413047-Underground-Commercial-Sex-Economy

1.4. The Linear Program
1.4.1. Sex Proxy Ratio Constraints
For each distinct pair of cities and choice of time index , we introduce upper and
lower bound ratio constraints bounding the relative sizes of the cash-based sex economies of cities and
cities .
These constraints codify that the ratio of values the sex variables must agree with the corresponding
ratios of the linear proxy , up to a slack margin of . In our analysis, we took , allowing
for a 20 percent deviation of the sex variable ratios from the proxy ratios. The setting of the slack margin
was determined to be reasonable based on an analysis of the mean standard deviation of the weekly gross
cash intake across pimps across cities/times (which is a constituent of linear proxy , as described in
section 1.2.1).
Additionally, for each city we introduce upper and lower bound ratio constraints on the relative
change in the cash-based sex economy of from to .
This yields a homogeneous system of
which concern relative sizes cash-based sex economies.
linear ratio inequalities on the 14 variables
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