413047-Underground-Commercial-Sex-Economy

1.1.1 Process for Deriving Estimates (In Depth)
The true value of the cash-based underground commercial sex economy in city during time is
denoted by . As it is almost impossible to measure directly, we seek to estimate it. During the
estimation process, we will think of it as a formal variable and argue that the variable is subject to
particular constraints. When we are thinking of it as a variable, it will be denoted in lowercase: .
The constraints on
will often be expressed in terms of directly measurable values of a linear
proxy for . Such proxies will be indicated via a superscript asterisk, i.e., . By solving systems of
constraints on the variable we hope to obtain an estimate for (the value for the size of the cash
UCSE); such an estimate will be denoted by a tilde:
. Analogous notational conventions apply to
the formalisms used during the analysis of cash-based underground economies for drugs guns ,
“other” , and total cash
1.2. Constraints by Proxy Ratios
Because , , and represent cash exchanged in a largely “dark transactions” in underground
commercial economies of goods and services (that is, for sex, drugs, and guns, respectively), it is difficult
to obtain data on the variables directly. Indeed, although the cash value represented by the variable
captures predominantly “visible transactions,” it too is intangible in the sense that we know of no reliable
direct measurement of it.
The key insight here is to pursue the possibility of four (4) proxy variables each of which may be
plausibly assumed to be linearly dependent on , , , and , respectively. This brings us to the next set
of assumptions:
Assumption (A3-W): There exists a variable which is a linear proxy for the cash
exchanged toward the purchase of guns—in region during time interval . We say that
a variable is a linear proxy for if it (a) sufficiently captures the ratio of cash exchanged
for guns in a given city across two distinct time intervals and :
and (b) sufficiently captures the ratio of cash exchanged for guns in a given time interval
across two distinct cities and :
Analogous assumptions (A3-D), (A3-O), and (A3-S) must be made regarding the existence of
linear proxies , , and (for , , and ) respectively. The construction of the four proxies
, , , and is treated separately in each of the four sections that follow: 1.2.1. Linear
Proxy , 1.2.2. Linear Proxy , 1.2.3. Linear Proxy , and 1.2.4. Linear Proxy ,
respectively.
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