413047-Underground-Commercial-Sex-Economy

These constraints codify that the ratio of values the gun 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 1 percent deviation of the gun variable ratios from the gun proxy ratios. The setting of the slack
margin was determined to be reasonable based on the fact that several coherent low-level proxies for guns
were aggregated to form (see 1.2.3. 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 gun economies.
linear ratio inequalities on the 14 variables
An Example of Gun Proxy-based Ratio Constraints
The two tables below (Table 3.16 Cross-City Gun Proxy Ratios) list the cross-city ratios of the guns proxy , in
2003 and 2007. The table tells us, for example, that in 2003 the proxy for the underground cash-based drug economy
in DC ( was 1.27 times what it was in Atlanta ( . This single ratio entry would give rise to two linear
constraints:
The next table (Table 3.17 Cross-Year Gun Proxy Ratios) lists the cross-year ratios of the guns proxy (value in
2007 over the value in 2003). The table tells us, for example, that the underground cash-based gun economy in Miami
in 2007 was 12 percent higher than it was in 2003. This single ratio entry would give rise to two linear
constraints:
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