ï»¿ WPS6488
Policy Research Working Paper 6488
Misunderestimating Corruption
Aart Kraay
Peter Murrell
The World Bank
Development Research Group
Macroeconomics and Growth Team
May 2013
Policy Research Working Paper 6488
Abstract
: Estimates of the extent of corruption rely largely questions reflect three probabilitiesâ€”that the respondent
on self-reports of individuals, business managers, and has done the sensitive act in question, that the respondent
government officials. Yet it is well known that survey exhibits reticence in answering sensitive questions, and
respondents are reticent to tell the truth about activities that a reticent respondent is not candid in answering
to which social and legal stigma are attached, implying a any specific sensitive question. These probabilities can
downward bias in survey-based estimates of corruption. be estimated using a method-of-moments estimator.
This paper develops a method to estimate the prevalence Evidence from the 2010 World Bank Enterprise survey in
of reticent behavior, in order to isolate rates of corruption Peru suggests reticence-adjusted estimates of corruption
that fully reflect respondent reticence in answering that are roughly twice as large as indicated by responses
sensitive questions. The method is based on a statistical to standard questions. Reticence-adjusted estimates of
model of how respondents behave when answering a corruption are also substantially higher in a set of ten
combination of conventional and random-response Asian countries covered in the Gallup World Poll.
survey questions. The responses to these different types of
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.
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MISUNDERESTIMATING CORRUPTION
Aart Kraay (The World Bank)
Peter Murrell (University of Maryland)
JEL Classification Codes: C83, O17, O43
Keywords: Corruption, reticence, random response questions
_____________________________
1818 H Street NW, Washington DC 20433, akraay@worldbank.org; Department of Economics, University of
Maryland, College Park, MD 20742, murrell@econ.umd.edu. We would like to thank Nona Karalashvili and Tatjana
Kleineberg for invaluable research assistance, and David McKenzie, Gale Muller, Luis Serven, Carlos Silva-Jauregui
and Rajesh Srinivasan for helpful comments. We are grateful to the World Bank's Enterprise Survey team (and
especially Jorge Meza, Federica Saliola, and David Francis) for fielding the random response questions discussed in
the paper. We are indebted to Gallup for their collaboration in fielding these questions in the Gallup World Poll
and making the data available to us, and especially to Nicole Naurath and Rajesh Srinivasan for their support of this
project. Financial support from the Knowledge for Change Program (KCP) of the World Bank is also gratefully
acknowledged. The views expressed here are the authors', and do not reflect those of the Gallup Organization, the
World Bank, its Executive Directors, or the countries they represent.
1. Introduction
In a classic study that compared survey responses to official records, Locander et al. (1976)
found that 19% of survey respondents in Chicago incorrectly claimed possession of a library card.
Recently after radio-monitoring meters were installed in cars in the US, the radio ratings company
Arbitron realized that past estimates of commuters' listening patterns had been significantly distorted
by the survey responses of men who were claiming to listen to more classical and jazz, and less oldies
and country music, than was actually the case. 1 Many studies have documented that survey responses
indicate much higher rates of church attendance than can be verified from time use diaries, particularly
in the United States (Brenner 2011). More seriously, Gong (2012) combines survey data on self-
reported sexual activity with the results of tests for sexually transmitted infections, and finds that the
latter provide clear evidence that survey respondents underreport their sexual activity. Imagine then
how distorted responses might be if a survey asked about breaking the law in a country where privacy
protections and legal rights were of concern to respondents. And how might we know the degree of
distortion in the absence of pertinent official records, metering, or testing?
Despite these obvious concerns, economics research on corruption usually ignores the
possibility that survey respondents are reluctant to give truthful answers to questions on sensitive
topics. Svensson (2003) is a telling example of the approach within economics, both because it is a
significant contribution to the literature, uncovering important relationships in the corruption behavior
of developing country firms, and because of the relative emphasis it places on different methodological
problems. The paper provides a careful assessment of different theories of bribe-giving and their
implications for econometric specification and interpretation of results. To obtain a representative
sample, data collection relied on the large stock of existing knowledge on sampling techniques. A
number of convincing robustness exercises were carried out. But based on the candor of survey
responses, the paper is forced to conclude that "â€¦cases of misreporting are likely to remain in the
sample. For this reason, the paper has not focused on the level of bribes per se, but rather on their
correlates" (Svensson 2003 p. 225).
That sums up the current status of economics research on the reticence of survey respondents.
Despite the large amount of survey data from firms that is used in empirical papers and is diffused by
popular databases such as the World Bank Enterprise Surveys, the discipline does not have much to say
about absolute levels of corruption when using data obtained directly from those who pay bribes or
those who receive them. 2 Our objective in this paper is to remedy that problem by developing a
methodology that allows estimation of the degree of candor and reticence of survey respondents, and
simultaneously to use these estimates to determine the degree to which corruption itself has been
1
"Never Listen to CÃ©line? Radio Meter Begs to Differ" By Stephanie Clifford. New York Times, December 16th,
2009.
2
An exception is Olken (2009), which compared Indonesian villagers' perceptions of corruption in local road-
building projects with estimates of actual "missing expenditures", i.e. gaps between what villages reported
spending on road-building projects and ex post estimates of the cost of materials based on physical audits of the
roads. For obvious reasons, opportunities to directly measure corruption and contrast it with survey-based
estimates are rare.
2
underestimated in the past. Although it is generally recognized that underestimation of corruption is a
problem, our results show that it is even more of a problem than seems to have been generally
recognized. Hence our paper's title, which borrows a neologism coined by former US President George
W. Bush, commenting on how his opponents in the presidential election had severely underestimated
him. 3
We implement our methodology using data from the 2010 World Bank Enterprise survey in
Peru. The baseline estimate of corruption from that survey is that 18% of firms answer that it is
common for similar firms to make informal payments to government officials. For terminological
convenience, we will refer to such an answer as "guilt" on the part of the respondent, because this is
usually interpreted as an admission of making informal payments, even though the question itself does
not specifically ask whether the respondent makes such payments. This standard interpretation of a
simple yes/no question about corruption assumes that all respondents are always candid when
answering all questions. In contrast, we estimate that 74% of respondents are reticent in answering
sensitive questions, that reticent respondents are not candid in answering 69% of sensitive questions,
and that 37% of respondents in fact find it common to make informal payments, a doubling of the
estimate of corruption. For some subsets of firms the results are even more dramatic. For example,
more than 90% of the respondents in small firms exhibit reticence, raising estimated guilt from 30% to
more than 90%.
These results assume that reticence and guilt are uncorrelated. However, estimates of the
probabilities of reticence and guilt for subsets of survey respondentsâ€”by firm sector or age, for
exampleâ€”show that a positive correlation is almost certainly the case. This is also intuitively plausible:
the guilty have more to hide. If that is the case, reticence-adjusted estimates of corruption are even
higher because the most corrupt are least likely to admit to its existence. Allowing for a positive
correlation leads to corruption estimates above 50%, in contrast to the 18% indicated by applying
standard analyses of the data that we use.
Of course, if rates of reticence were similar across countries, the findings from Peru would not
be particularly worrisome for cross-country analysis: corruption would be underestimated in all
countries, but by more or less the same amount. However, if rates of reticence vary across countries
then comparisons of corruption could be quite misleading. Hence, we also apply the methodology to a
set of Asian countries using data from the Gallup World Poll. Effective reticenceâ€”the proportion of
reticent respondents times the probability that they are not candid on any specific sensitive questionâ€”
varies dramatically between countries, with a rate of 21% in Indonesia and 48% in India, meaning that
existing estimates of corruption are downward biased by less than 2 percentage points in some
countries but by more than 20 percentage points in others.
We note at the outset that these findings do not imply that survey-based estimates of
corruption are without value. Indeed, the illegal nature of bribery implies that those involved have
strong incentives to hide any evidence of such behavior, so that direct measurement of corruption is in
3
See http://en.wikipedia.org/wiki/Bushism, retrieved May 11, 2013.
3
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 paperâ€”
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. 4 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 designersâ€”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. 5
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.
4
Our methodology advances on all these insights. We follow the Azfar-Murrell (2009) definition
of reticenceâ€”a reticent respondent is one who gives knowingly 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. This definition directly leads to a precise specification
of how different types of respondents answer sensitive questions and therefore explicit predictions on
how survey answers vary with respondent reticence and guilt. We frame these predictions in terms of
three moment functions: the expected value of the response to a sensitive CQ and the expected mean
and variance of the number of yes responses on a set of sensitive RRQs. The expected moments are
functions of three probabilitiesâ€”that a respondent is guilty on the sensitive acts, that a respondent
exhibits reticence in answering sensitive questions, and that a reticent respondent is not candid in
answering any specific sensitive question.
Using those three moment conditions within a standard method of moments estimator, we
estimate the three probabilities. We follow Azfar and Murrell (2009) and Clausen et al. (2011) in using a
set of seven RRQs, the resultant pattern of responses facilitating identification of reticence.
Identification of reticence-adjusted guilt rests on the same insight as that of Clarke and Deshairnais
(1998)â€”that identification requires RRQs with different randomization probabilities. In our
implementation we use seven RRQs and one CQ, noting that a CQ is a limiting case of an RRQ.
Our paper proceeds in the following way. In Section 2, we briefly describe the Peru Enterprise
Survey, discussing in some detail the CQ and RRQs that we use to develop our estimates of reticence
and guilt. In Section 3, we lay out the statistical model of respondent behavior and show how
observable moments in the data from the CQ and RRQs reveal information about the prevalence of
respondent reticence, reticent behavior on any specific question, and guilt. Section 4 contains our main
results from the Peru Enterprise Survey, while Section 5 provides cross-country evidence from the
Gallup World Poll. In Section 6 we generalize our statistical model to allow for the realistic possibility
that guilt and reticence are correlated across respondents and show how this leads to even higher
estimates of guilt in the Peruvian data. Section 7 offers concluding remarks. Details on the survey
questions and on the derivations of the relevant moments are in Appendices A and B.
2. The Context
We implement our methodology using data from the 2010 World Bank survey of Peruvian firms
(World Bank Enterprise Surveys 2012). Peru is an upper middle-income country with a population of 23
million and an economy that has been one of the fastest-growing in Latin America in the last decade.
The survey polled business owners and top managers in a sample of 1,000 firms representative of the
economy's private sector. Interviews occurred from April 2010 through April 2011. Given the sensitive
nature of some of the data collected, the World Bank Enterprise Survey team emphasizes the efforts
made to ensure confidentiality of responses. Its description of the survey methodology notes
"Confidentiality of the survey respondents and the sensitive information they provide is necessary to
ensure the greatest degree of survey participation, integrity and confidence in the quality of the data.
5
Surveys are usually carried out in cooperation with business organizations and government agencies
promoting job creation and economic growth, but confidentiality is never compromised." 6
We use a CQ that is the basis of a very common measure of corruptionâ€”the first item of data
that the reader encounters when perusing the World Bank's summary of results from the Peruvian
survey. 7 The question asks whether firms are expected to give gifts to public officials "to get things
done". Appendix A contains the precise wording of all survey questions used in this paper. Of the 134
countries that the World Bank has surveyed on this question, Peru is ranked the 44th most corrupt. In
the subsample of firms that we useâ€”the 707 firms for which we have complete data for both the CQ
and all RRQsâ€”18% of firms expect to give informal payments to government officials. 8 Absent any
concerns about respondent reticence, this would be our baseline estimate of corruption in Peru.
However, as we shall see, our estimates of the incidence of reticence imply that this is a serious
underestimate of the actual prevalence of corruption.
Our RR methodology presents survey participants with a series of ten sensitive questions, listed
in Table 1. Respondents privately toss a coin before answering each question and are instructed to
answer "Yes" if the coin comes up heads. If the coin comes up tails, they are instructed to answer the
sensitive question truthfully. 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 1, but were not so
highlighted in the questionnaire itself.
As discussed above, the conventional rationale for deploying RRQs is that they give respondents
the opportunity to "camouflage" their responses: the interviewer will not know whether a "Yes"
response is actually an admission of guilt or simply the outcome of a coin toss. This in turn is expected
to encourage greater candor on the part of respondents. However, as noted above, the success of RRQs
in reducing reticent behavior has been shown to be limited. Instead, we initially follow the insight of
Azfar and Murrell (2009) who infer the prevalence of reticent behavior from the number of respondents
whose answers contain the highly improbable seven "No's" to the seven sensitive RRQs. Based on this,
a baseline estimate of reticence is 23.6%.
The top panel of Figure 1 exhibits the justification for this methodology and why this baseline
estimate does not capture all those who are reticent. It shows the actual distribution of "Yes" responses
in the Peru survey, and the actual distribution for those who answered yes to at least one question. In
addition, it superimposes the hypothetical distribution of responses that would be observed if there
were no reticent behavior, and if no respondents had actually done any of the sensitive acts described in
the questions. Under this null hypothesis, the number of "Yes" responses should be binomially
6
Full details of the methodology can be found at http://www.enterprisesurveys.org/Methodology.
7
http://www.enterprisesurveys.org/Data/ExploreEconomies/2010/peru
8
Our estimates differ from those on http://www.enterprisesurveys.org/Data/ExploreEconomies/2010/peru for
two reasons. First, we restrict our sample to those who have answered the RRQs. Second, we do not apply the
sampling weights that are used to produce the World Bank estimates.
6
distributed, with a success probability of 0.5 -- i.e. respondents answer "Yes" if and only if the coin
comes up heads.
The actual distribution differs from this hypothetical distribution in a very obvious way. There is
a large mass of 23.6% of respondents with zero "Yes" responses. This is clear evidence of reticent
behavior -- respondents are supposed to answer "Yes" every time the coin comes up heads, and so the
probability of observing no "Yes" responses over seven coin tosses should only be 0.008 if respondents
were correctly following the protocol of the question. Based on this insight, Azfar and Murrell (2009)
identify these respondents as reticent, and the remainder as possibly candid. However, even among the
possibly candid, the actual distribution of responses still yields too few "Yes" responses. For example,
37% of the possibly candid respondents answer "Yes" as few as one or two times, while under the null
hypothesis that they are candid only 22% of respondents should do so. This point is amplified if we
assume further that some respondents are guilty on the sensitive acts. This is because the candid who
are guilty are expected to answer yes more often than the candid who are innocent. This is clearly seen
in the bottom panel of Figure 1, which uses 18.25% as the rate of guilt, which is the sample rate of
admission on the CQ. In this case, we would expect just 11% of candid respondents to answer "Yes"
only one or two times, but in fact 37% of the possibly candid do so.
In sum, Figure 1 shows that there are a significant number of reticent respondents in the
sample. It also indicates that reticent respondents are not always reticent on every question, but rather
are sometimes willing to give an answer that might lead to an inference of guilt. Hence, this suggests a
model that has at least two parameters, a probability that a respondent is reticent and a probability that
a reticent respondent answers yes in any particular instance. However, as comparison of the theoretical
distributions in the two panels of Figure 1 suggests, the distribution of yes answers is also affected by
guilt rates. Thus, rates of reticent behavior cannot be estimated without taking into account the effects
of a third parameter, the probability of guilt.
3. Modeling the Interview Process
In this section we develop a statistical model of the interview process for CQs and RRQs. Our
objective is to provide some structure to describe the interaction between an interviewer, who would
like to elicit information, and the respondent, who may prefer not to disclose this information. In our
model, we focus exclusively on respondent characteristics that determine the answer to a given
question. 9 In particular, the probability that respondents answer "Yes" to a given question depends on
(i) whether they have in fact done the sensitive act in question, i.e. whether they are "guilty", and (ii)
whether they are willing to divulge this information, i.e. whether they are "reticent", and (iii) whether
they choose to behave reticently on a specific question.
9
It is of course very plausible that interviewer characteristics matter as well. Indeed, survey firms typically spend
considerable effort training interviewers in ways to establish rapport with respondents in order to elicit truthful
responses. And it is also quite plausible that some interviewers are able to do this better than others. However,
we do not seek to model interviewer characteristics here.
7
With respect to guilt, we assume that there is a probability í µí±” â‰¥ 0 that the respondent has done
the sensitive act in question. Moreover, we assume that the event of being guilty is independent across
questions: the probability of having done a sensitive act referenced in one question does not affect the
probability of having done another sensitive act referenced in another question. This is a strong
assumption, and in Section 6 we will consider a more general framework in which there are different
"types" of respondents, some of whom might have a high likelihood of guilt across questions while
others have a low likelihood of guilt across questions.
With respect to reticence, we assume that reticent respondents differ from candid respondents
in that they are less likely to be willing to answer "Yes" to either CQs or RRQs. Specifically, recall that all
respondents are supposed to answer "Yes" to the CQ if they have done the sensitive act in question, and
they are supposed to answer "Yes" to the RRQ if either they have done the sensitive act in question or if
the coin toss comes up heads. Candid respondents always answer "Yes" when they are supposed to. In
contrast, we assume that reticent respondents answer "Yes" when they are supposed to with
probability (1 âˆ’ í µí±ž ) < 1. We also assume that the event of inappropriately failing to answer "Yes" is
independent across all the relevant questions. Finally, we assume that a proportion í µí±Ÿ of respondents
are reticent, while a proportion 1 âˆ’ í µí±Ÿ are candid. Thus reticence is an unobserved trait that is fixed for
a given respondent, but reticent behavior, i.e. failure to answer "Yes" when supposed to, may vary
across questions.
With these assumptions and notation in hand, it is straightforward to summarize the interview
process using probability trees. In the top panel of Figure 2, we show the relevant probability tree
describing how a reticent respondent answers a CQ. In this case, the tree is simple. The first branch
captures whether the respondent has done the sensitive act in question or not, while the second branch
captures whether the reticent respondent inappropriately fails to answer "Yes". Combining these two
steps, it is clear that the respondent answers "Yes" with probability í µí±”(1 âˆ’ í µí±ž): with probability í µí±” the
respondent has done the sensitive act, and the reticent respondent admits to it with probability 1 âˆ’ í µí±ž.
The corresponding tree for a candid respondent is the special case where í µí±ž=0, i.e. the candid
respondent answers "Yes" if and only if he is guilty, which occurs with probability í µí±”.
In the bottom panel of Figure 2, we show the probability tree describing how a reticent
respondent answers an RRQ. The branches of the tree corresponding to guilt and reticent behavior are
identical to those in the top panel. The only difference is that each question is preceded by a coin toss.
If the coin comes up heads, all respondents are supposed to answer "Yes", but only a fraction 1 âˆ’ í µí±ž of
reticent respondents do so. If the coin comes up tails, all guilty respondents are supposed to answer
"Yes", but only a fraction 1 âˆ’ í µí±ž of the reticent respondents do so. This means that the overall
probability of observing a "Yes" response on a single RRQ is 0.5(1 âˆ’ í µí±ž ) + 0.5(1 âˆ’ í µí±ž )í µí±” =
0.5(1 âˆ’ í µí±ž )(1 + í µí±”). As before, for candid respondents í µí±ž = 0. In this case, candid respondents always
answer "Yes" when the coin comes up heads (with probability 0.5), and they also answer "Yes" if the
coin comes up tails and they have done the sensitive act in question (with probability 0.5í µí±”), for a total
probability of 0.5(1 + í µí±”).
8
Of course, for a given respondent, reticence and guilt are unobservable. Nevertheless, we can
make inferences about the prevalence of reticence, í µí±Ÿ, reticent behavior, í µí±ž, and guilt, í µí±”, from the
observed responses to CQs and RRQs. Specifically, we will show how the population mean and variance
of responses to the RRQ, together with the population mean response to the CQ, combine to identify
the three parameters of interest. This then motivates a standard method-of-moment estimator in
which sample moments are equated with population moments, and the resulting system of nonlinear
equations can be solved for the parameters of interest.
A little more notation aids the exposition. Let í µí±§ denote a binary random variable equal to one if
a specific respondent is reticent, and zero otherwise. í µí±§ will be one with probability í µí±Ÿ. Let í µí±† be a binary
random variable equal to one if the respondent answers "Yes" on the CQ. From the probability tree
above, í µí±† is a mixture of two Bernoulli random variables:
(1) í µí±† = í µí±§í µí±† í µí±… + (1 âˆ’ í µí±§)í µí±† í µí°¶
where í µí±† í µí±… is a Bernoulli random variable with success probability í µí±”(1 âˆ’ í µí±ž), i.e. the reticent respondent
has in fact done the sensitive act and in addition chooses to respond truthfully; and í µí±† í µí°¶ is a Bernoulli
random variable with success probability í µí±”, i.e. the candid respondent is guilty and accordingly answers
"Yes".
Turning to the RRQ, recall that we ask a series of í µí±› questions. Let í µí±‹ be a random variable
reflecting the number of "Yes" responses on the RRQs, which is a mixture of binomial random variables:
(2) í µí±‹ = í µí±§í µí±‹ í µí±… + (1 âˆ’ í µí±§)í µí±‹ í µí°¶
where í µí±‹ í µí±… is a binomial random variable with í µí±› trials and success probability 0.5(1 âˆ’ í µí±ž )(1 + í µí±”),
capturing the number of "Yes" responses given by a reticent respondent; and í µí±‹ í µí°¶ is a binomial random
variable with í µí±› trials and success probability 0.5(1 + í µí±”) capturing the number of "Yes" responses given
by a candid respondent. With this notation, it is straightforward to compute the population mean "Yes"
responses to the CQ and the sequence of RRQs:
(3) í µí°¸ [í µí±†] = í µí±”(1 âˆ’ í µí±Ÿí µí±ž )
and
(4) í µí°¸ [í µí±‹/í µí±›] = 0.5(1 + í µí±”)(1 âˆ’ í µí±Ÿí µí±ž)
The intuition for these expressions is straightforward given the preceding discussion. On the
CQ, respondents answer "Yes" only if they have done the sensitive act in question, which occurs with
probability í µí±”. Among these, a fraction í µí±Ÿ are reticent, and respond "Yes" with probability 1 âˆ’ í µí±ž, while
the remaining 1 âˆ’ í µí±Ÿ are candid and answer "Yes" with probability 1. This gives an overall frequency of
"Yes" responses of í µí±”ï¿½í µí±Ÿ(1 âˆ’ í µí±ž ) + (1 âˆ’ í µí±Ÿ)ï¿½ = í µí±”(1 âˆ’ í µí±Ÿí µí±ž ). Thus í µí±Ÿí µí±ž is an "effective" rate of reticenceâ€”the
probability that an individual is reticent times the likelihood of behavior in a reticent manner on a given
question. Similarly, on the sequence of RRQs, respondents are supposed to answer "Yes" with
9
probability 0.5(1 + í µí±”), reflecting both guilt and the instruction to answer "Yes" whenever the coin
comes up heads. However, only candid respondentsâ€”a proportion equal to 1 âˆ’ í µí±Ÿâ€”always follow these
instructions, while the proportion í µí±Ÿâ€”the reticent respondentsâ€”do so only with probability 1 âˆ’ í µí±ž, for
an overall probability of 0.5(1 + í µí±”)(1 âˆ’ í µí±Ÿí µí±ž).
A first observation that follows immediately from Equations (3) and (4) is that the frequency of
guilt can be inferred from the mean "Yes" responses to the two types of questions. Specifically, taking
the ratio of these two expressions and rearranging gives
í µí±” 1 í µí°¸ [í µí±†]
(5) =
1 + í µí±” 2 í µí°¸ [í µí±‹/í µí±›]
The intuition for this expression follows from noting that we should expect that the average rate
of "Yes" responses on the battery of RRQs will be higher than the rate of "Yes" responses on the CQ.
This is because, for a given rate of effective reticence (í µí±Ÿí µí±ž), we will see more "Yes" responses on the RRQ
coming from the cases where the respondent tosses "Heads" and follows the protocol of answering
"Yes" even if not guilty.
The key point is that the difference in the rate of "Yes" responses across the two types of
questions is informative about the prevalence of guilt. To see this, consider the extreme case where the
average rate of "Yes" responses is the same on the CQ and the RRQ battery. The only way this can occur
is if the probability of guilt is equal to one, since then there will be no inaccurate "Yes" responses in the
RRQ coming from the "Heads" outcome. Any deviation from this benchmark tells us that the probability
of guilt is less than one. For example, at the other extreme, suppose that we observe a much higher
incidence of "Yes" responses on the RRQ battery than on the CQ. The only way this can happen is if the
true rate of guilt is low.
A crucial identifying assumption here is that the rate of guilt is the same across all of the RRQs
and the CQ. As with most identifying assumptions, this is untestable. We discuss the plausibility of this
assumption in our empirical context in Section 4.
Given that the population frequency of guilt is identified by the ratio of the two means, it is
straightforward to retrieve an estimate of the rate of effective reticence, í µí±Ÿí µí±ž, from one or the other of
the two means. However, thus far we do not have sufficient information to separately identify the
proportion of reticent respondents, í µí±Ÿ, and the frequency of reticent behavior, í µí±ž. Intuitively, if for a
given rate of guilt we observe a low rate of "Yes" responses on either the CQ or the RRQs, we cannot tell
if this is because there are many reticent respondents, i.e. í µí±Ÿ is high, or if this is because reticent
respondents are very likely to behave in a reticent manner on a given question, i.e. if í µí±ž is high. All we
know is that the effective rate of reticent behavior is high.
We next show that it is possible to separately identify í µí±Ÿ and í µí±ž by drawing on additional
information contained in the variance of the number of "Yes" responses in the RRQ battery. The
intuition for identification comes from our assumption that reticence is an individual-specific trait which
is fixed across questions for a given respondent, while the event of reticent behavior, i.e. failure to
answer "Yes" when supposed to, is independent across questions. This immediately has the implication
10
that the presence of reticence will be reflected in some positive covariance of responses across
individual questions in the RRQ battery: reticent respondents are less likely to answer "Yes" to RRQs
precisely because they are reticent. This in turn will be reflected in the variance of the number of "Yes"
responses over the individual RRQs.
To show this formally, the variance of the average number of "Yes" responses is:
1
í µí±‰[í µí±‹/í µí±›] = 0.5(1 + í µí±”)(1 âˆ’ í µí±Ÿí µí±ž )ï¿½1 âˆ’ 0.5(1 + í µí±”)(1 âˆ’ í µí±Ÿí µí±ž )ï¿½
í µí±›
(6)
(í µí±› âˆ’ 1)
+ (0.5(1 + í µí±”)í µí±ž )2 í µí±Ÿ(1 âˆ’ í µí±Ÿ)
í µí±›
This equation has a straightforward intuition. The first line is recognizable as the variance of the
mean of a binomial random variable with í µí±› trials and a success probability 0.5(1 + í µí±”)(1 âˆ’ í µí±Ÿí µí±ž ). The
second line captures the covariance across responses to individual RRQs that is due to the presence of
reticent respondents. To see this, consider the polar case where there are no reticent respondents, i.e.
í µí±Ÿ = 0. In this case, all respondents are candid and answer "Yes" to each RRQ with probability
0.5(1 + í µí±”). Since guilt and the coin toss are both independent across questions, the average rate of
"Yes" responses is simply a binomial distribution with this success probability and with variance as given
in the first line of Equation (6), setting í µí±Ÿ = 0. And in this polar case the covariance term in the second
line is of course also zero. The same is true for the opposite polar case where í µí±Ÿ = 1. In this case all
respondents are reticent, and they answer "Yes" to each RRQ with probability
0.5(1 + í µí±”)(1 âˆ’ í µí±ž). Again answering "Yes" is independent across questions and so Equation (6) again
simplifies to the variance of a binomial distribution and the covariance term in the second line is zero.
However in the intermediate case 0 < í µí±Ÿ < 1, the covariance term does not vanish, precisely
because individual-specific reticence induces a positive covariance across RRQs, and this in turn
contributes to the variance of mean "Yes" responses in the RRQ battery. Crucially, this covariance term
depends on í µí±ž and í µí±Ÿ separately, and this is how the variance allows us to separately identify these two
parameters. Specifically, slight rearrangement of the last term in Equation (6) shows that the variance
depends on í µí±”, í µí±Ÿí µí±ž, and 1/í µí±Ÿ, and moreover is linear in 1/í µí±Ÿ. Since we have already seen that the
moment conditions in Equations (3) and (4) can be solved for í µí±” and í µí±Ÿí µí±ž, this establishes that Equations
(3), (4), and (6) can together be solved for í µí±”, í µí±Ÿ, and í µí±ž.
Note also the important role played by having multiple questions in the RRQ battery. If we had
only one RRQ, i.e. í µí±› = 1, the covariance term in the second line of Equation (6) disappears, simply
because there is just one RRQ and so its covariance with another is not defined. As the number of RRQs
becomes large, the first term in Equation (6) disappears. This is due to the law of large numbers given
our assumptions that both the coin toss and reticent behavior are independent across questions.
However, the second term does not decline with í µí±› as it captures the individual-specific reticence effect
which does not average out across multiple RRQs. In fact, the larger is the number of RRQ questions,
11
the more informative about the proportion of reticent respondents is the variance in the number of
"Yes" responses in the RRQ battery. 10
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, í µí±”, the probability that a respondent is reticent, í µí±Ÿ, 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 respondentâ€”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 momentsâ€”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). 11 Estimation of the three parameters í µí±”, í µí±Ÿ, and í µí±ž using the method of moments with three moment
conditions is therefore straightforward.
The estimation uses the identifying assumption that the parameter í µí±” 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 implementationâ€”finding a large number of sensitive questions
with guilt rates similar to that of the CQ and then administering all these as RRQsâ€”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.
12
degree of sensitivity as the average of the RRQs. Later in this section, we present a robustness exercise
that justifies this point.
Our core results appear in Table 2. In addition to estimates of í µí±”, í µí±Ÿ, and í µí±ž, we present estimates
for one composite parameter, effective reticence (í µí±Ÿí µí±ž), which reflects the proportion of sensitive
questions that are not answered candidly for the whole sample. This proportion is approximately 50%
in our estimates. Therefore the predicted guilt rate on making informal payments to public officials
approximately doubles, from the 18% that comes from naively accepting the answers to the CQ to the
37% in Table 2. Remarkably, 74% of survey respondents exhibit markers of reticent behavior, with those
respondents acting in this way on 69% of sensitive questions.
Although these results make a strong argument that corruption estimates must take into
account reticence, results for subsets of the sample do so even more strongly. Table 3 presents
estimates for five different disaggregations of the sampleâ€”sector, firm size, region, firm age, and
gender of respondent. 12 Thus, for example, while baseline estimates suggest that Arequipa is 40% more
corrupt than Lima, reticence-adjusted estimates suggest that the former has triple the rate of corruption
of the latter. Similarly, while standard estimates suggest that very small firms have three times the rate
of corruption of large firms, our results indicate the difference is six-fold. One important qualification
however is that the sample sizes within some of these groups are quite small, so that the group-specific
parameters are less precisely estimated. This means that in most cases we cannot reject the null
hypothesis that the group-specific parameters are significantly different from the corresponding point
estimates in the full sample.
One interesting way to reflect on these data is to examine whether there are any reversals in
the ordering of estimates of corruption, in the sense that some sub-sample seems more corrupt than
another in the baseline estimates but less corrupt in the reticence-adjusted estimates. Figure 3 provides
an easy visualization of the phenomenon. Of the 19 subsamples, 13 exhibit reversals but in most cases
only in minor ways. The reason for few significant reversals is that guilt and effective reticence are so
highly correlated across subsamples, as Figure 4 clearly shows. Arequipa is an important exception to
these stylized facts. According to the baseline estimates, it is ranked the thirteenth most corrupt of the
nineteen subsamples but the reticence-adjusted estimates give it fourth place because it receives the
highest estimated rate of effective reticence in the subsamples.
As a check on a major identifying assumption used in the empiricsâ€”that the rates of guilt on the
CQ and the RRQs are roughly comparableâ€”we obtain estimates equivalent to those in Table 2, but use a
subset of four RRQs, dropping the three with the lowest rates of yes responses of the original seven that
are used. (From equation (5), this will lead to a decrease in the estimated rate of guilt.) The resultsâ€”in
Table 4â€”are very similar to those of our core results, with guilt and effective reticence more than 90%
of that in Table 2.
12
Four cities are represented in the survey, but for two, Chiclayo and Trujillo, estimates of guilt are above one. We
omit results from these regions.
13
5. Results from the Gallup World Poll
In the previous section we saw in the Peruvian data that there were both (i) considerable
differences across subgroups of the population in terms of naive estimates of guilt based on a literal
interpretation of conventional survey questions about corruption, and (ii) substantial differences across
subgroups in the gap between reticence-adjusted and naive estimates of corruption. This suggests that
naive estimates of corruption not only underestimate its true prevalence, but may even lead to an
incorrect ranking of subgroups of a population according to estimates of the prevalence of corruption.
We now investigate the same issue in a cross-country setting. Our dataset consists of household
survey data from a set of Asian countries included in the 2010 wave of the Gallup World Poll (GWP). The
GWP is a large cross-country survey fielded annually since 2006 in over 150 countries representing 95%
of the world's adult population. The GWP gathers respondents' views on a wide range of topics, using
in-depth face-to-face interviews, except in some developed economies where the survey is
implemented by telephone. The core GWP questionnaire is designed to be comparable across all
countries. Within each country the sample is constructed to be representative of the population aged
15 and over.
The majority of questions in the GWP are non-political, focusing on respondents' well-being,
happiness, life satisfaction, expectations about the future, etc. The GWP also asks a number of
questions about respondents' confidence in public institutions, as well as a specific question about
respondents' personal experiences with corruption. This question, which asks whether the respondent
has been in a situation in the past year where a bribe was expected, is used as the CQ.
With the generous collaboration of Gallup, we also placed a 10-question RRQ on the
questionnaires used in 12 Asian countries included in the 2010 wave of the GWP. The RRQ followed the
same structure as the RRQ placed in the Peru Enterprise Survey. However, the specific sensitive
questions were modified to reflect the fact that the respondents were randomly-selected individuals
rather than firm managers. The 10 specific questions included in the coin toss battery, together with the
average number of "Yes" responses, is reported in Table 5. The seven more sensitive questions that we
use in the empirical analysis are indicated in bold.
The pattern of responses to the RRQ indicates that reticent behavior is likely to be present
among GWP respondents. While full compliance with the coin toss question would result in "Yes" rates
of at least 50%, this is rarely the case, and particularly on the sensitive questions indicated in bold. For
example, in all 12 countries, the average "Yes" rate is less than 50% on three of the sensitive questions,
dealing with theft of property and with insulting a family member. The same is true in 11 out of 12
countries for the questions dealing with cheating and hiding money from family members. Taken
together, fully 73 out of 84 average responses to the seven sensitive questions in 12 countries result in
"Yes" rates of less than 50%.
Using the methodology described in Section 3, we compute estimates of reticence and guilt for
10 of the 12 countries where we have data on both the RRQ and the CQ. We lose one country because
the CQ dealing with personal experiences with corruption was not asked in China. We also do not
14
report results for Afghanistan where our estimate of the rate of guilt is greater than one and thus falls
outside the feasible parameter space. The results appear in Table 6, which reports estimates of í µí±”, í µí±Ÿ and
í µí±ž, as well as effective reticence, í µí±Ÿí µí±ž. This latter measure is particularly relevant because it indicates the
proportion of sensitive questions that are not answered candidly. Finally, for reference the Table also
reports naive estimates of guilt. 13
The estimated rate of effective reticence, í µí±Ÿí µí±ž, ranges from 21% in Indonesia to 48% in India.
While these rates are all lower than the estimated rate of effective reticence of 51% in Peru, they still
indicate that a substantial fraction of questions are not answered candidly in these countries. Naturally,
this prevalence of reticent behavior implies that estimated rates of guilt are higher than those implied
by average responses to the CQ. Looking across countries, the fraction of respondents reporting
personal experience with corruption ranges from a low of 7% in Indonesia to a high of 23% in India.
However, our estimates of guilt range from 9% in Indonesia to 44% in India.
It is also interesting to note that many of the cross-country differences in estimated guilt and
reticence are large relative to the corresponding standard errors of the estimates. To illustrate this, we
test the null hypothesis that each of the estimated parameters in Table 6 is equal to the corresponding
point estimates that we would obtain if we were to pool data from all 10 countries in our estimation.
We then indicate with * (**) (***) those cases where we can reject this null hypothesis of parameter
equality at the 90 (95) (99) percent significance level. Consider for example the estimated rate of guilt,
g. The pooled estimate combining data for all countries is 0.286, and we reject the null hypothesis that
the country-specific estimates of g are equal to the pooled estimate in 5 out of 10 countries. For
effective reticence, the pooled estimate of rq is equal to 0.381, and we find that in 8 out of 10 countries,
country-specific estimates are significantly different from this pooled estimate.
Figure 5 illustrates the consequences of reticent behavior for estimates of the prevalence of
corruption for the full set of 10 countries included in our analysis. The top panel compares naÃ¯ve and
reticence-adjusted estimates of guilt. Consider for example the comparison of Indonesia and Malaysia,
which have similar naive estimates of the prevalence of corruption of 7% and 9% respectively. However,
our estimates suggest that effective reticence is much more common in Malaysia (44%) than it is in
Indonesia (21%). As a result, our reticence-adjusted estimates of corruption increase much more in
Malaysia (to 15%) than they do in Indonesia (to 9%). Note also that the corruption ranking of six of the
ten countries differs between the naÃ¯ve and the estimated rates of guilt. Overall, our estimates from the
GWP show that reticent behavior is likely to lead to substantial downward biases in estimates of
corruption based on CQs, and moreover that the size of these biases can differ non-trivially across
countries.
13
In our estimates, we restrict our sample to those who have answered the RRQs, and we also do not apply the
sampling weights that are used to produce the GWP estimates. As a result, the sample means of the CQ reported
in the last row of Table 6 differ from those reported by Gallup.
15
6. Extension to Correlated Guilt and Reticence
In this section, we suggest a realistic extension of the basic statistical model we developed in
Section 3 of the paper, which is motivated by the results of the empirical applications in Sections 4 and
5. This extension moves to greater realism in two dimensions. First, it relaxes our previous strong
assumption that guilt is independent across questions. This captures the plausible notion that
individuals who are willing to do certain bad things are also more likely to be willing to do other bad
things. Second, by allowing guilt to be a persistent individual-specific trait, we are now also able to
allow reticence and guilt to be correlated across individuals. This captures the plausible idea that
individuals who have done bad things are also more likely to be reticent since they have something to
hide. Alternatively, it allows for the case where individuals who are unprincipled in the sense of being
willing to do bad things are also brazen about their misdeeds. In either case, this extension of the model
allows us to consider some non-zero correlation between guilt and reticence, which was not possible in
the model of Section 3.
We assume that a fraction í µí±? of respondents are "principled" in the sense that they have never
done any of the sensitive acts referred to in the CQ and RRQs, while a fraction 1 âˆ’ í µí±? of respondents are
"unprincipled" in the sense that they have done all of the sensitive acts referred to in these questions.
In terms of the notation of Section 3, this amounts to assuming that a fraction í µí±? of respondents has
í µí±” = 0 while the remaining 1 âˆ’ í µí±? has í µí±” = 1.
Figure 6 shows the basic probability tree that sorts respondents into types. The first branch of
the tree distinguishes principled and unprincipled respondents, while the second branch distinguishes
reticent from candid respondents. The key innovation here is that principled respondents are assumed
reticent with probability í µí±Ÿ âˆ’ í µí¼€, while unprincipled respondents are reticent with probability í µí±Ÿ + í µí¼€. Thus
if í µí¼€ > 0 (í µí¼€ < 0) the correlation between guilt and reticence is positive (negative). We leave implicit the
natural restriction that í µí±Ÿ + í µí¼€ and í µí±Ÿ âˆ’ í µí¼€ are both bounded between zero and one.
Depending on the type of the individual, the remainder of the question-response process is the
same as in Section 3. The probability trees describing this process are the same as those shown in
Figure 2, but specializing to the appropriate choice of í µí±”. In particular, the decision tree for reticent and
principled respondents is the same as shown in Figure 2, but setting í µí±” = 0 since we have assumed that
principled respondents never do any of the sensitive acts. Similarly, the decision tree for reticent and
unprincipled respondents, whom we assume have done all of the sensitive acts, is also the same as
shown in Figure 2, but setting í µí±” = 1. Finally, the corresponding decision trees for candid respondents
are as before in the special case of setting í µí±ž = 0.
We now extend the notation of Section 3 to capture the responses of principled and
unprincipled respondents. As before let í µí±§ be a Bernoulli random variable taking the value 1 if the
respondent is reticent, and zero otherwise, and now let í µí±¤ be a Bernoulli random variable taking the
value 1 if the respondent is principled, and zero if unprincipled. We can then write the number of "Yes"
responses on the CQ as a mixture of four Bernoulli random variables taking the value of 1 if the
corresponding type of respondent answers "Yes":
16
(7) í µí±† = í µí±§í µí±¤í µí±† í µí±…í µí±ƒ + í µí±§(1 âˆ’ í µí±¤ )í µí±† í µí±…í µí±ˆ + (1 âˆ’ í µí±§)í µí±¤í µí±† í µí°¶í µí±ƒ + (1 âˆ’ í µí±§)(1 âˆ’ í µí±¤)í µí±† í µí°¶í µí±ˆ
where í µí±† í µí±…í µí±ƒ and í µí±† í µí°¶í µí±ƒ have a success probability of zero (principled individuals never do any sensitive acts
and so never say "Yes", whether they are reticent or candid); and í µí±† í µí±…í µí±ˆ and í µí±† í µí°¶í µí±ˆ have success
probabilities of 1 âˆ’ í µí±ž and 1, respectively. (Unprincipled respondents are always guilty, but only a
fraction 1 âˆ’ í µí±ž of the reticent ones admit to it.)
We can similarly write the number of "Yes" responses on the RRQ battery as a mixture of four
binomial random variables corresponding to the four types of respondents:
(8) í µí±‹ = í µí±§í µí±¤í µí±‹ í µí±…í µí±ƒ + í µí±§(1 âˆ’ í µí±¤ )í µí±‹ í µí±…í µí±ˆ + (1 âˆ’ í µí±§)í µí±¤í µí±‹ í µí°¶í µí±ƒ + (1 âˆ’ í µí±§)(1 âˆ’ í µí±¤)í µí±‹ í µí°¶í µí±ˆ
where í µí±‹ í µí±…í µí±ƒ and í µí±‹ í µí°¶í µí±ƒ have a success probability of 0.5(1 âˆ’ í µí±ž) and 0.5 respectively. (Principled
individuals never do any sensitive acts, and so the candid ones answer "Yes" only when the coin comes
up heads, while the reticent ones do so only when the coin comes up heads and they choose not to
behave reticently.) í µí±‹ í µí±…í µí±ˆ and í µí±‹ í µí°¶í µí±ˆ have success probabilities of 1 âˆ’ í µí±ž and 1 respectively. (Unprincipled
individuals are guilty of all of the sensitive acts, and so they should say "Yes" whether the coin comes up
heads or tails, but the reticent ones do so only with probability 1 âˆ’ í µí±ž .)
With this notation it is straightforward to calculate the average number of "Yes" responses on
the CQ and RRQ battery as before:
(9) í µí°¸[í µí±†] = (1 âˆ’ í µí±?)(1 âˆ’ (í µí±Ÿ + í µí¼€ )í µí±ž)
and
(10) í µí°¸ [í µí±‹/í µí±›] = (1 âˆ’ í µí±?)(1 âˆ’ (í µí±Ÿ + í µí¼€ )í µí±ž ) + í µí±?0.5(1 âˆ’ (í µí±Ÿ âˆ’ í µí¼€ )í µí±ž )
These expressions are the natural generalizations of Equations (3) and (4) in Section 3. First, note that
they are exactly equivalent to (3) and (4) when í µí¼€ = 0, after making the substitution (1 âˆ’ í µí±?) = í µí±”.
Hence, in the benchmark case of zero correlation between reticence and guilt, the ratio of these two
moment conditions identifies 1 âˆ’ í µí±? and given this estimate of í µí±?, we can retrieve an estimate of í µí±Ÿí µí±ž from
one of the two means. Finally, we can separately identify í µí±Ÿ and í µí±ž from the variance of the RRQ, as we
did in the previous model. There is however one difference here even in the case where í µí¼€ = 0. In this
generalized version of the model a fraction 1 âˆ’ í µí±? of respondents are always guilty, and so if they were
candid they would be answering "Yes" to all of the questions in the RRQ battery, thereby increasing the
variance of í µí±‹. Since not many respondents answer in this way, matching the variance of í µí±‹ entails
inferring that there is a smaller proportion of candid respondents in the sample.
This is precisely what we find in Table 7, when we return to the Peruvian data. In the first
column, we consider the basic case where í µí¼€ = 0, i.e. reticence and guilt are uncorrelated. We find that
the proportion of principled respondents is 0.63, implying a proportion of unprincipled respondents,
1 âˆ’ í µí±? = 0.37, which is the same as the estimated rate of guilt from our basic model in Sections 3 and 4.
17
Moreover, the estimated rate of effective reticence, í µí±Ÿí µí±ž, is the same as it was in the basic model.
Consistent with the intuition given above, however, we find a higher proportion of reticent respondents,
with í µí±Ÿ = 0.82, as opposed to í µí±Ÿ = 0.74 in the basic model.
More generally, for , given guilt and reticence rates, the average number of "Yes" responses on
the CQ will be lower if the correlation between reticence and guilt is positive, i.e. if í µí¼€ > 0. This is
because reticent behavior is now more likely among those respondents who otherwise would have
answered "Yes", the unprincipled individuals (who have done the sensitive act). The average number of
"Yes" responses on the RRQ battery is a weighted average of the responses of principled and
unprincipled individuals. Unprincipled individuals are always guilty and are reticent with probability +í µí¼€ .
The first term in Equation (10) is thus 1 âˆ’ í µí±? times the average response on the RRQ in Equation (4), but
with í µí±” = 1 and replacing í µí±Ÿ by í µí±Ÿ + í µí¼€ . Similarly, principled individuals are never guilty, and also are
reticent with probability í µí±Ÿ âˆ’ í µí¼€, and so the second term in Equation (10) isí µí±? times Equation (4), but
setting í µí±” = 0 and replacing í µí±Ÿ with í µí±Ÿ âˆ’ í µí¼€.
In the remaining columns of Table 7 we impose alternative values of í µí¼€ , which governs the
correlation between guilt and reticence. In columns (2) and (3) we consider values of í µí¼€ = 0.2 and
í µí¼€ = 0.4, corresponding to successively stronger correlations between reticence and guilt. The main
effect of this change is to substantially decrease our estimate of the proportion of principled individuals,
which falls from í µí±? = 0.63 in the baseline to í µí±? = 0.34 when í µí¼€ = 0.4. This of course implies an increase
in the estimated proportion of guilty individuals, to 1 âˆ’ í µí±? = 0.66. This figure is substantially higher than
the corresponding estimate of í µí±” = 0.37 in the basic model in Table 2. The intuition for this increase is
straightforward: if guilt and reticence are positively correlated then more of the "No" responses that we
observe in the data are coming from individuals who did in fact do the sensitive act in question. Thus for
a given observed rate of "No" responses, the proportion of unprincipled respondents in the data must
be higher than in the case where reticence and guilt are assumed to be independent across
respondents.
If on the other hand we assume that guilt and reticence are negatively correlated, we obtain the
opposite finding. Under this assumption, "Yes" responses are more likely to signal actual guilt, since
unprincipled respondents are assumed to be more likely to be willing to admit to having done sensitive
acts. In this case, for a given observed rate of "Yes" responses, we must conclude that the proportion of
unprincipled respondents is lower than under the benchmark where guilt and reticence are
independent. This can be seen in column (4) of Table 7, where í µí¼€ = âˆ’0.1. However, in this case we also
find that the estimated proportion of reticent respondents becomes implausibly high. In column (4) the
proportion of principled respondents who are reticent, í µí±Ÿ âˆ’ í µí¼€, is 0.88 âˆ’ (âˆ’0.1) = 0.98, with the
implication that essentially all principled respondents are reticent. 14 Given that this conclusion is
absurd, we think the case where reticence and guilt are positively correlated is much more likely to
characterize the Peruvian observations.
14
In fact, if we go to values of í µí¼€ = âˆ’0.2 or lower, we find that the estimated proportion of principled and reticent
respondents, í µí±Ÿ âˆ’ í µí¼€, becomes greater than one, which is in the inadmissible region of the parameter space.
18
The estimates of Section 4 suggest that the actual rate of corruption is more than double that
derived from the usual procedure of naÃ¯vely using the responses of survey respondents. However,
estimates from subsamples of the Peruvian data and the current discussionâ€”and basic common-
senseâ€”strongly suggest that there is a positive correlation between reticence and guilt. Hence, the
change from the 18% of the naÃ¯ve estimates to the 37% of Section 4 is itself probably a
misunderestimation of the effect of reticence on the measurement of corruption.
7. Conclusions
This paper is motivated by the uncontroversial observation that survey respondents may not
always respond candidly when asked sensitive questions about their personal behavior. This is true
across a broad range of topics, and we specifically focus on the implications of this observation for
survey-based data on corruption. Such data, gathered systematically in many different surveys of
households and firms, are intensively used in policy analysis and in public discourse about the
prevalence of corruption and the success (or failure) of policies to reduce it. While there is widespread
agreement that respondent reticence implies downward biases in survey-based estimates of corruption,
little is known about the magnitude of these biases. Moreover, it is also well-understood in the survey-
research literature that standard solutions to address respondent reticence, such as random response
questions, have had, at best, mixed success.
In this paper we have proposed a novel methodology for estimating the frequency and
consequences of reticent behavior. We develop a statistical model of how responses to sensitive survey
questions are influenced by three characteristics of respondents that are not directly observable:
whether they are reticent, whether they behave reticently in response to a particular question, and
whether they are guilty in the sense of having done the sensitive act in question. We show how the
population frequency of these three characteristics can be estimated using a method of moments
estimator that exploits information in average responses to a CQ and RRQs as well as the variance of
RRQs.
We implement this methodology in the World Bank's Enterprise Survey for Peru and in a sample
of 10 Asian economies covered by the Gallup World Poll. In both applications, we find that reticent
behavior is common: around two-thirds of firm managers surveyed in Peru exhibit signs of reticent
behavior, while in the Gallup World Poll the fraction of individuals exhibiting reticence ranges from 40%
in Indonesia to 81% in India. This in turn implies that the simple average of responses to standard
questions about corruption substantially underestimates the prevalence of corruption. Our reticence-
adjusted estimates of corruption in Peru are twice as high as standard estimates (37% versus 18%), and
similarly we see much higher estimates of corruption in the Gallup World Poll after we adjust for
reticent behavior. Moreover, corruption estimates are even higher in models that allow for a positive
correlation between reticence and guilt, which is indicated strongly by our results.
An immediate implication of our findings is that self-reported survey data on the incidence of
corruption substantially underestimate its actual prevalence. More practically, our findings underscore
the importance of refining survey techniques to improve the measurement of corruption. This includes
19
finding credible and easy-to-implement markers of reticent behavior that can be routinely included in
surveys that aim to gather sensitive data, as well as deploying novel survey techniques to encourage
greater candor (for example using computer-assisted interviewing to reduce the sensitivity of face-to-
face interactions between respondents and interviewers). 15 This research agenda is particularly
important in the case of corruption, where alternatives to self-reported survey-based data are rare.
15
Tourangeau and Yan (2007) provide a valuable survey of the results from many different experiments to improve
the accuracy of responses on sensitive questions, concluding that "The need for methods of data collection
that elicit accurate information is more urgent than ever."
20
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21
Appendix A: The Survey Questions
The Random Response Questions in Peru
The questionnaire was administered in a face-to-face interview with a professional surveyor. The
interviewer was asked to read the following to the respondent:
"We have designed an alternative experiment which provides the opportunity to answer questions based
on the outcome of a coin toss. Before you answer each question, please toss this coin and do not show
me the result. If the coin comes up heads, please answer "yes" to the question regardless of the question
asked. If the coin comes up tails, please answer in accordance with your experience. Since I do not know
the result of the coin toss, I cannot know whether your response is based on your experience or by
chance."
The ten sensitive questions used in this battery of questions are given in Table 1. Respondents who
refused to respond were dropped from the sample. This left 785 respondents who answered all seven
sensitive questions.
The Conventional Question in Peru
The variable we use is constructed in the same way that the World Bank constructs the following
variable: "Percent of establishments that consider that firms with characteristics similar to theirs are
making informal payments or giving gifts to public officials to "get things doneâ€? with regard to customs,
taxes, licenses, regulations, services, etc." See page 22 of
http://www.enterprisesurveys.org/Data/ExploreEconomies/2010/~/media/FPDKM/EnterpriseSurveys/D
ocuments/Misc/Indicator-Descriptions.pdf.
The interviewer reads the following to the respondent:
" It is said that establishments are sometimes required to make gifts or informal payments to public
officials to â€œget things doneâ€? with regard to customs, taxes, licenses, regulations, services etc. On
average, what percentage of total annual sales, or estimated total annual value, do establishments like
this one pay in informal payments or gifts to public officials for this purpose?"
The respondent is then given the option of responding either as a percentage of annual sales or a total
monetary amount in domestic currency units, but not both. The constructed dummy variable then
equals one if either the percentage or the monetary amount is greater than zero, or if the respondent
refuses to answer. If the response was either 0% or a zero monetary amount then the dummy variable
equals zero. Don't knows are treated as missing. This resulted in 881 observations. 707 of these also
answered the RRQ battery.
22
The Random Response Questions in the Gallup World Poll
The questionnaire was administered in a face-to-face interview with a professional surveyor. The
interviewer was asked to read the following to the respondent:
I am going to read out a set of questions that describes acts or behaviours that people have expressed.
Unlike other questions where you would just respond with a â€œyesâ€? or â€œno,â€? this set has a slight variation
to it. Before you answer each question, you will toss this coin, and based on which side comes up, I will
give you an instruction to provide the appropriate response. Are you ready? I will now read the first
question. Please toss the coin, and if the coin comes up heads, just say YES regardless of whether you
have done this or not. If the coin comes up tails, please just answer the question. Please do not let me see
the coin. This is very important.
The 10 subsequent questions posed using this random response methodology are listed in Table 5.
Response rates were exceedingly high, with less than 100% response rates on the RRQ battery only in
China, Mongolia, and the Philippines.
The Conventional Question in the Gallup World Poll
The conventional question seeks to obtain information on the respondent's personal experience with
corruption, as follows:
Sometimes people have to give a bribe or a present in order to solve their problems. In the last 12
months, were you, personally, faced with this kind of situation, or not (regardless of whether you gave a
bribe/present or not)?
Responses included Yes/No/Don't Know/Refused. We coded all "Yes/Refused " responses as 1 and "No
" as zeros, and treated Don't Know's as missing. This is consistent with the coding of the CQ for Peru.
Response rates were very generally very high, less than 2% in the median country.
23
Appendix B: Derivations
In this appendix we show how to derive the expressions for the means of the CQ and RRQ, and the
variance of the RRQ. These derivations all rely on application of the law of iterated expectations to the
random variables defined in Equations (1),(2),(7) and (8), combined with the expressions for the mean
and variance of binomial random variables, i.e. if í µí±‹~í µí°µ(í µí±›, í µí±?), í µí°¸ [í µí±‹] = í µí±›í µí±? and í µí±‰[í µí±‹] = í µí±›í µí±?(1 âˆ’ í µí±?).
Mean of CQ in Section 3 (Equation (3))
í µí°¸ [í µí±†] = í µí°¸ï¿½í µí°¸[í µí±†|í µí±§]ï¿½ = í µí°¸ï¿½í µí±§í µí°¸[í µí±† í µí±… ] + (1 âˆ’ í µí±§)í µí°¸[í µí±† í µí°¶ ]ï¿½
(11) = í µí°¸ [í µí±§í µí±”(1 âˆ’ í µí±ž ) + (1 âˆ’ í µí±§)í µí±”]
= í µí±”ï¿½í µí±Ÿ(1 âˆ’ í µí±ž ) + (1 âˆ’ í µí±Ÿ)ï¿½ = í µí±”(1 âˆ’ í µí±Ÿí µí±ž)
The first line is the application of the law of iterated expectations. The second line uses the fact that
í µí±† í µí±… ~í µí°µï¿½1, í µí±”(1 âˆ’ í µí±ž )ï¿½ and í µí±† í µí°¶ ~í µí°µ(1, í µí±”). The last line uses the fact that í µí±§~í µí°µ(1, í µí±Ÿ).
Mean of RRQ in Section 3 (Equation (4))
í µí°¸ [í µí±‹/í µí±›] = í µí°¸ï¿½í µí°¸[í µí±‹/í µí±›|í µí±§]ï¿½ = í µí°¸ï¿½í µí±§í µí°¸ [í µí±‹ í µí±… /í µí±›] + (1 âˆ’ í µí±§)í µí°¸ [í µí±‹ í µí°¶ /í µí±›]ï¿½
(12) = í µí°¸ [í µí±§0.5(1 âˆ’ í µí±ž )(1 + í µí±”) + (1 âˆ’ í µí±§)0.5(1 + í µí±”)]
= 0.5(1 + í µí±”)ï¿½í µí±Ÿ(1 âˆ’ í µí±ž ) + (1 âˆ’ í µí±Ÿ)ï¿½ = 0.5(1 + í µí±”)(1 âˆ’ í µí±Ÿí µí±ž)
The first line is the application of the law of iterated expectations. The second line uses the fact that
í µí±‹ í µí±… ~í µí°µ(í µí±›, 0.5(1 âˆ’ í µí±ž )(1 + í µí±”)) and í µí±‹ í µí°¶ ~í µí°µ(í µí±›, 0.5(1 + í µí±”)). The last line uses the fact that í µí±§~í µí°µ(1, í µí±Ÿ).
Variance of RRQ in Section 3 (Equation (6))
í µí±‰[í µí±‹/í µí±›] = í µí°¸ï¿½í µí±‰[í µí±‹/í µí±›|í µí±§]ï¿½ + í µí±‰ï¿½í µí°¸[í µí±‹/í µí±›|í µí±§]ï¿½
1
= í µí°¸ï¿½í µí±§ 2 í µí±‰[í µí±‹ í µí±… ] + (1 âˆ’ í µí±§)2 í µí±‰[í µí±‹ í µí°¶ ]ï¿½
í µí±›2
+ í µí±‰ï¿½í µí±§í µí°¸ [í µí±‹ í µí±… /í µí±›] + (1 âˆ’ í µí±§)í µí°¸[í µí±‹ í µí°¶ /í µí±›]ï¿½
1
= í µí°¸ï¿½í µí±§ 2 í µí±›0.5(1 âˆ’ í µí±ž )(1 + í µí±”)ï¿½1 âˆ’ 0.5(1 âˆ’ í µí±ž )(1 + í µí±”)ï¿½
í µí±›2
+ (1 âˆ’ í µí±§)2 í µí±›0.5(1 + í µí±”)ï¿½1 âˆ’ 0.5(1 + í µí±”)ï¿½ï¿½
(13)
+ í µí±‰ï¿½í µí±§ï¿½0.5(1 âˆ’ í µí±ž )(1 + í µí±”) âˆ’ 0.5(1 + í µí±”)ï¿½ï¿½
1
= ï¿½í µí±Ÿ0.5(1 âˆ’ í µí±ž )(1 + í µí±”)ï¿½1 âˆ’ 0.5(1 âˆ’ í µí±ž )(1 + í µí±”)ï¿½
í µí±›
+ (1 âˆ’ í µí±Ÿ)0.5(1 + í µí±”)ï¿½1 âˆ’ 0.5(1 + í µí±”)ï¿½ï¿½
2
+ í µí±Ÿ(1 âˆ’ í µí±Ÿ)ï¿½0.5(1 âˆ’ í µí±ž )(1 + í µí±”) âˆ’ 0.5(1 + í µí±”)ï¿½
24
The first equality is the law of iterated expectations applied to variances. The second equality uses the
definition of í µí±‹. The third equality follows from using the fact that í µí±‹ í µí±… ~í µí°µ(í µí±›, 0.5(1 âˆ’ í µí±ž )(1 + í µí±”)) and
í µí±‹ í µí°¶ ~í µí°µ(í µí±›, 0.5(1 + í µí±”)). The fourth equality follows from the fact that í µí±§~í µí°µ(1, í µí±Ÿ). Finally, Equation (6) in
the main text follows from rearranging the resulting terms in the last line.
The derivation of the corresponding moments in the model of Section 6 follows the same structure. In
particular, Equation(9) follows by applying the law of iterated expectations to Equation (7), and relying
on the fact that í µí±† í µí±…í µí±ƒ ~í µí°µ(1,0), í µí±† í µí°¶í µí±ƒ ~í µí°µ(1,0), í µí±† í µí±…í µí±ˆ ~í µí°µ(1,1 âˆ’ í µí±ž) and í µí±† í µí°¶í µí±ˆ ~í µí°µ(1,1). To derive the mean and
variance of the RRQ, it is useful to re-write Equation (8) as:
(14) í µí±‹ = í µí±¤í µí±‹ í µí±ƒ + (1 âˆ’ í µí±¤ )í µí±‹ í µí±ˆ
where í µí±‹ í µí±ƒ â‰¡ í µí±§í µí±‹ í µí±…í µí±ƒ + (1 âˆ’ í µí±§)í µí±¤í µí±‹ í µí°¶í µí±ƒ and í µí±‹ í µí±ˆ â‰¡ í µí±§í µí±‹ í µí±…í µí±ˆ + (1 âˆ’ í µí±§)í µí±‹ í µí°¶í µí±ˆ .
Next observe that í µí±‹ í µí±ƒ corresponds to the number of "Yes" responses for a principled individual, i.e. one
who is reticent with probability í µí±Ÿ âˆ’ í µí¼€ and is guilty with probability 0. This means that the mean and
variance of í µí±‹ í µí±ƒ are given by Equations (4) and (6) in the main text, but replacing í µí±Ÿ with í µí±Ÿ âˆ’ í µí¼€, and setting
í µí±” = 0. Similarly, í µí±‹ í µí±ˆ corresponds to the number of "Yes" responses for an unprincipled individual, and
so the mean and variance of í µí±‹ í µí±ˆ are given by Equations (4) and (6) in the main text, but replacing í µí±Ÿ with
í µí±Ÿ + í µí¼€, and setting í µí±” = 1.
The expression for the mean of the RRQ in (10) then simply follows from applying the law of iterated
expectations to Equation (14), while the variance of the RRQ (which is not reproduced in the text)
follows from applying the variance form of the law of iterated expectations in Equation (13) to Equation
(14), i.e.
í µí±‹
í µí±‰ ï¿½ ï¿½ = í µí°¸ï¿½í µí±‰[í µí±‹/í µí±›|í µí±¤ ]ï¿½ + í µí±‰ï¿½í µí°¸[í µí±‹/í µí±›|í µí±¤ ]ï¿½
í µí±›
1
= 2 í µí°¸ï¿½í µí±¤ 2 í µí±‰[í µí±‹ í µí±ƒ ] + (1 âˆ’ í µí±¤ )2 í µí±‰[í µí±‹ í µí±ˆ ]ï¿½
í µí±›
í µí±‹ í µí±ƒ í µí±‹ í µí±ˆ
(15) + í µí±‰ ï¿½í µí±§í µí°¸ ï¿½ ï¿½ + (1 âˆ’ í µí±§)í µí°¸ ï¿½ ï¿½ï¿½
í µí±› í µí±›
1
= (í µí±?í µí±‰[í µí±‹ í µí±ƒ ] + (1 âˆ’ í µí±?)í µí±‰[í µí±‹ í µí±ˆ ])
í µí±›2
+í µí±?(1 âˆ’ í µí±?)(í µí°¸ [í µí±‹ í µí±ƒ /í µí±›] âˆ’ í µí°¸ [í µí±‹ í µí±ˆ /í µí±›])2
Inserting the means and variances of í µí±‹ í µí±ƒ and í µí±‹ í µí±ˆ described above gives the variance of the average
number of "Yes" responses on the RRQ in the model of Section 6.
25
Figure 1: Actual and Hypothetical Distributions of Responses to the
RRQ in the Peruvian Enterprise Survey
Panel A: Assuming No Guilt
30
25
All respondents in the
20 Peruvian survey
Percent
15
Predicted given no
reticence
10
Respondents in the
5
Peruvian survey with at
least one "yes"
0
0 1 2 3 4 5 6 7
Number of Yes Responses
Panel B: Assuming Guilt Rate of 18.25%
35
30
25 All respondents in the
Peruvian survey
20
Percent
Predicted given no
15
reticence
10
Respondents in the
5 Peruvian survey with at
least one "yes"
0
0 1 2 3 4 5 6 7
Number of Yes Responses
Notes: This figure shows the actual distribution of the total number of "Yes" responses across seven sensitive RRQs, the
hypothetical distribution of responses that would be observed if respondents were candid and if the probability of guilt
were zero (top panel) or 0.1825 (bottom panel), and the actual distribution of the number of "Yes" responses among
those respondents who answered "Yes" at least once.
26
Figure 2: Probability Trees for Reticent Respondents
Panel A: Conventional Question (CQ)
Panel B: Random Response Question (RRQ)
q â€œNoâ€?
g
1-q â€œYesâ€?
q â€œNoâ€?
Heads (0.5)
1-g â€œYesâ€?
1-q
q â€œNoâ€?
g
1-q â€œYesâ€?
Tails (0.5) q â€œNoâ€?
1-g â€œNoâ€?
1-q
Coin Guilt Reticent
Toss Behaviour
27
Figure 3: Reticence-Adjusted and Unadjusted (NaÃ¯ve) Estimates of Guilt
for Subsamples of the Peruvian Data
1
very small
Rate of guilt (g) estimated from model
.8
other manuf.
transport
.6
Arequipa service
female food
2000's 1990's
.4
male
chemicals small
medium 1980's
old text. & garments
Lima
.2
large
metals
0
0 .2 .4 .6 .8 1
Naive rate of guilt directly from survey
Note: This graph plots the mean response to the CQ (horizontal axis) and the estimated rate of guilt (vertical axis), for the
indicated subsets of the Peru Enterprise Survey data. The corresponding data are also reported in Table 3.
28
Figure 4: Effective Reticence and Reticence-Adjusted Estimates of Guilt
for Subsamples of the Peruvian Data
Rate of effective reticence (rq) estimated from the model
.8 1
Arequipa
transport very small
service other manuf.
.6
female
old chemicals 2000's
food
1980's male
text. & garments 1990's
large medium small
.4
Lima
metals
0 .2
0 .2 .4 .6 .8 1
Rate of guilt ( g) estimated from model
Note: This graph plots the estimated rate of guilt (horizontal axis) against the estimated effective reticence rate (vertical axis),
for the indicated subsets of the Peru Enterprise Survey data. The corresponding data are also reported in Table 3.
29
Figure 5: Reticence-Adjusted and Unadjusted (NaÃ¯ve) Estimates of Guilt and Effective
Reticence for the Gallup World Poll Countries
India
.4
Rate of guilt (g) estimated from model
Mongolia
Philippines
Pakistan
Cambodia Thailand
.2
Bangladesh
Malaysia Sri Lanka
Indonesia
0
0 .1 .2 .3 .4 .5
Naive rate of guilt directly from survey
Rate of effective reticence (rq) estimated from the model
.5
India
Malaysia
Pakistan
.4
Philippines
Cambodia
.3
Bangladesh Mongolia
Sri Lanka
Thailand
Indonesia
0 .1 .2
0 .1 .2 .3 .4 .5
Rate of guilt ( g) estimated from model
30
Figure 6: Probability Tree for Reticent and Principled Respondents
31
Table 1: Summary Results from Random Response Questions in Peru
Percentage of Respondents
Answering "Yes"
Have you ever paid less in personal taxes than you should have under the law? 37.8
Have you ever paid less in business taxes than you should have under the law? 36.8
Have you ever made a misstatement on a job application? 31.7
Have you ever used the office telephone for personal businesses? 74.8
Have you ever inappropriately promoted an employee for personal reasons? 36.1
Have you ever deliberately not given your suppliers or clients what was due to them? 31.5
Have you ever lied in your self-interest? 50.3
Have you ever inappropriately hired a staff member for personal reasons? 33.8
Have you ever been purposely late for work? 48.4
Have you ever unfairly dismissed an employee for personal reasons? 28.4
Note: Responses from 707 Peruvian firms, April 2010-April 2011.
The seven sensitive questions used in the paper's empirics are in bold.
32
Table 2: Estimates of Reticence and Guilt from the Peruvian Enterprise Survey
Reticence (r ) 0.737***
(14.12)
Probability reticent person 0.689***
answers question reticently (q) (40.62)
Guilt (g) 0.371***
(5.11)
Effective reticence (rq) 0.508***
(13.05)
Number of Observations 707
Notes: z-statistics based on heteroskedasticity-consistent standard errors clustered at the strata level (for a total of 99 clusters)
are reported in parentheses
* p<0.05 ** p<0.01 *** p<0.001
33
Table 3: Estimates of Reticence and Guilt for Subsets of Responding Firms in the
Peruvian Enterprise Survey
"NaÃ¯ve" Prob. question Effective
estimate of guilt Reticence answered Guilt reticence Number of
rate r reticently g rq observations
Sectors
food 0.242 0.814*** 0.632*** 0.499** 0.514*** 128
text. & garments 0.144 0.668*** 0.681*** 0.264* 0.455*** 139
chemicals 0.165 0.759*** 0.689*** 0.347*** 0.523*** 121
metals 0.106 0.433*** 0.778*** 0.159* 0.337*** 104
service 0.211 0.819*** 0.719*** 0.514* 0.589*** 123
transport 0.208 0.884*** 0.775*** 0.66 0.685** 24
other manuf. 0.255 0.881*** 0.752*** 0.754 0.663*** 55
Size of firm
very small 0.303 0.919*** 0.757*** 0.995** 0.696*** 175
small 0.188 0.673*** 0.689*** 0.349*** 0.464*** 176
medium 0.144 0.633*** 0.717*** 0.265*** 0.454*** 180
large 0.097 0.646*** 0.653*** 0.167*** 0.422*** 176
Regions
Lima 0.114 0.529*** 0.683*** 0.178*** 0.361*** 510
Arequipa 0.157 0.831*** 0.862*** 0.552* 0.716*** 83
Age of firm
old 0.121 0.694*** 0.731*** 0.246*** 0.507*** 173
1980's 0.168 0.741*** 0.669*** 0.332*** 0.496*** 173
1990's 0.220 0.744*** 0.674*** 0.441*** 0.501*** 200
2000's 0.213 0.766*** 0.681*** 0.444** 0.522*** 160
Gender of respondent
male 0.177 0.721*** 0.688*** 0.352*** 0.496*** 593
female 0.211 0.813*** 0.700*** 0.488** 0.569*** 114
Notes: z-statistics based on heteroskedasticity-consistent standard errors clustered at the strata level are reported in parentheses
* p<0.05 ** p<0.01 *** p<0.001
Estimated guilt rates for Chiclayo and Trujillo were above 1.0. Therefore results for these regions are omitted.
34
Table 4: Using only Four RRQs to Obtain Estimates of Reticence and Guilt from the
Peruvian Enterprise Survey
Reticence (r) 0.677***
(9.71)
Probability reticent person 0.680***
answers question reticently (q) (28.99)
Guilt (g) 0.338***
(5.12)
Effective reticence (rq) 0.460***
(10.78)
Number of Observations 707
Notes: z-statistics based on heteroskedasticity-consistent standard errors clustered at the strata level (for a total of 99 clusters)
are reported in parentheses
* p<0.05 ** p<0.01 *** p<0.001
35
Table 5: Summary Results from the Random Response Questions in Gallup World Poll Asian Countries
Afghanistan Bangladesh Cambodia China India Indonesia Malaysia Mongolia Pakistan Philippines Sri Lanka Thailand
Proportion of Respondents Answering "Yes" to:
1. Have you ever lied to protect yourself? 63.9 61.2 68.3 59.1 64.3 66.7 68.5 61.2 64.1 63.8 67.7 68.8
2. Have you ever deliberately spoken ill of a member of your family or a friend? 56.1 40.1 51.7 45.5 45.2 51.5 32.3 45.9 47.6 56.8 49.7 51.4
3. Have you ever deliberately tried to cheat another person? 54.9 39.2 38.0 42.9 34.1 43.0 38.6 44.4 34.4 32.4 42.0 41.4
4. Have you ever broken a promise? 31.4 47.9 57.6 51.2 48.7 55.9 56.9 54.1 44.6 61.2 49.4 59.4
5. Have you ever taken something that is not yours without permission and kept 32.1 39.8 40.6 37.7 34.6 38.9 30.8 37.9 39.7 31.9 41.6 46.3
it?
6. Have you ever bought, sold, bartered or been given something that you knew 31.0 37.9 35.0 37.8 31.4 39.4 25.8 37.8 32.7 31.1 37.3 42.2
was stolen?
7. Have you ever mistreated someone because they did not share your opinions 47.8 54.7 40.1 37.2 42.6 42.2 44.2 62.1 37.2 49.6 45.6 50.9
or values?
8. Have you ever been nice to a person only because you thought it would bring 78.6 62.8 66.5 46.0 49.6 48.4 52.2 59.0 41.3 52.0 53.2 52.5
you some benefit?
9. If you received some extra money that your family did not know about, would 38.5 42.6 42.5 40.3 39.0 44.0 32.2 48.6 38.4 37.8 41.4 54.5
you ever hide it from them and spend it on your own enjoyment?
10. Have you ever insulted your parents, relatives or other elders ? 28.3 40.0 36.8 34.6 35.3 41.0 24.0 49.1 36.8 37.6 39.1 39.2
Note: The seven sensitive questions used in the empirical part of this paper are indicated in bold.
36
Table 6: Estimates of Reticence and Guilt For Asian Gallup World Poll Countries
Pakistan Indonesia Bangladesh India Philippines Sri Lanka Thailand Cambodia Malaysia Mongolia
Guilt (g) 0.263 0.0919*** 0.191*** 0.435*** 0.275 0.150*** 0.272 0.248 0.155*** 0.287
(5.80) (2.86) (7.24) (8.51) (4.51) (5.40) (3.80) (9.15) (4.18) (3.88)
Reticence (r ) 0.607 0.413** 0.617 0.814*** 0.528 0.624 0.666 0.631 0.588* 0.507*
(9.03) (3.26) (10.93) (29.48) (5.08) (9.50) (3.54) (17.77) (11.77) (5.09)
Probability reticent person 0.653*** 0.510 0.479* 0.586 0.709*** 0.422*** 0.400*** 0.552 0.746*** 0.555
answers question reticently (q) (20.34) (5.80) (9.58) (20.89) (19.42) (10.61) (10.18) (29.08) (26.32) (12.48)
Effective reticence (rq) 0.396 0.211** 0.296** 0.477*** 0.375 0.263*** 0.267* 0.348* 0.439* 0.281*
(9.18) (2.93) (7.23) (14.88) (6.04) (8.46) (3.84) (17.93) (13.67) (5.13)
Number of Observations 937 1048 987 5760 495 1024 967 983 956 969
Number of Clusters 72 14 49 99 38 31 21 105 121 8
NaÃ¯ve guilt rate estimated 0.159 0.073 0.135 0.228 0.172 0.110 0.200 0.162 0.087 0.206
directly from survey responses
Notes: z-statistics based on heteroskedasticity-consistent standard errors clustered at the primary sampling unit level are reported in parentheses.
The corresponding number of clusters is reported in the penultimate row of the table.
All coefficients are significantly different from zero at 99% levels.
* p<0.05 ** p<0.01 *** p<0.001 denote the p-values for the null hypothesis that the country-specific estimate of the indicated parameter is equal to the corresponding point estimate
obtained pooling data for all countries. These pooled estimates are í µí±” ï¿½ = 0.563, and í µí±Ÿí µí±ž
ï¿½ = 0.286, í µí±ŸÌ‚ = 0.676, í µí±ž ï¿½ = 0.381.
37
Table 7: The Effects of Varying the Correlation Between Guilt and Reticence
Value of Îµ 0 0.2 0.4 -0.1
Probability of being principled (p) 0.629*** 0.481*** 0.341*** 0.678***
(8.67) (5.81) (5.26) (10.89)
Reticence (r ) 0.824*** 0.690*** 0.518*** 0.879***
(22.96) (45.81) (67.94) (18.00)
Probability reticent person 0.616*** 0.729*** 0.787*** 0.555***
answers question reticently (q) (22.36) (43.84) (54.87) (19.49)
Effective reticence (rq) 0.508*** 0.508*** 0.508*** 0.508***
(13.05) (13.05) (13.05) (13.05)
Note: 707 observations in all four estimates
z-statistics based on heteroskedasticity-consistent standard errors clustered at the strata level (for a total of 99 clusters) are reported in parentheses
* p<0.05 ** p<0.01 *** p<0.001
38