metadata: authors: 0: author: Karalashvili,Nona
1: author: Kraay,Aart C.
2: author: Murrell,Peter
count: World
docna: 0: docna: Doing the survey two-step : the effects of
            reticence on estimates of corruption in two-stage survey questions
docty: Policy Research Working Paper
subtopic: Judicial System Reform,Health Care Services Industry,Employment and Unemployment,Crime and Society
teratopic: Public Sector Development,Governance,Macroeconomics and Economic Growth
abstracts: cdata!: This paper develops a structural
            approach for modeling how respondents answer survey
            questions and uses it to estimate the proportion of
            respondents who are reticent in answering corruption
            questions, as well as the extent to which reticent behavior
            biases down conventional estimates of corruption. The
            context is a common two-step survey question, first
            inquiring whether a government official visited a business,
            and then asking about bribery if a visit was acknowledged.
            Reticence is a concern for both steps, since denying a visit
            sidesteps the bribe question. This paper considers two
            alternative models of how reticence affects responses to
            two-step questions, with differing assumptions on how
            reticence affects the first question about visits.
            Maximum-likelihood estimates are obtained for seven
            countries using data on interactions with tax officials.
            Different models work best in different countries, but
            cross-country comparisons are still valid because both
            models use the same structural parameters. On average, 40
            percent of corruption questions are answered reticently,
            with much variation across countries. A statistic reflecting
            how much standard measures underestimate the proportion of
            all respondents who had a bribe interaction is developed.
            The downward bias in standard measures is highly
            statistically significant in all countries, varying from 12
            percent in Nigeria to 90 percent in Turkey. The source of
            bias varies widely across countries, between denying a visit
            and denying a bribe after admitting a visit.
repnme: repnme: Doing the survey two-step : the effects of
            reticence on estimates of corruption in two-stage survey questions
display_title: Doing the survey two-step : the
            effects of reticence on estimates of corruption in two-stage
            survey questions
listing_relative_url: /research/2015/05/24531877/doing-survey-two-step-effects-reticence-estimates-corruption-two-stage-survey-questions
topicv3: Justice m1326106 840,Criminal Justice m1326993 1014,Crime m1439217 3041,Enterprise Surveys m1504072 2762,Health m1504661 3480
publishtoextweb_dt: 2015-05-22T00:00:00Z
historic_topic: Public Sector Development,Governance,Macroeconomics and Economic Growth
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
no_of_pages: 43
author_keys: 0: author_key: 1304920
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2: author_key: 454682
model_extractions: WPS7276 Policy Research Working Paper 7276

# Doing the Survey Two-Step

The Effects of Reticence on Estimates of Corruption in Two-Stage Survey Questions _Nona Karalashvili Aart Kraay Peter Murrell_ Development Research Group Macroeconomics and Growth Team May 2015
Policy Research Working Paper 7276

# **Abstract**

This paper develops a structural approach for modeling how respondents answer survey questions and uses it to estimate the proportion of respondents who are reticent in answering corruption questions, as well as the extent to which reticent behavior biases down conventional estimates of corruption. The context is a common two-step survey question, first inquiring whether a government official visited a business, and then asking about bribery if a visit was acknowledged. Reticence is a concern for both steps, since denying a visit sidesteps the bribe question. This paper considers two alternative models of how reticence affects responses to two-step questions, with differing assumptions on how reticence affects the first question about visits. Maximum-likelihood estimates are obtained for seven countries using data on interactions with tax officials. Different models work best in different countries, but cross-country comparisons are still valid because both models use the same structural parameters. On average, 40 percent of corruption questions are answered reticently, with much variation across countries. A statistic reflecting how much standard measures underestimate the proportion of all respondents who had a bribe interaction is developed. The downward bias in standard measures is highly statistically significant in all countries, varying from 12 percent in Nigeria to 90 percent in Turkey. The source of bias varies widely across countries, between denying a visit and denying a bribe after admitting a visit.

This paper is a product of the Macroeconomics and Growth Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at akraay@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Doing the Survey Two-Step:  The Effects of Reticence on Estimates of Corruption in Two-Stage Survey Questions**

Nona Karalashvili (University of Maryland and The World Bank) Aart Kraay (The World Bank) Peter Murrell (University of Maryland)

**JEL Classification Codes:** C83, O17, O43

**Keywords:** Corruption, reticence, random response questions

The authors can be contacted at nona.karalashvili@gmail.com, akraay@worldbank.org, or <u>murrell@econ.umd.edu. A first version of this paper was presented at the Conference on “Ethics and</u> Corporate Malfeasance: Interdisciplinary Perspectives", organized by the Center for the Study of Business Ethics, Regulation, and Crime (C-BERC), University of Maryland, September 12, 2014. We thank participants at that conference for helpful suggestions. Financial support from the Knowledge for Change Program of the World Bank is gratefully acknowledged.
Economics studies facts, and seeks to arrange the facts in such ways as make it possible to draw conclusions from them. As always, it is the arrangement which is the delicate operation. Facts, arranged in the right way, speak for themselves; unarranged they are as dead as mutton.

_The Social Framework_ , 1950

# **1. Introduction**

Cross-country estimates of the extent of corruption rely largely on the self-reports of households, business managers, and government officials. But a long-recognized problem in survey research is that individuals are reticent to tell the truth about sensitive topics, which extend from illegal activities to behaviors in which a person is simply morally invested. An old example was exaggeration in reports of possession of a library card (Locander et al. 1976), but recent examples abound. Pregnant women, especially those in higher social classes, under-report smoking, even when access to free smoking cessation services depends on such reports (Shipton et al. 2009). A significant number of girls, and even more boys, profess knowledge of the mathematical concepts of declarative fractions and subjunctive scaling, which are fictions (OECD 2015). Either conservatives exaggerate how happy they are or liberals downplay how happy they are, or both (Wojcik et al. 2015).

In attempting to counter the problem of reticence on sensitive topics, the traditional approach in survey research has been to find ways to make respondents more comfortable when answering questions, in order to elicit more candor. For example, researchers have experimented with selfadministered questions, telephone interviewing, and variations in the wording of questions (Tourangeau and Yan 2007). One important approach in trying to increase respondent comfort level has been the use of unconventional questions that elicit answers that do not reveal precise facts about individuals but yield relevant sample statistics. Such techniques range from the venerable random-response question of Warner (1965) to the new item sum technique of Trappmann et al. (2014). These different approaches have made varying contributions to alleviating the problem of reticence, but it is fair to conclude that none comes close to solving that problem. As Tourangeau and Yan (2007, p. 878) state "The need for methods of data collection that elicit accurate information is more urgent than ever." This urgency appears no more so than in the area on which this paper focuses, measures of corruption that are comparable across countries. These measures perform a vital function. Policy makers and politicians use corruption indicators to monitor governance quality, with consequences for implementation of reforms and for the provision of aid by such entities as the Millennium Challenge Corporation, USAID, and the World Bank. Cross-country measures of corruption are often prominent in political debate, as for example in attitudes towards Greece within Europe.<sup>1</sup> Innovative attempts have been made to obtain evidence on corruption that does not rely on self-reports (Reinikka and Svensson 2004; Olken 2009). However, the effort required to gather such

> 1 "Corruption still alive and well in post-bailout Greece" _The Guardian_ December 3, 2014 <u>http://www.theguardian.com/world/2014/dec/03/greece-corruption-alive-and-well</u>

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evidence is large and there is great reliance on peculiar country-specific institutional features that create specific opportunities for measurement. Hence, self-reports from surveys will continue to provide the basis for most research on and assessment of corruption in the future. This is especially the case when the focus is on comparisons across countries.

Existing survey evidence indicates that acts of corruption are amazingly common across the globe. Rose and Peiffer (2015) estimate that over a quarter of the world's population regularly pays bribes for public services. Such acts are by definition illegal. Moreover, for obvious reasons, corruption is much more common in countries where the reach of the rule of law is tenuous. But these are exactly the countries where respondents have the most reason to fear that government officials can force survey firms to violate confidentiality agreements. They are the countries where the evidence necessary to support criminal prosecution—or simply political or administrative persecution—is the weakest. They are the places where legal defense against such prosecution or persecution is least likely to be effective. Hence, in the highest corruption environments, there is very good reason to believe that the traditional approach of survey research—increasing respondent comfort—will not eliminate respondent reticence on corruption questions.

Therefore, in aiming to develop valid, self-report-based, cross-country-comparable measures of corruption, we adopt an approach diametrically opposite to the traditional one. We accept that there will always be large numbers of respondents who have a propensity to give false answers to questions on sensitive issues, and we embrace that fact. Instead, we rely on a methodology that allows us to estimate the rate of false answers and therefore the rate of commission of the corrupt act.

The intuition behind our approach is as follows. We formulate a structural model of the behavior of reticent respondents in answering sensitive survey questions. We then apply the model to data that simultaneously reflects the answers to two different types of questions. First, there is a conventional question (CQ) that asks explicitly whether a particular act of corruption has taken place. Naturally, if respondents are reticent, the distribution of yes/no responses on this question will depend on both the level of corruption and the level of reticence. Using this question alone one cannot disentangle the two. We therefore employ the CQ in tandem with a second type of question, a forcedresponse random-response question (RRQ; Warner 1965, Boruch, 1971). Importantly, we assume that responses to both the RRQ and the CQ are affected by the same degree of respondent reticence.<sup>2</sup> Then, the distribution of responses on the RRQ will depend on the same corruption and reticence parameters as the distribution for the CQ, but in a different way. Hence, by applying our model to the combination of the responses to the two types of questions, we obtain estimates of structural parameters that separately reflect levels of corruption and degree of respondent reticence. Our analytical approach is fully described in Sections 3 and 4, where we set up the model of respondent

> 2 In Appendix B, we argue that this is a reasonable assumption and also summarize some simulation results that show that our estimates of the degree of downward bias in standard measures of corruption are lower than those that would be obtained should the RRQ work as designed.

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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.

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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
corruption are 157% higher than standard estimates. This is due to the combination of a rise in the perception of visits by 49% and a rise in the perception of corruption on a visit of 72% (2.57 approximately equals 1.49 times 1.72). In other countries, Turkey, for example, there is no change in the perception of visits and all the rise in effective corruption is due to an increase in the perception of levels of corruption on an official's visit.

# **2. The Data**

We implement our methodology using data from surveys conducted by the World Bank Enterprise Survey unit (WBES, 2015) on Bangladesh, India, Nigeria, Peru, Sri Lanka, Turkey, and the Ukraine. Over the past several years, with the generous cooperation of the WBES team, we have placed forced-response random-response questions in these surveys. Each survey polled business owners or top managers in a sample of officially registered firms that is representative of the economy's formal private manufacturing and services sectors.<sup>4</sup> Interviews were conducted face-to-face and covered a wide range of topics, including corruption. The data from the seven surveys were collected in different waves of the WBES between 2007 and 2014. Information on the timing of interviews, the type of interview, and the number of observations included in our analysis for each country is given in Table 1. Full details of the subsample of firms used in the analysis are given in Appendix A.

We use responses to two types of question. The first is a two-step conventional question (CQ) regarding whether an interaction with a government official occurred and if it did whether a bribe interaction took place. Two-step questions with this structure are very common in survey work, appearing for example in the surveys conducted by Transparency International, the World Justice Project, the US Federal Reserve, the US Agency for International Development, and the World Health Organization, as well as the Gallup World Poll and the National Crime Victimization Survey.<sup>5</sup> In the World Bank’s Enterprise Surveys, there are a number of such questions with identical structure, varying only in the type of official who is the subject of enquiry. The example used in this paper concerns interactions with tax officials, a question that is in the core questionnaire for the World Bank’s Enterprise Surveys and has been asked in a large number of countries. This two-step CQ asks whether

> 4 Full details of the methodology can be found at http://www.enterprisesurveys.org/methodology.  Stratified random sampling was used, with strata based on firm size, geographical location, and economic sector. Given the small sample size and the oversampling of some industries, the pattern of sampling weights is highly skewed. To prevent a small number of firms with very high weights from dominating our results, we report unweighted results throughout the paper. As a result, our results should be interpreted as representative only of the sample of firms in the data.

> 5 See, for example, Transparency International's survey for the Global Corruption Barometer <u>http://files.transparency.org/content/download/604/2549/file/2013_GlobalCorruptionBarometer_EN.pdf, the</u> questions on gambling in the Fed's Survey of Household Economics and Decisionmaking <u>http://www.federalreserve.gov/econresdata/2014-economic-well-being-of-us-households-in-2013-appendix2.htm, the questions on health behaviour in the World Health Survey of the WHO http://www.who.int/healthinfo/survey/en/, the World Justice Project's questions on corruption http://worldjusticeproject.org/sites/default/files/gpp_2013_final.pdf, the questions on unwanted sexual acts in</u> the National Crime Victimization Survey http://www.bjs.gov/index.cfm?ty=dcdetail&iid=245, and the questions on sexual behaviour in the Demographic and Health Surveys of USAID http://dhsprogram.com/What-We-Do/Survey- <u>Types/DHS-Questionnaires.cfm.</u>

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firms had an interaction with tax officials over the last year and if so, whether the firms were expected or requested to give gifts to the officials. Responses to this question are the basis of one of WBES’s prominent corruption indicators—“Percent of firms expected to give gifts in meetings with tax officials”.<sup>6</sup> Appendix A contains the precise wording of all survey questions used in this paper and further details on the samples used in the analysis, including information for each country on how many observations were dropped because questions were not answered.

For simplicity in presentation, and following previous papers, we will rather inaccurately refer to a firm as 'guilty' when it was expected or requested to give gifts in the meeting with tax officials. This is the measure of corruption. The standard approach in the literature is simply to assume that all answers to the CQs are honest and to report statistics based on such answers.<sup>7</sup> These we call 'standard' estimates of corruption or guilt in what follows.

The second type of question is a forced-response random-response question (RRQ). For reasons made clear below, our methodology requires responses to more than one random-response question. The ones we use are intended to be on issues that are similarly sensitive to the subject matter on the CQ. This identifying assumption is important because we will assume that the probability of reticent behavior is the same for the CQ and the RRQs. The questions are listed in Table 2, together with summaries of the responses to each question in each of the countries.<sup>8</sup> Following Azfar and Murrell (2009), Clausen, Kraay, and Murrell (2011), and Kraay and Murrell (2015), survey respondents were presented with a series of ten sensitive questions. They privately toss a coin before answering each question, having previously been instructed to answer "Yes" if the coin comes up heads and otherwise answer the sensitive question. The series of ten questions includes three that ask about less sensitive acts. We do not use the data from these three questions: their inclusion is to give sophisticated reticent respondents the chance to answer "Yes" occasionally without affecting the data that we use. The seven more-sensitive questions used in the analysis are identified in bold in Table 2, but were not so highlighted in the questionnaire itself.

The data in Table 2 provide immediate justification for our assumption that the RRQs do little to encourage respondent candor. Absent reticent behavior, the rate of “Yes” responses on each of the RRQs should be at least 50 percent given that half of the responses would reflect the outcome of obtaining a heads on the coin toss, which should force a “Yes” response. Yet “Yes” response rates are below 50 percent in 47 of the 49 relevant cases in Table 2 (7 RRQs for each of 7 countries). Moreover, if a positive fraction of respondents had in fact done the sensitive acts in question, we should expect even

> 6 Several measures of corruption produced and used by the World Bank are available at: <u>http://www.enterprisesurveys.org/data/exploretopics/corruption</u>

> 7 With one caveat: refusals to answer are sometimes treated as admissions of guilt, as for example in analysis conducted by the World Bank’s Enterprise Surveys unit.

> 8 Because these RRQs are not part of the core questionnaire for the World Bank’s Enterprise Surveys, we placed these questions in selected Enterprise Surveys over the past several years, in collaboration with the Enterprise Survey team at the World Bank.  We are particularly grateful to Giuseppe Iarossi, Jorge Rodriguez, Veselin Kuntchev and Arvind Jain for their cooperation in placing these questions.

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higher rates of “Yes” responses. This provides a first clear indication that a significant proportion of responses reflect reticent behavior.

The data underlying Table 2 also provide justification for another assumption that we use in our model, that reticent respondents do not always behave reticently, but sometimes answer questions candidly. In Sri Lanka for example, the existence of reticence itself is clear from the 7.5 percent of respondents with zero "Yes" responses on all the seven sensitive questions, since if there were no reticence less than 1 percent would answer the RRQs in this way.<sup>9</sup> Importantly, another 31.5 percent of respondents answer "Yes" one or two times, while if there were no reticence, only 22 percent of respondents should do so.<sup>10</sup> This is evidence of significant reticence but also of reticent respondents who answer some questions candidly and others reticently. These points are further amplified if we assume that some respondents have done some of the sensitive acts in question, because candor would then require more “Yes” answers.

# **3. Modeling Survey Responses**

Our goal in this section is to provide some structure in describing the interaction between an interviewer, who would like to elicit accurate information, and the respondent, who may prefer not to disclose this information. Our particular approach in addressing the problem of respondent reticence means that providing such structure is intrinsic in our methodology. But as we proceed below, it will become obvious that _every_ attempt to construct a measure of corruption from similar questions involves making assumptions, either implicitly or explicitly, on the way in which reticent behavior influences respondents’ answers. The virtue of an explicit structure is that our assumptions become clear.

We follow the Azfar-Murrell (2009) definition of reticence—a reticent respondent is one who knowingly gives false answers with a nonzero probability when honest answers to a specific set of survey questions could generate the inference that the respondent might have committed a sensitive act. We assume that the probability that respondents answer "Yes" to a given question depends on (i) whether they are reticent individuals, in the sense that they are sometimes unwilling to truthfully answer a sensitive question, (ii) whether those who are reticent individuals choose to behave reticently on a specific question, and (iii) whether they have in fact done the sensitive act in question, i.e. whether they are guilty, allowing for guilt rates to be different for reticent and candid respondents. These are natural assumptions. The first is implied by all of the literature on the under-reporting of sensitive acts. The second—that reticent respondents are not always reticent—is strongly suggested by patterns in the data analyzed in previous research and noted above (Azfar and Murrell 2009; Clausen et al. 2011; Kraay

> 9 Specifically, under the assumption that the respondent has done none of the sensitive acts, the probability of observing seven “No” responses is 0.5<sup>7</sup> < 0.01.

> 10 Specifically, under the assumption that the respondent has done none of the sensitive acts, the probability of observing one or two “Yes” responses can readily be calculated from the binomial distribution with seven trials and a success probability of 0.5.

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and Murrell 2015). The third is completely intuitive: the guilty may very well have more incentive to behave reticently.

There are five parameters in our model: the probabilities of (i) receiving a visit, (ii) being reticent, (iii) behaving reticently on a given question, (iv) being guilty if reticent, and (v) being guilty if candid. We make the identifying assumption that the answers to all questions—CQs and RRQs—can be modeled using the same parameter values. This is a strong assumption, but all approaches to using survey data in the face of reticence would need to make some such assumptions. In Appendix B, we review some literature relevant to this assumption and present results that show that our general conclusions are robust to violations of this assumption.

Reticence is an individual-specific trait, with respondents being reticent or candid with probabilities and . Candid respondents are always honest. However, with probability , reticent respondents choose to behave reticently on any given sensitive question—that is, they answer in a way rr 1 −rr qq that obscures any possible inference of guilt. Sometimes, however, reticent respondents behave candidly, and provide honest answers with probability . We assume that the decision to behave reticently on the two-step CQ is made once, and is independent of the similar decisions on the 1 −qq< 1 RRQs. Notice that this set-up makes a distinction between reticence and behaving reticently: reticence is a fixed trait for a single individual, but any reticent individual sometimes behaves reticently and sometimes candidly across different questions. Tax officials visit or inspect businesses with probability .<sup>11</sup> We differentiate between two classes of businesses in order to allow for the possibility that guilt and reticence are correlated across ww respondents. First, businesses asked for a bribe with probability have reticent respondents. Second, those asked for a bribe with probability ( ) have candid respondents. A less than 0 ≤gg≤1 one induces the correlation between reticent behavior and guilt. However, our estimation procedure kkgg 0 ≤kk≤1 kk does not preclude as a special case. We can therefore test whether, in fact, the guilty are more likely to give dishonest responses. kk= 1

# _3.1 Modeling Responses to the Conventional Question_

In this subsection we develop two alternative models of how reticent behavior affects the interview process for the two-step CQ, a boiled-down version of which is "(1) was your firm visited by tax officials and (2) if yes, did they expect an informal payment?". Importantly, if no visit is acknowledged in the first step, no bribe question is asked in the second step. This means that reticent respondents can avoid the bribe question, if they so choose, by denying that a visit occurred. Thus, in contrast with Kraay and Murrell (2015), we must not only decide how to model reticent behavior, but also specify which parts of the two-step CQ are affected by reticent behavior.

> 11 It is of course plausible that businesses of different characteristics (size, activity, etc.) have different probabilities of getting a visit or inspection by tax officials. However, we do not model tax officials’ choices here.

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We consider two distinct possibilities. In the first, which we refer to as Model A, reticent respondents are always candid in responding to the first part of the CQ, i.e. the question about the visit. However, they may behave reticently when responding to the sensitive second part of the CQ, i.e. the question about the bribe. The second possibility, which we refer to as Model B, allows reticent respondents to avoid answering the sensitive second part of the CQ by responding “No” to the first part of the CQ even if a visit did occur. Although the first part of the CQ is not _per se_ sensitive, a “No” answer can put the respondent in the position of avoiding an inquiry on a sensitive act.<sup>12</sup> Specifically, we assume that reticent respondents who received a visit but not a request for a bribe respond candidly to both parts of the CQ. In contrast, reticent respondents receiving a visit and a bribe request and choosing to behave reticently deny that the visit occurred and thereby avoid the sensitive second question.<sup>13</sup> For notational convenience, we now define a random variable that fully summarizes the possible responses to the two-part CQ. Specifically, if no visit is acknowledged, if a visit is DD acknowledged but no bribe is reported, and if a visit and a bribe are both acknowledged. Note DD= 1 DD= 2 that is defined in such a way that it is non-missing for all respondents that answered either part of the DD= 3 CQ. This is in contrast with the bribe question itself, which is non-missing only for those respondents DD who acknowledge a visit in the first part of the CQ. The use of a structural model integrating responses on both parts of the CQ therefore will allow us to use the data on all respondents in estimating rates of corruption. This is in contrast to standard estimates that focus only on the subset of the sample corresponding to respondents who acknowledge a visit.

Table 3 spells out our assumptions on the likelihood of observing these three possible responses to the CQ. The panels of the table reflect combinations of the models (A and B) and the types of respondents (candid and reticent), with only three panels needed since candid respondents behave the same in both models. Within panels, the rows reflect the three possibilities for the respondents' actual experiences on visits and bribery, i.e. (i) a visit actually did not occur, (ii) a visit did occur without a bribe request, or (iii) a visit did occur and a bribe was requested. Of course, these actual experiences are unobserved for the researcher, who only sees survey responses. The columns of the table correspond to the three possible responses to the CQ, which are observed by the researcher. The cell entries spell out the probability of the (observed) response corresponding to the column, given the model, the type of respondent, and the (unobserved) actual experience indicated in the row of the table. Of course, even though the probability of two different values of D can both be positive, the value of D is unique in any given observation in the survey.

> 12 On the WBES questionnaires, this tax question appears in the middle (or in Nigeria, at the end) of a series of twopart questions each of which is identical in structure to the question on taxes, but referring to other government agencies.  Thus by the time the respondents reach the tax question they should know that acknowledgement of a visit will be followed by a question about a bribe request.

> 13 We also considered a third model, similar to model B except that all reticence respondents who chose to behave reticently did so on the visit question whether or not a visit had resulted in a bribe request.  When evaluating the performance of each model—see Section 6—this third model was the least preferred for all countries and therefore we have not reported any results for this model.

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Consider the behavior of candid respondents, summarized in Panel 1 of Table 3. Candid respondents always answer truthfully, so there are ones on the diagonal and zeros otherwise, indicating that candid respondents always answer truthfully e.g. if there was no visit, they say there was no visit with probability 1. At the bottom of this panel we report the corresponding population probabilities of observing the three possible responses on the two-part CQ, conditional on respondents being candid, i.e. for the three outcomes , with the conditional _C_ indicating a candid respondent. Since candid respondents respond truthfully, the probability of observing a “Yes” response to the visit PP[DD= jj|CC] jj= 1,2,3 question is simply , i.e. the true probability of a visit. Similarly, the probability of reporting a visit but not a bribe is , i.e. a visit occurs with probability and a PP[DD= 1|CC] = ww bribe does not occur with probability . Naturally, the probability of reporting a visit and a bribe is PP[DD= 2|CC] = ww(1 −kkgg) ww simply the product of the probability of these two events, i.e. . 1 −kkgg The second and third panels of Table 3 present the same analyses for reticent respondents, PP[DD= 3|CC] = wwkkgg

The second and third panels of Table 3 present the same analyses for reticent respondents, whose behavior differs between the two models. Under the assumptions of both Model A and Model B, reticent respondents truthfully respond that there was no visit if indeed no visit occurred, as summarized by the 1 in the top-left cell of each the second and third panels. Similarly, if there was a visit and no bribe request occurred, they truthfully acknowledge the visit in the first part of the CQ, and truthfully state that there was no bribe in response to the second part of the CQ. This is represented by a 1 in the center cell of both panels. If a visit and a bribe occurred, under the assumptions of Model A reticent respondents admit the visit but behave reticently with probability on the second part of the CQ. Specifically, with probability the reticent respondent denies the bribe, or otherwise the bribe is qq acknowledged (hence with probability ). On the other hand, under the assumptions of Model B, qq reticent respondents who are guilty might manifest reticent behavior in the first part of the CQ: they 1 −qq deny that the visit occurred with probability , or otherwise admit to the visit and the bribe (hence with probability ). qq The different assumptions of Model A and Model B imply different probabilities of observing the 1 −qq three possible responses to the CQ among reticent respondents. In Model A, reticent respondents are always candid about the visit question, and so the probability of denying a visit is just one minus the true probability of a visit, i.e. , the _A_ subscript referencing the model and the conditional _R_ indicating a reticent respondent. In contrast, in Model B reticent respondents who (i) AA PP [DD= 1|RR] = 1 −ww received a visit (with probability ), _and_ (ii) received a bribe request (with probability ), _and_ (iii) choose to behave reticently (with probability ) will deny that the visit occurred. These responses are in ww gg addition to those of respondents who in fact did not receive a visit (a proportion of respondents), qq so the overall probability of a response that a visit did not occur is 1 −ww . BB PP [DD= 1|RR] = 1 −ww+ wwggqq≥ AA PP [DD= 1|RR] In Model B, reticent respondents always acknowledge a visit when a bribe does not occur, so the probability of a response that a visit occurred without a bribe is simply the product of the probability of a visit and the probability of a bribe not occurring, i.e. . However, in Model A, there are also some reticent respondents who experienced a visit and a bribe request, but decided to BB PP [DD= 2|RR] = ww(1 −gg) behave reticently on the second part of the CQ and deny that the bribe occurred. This implies a greater

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likelihood of observing a “No” response to the second part of the CQ in Model B, i.e. . Finally, in both models, reticent behavior reduces the likelihood of AA PP [DD= 2|RR] = respondents admitting both the visit and the bribe by the same amount, i.e. BB ww(1 −gg+ qqgg) ≥PP [DD= 2|RR] . In both cases, a visit _and_ a bribe occur with probability , and reticent AA PP [DD= 3|RR] = respondents acknowledge this with probability . In Model A, the remaining proportion of BB PP [DD= 3|RR] = wwgg(1 −qq) wwgg respondents admit to the visit but deny the bribe, while in Model B these respondents manifest their 1 −qq qq reticence by denying the visit, thereby avoiding the question about the bribe.

Combining these observations, we can now summarize how the presence of reticent respondents affects the interpretation of responses to both parts of the CQ. Note first that the probability that a visit is reported in the first part of the CQ is: In Model A, both candid and reticent respondents are candid in their responses to the question about visits, and so the observed rate of “Yes” responses is a valid estimate of the frequency of visits, . However, in Model B, a fraction of respondents are reticent, experience a bribe with probability , and ww with probability choose to behave reticently by denying that the visit occurred. As a result, the rr gg observed frequency of visits in the data is an underestimate of the true frequency of visits, and the qq extent of the downward bias depends on the prevalence of reticent respondents, the likelihood of reticent behavior on the part of reticent respondents, and the frequency of bribery itself.

The interpretation of responses on the second part of the CQ is similarly clouded by reticent behavior. Consider the rate of admission of bribery among those respondents who acknowledge a visit, which is exactly the standard estimate of corruption. Using our notation, this is: In Model A, all respondents who were visited by an inspector admit to the visit. Among these, a proportion are candid and truthfully admit that a bribe occurred with probability . In contrast, a proportion of respondents are reticent. For these, a bribe occurs with probability but only a 1 −rr kkgg proportion of reticent respondents chooses to behave candidly and answer the question rr gg truthfully. The only difference in Model B is that reticent respondents who are guilty and choose to 1 −qq behave reticently deny that the visit occurred rather than admitting the visit but denying the bribe. The probability of this occurring is . In Model A these respondents would have admitted the visit in the first part of the question, but would have responded “No” to the bribe question in the second stage. In rrggqq Model B these respondents do not advance to the second stage and so the rate of “Yes” responses in the second stage is higher by a factor of . 1/(1 −rrggqq) ≥1 12
# _3.2 Modeling Responses to the Random-Response Questions_

For both models, the interview process for RRQs is modeled as in Kraay and Murrell (2015). The key assumption here is that reticent behavior is equally prevalent in responses to the RRQ as it is in the CQ. Recall that on each of the questions in the RRQ, the respondent is instructed to answer the sensitive question if the coin comes up tails, and to answer “Yes” if the coin comes up heads. Our definition of a reticent respondent is one who gives knowingly false answers with a nonzero probability when honest answers to a question could generate the inference that the respondent might have committed a sensitive act. Given the assumptions above and this definition, there is therefore a probability that a reticent respondent will respond “No” even when the coin comes up heads. Similarly, when the coin comes up tails, there is a probability that the reticent respondent will answer qq “No” even if the respondent has done the sensitive act in question. The data in Table 2 provide qq reassurance on this assumption. If the outcome of a head on the coin toss actually encourages candor, then all entries in that table would lie above 50%. However, as discussed in the previous section, for the truly sensitive questions the responses are greater than 50% only in two out of 49 cases (seven sensitive questions in seven countries).<sup>14</sup> As discussed in more detail in Kraay and Murrell (2015), these assumptions imply that the probability of a “Yes” response on any single RRQ is . To see this, note that respondents are supposed to answer “Yes” either if they are guilty (with probability ) or if they are not 0.5(1 + gg)(1 −qq) guilty and the coin comes up heads (with probability ). These two probabilities sum to gg but must be scaled down by , the probability that a reticent respondent provides an 0.5(1 −gg) honest “Yes” response. For candid respondents, the probability of a “Yes” response on a given RRQ is 0.5(1 + gg) (1 −qq) . Candid respondents can have a lower guilt probability than reticent respondents (i.e., ), but always answer honestly (i.e. is not relevant to them). 0.5(1 + kkgg) Define the random variable as the number of “Yes” responses on the 7 sensitive RRQs that are kkgg≤gg qq given in bold in Table 2. Since both the coin toss and the decision to behave reticently on a given XX question are independent across questions in the battery of RRQs, is binomially distributed, with different success probabilities for reticent and candid respondents as noted above, i.e. a success XX probability of for candid respondents and for reticent respondents. It is also useful to briefly note why we use several RRQs and not just a single RRQ. As discussed 0.5(1 + kkgg) 0.5(1 + gg)(1 −qq) in Section 2, in modeling the data generating process it is important to allow for the possibility that the reticent do not always behave reticently, that is to include in the model a parameter But then if , which is a possibility that we do not want to rule out _a priori_ , the effects of and on data qq< 1. gathered on any single CQ or single RRQ are identical.<sup>15</sup> Hence, these parameters would not be kk= 1 qq rr

> 14 Since the assumption that rates of reticence on the CQ and the RRQ are the same is so critical to our procedures, and is non-standard in the context of the existing literature on RRQs, we elaborate on this point in Appendix B. Importantly, in that appendix we report the results of some simulations showing that if our assumption is not correct in the sense that reticent behaviour is less prevalent in the RRQ, then we _underestimate_ the degree of downward bias in standard estimates of corruption.

> 15 This point is trivial to show using equations (1) and (2) and the information appearing in the paragraphs immediately above .

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=| pip = scl Je ~~l»)~~
_guilt_ , which is the probability that a random respondent will be asked for a bribe given that this respondent is being visited by a tax official. Third we estimate the unconditional probability that a randomly selected respondent will be both visited by a tax official and asked for a bribe, which is average guilt times the probability of a visit, i.e. . We call this _effective corruption_ , reflecting the fact that in countries where corruption is widespread part of the underlying motive for wwgg(rr+ (1 −rr)kk) visits by tax officials is to extract a bribe.

# **5. Results: Standard Estimates and Alternative Models of Reticence**

Tables 4-10 report estimates of Model A and Model B for the seven countries in our data set. In each table we report estimates for the five model parameters, , k, , , and , and for the three composite parameters, _effective reticence_ , _average guilt_ , and _effective corruption_ . Our discussion gg rr qq ww focuses mainly on the three composite parameters since these are most informative about overall levels of corruption and reticence. Effective reticence ( ) reflects the proportion of sensitive questions that are not answered candidly in the whole sample. This proportion varies from 28% for Model A in Sri Lanka to 67% for rrqq Model A in India. Variation is much greater between countries than between models within a country, the two models telling a quite consistent story about rates of effective reticence. One element of this story is that the countries seem to fall naturally into two groups. Turkey and India have rates of effective reticence approximately twice as high as the rates in all other countries. The estimates for these two countries imply that approximately 64% of the time a respondent would answer the secondpart of the CQ misleadingly if the respondent had in fact been asked for a gift or informal payment. The analogous percentage for the other countries varies between around 30% and 40%. In all countries, these are high rates of misleading answers. The obvious implication is that overall rates of corruption in standard measures are downward biased, with the degree of underestimation varying markedly between countries.

Examining average guilt, which is the probability that a request for a bribe is made on any visit, our estimates average approximately twice those that would be reported using standard methods. But as expected there also is large variation between countries. For Turkey, the estimate of average guilt is increased either tenfold (Model A) or fourfold (Model B) relative to standard estimates. In Peru, on the other hand, effective guilt is “only” 50 percent higher than conventional estimates. The significance of allowing for reticence is perhaps best shown by the results for Sri Lanka, because that country generally scores reasonably well in cross-country rankings of corruption, and has relatively low rates of reticent behavior. Even then, average guilt is 84% above standard estimates in Model A and 63% above in Model B.

Effective corruption reflects the unconditional probability of being personally involved in a corrupt exchange with tax officials, that is, it is the probability of having been visited by tax officials and 15
having been expected to give a gift on such a visit.<sup>16</sup> This proportion varies from 6.6% for Model A in Peru to 48% in Model A for Bangladesh. In contrast, standard estimates in these instances give 4.2% for Peru and 26% for Bangladesh. Estimates for Model A increase the perception of overall corruption by approximately 100% on average whereas the corresponding figure for Model B is 75%. Thus the risk of being personally involved in corruption is usually greatly underestimated. But it is not uniformly underestimated. In Turkey, which has low rates of corruption and high rates of reticence based on any yardstick, estimates of effective corruption are tenfold the standard estimates in Model A and fourfold in B. In contrast, Ukraine's estimate of effective corruption in Model B is marginally less than that in standard estimates.

We now turn to brief comments on the estimates of the individual parameters. For _w_ , the probability of a visit by tax officials, estimates vary much more between countries than between models. As discussed in Section 3, Model A's estimates are by construction identical to standard estimates, whereas Model B's estimates are usually in the range of 5-10% higher than standard ones. One exception to this is India, a high corruption, high reticence country, where our estimate of visits by tax officials is more than 50% greater than conventional ones. Such an observation changes perceptions about the mechanisms of corruption in a country, suggesting that the decision of a tax official to visit a business might be an element of that mechanism.

For _k_ , the parameter capturing (inversely) the correlation between reticence and guilt, results vary more between models than for any other of the parameters. For three countries, Model A tells a different story than Model B. For example, in Ukraine Model B finds no significant correlation ( _k_ not significantly different from 1), while Model A suggests that the reticent are four times as likely to be guilty as the candid. However, in general, estimates of _k_ are quite low, implying a strong correlation between reticence and guilt, which is hardly surprising.<sup>17</sup>

# **6. Results: Preferred Estimates and Analysis**

In this section we draw together the preferred estimates for each country. We choose either Model A or Model B as the preferred model, based on which has the largest value of the maximized loglikelihood.<sup>18</sup> Table 11 first indicates our preferred model and then the following five rows summarize the preferred estimates of the five parameters of the model, i.e. , , , , and , and the corresponding estimate of effective reticence, . In the remaining rows we focus on accounting for the ww rr qq gg kk 16 This composite parameter is different from the measure of corruption in dealing with tax officials that is usually rrqq publicized (e.g. by the WBES ) in that it takes into account the fact that not every business is necessarily involved in the contexts that potentially involve corruption. Average guilt, estimates of which are provided in Tables 4-10, is the concept that it is usually reported.

> 17 This general point is strongly reinforced when we examine the set of preferred estimates in the ensuing section. It is also a strong conclusion in Kraay and Murrell (2015).

> 18 Formally, we perform the Vuong (1989) model selection test for non-nested models estimated by maximum likelihood.  The test is very simple and involves forming the difference between the maximized value of the likelihood function between the two models for each observation, and then performing a standard t-test of the null hypothesis that the mean difference is zero.  The differences in the maximized values of the log likelihoods for the two models is statistically significant at the 10% level in Sri Lanka, and at the 5% level in Ukraine.

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primary question of interest in this paper, which concerns the size and source of downward biases present in measures of corruption that do not take reticent behavior into account. We focus here on estimates of effective corruption, i.e. the likelihood that a firm is visited by a tax inspector and a bribe request takes place. The standard way to estimate effective corruption without taking reticence into account would be to simply calculate the proportion of all respondents who admit to both a visit and a bribe request. The population frequency of this is in the notation of Section 3. Note that the standard estimate of effective corruption differs from the standard estimate of corruption conditional PP[DD= 3] on a visit occurring, which is described in Equation (2) above and is commonly reported in analysis of the Enterprise Survey data.

The left-hand side of this expression is the ratio of measured corruption to true effective corruption, which is less than one if there is reticent behavior. The first term on the right-hand side is the ratio of the population value of the standard estimate of the probability of a visit to the true probability, and so measures the downward bias in reported visits due to reticence. The second term on the right-hand side is the ratio of the population value of the standard estimate of bribery conditional on a visit to the corresponding true probability, and so measures the downward bias in reported bribe interactions conditional on a visit being reported.

These two sources of bias are different in the two models we have considered. In particular from Equation (1) we see that the bias in reported visits is: In Model A we assumed there is no reticence in responding to the visit question so there is no bias relative to the true incidence of visits. However in Model B reticent respondents who experienced a bribe behave reticently with probability , and so there is a downward bias, i.e. . We report standard and reticence-adjusted estimates of the probability of a visit, and the ratio of the two, in the qq 1 −rrqqgg< 1 first part of Panel B of Table 11. This ratio is equal to 1 for Sri Lanka, Turkey, and Ukraine where Model A is the preferred model. However, for the remaining four countries this ratio is less than one, and substantially so in India (67%) and Bangladesh (73%). On average, for the four countries where Model B is the preferred model, reticent behavior implies that only 81% of visits that actually occur are acknowledged by respondents.

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In both Model A and Model B, the frequency of reported bribes among those who report a visit is biased down relative to the true probability of a bribe occurring, i.e. this ratio is less than one when there is reticent behavior. Comparing Model A and B, the downward bias is greater in Model A. As discussed in Section 3, this is because some reticent respondents simply denied the visit altogether in Model B rather than admit the visit and then deny the bribe. We summarize the estimated downward biases in the second part of Panel B in Table 11, reporting standard and reticence-adjusted estimates of rates of bribery among those who admit to a visit, as well as the ratio of the two. This ratio naturally is less than one, but varies widely across countries. At the one extreme, in Turkey we estimate that only 10% of the bribes that actually occur are reported in responses to the second part of the question. At the other extreme, in Nigeria virtually all bribe interactions are acknowledged in the second part of the question. On average across the seven countries, we estimate that 58% of bribes that actually occur are acknowledged.

Inserting Equations (5) and (6) into Equation (4), we find that the overall bias in standard estimates of effective corruption relative to actual effective corruption is the same function of the parameters in both Models A and B, i.e.

for both models. Standard estimates of effective corruption are biased downward as long as , i.e. as long as there is reticent behaviour. We report the standard estimates, estimated true effective corruption, and the ratio of the two in the last Part of Table 11. The downward bias is substantial, with the ratio of standard estimates to actual effective corruption averaging 50% across the seven countries. Naturally, this ratio also varies considerably across countries, from a low of 10% in Turkey to a high of 88% in Nigeria. To assess the significance of these overall downward biases, we also report the z- statistic for the test of the null hypothesis that the ratio on the right-hand side of equation (7) is equal to one. This null hypothesis is overwhelming rejected in all seven countries.

Figure 1 depicts the extent to which standard estimates of corruption are biased in the seven countries, how much the degree of bias varies, and the source of the bias, in terms of reticence on visits and reticence on bribes given visits. The solid, blue bar shows our preferred estimates of effective corruption while the white bar shows standard estimates. The varying heights of the first bar show how much corruption levels vary between countries, the contrast between Bangladesh and Peru, for example, being very striking. The ratios of the last to the first bars show how much the underestimation 18
of corruption due to reticence varies between countries, with the contrast between Nigeria and Turkey standing out. Finally, the decomposition of bias is depicted in two steps, when moving from the white bar to the cross-hatched, red bar to the solid blue bar, with under-reporting due to reticence on the bribe question first corrected and then under-reporting due to reticence on visits corrected. While Bangladesh, India, and Nigeria evidence a significant portion of their bias from under-reporting on visits, Peru and the three countries with the preferred Model A do not.

# **7. Conclusions**

We conclude with three points not emphasized above. First, when aiming to produce valid cross-country comparisons of corruption, we highlight how important it is to model responses in terms of structural parameters. Second, we underscore how much cross-country perceptions of corruption can change when such perceptions are cast in terms of structural parameters estimated using models that acknowledge the effect of reticence. Third, we emphasize the broader applicability of these techniques to other survey settings where reticent behavior is a concern.

Our summary in Section 6 reflects the results from the single preferred model for each country, basing the choice on which model maximizes the likelihood. As it happens, the preferred model differs between countries. In 3 of the 7 cases the preferred model has no reticence on visits and in the remainder there is reticence on visits when a bribe occurred in the subsequent interaction.<sup>19</sup> This fact speaks to the virtue of our approach of estimating structural parameters that have identical meanings across countries but enter different models in different ways. Because respondent behavior on reticence differs across countries, standard statistics, which reflect varying combinations of those structural parameters, have different meanings across countries. By focusing on the estimates of structural parameters themselves, we are able to generate valid comparisons between countries. Since the design of any anti-corruption program would need access to those structural parameters, such programs would be much better informed by the estimates we present here than by simple summary statistics from two-step questions. Indeed, as we have shown above, the intuitively appealing standard summary statistics might contain little useful information given the biases induced by reticent behavior.

Figure 2 depicts how much perceptions of differences in effective corruption across countries can change when using comparisons of rigorously-estimated structural parameters rather than comparisons of the intuitively appealing, but informationally obscure, standard estimates. On the horizontal axis we graph the standard estimates of effective corruption and on the vertical axis we report our preferred reticence-adjusted estimates, those appearing in Table 11. The upward sloping line traces out the points where reticence-adjusted estimates equal standard estimates of guilt. The large differences between model-based estimates of effective corruption and standard estimates are readily apparent in the large vertical distance between any data point and the upward-sloping line. More notably, there are very significant reversals of orderings. In standard estimates, Nigeria appears much more corrupt than both India and Ukraine, whereas in our estimates Nigeria is less corrupt than those

> 19 As noted above, the data for all countries reject a model that reticent respondents treat the visit as a sensitive issue in exactly the same way that they would confront a question on bribes

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two countries. Whereas standard estimates place Turkey as the least corrupt of our seven countries, we place the levels of corruption of Sri Lanka and Peru below those of Turkey. Given that aid allocations are partially based on such rankings, it would seem prudent to use rankings based on models using structural parameters when the data are from sensitive questions asked on surveys.

Finally, we emphasize the applicability of our methodology to other survey settings where responses to sensitive questions may be influenced by reticent behavior. As noted earlier, two-stage questions regarding sensitive acts are common in many other settings, and our methodology provides a framework for handling reticence in either stage of the question. When considering applications of this methodology in other contexts, we can offer at least some hints of the wider external validity of this approach. For three of the countries included here, Bangladesh, India, and Sri Lanka, we have also applied our methodology in household surveys conducted by the Gallup World Poll. Despite the very different context of household (as opposed to firm) surveys, we find a rank ordering of countries by effective reticence that is remarkably consistent with this paper, with Sri Lanka the lowest, Bangladesh next, and India having much higher rates than the other two.

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