413047-Underground-Commercial-Sex-Economy

These constraints codify that the ratio of values the other 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% deviation of the other variable ratios from the other proxy ratios.
The setting of the slack margin was determined by considering the variation in low-level proxies
aggregated to form (see section 1.2.4. Linear Proxy ).
Additionally, for each city we introduce upper and lower bound ratio constraints on the relative
change in the cash-based gun economy of from to .
This yields a homogeneous system of
which concern relative sizes of cash-based “other” economies.
An Example of Other Proxy based Ratio Constraints
linear ratio inequalities on the 14 variables
The two tables below (Table 3.18 Cross-City Other Proxy Ratios) list the cross-city ratios of the other proxy , in
2003 and 2007. The table tells us, for example, that in 2003 the proxy for the underground cash-based other economy
in Seattle ( was 1.37 times what it was in Denver ( . This single ratio entry would give rise to two linear
constraints:
The next table (
Table 3.19 Cross-Year Other Proxy Ratios) lists the cross-year ratios of the other proxy O^* (value in 2007 over the
value in 2003). The table tells us, for example, that the underground cash-based other economy in San Diego (c_4) in
2007 was 10 percent higher than it was in 2003. This single ratio entry would give rise to two linear constraints:
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