413047-Underground-Commercial-Sex-Economy

1.2.4. Linear Proxy
We followed the exact same procedure to estimate as we did to estimate . Again, we had fewer proxy
variables available, with . The computed values of the other proxy are given in the table
below.
Table 3.10 Final Values of Proxy O*
Year Atlanta Dallas Denver Miami San Diego Seattle DC
2003 0.961 1.121 0.496 1.019 0.564 0.643 0.979
2007 1.120 1.324 0.481 1.027 0.568 0.695 1.179
1.3. The Left Hand Side : Estimating Total Cash in Circulation
The approach used to estimate total cash in circulation evolved over time. For a more complete
description of this process, see chapter 2. In the end, we estimated the average ratio of currency in
circulation to real GDP using national data. We then multiplied this ratio by each city’s real GDP,
available from the Bureau of Economic Analysis, to yield a city-level estimate of currency in circulation.
Because city-level currency data is not available, it must be estimated using national data. A naïve
approach might be simply to multiply the national currency-GDP ratio by city-level GDP. In other words,
one might calculate city-level currency in city at time using this formula: 40
However, the currency-GDP ratio varies over time. Specifically, it is likely that the national currency-GDP
ratio varies systematically with economic conditions, such as personal income, employment rates, and
inflation rates. If cities differ along these dimensions, this information can help generate more accurate
estimates of city-level currency volumes.
To identify this systematic variation, we used quarterly data from the St. Louis Federal Reserve Bank’s
Federal Reserve Economic Data (FRED). We used all available years (1959–2012) and a simple linear
model to estimate systematic covariation between economic variables and the national currency-GDP
ratio. Specifically, we estimated the following model: 41
Variable
Coefficient
estimate
Standard
error
t-statistic
Intercept 0.319*** 0.052 6.18
Per capita personal income -6.96*** 1.507 4.62
Per capita real GDP 6.458*** 1.309 4.94
Ratio of GDP to personal income -0.227*** 0.048 4.68
Employment-population ratio -0.084*** 0.013 6.5
Business income as percent of total income 0.28*** 0.03 9.48
Inflation rate -0.032*** 0.007 4.63
40 Alternatively, one might use the national currency-GDP ratio from year . This does not substantially change the results.
41 We experimented with a range of additional variables which had little predictive power. We also considered several specifications
of temporal effects (such as linear or quadratic time trends and decade-specific intercepts). These did not significantly change the
results.
36