the more informative about the proportion of reticent respondents is the variance in the number of "Yes" responses in the RRQ battery.<sup>10</sup> To summarize, in this section we have suggested a simple statistical model of how respondents behave when asked sensitive questions in both the CQ and the RRQ format. In the model, there are three key parameters of interest: the probability a respondent is guilty in the sense of having done the act referred to in the sensitive question, g , the probability that a respondent is reticent, r , and the probability that a reticent respondent chooses to behave reticently in response to a specific sensitive question. We have shown how there is a unique mapping between these three parameters and three population moments: the variance of the mean number of "Yes" responses in the RRQ battery, that mean itself, and the mean rate of "Yes" responses in the CQ. In the next section we exploit this mapping to retrieve empirical estimates of these parameters using a standard method of moments estimator that equates the population moments with their sample counterparts and then solves for the parameters of interest.

# **4.  Results from the Peru Enterprise Survey**

In this section we use the Peruvian enterprise data to estimate reticence and guilt. The data are the individual observations from the 707 respondents who answer all seven sensitive RRQs listed in Table 1 and the sensitive CQ on whether firms are expected to give gifts to public officials "to get things done". We measure the values of two variables for each respondent—a dummy indicating a "Yes" response on the CQ and the mean of the seven dummies capturing "Yes" responses on the seven RRQs. We then calculate three sample moments—the means of these two variables and the variance of the mean of the seven RRQ dummies. These are the sample analogs of the moment expressions (3), (4), and (6).<sup>11</sup> Estimation of the three parameters g , r , and q using the method of moments with three moment conditions is therefore straightforward.

The estimation uses the identifying assumption that the parameter g is the same for all seven RRQs and for the CQ. For two reasons, any application of our procedure would always require such an assumption. First, each of the seven RRQs must be distinct. Second, asking the sensitive part of one of the RRQs again as a CQ would introduce the concern that some respondents might begin to question the integrity of the survey procedure itself.

The CQ asks about instances of bribing government officials, which would normally be regarded as a worse offense than the breaking of tax laws. Judging by the distribution of responses given in Table 1, the two questions on the breaking of tax laws are the least serious in our set of seven RRQs, at least in the perception of the respondents. Thus, it is reasonable to assume that our CQ has roughly the same 10 In practical applications, this leads to a trade-off in experimental design. The above statistical considerations suggest a large number of RRQs. Practicalities in implementation—finding a large number of sensitive questions with guilt rates similar to that of the CQ and then administering all these as RRQs—suggests a small number of RRQs.

11 For ease of implementation in estimation, we use the moment condition for the square of the seven dummies rather than the variance. Given that the mean of the seven dummies is one of the moment conditions also, this is formally equivalent to using the variance. The intuition of our procedure is better captured using the variance.

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