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These three selection levels introduce a bias in our analysis. Arrested clients could be on average less experienced in buying sex from street sex workers than non-arrested clients and therefore end up being caught. Moreover arrested clients motives for seeking sex workers could be different from those who were not caught. Here we do not deal explicitly with selection bias issues, which we leave for future work. Table 1 compares the sample of clients with a National sample taken from the National Health and Social Life Survey, conducted in 1992, using a nationally representative sample17 which contains extensive information on the US population aged 18–59 able to complete an interview in English.

Let Unj be the utility for client n of being j-type of client. When j = 1, the client is a ‘regular’ 50 Empirical application client and when j = 0 he is an ‘experimenter’. We will assume that Unj is given by: Unj = xn γj + εnj ; j = 0, 1; n = 1, 2, . . , N. (34) The vector xn is the same as in the ordered logit presented above, expect that it includes 1 to allow for a constant, and γj is a vector of alternative specific coefficients. By assuming that nj is extreme value distributed (the double exponential distribution) with zero expectation and a constant variance, and by assuming utility maximization, we get the following probability for being a ‘regular’ customer: K exp k=0 P(Un1 ≥ Un0 ) = K exp k=0 γ0k xnk + exp K exp = 1 + exp γ1k xnk K k=0 γ1k xnk γk xnk k=0 K k=0 (35) γk xnk where γk = γ1k − γ0k , and xn0 = 1.

7) where: a1 = α1 2α11 α3 2α33 α4 , a11 = , a3 = , a33 = , a4 = . α2 α2 α2 α2 α2 (8) Here a1 , a3 and a4 are all positive,11 and in order to have a quasiconcave utility function the following must hold: a11 + a33 < 0 (9) with a11 < 0 the marginal utility of consuming paid sex is diminishing with consumption, given reputation. If a33 < 0, the marginal utility 22 A reputation approach to the analysis of the sex market of a higher reputation capacity declines with the size of this capacity. Note, however, that it is not necessary for the quasi-concavity of the utility function that both these two parameters are negative, only the sum of them has to be negative.

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