Section 3 details how we model a respondent formulating a response to the two-step question. We consider two alternative models with different assumptions on how reticence affects the respondent's approach to the first part of the question on whether a visit occurred. Our first model assumes respondents are reticent only on direct questions on corruption and are candid on questions about the visit of a government official. Our second model assumes that a question about a visit is innocuous to all respondents who have not subsequently experienced a bribe request, but a reticent respondent who has experienced a bribe request will be reticent about reporting visits. We show that estimates of corruption and reticence depend upon which model of respondent behavior is used. Section 3 also describes how we model the responses to RRQs, showing that such responses are a function of the same parameters as responses to the two-part CQ.

Section 4 describes the maximum likelihood estimation procedure. Section 5 presents estimates of the two different models for each of the countries, comparing these to standard estimates of corruption that assume all answers were candid. Section 6 presents summary cross-country results based on estimates for the preferred model for each country. We estimate that the rate at which questions on bribes are answered reticently runs from a low of 27% in Bangladesh to a high of 64% in India. Not surprisingly these rates of reticence cause corruption to be significantly underestimated in all countries.

We introduce the concept of effective corruption, a derived parameter. Effective corruption is the unconditional probability of a randomly-selected firm being directly involved in a corrupt interaction with a government official from a specific agency. It is equal to the probability of a visit by an official times the probability of a bribe being solicited on a given visit. The latter probability—that is, the conditional and not the unconditional one—is the one reported in standard sources in the literature, for example by the WBES. Effective corruption adds insights by taking into account the frequency of visits by officials, which is especially important because our estimates show that respondents can be reticent in answering questions about whether visits have occurred. This implies that simple reported rates of visits by government officials cannot be taken at face value, but must be corrected for reticence in a manner similar to that used for reported rates of bribe frequency.

We obtain maximum likelihood estimates of the degree of downward bias of effective corruption in standard (non-reticence-adjusted) measures of corruption. These estimates range from a low of 12% in Nigeria to a high of 90% in Turkey. That is, only 10% of corruption by tax officials is reported in standard estimates for Turkey. Thus our methods produce startling changes in perceptions of relative corruption: Peru is perceived as more than twice as corrupt as Turkey in standard estimates, while Turkey appears more than twice as corrupt as Peru in our estimates. Estimates of the propensity of officials to make visits to firms are also affected. In India, for example, tax officials visit 50% more firms than standard estimates suggest.

Since effective corruption is the probability of a bribe being solicited by a visiting official times the probability of a visit, we can use our methods to decompose any bias in the perception of effective corruption between bias on estimates of bribes and bias on estimates of visits. In India, our estimates of 5