behavior, apply the model to the two types of questions, and show how the key parameters of the model can be estimated.

The analysis follows and expands on that of Kraay and Murrell (2015). Their initial implementation of the above methodology focused on a CQ that asks all respondents (for example, company officials acting on behalf of firms) whether a bribe is required when government officials provide some sort of service.<sup>3</sup> This is a very general question that does not generate information on any specific government agency, and as such is not a good guide to specific anticorruption measures aimed at particular government agencies. To be more useful to policy makers, the CQ must be more specific, asking, for example, about levels of corruption in a named government agency. But then a problem of analysis immediately arises. Whereas most firms are likely to have had interactions with at least one government official and therefore can answer a nonspecific question, not every firm will interact with any given agency's officials. This necessitates a subtle change in the nature of the survey question asked, which in turn has significant implications for modeling how respondents answer survey questions.

Consider the subject matter of this paper. The World Bank Enterprise Surveys project (World Bank, 2015; henceforth WBES), from which our data come, asks a two-step question about each of a series of government officials. First, it asks whether the firm has been visited by a specific type of official in the past 12 months. Then, the survey goes on to inquire about whether a gift or payment was required only if the respondent acknowledged that a visit occurred. For such two-step questions, modeling respondent behavior is more complex because respondents might be reticent in answering the question about a visit in order to forestall being asked the follow-up question about the bribe. Additionally, this reticence in acknowledging the visit might depend on whether a request for a bribe had occurred. This adds more complexity to the modeling process, because evaluating the answers to one question (the bribe) cannot be done independently of evaluating the answers to another (the visit). In this paper, we extend the Kraay-Murrell (2015) analytics to cover the case of two-step questions. We use the example of a two-step question asking about interactions with tax officials, but as we note below analogous two-step questions are very common across a whole range of well-known surveys, and so our methodology is broadly applicable in these other settings as well.

In Section 2, we provide the background to the current exercise, describing the data sets and survey questions used. We use data from seven countries included in the World Bank Enterprise Surveys project— Bangladesh, India, Nigeria, Peru, Sri Lanka, Turkey, and the Ukraine -- where we have fielded the random response questions essential to the implementation of our methodology. Thus one contribution of this paper is to compare rates of reticence across countries, then examining the degree to which the underestimation of corruption varies across nations. This has important implications for the production of valid cross-national comparisons of corruption.

> 3 Kraay and Murrell (2015) used two different data sets in their implementation.  For brevity, we focus on their implementation that uses data from the World Bank's Enterprise Surveys project (World Bank, 2015), since this project also provides the data for the set of countries on which this paper focuses.

4