, we could deduce:<br />

Thus (hypothetically) we could conclude that in 2012, the size of the cash-UCSE in Atlanta is approximately<br />

1.875 times the size of the cash-based UCSE in Kansas City.<br />

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