most cases infeasible without prohibitively costly and intrusive audits. In the absence of practical alternatives, survey data on corruption will continue to be an important source of information about corruption. This in turn underscores the need for more research with the same goal as in this paper— seeking to address potential biases in survey data on corruption.

The reticence of respondents in answering sensitive questions has been a concern of survey researchers for a long time.<sup>4</sup> Much attention has been placed on techniques that aim to mitigate the problem, such as better wording of questions, the optimal structure of interviews, the use of computers, etc. (Tourangeau and Yan 2007). One fundamental contribution was made by Warner (1965), who developed the random-response question (RRQ). In the form used in our empirical work, a RRQ poses an innocuous question alongside a sensitive question and has the respondent answer only one of these. Which question is answered is dictated by the realization of an event (e.g. toss of coin) known only to the respondent, but whose probability of occurrence is known to the surveyor. The motivation for RRQs is the theory that a respondent will be less reticent if the interviewer and recipients of the survey data do not know which question was answered. If that theory is correct and respondents are candid and if the distribution of answers to the innocuous question is known a priori (e.g. probability of heads on a coin-toss), it is trivial to derive unbiased estimates of the prevalence of the sensitive behavior.

Random-response has had some successes. However, respondents often show reticence even when answering such questions. In studies where external validation of survey responses is possible, Lensvelt-Mulders et al. (2005) found that RRQs had 90% of the reticence of conventional face-to-face interview questions (CQs). RRQs performed no better than CQs on such issues as library cards, voting in elections, and arrest records. However, there is one feature of an RRQ that provides opportunities for uses different from the intentions of its designers—the randomization probability embodied in the question affects the relationship between reticence and responses. Using this insight, Clarke and Deshairnais (1998), Moshagen and Musch (2012), and Moshagen, Musch, and Erdfelder (2012) suggest creating subsamples of respondents and asking them RRQs with different randomization probabilities. They then derive insights into levels of reticence and guilt.<sup>5</sup> In the economics literature, Azfar and Murrell (2009) and Clausen, Kraay, and Murrell (2011) used a series of seven RRQs, in firm surveys in Romania and Nigeria respectively. They noted that a "No" answer on any single question implied a coin coming up tails. Since the occurrence of seven tails has a very low probability, these papers classified those responding with seven "No's" as reticent. In these surveys, those so classified reported significantly lower rates of commission of sensitive acts and claimed higher levels of personal ethics. These papers did not estimate population rates of reticence and guilt, since their primary goal was to show how to identify a set of respondents who were reticent with near certainty, to show that there were significant numbers of such respondents, and to examine the distinctive ways in which these respondents answered sensitive questions.

> 4 See for example, Warner (1965), Campbell (1987), Clark and Desharnais (1998), and Tourangeau and Yan (2007). 5 Moshagen and Musch (2012) estimate the proportion of respondents who do not follow the RRQ procedure faithfully (non-adherents), which is thought to happen because that procedure places even innocent respondents in a position that looks like they are admitting to the sensitive act.  Moshagen, Musch, and Erdfelder (2012) estimate rates of reticence assuming that there are no non-adherents.

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