How Much Do Perceptions of Corruption Really Tell Us?

Regressions and tests performed on data from Transparency International Global Corruption Barometer (GCB) 2004 survey show that personal or household experience of bribery is not a good predictor of perceptions held about corruption among the general population. In contrast, perceptions about the effects of corruption correlate consistently among themselves. However, no consistent relationship between opinions about general effects and the assessments of the extent with which corruption affects the institutions where presumably corruption is materialized is found. Countries are sharply divided between those above and below the US$ 10,000 GDP per capita line in the relationships between variables concerning corruption. Among richer countries, opinions about institutions explain very well opinions concerning certain effects of corruption, while among poorer countries the explanatory power of institutions for the effects of corruption falls. Furthermore, tests for dependence applied between the variables in the sets of respondents for each of 60 countries also show that, for most of them, it is likely that experience does not explain perceptions. On the other hand, opinions tend to closely follow the trend of other opinions. Additionally, it is found that in the GCB opinions about general effects of corruption are strongly correlated with opinions about other issues. The correlation is so strong as to justify the hypothesis that it would suffice to measure the average opinion of the general public about human rights, violence etc. to accurately infer what would be the average opinion about least petty and grand corruption. The findings reported here challenge the value of perceptions of corruption as indications of the actual incidence of the phenomenon. --


Introduction
Perceptions of corruption are often taken as reliable proxies for the actual phenomenon of corruption occurring in countries. Regressions and tests performed on data from the Global Corruption Barometer 2004 (GCB), 1 however, show that personal or household experience of bribery is not in fact a good predictor of perceptions held about corruption among the general population. Countries are sharply divided between those above and below the US$ 10,000 GDP per capita line in the relationships between variables concerning corruption, and especially those involving experience vs.
opinions. It is found that the connection between the experience variable and the others mostly remains weak or non-significant in both groups. Controlling for GDP per capita leads to very small and non-significant correlations almost completely across the board. In contrast, perceptions about the effects of corruption correlate consistently among themselves, the exception being the outlook towards the future, which does not appear to be connected to any of the other factors.
No consistent relationship between opinions about general effects and the assessments of the extent with which corruption affects the institutions where presumably corruption is materialized is found. Among richer countries, opinions about institutions explain very well opinions concerning certain effects of corruption, while among poorer countries the explanatory power of institutions for the effects of corruption falls, sometimes radically. Furthermore, tests for dependence applied between the variables in the sets of respondents for each of 60 countries (48,232 in all) show that, for most of them, it is likely that experience does not explain perceptions. On the other hand, again opinions tend to closely follow the trend of other opinions. For example, in most countries, an opinion that petty corruption is a problem is not significantly more frequent among respondents that have had experience with bribery than otherwisewhile for most countries the opposite happens concerning the relationship between perceptions.
Additionally, it is found that in the GCB opinions about general effects of corruption are strongly correlated with opinions about other issues, as much as to justify the hypothesis that it would suffice to measure the average opinion of the general public about human rights, violence etc. to accurately infer what would be the average opinion about at least petty and grand corruption. Every time these indices are announced, they are presented in the press as indices "of corruption". More often than not, the "perceptions" part is forgotten. 3 This leads most lay persons to take such indices as reflecting actual levels of corruption affecting countries -even if, as pointed out by many authors, 4 the meaning of "actual level of corruption" is not at all clear.
Taking perceptions as indications of actual phenomena by default can become a habit. Thus, after arguing that (for instance) "conviction rates are not an adequate indicator for the actual incidence of corruption, but rather, reflect the quality of the judiciary" (which in itself is sensible), Lambsdorff (1999) proceeds to state that "perceptions are commonly a good indicator of the real

The Data and the Model
The Global Corruption Barometer 2004 6 was a public opinion survey conducted between July and September 2004 by Gallup International on behalf of Transparency International among 52,682 respondents from 64 countries. The survey questionnaire uses in part Gallup's "Trust in Institutions" survey, which have been done several times in Iberoamerica (14 Latin American countries plus Spain and Portugal), 7 added by one question concerning experience with bribery and numerous questions about perceptions of corruption and other issues. National samples varied from national to urban to metropolitan, the majority of them being urban. Three methods were used: Face-to-face interviews, telephone interviews, in one case (Japan) self-applied questionnaires and in another (Norway) web interviews. Samplings were mostly based on demographic quotas, while in a few cases they were probabilistic. Thus, margins of error vary considerably from country to country.
The informed overall margin is ±4.4 pp.
The questions asked in the survey were the following: 1. These days, citizens face a number of problems. In your opinion, how would you describe the following problems facing your country? For each of the problems that I read out would you say that it is a very big problem in your country, a fairly big problem, not a particularly big problem or not a problem at all, Do not Know/Did not Answer.
1.b. Petty or administrative corruption that is corruption in ordinary people's daily lives, such as bribes paid for licences, traffic violations, etc./ Grand or political corruption that is corruption at the highest levels of society, by leading political elites, major companies, etc.
2. Some people believe that corruption affects different spheres of life in this country. In your view, does corruption affect […] not at all, to a small extent, to a moderate extent or to a large extent, DK/DA? Your personal and family life; The business environment; Political life.
3. To what extent do you perceive the following sectors in this country to be affected by corruption? Please answer on a scale from 1 to 5 (1 meaning not at all corrupt, 5 meaning extremely corrupt). Of course you can use in-between scores as well. Customs/Education system/Legal system-Judiciary/Medical services/Police/Political parties/Parliament-Legislature/Registry and permit services (civil registry for birth, marriage, licences, permits)/ Utilities (telephone, electricity, water etc.)/Tax revenue/Business-private sector/Media/The military/NGOs (non governmental organizations)/Religious bodies 4. Do you expect the level of corruption in the next 3 years to change? Will it increase a lot, increase a little, stay the same, decrease a little, decrease a lot. DK/DA? 5. In the past 12 months, have you or anyone living in your household paid a bribe in any form? (Living in household = people included in your house e.g. parents, children, etc.).

[Yes/No/DK/DA]
We are interested in the following events built from the above (dummies). Abusing the language, we will refer to the corresponding dummy variables by the same names. We will also group variables into categories. The dummies are presented already grouped.

Group 1. Effects of corruption
Petty, Grand: Respondents answering "a very big problem" and "a fairly big problem" to question 1.b.
Life, Business and Politics: Respondents answering "to a moderate extent" and "to a large extent" to question 2.
Perspective: Respondents answering "will increase a lot" and "will increase a little" to question 4.

Group 2. Institutions
Customs, Education, Judiciary, Health, Police, Parties, Parliament, Civil Registry, Utilities, Taxes, Private Sector: Respondents giving scores of 4 and 5 to question 3. We will not use the variables Media, Military, NGOs and Religions. www.economics-ejournal.org

Group 4. General issues
Prices, Poverty, Environment, (Human) Rights, Violence and Jobs: Respondents answering "a very big problem" and "a fairly big problem" to question 1.a.
All groups but Group 3 concern opinions. Our attention is focused on the relationship between experience with bribery and opinions about corruption, both concerning Effects and Institutions.
The aim is to find out the extent with which personal/household experience with bribery informs the opinions of people. Another field of interest is the relationship between opinions.
The analysis is restricted to 60 of the 64 countries depicted in the GCB (48,232 individual respondents). The survey conducted in three of these countries did not include some or all the questions we are interested in and for one (Kosovo) there are no economic data easily available. For GDP per capita we use the International Monetary Fund's data. We also use Transparency International Corruption Perceptions Index and the recent index proposed in Dreher et al. (2007). GDP-PC is used to group countries into two categories, divided by the US$ 10,000 line. There would be 24 countries in the upper tier and 36 in the lower group. Because for almost all variables two countries in the upper tier (Greece and South Korea) behave much closer to the bottom tier than to the top, we grouped then together with the lower-income group. Thus, we ended up with a "Top 22" and a "Bottom 38" assemblies.
Besides testing aggregated data, we performed tests for dependence between variables within each country's set of individual responses. The method used to do this is described in Annex I.

Cross-Country Analysis
Understanding the phenomenon of corruption is difficult because of its secret character. Not being amenable to direct measurement, corruption is addressed by indirect means, the most promi- Because of the scarcity of data, few studies on the relationship between perceptions and experience with corruption across assemblages of countries were conducted. Recently, Mocan (2004) studied data from ICVS and compared them with four perceptions indices, collected along different periods. His conclusion is that the perception of corruption in a country is mainly influenced by the quality of its institutions (proxyed by the risk of expropriation), and that, when this factor is compensated for, actual experience has no impact on the level of perceived corruption.
The Global Corruption Barometer presents a valuable opportunity to compare perceptions and experience within the same samples. The importance of establishing the relationship, if any, between experience and opinions cannot be minimized, as reporting instances of bribery provides a presumably objective assessment of the actual incidence of corruption upon populations. Compar-9 KK also uses surveys among the general population. 10 Those indices hold very high pairwase correlations -which is only to be expected, as often they are based on similar or even identical samples. Starting in 2006, KK is using the GCB as one of its sources. 11 See e.g. Johnston (2000), Søreide (2003) and(2006) and Weber Abramo (2007). www.economics-ejournal.org ing experience with perceptions within the same sample allows one to investigate how the former relates to the latter.

Basic Statistics
We start with the averages. Table 1 shows the averages of the variables belonging to the Effects group, plus Experience (base percentages weighted). Table 2 has the corresponding numbers for the variables of the Institutions group. tive. This variable systematically behaves at odds with the others, and in the sequel will be treated separately. Harsher evaluations among Bottom countries are also the norm for the variables from the group of Institutions (Table 2). It is also interesting to observe a few of the evaluations some of the GDP per capita correlates better with the subjective variables, and in almost all cases better among Top countries than among Bottom countries (Table 3), the exception being Perspective.
Business and Politics correlate positively with GDP-PC in the Bottom subset (the higher the income, the more pessimistic is the perceived effect of corruption), but in the case of Business the correlation is not significant. Observe that almost all correlations in the Bottom set are not significant. ceptions, the other variables also exhibit low correlations with GDP-PC. Thus, in general, as far as the predictive power of income for opinions goes, it is stronger for perceived Effects of corruption than for Institutions and stronger among countries that are richer and less objectively affected by bribery than among poorer and (presumably) more prone to bribery ones. The correlations with variables of the Institutions group are generally weaker, but the disparity between the income groups remains.

Experience as Predictor of Opinions
One of our principal aims here is to ascertain how pragmatic experience as reported by respondents relate to their opinions. We will then begin with the relationships of the Experience variable with those concerning opinions about the Effects of corruption (Table 4). www.economics-ejournal.org

Opinions as Explanations for Other Opinions
In marked contrast with the correlations involving Experience, those holding between the subjective variables are considerably higher. Not only that, they also vary much less across the income subsets. Table 6 describes the relationships within the Effects group, excluding Perspective. As an opinion about Effects might be informed by more than one single opinion about Institutions, we will pursue the matter of how much the latter explains the former by performing multiple www.economics-ejournal.org regressions on them. We will address each Effects variable in turn. We will use the following terminology: "Expected" will refer to a set of explanations that one would reasonably expect for any given effect, given its nature. For instance, while it would be natural to expect that corruption in Education and in Health impact on the perceptions about the extent of over-the-counter bribery and also on the significance of corruption in day-to-day life (and so these variables, among others, would comprise the Expected set of explanations for both Petty and Life), prima facie it would not be expected that assessments about corruption in the health system would have a sizable impact on opinions about the political life, say.
So, for the various Effects variables we will use the following variables from the Institutions set to form their respective Expected groups: Petty -Education, Health, Police, Civil Registry and Taxes.
Life -The same as Petty.
Grand -Parliament, Parties and Judiciary.
Business -Taxes, Utilities, Customs, Parties, Parliament, Private Sector and Judiciary.
Politics -Parliament, Parties and Judiciary.
The regressions with the Expected sets are performed with and without the addition of the variable Experience. 13 Table 7 summarises the results. 13 Although the standard procedure is to find the least ensemble of independent variables that explains the dependent variable (thus getting "parsimonious" explanations), we will not pursue this path.
www.economics-ejournal.org The regression for Petty using all variables over the whole set of countries leads to a multiple adjusted R 2 of 0.811, which is a good fit, but the standard error is big, 0.101. Taking just the Expected variables for Petty (Education, Health, Police, Civil Registry and Taxes) and running the regression over that set, we get an adjusted R 2 = 0.787 and standard error of 0.107. Within these limits, we can say that taking the whole set of countries, these variables reasonably explain the evaluations about Petty (and Grand) corruption. However, the picture changes when we focus on the income subsets. Whereas evaluations of institutions reasonably explain opinions about the extent of Petty corruption if we keep to richer countries, the explanatory power of such institutional assessments falls dramatically for the set of poorer countries. When Experience is added to the regression, the fit slightly deteriorates. In fact, controlling Petty vs. Experience in the income subsets for the variables from Petty's Expected set, the correlations totally cease to be significant (respectively -0.087 and 0.084).
For Grand, we find that the explanatory power is very good within Top countries, falling for Bottom ones. This is one of the two exceptions where adding the Experience variable to the regression improves the fit, but only for the Top group. Adding Private Sector to the Expected set improves the fit when the regression is performed over the whole set and for the Bottom countries, but deteriorates it in the Top subset.
Taking Life, the explanatory power falls for both sets of independent variables. Expected is the same as was used for Petty. The differences of predictive power across the income divide are less than for Petty, but standard errors are bigger. Here, Experience adds to the goodness of fit in the Top group. Controlling Life vs. Experience in the income subsets for the variables from its Expected set, the correlations become, respectively, -0.291 and -0.103.

www.economics-ejournal.org
The situation for the effects of corruption on Business is much worse than for the previous variables (the Expected set is formed by Taxes, Utilities, Customs, Parties, Parliament, Private Sector and Judiciary). Table 7 shows that the opinions about the effects of corruption on Business are not very well explained in the Top subset and remain unexplained in the Bottom subset. Experience deteriorates the fits. Limiting the Expected set to fewer independent variables results in even worse outcomes.
Lastly, the effects of corruption on Politics. It would be reasonable to find explanations in Parliament, Parties and Judiciary. The best fits involve all variables. The fit is moderately good with the Expected set for Top countries but not so for Bottom ones. Adding Private Sector improves the fit in the income subsets, while Experience deteriorates it.

So, in summary:
Petty is indeed acceptably explained by those perceptions of the incidence of bribery in institutions one would associate with it, but only in the set of richer countries. Among poor countries, the explanatory power is irrelevant whichever set of independent variables one chooses.
Grand is exceptionally well explained by the chosen Institutions variables in the Top group, but the predictive power sharply falls among the Bottom countries, although still maintaining an arguable connection, with low standard errors. Estimating Grand for Top countries by the variables of its Expected group leads to a very good fit (adjusted R 2 = 0.914, standard error = 0.073, as shown in Graph 3). www.economics-ejournal.org Estimated Grand

Grand (To p o nly)
Life does not work especially well neither in the Top nor in the Bottom subset (adjusted R 2 of, respectively, about 0.5 and 0.4 for the Expected set of explaining variables, with a standard error of 0.136 for the latter case).
The opinions about the impact of corruption on Business remain unexplained for the Bottom subset and moderately explained in the Top one by its Expected set.
Politics shows a slightly worse result within the Top for the Expected set of explanations, such deterioration being considerably more acute among Bottom countries.
With the exception of Grand and Life for the Top subset, the addition of Experience deteriorates all regressions.

The Unusual Behaviour of Perspectives about the Future
Every analysis performed over the variables led to distinctly peculiar results concerning the Perspectives variable. Around 40% of respondents in both income subsets consider that the future is bleak concerning the evolution of corruption, but the relationships of such opinion with the other perceptual evaluations of Effects of corruption are weak (

Intra-Country Relationships between Variables
Weak or strong relationships between country averages give no information about the linkages among the same variables within each country. Thus, for example, from the generally low degree of relationship between Experience and opinions one cannot conclude that personal/household experience has little connection with opinions in any given country, but only that, if experience informs opinions, it does it differently across countries. It could be that, staying within each country, one would find stronger links between the variables in question. If we were to confirm this, then we would become endowed with country-specific numerical factors that, applied to each country, would permit to normalize results in order to allow comparing opinions across countries.
In order to test whether or not this happens, we submitted the survey's country data to tests of dependence between variables. To do that, the crosstab statistics for each pair of variables was studied. Given a country and given two variables (say, Petty and Experience), we are interested in ascertaining whether or not respondents that reported having paid bribes are significantly more likely to hold a pessimistic opinion about the extent with which petty corruption is a problem than otherwise.
The most common way to do that is by means of the χ 2 (chi-square) test. Here we slightly depart from the usual path and directly explore the hypergeometric distribution, characteristic of sampling procedures. This allows for a better discrimination of cases than the χ 2 procedure. 14 We proceed exactly as with χ 2 , comparing the frequency of the event Petty in the overall sample with the same event in the sub-sample defined by those who reported having had experience. If the frequency of the event Petty in the sub-sample is significantly higher (or lower) than the frequency in the overall sample, then we conclude that the two events are dependent. Thus, the outcome of a test pivots on how we define the level of significance, that is, the range of frequencies that establishes whether we are willing to accept the hypothesis that the events are dependent. The margin used is n is the length of the sequence (the size of each country's sample); f is the frequency of the studied event in the sequence (say, the percentage of respondents that considered Petty corruption to be problematic); 15 r is the size of the sub-sample (say, the number of respondents that reported Experience); λ π is the parameter of the elected level of confidence, corresponding to , where ϕ is the normal distribution function.
The difference between this test and χ 2 is that for the latter the parameter n is taken as being much bigger than r, leading to a margin of We want to be as accommodating as possible concerning the rigour of the tests we want to apply, in order not to be guilty of bias towards rejection. Accordingly, for these tests we used a level of confidence of 90% (we will accept as dependent as many as 10% of all possible outcomes), corresponding to λ π = 1.645. To apply a test, the absolute value δ of the distance between the sampled frequency and the frequency of the event in the original sequence is compared with ε(r). If δ > ε(r), the sequence is dependent relative to the test. For instance, take the variables Health and Experience in Argentina. The numbers are: n = 1005 (all respondents from that country); f = 0.406 (the frequency of respondents that answered that corruption is a problem for Health in Argentina); r = 71 (respondents that reported having paid bribes). Therefore, ε(71) = 0.092. Now we use the micro data to compute the frequency of the event Health among the 71 respondents that reported having had Experience. It is 43/71 = 0.606, and so δ = |0.406 -0.606| = 0.200. Since δ > ε(r), we conclude that there is dependence between the two variables at the chosen level of confidence of 90%. Ob-serve that dependence is symmetrical -the same conclusion is reached by interchanging f and r/n, as it should.
Our intention is to ascertain whether or not the perceptions variables connected with corruption are dependent on the Experience variable and also among themselves. The rationale for applying the procedure is that, if Experience informs perceptions, then those who have had household contacts with bribery would be more likely to hold pessimistic views than those who haven't. Similarly, we compare each of the variables of the Effects group with their respective sets of Expected variables (see the previous section) selected from the Institutions group. The tests could produce three types of outcomes: Randomness. If for country A Experience is random relative to Petty (say), then one cannot say that it is likely that actual experience with bribery significantly informed the opinions of the persons pertaining to that country's sample.
Dependence by excess. When the frequency of the event under scrutiny (e.g. persons saying that corruption constitutes a problem in Life) within the subset of respondents that have had Experience with bribery is significantly higher than the frequency in the entire sample. Dependence by excess is what we are looking for.
Dependence by deficiency, or lack. When the frequency of the event under scrutiny within the subset of respondents that have had Experience with bribery is significantly lower than the frequency in the entire sample.

Dependence between Effects and Experience
We begin with the relationship of the Experience variable with the Effects group. The outcomes of the tests are summarised in Table 9. The numbers correspond to the amount of countries that fall into each of the three possible outcomes of the test.
www.economics-ejournal.org It turns out that in only 15 out of 60 countries' respondents that have had Experience with bribery were significantly more likely to answer that Petty corruption is a problem in their country than the country's overall sample. There were five countries (Guatemala, India, Indonesia, the Philippines and USA) where for respondents that reported having had Experience with bribery, it was significantly less likely that they would consider Petty corruption a problem than otherwise. For no less than 40 countries, the answers about Experience and Petty corruption were relatively random.
The panorama for the Grand variable is essentially the same, with only 12 countries exhibiting dependence between the variables. For seven there is non-randomness by lack of sufficient coincident answers (Germany, Guatemala, India, South Korea, Philippines, Portugal and USA), that is, respondents that experienced bribery were less likely to consider Grand corruption a problem in their countries than the incidence in the respective overall samples. The better-behaved instance concerns the variable Life, but even then only 25 countries showed dependence with Experience. On average, 72% of the relationships of the subjective Effects variables with Experience are either random of deficient, only 28% being dependent.
In what regards the comparative picture between Top and Bottom countries, a partial summary is presented in www.economics-ejournal.org Adding Perspective, the number is 13.
In the previous section we have seen that the correlations between the Effects variables and Experience are low and/or non-significant. Perhaps we could find better relationships if we limited the countries to those that exhibit dependence between Experience and each Effects variable in turn. Table 11 shows that the correlations obtained are even worse than previously. Only Grand, with 0.415 among 12 countries, escapes from generally negative or near zero correlations.
16 Even at the 70% confidence level (accepting as dependent 30% of all possible outcomes of the tests), the distribution of dependences of Experience vs. the subjective variables is: Petty -24 countries; Grand -31; Life -34; Business -28; Politics -26; Perspective -25. However, there is a trade-off, as dependences by deficiency also grow: Petty -9; Grand -9; Life -4; Business -5; Politics -7; Perspective -6. With this, as much as 56% of the relationships turns out to be non-positively-dependent even at that more than permissive level of confidence. www.economics-ejournal.org

Dependence between Institutions and Experience
The same procedure, now applied to the Institutions variables, leads to similar results ( www.economics-ejournal.org

Dependence between Effects
In sharp contrast with Experience, the tests for dependence among the perceptions variables of the Effects group produce much more consistent results, with the exception -again -of Perspective (Table 14). Thus, for instance, only six out of 60 countries fail to exhibit pairwise dependences between Grand, Business and Politics. This means that it is likely that asking one single question (say, impact of corruption in Business) will suffice to give a very good clue about opinions on Grand corruption or Politics. By the same token, given that in 49 countries Petty corruption and impact on personal/family Life are dependent, it probably suffices to ask one question in order to get a good indication of the other. This will be addressed in more detail further on.
www.economics-ejournal.org We observe that, once again, Perspective stands apart. For this variable, Table 14 shows that the field is more or less evenly divided between randomness and dependence. Thus, the answers to questions about the future of corruption in countries do not consistently help to understand either experiences with bribery or other opinions about the subject, thus being probably related to other aspirations, hopes and general outlooks not captured by the other corruption variables.

Dependence between Effects and Institutions
Additional tests on dependence can be performed on the countries' raw data. Thus, for instance, we can study dependences between the variables restricted to the subsets of respondents that experienced bribery. The outcomes are presented in Table 15. www.economics-ejournal.org The interpretation of this table is as follows. In the subset of respondents that reported having had Experience with corruption (country average of about 1.5% in the Top and 17.3% in the Bottom group), assessments of Petty corruption (say) are shown to be related to assessments of Grand corruption (say) in just one country. Impact on Life, on the other hand, seems to be connected by dependence with three other variables (Business, Politics and Perspective) in no less than 55 countries. Therefore, for people who experienced bribery, asking questions about the impact of corruption in Life suffices to inform about opinions on impact on Business and on Politics, as well as their Perspective about the future. However, among respondents that have had contact with bribery, the same variable Life does not show to be dependent towards Petty and Grand in a great many number of countries (respectively 19 and 14).
Besides concluding once again that Experience does not appear to be significantly connected with opinions in the majority of countries and that the outlook about the future shows no discernible pattern vis à vis other variables, the results of this section have a further important consequence, namely, that since the relationship between perceptions and Experience widely vary, ranking countries according to perceptions collected among the general population does not furnish reliable information about the comparative levels of actual over-the-counter bribery occurring in those countries. However, they do inform about other opinions. This is the case between opinions about the Effects of corruption and also between Institutions and Effects. Whereas there is lack of evidence that perceptions are linked with experience, it is likely that opinions depend on other perceptionswww.economics-ejournal.org so that, in order to change perceptions, one gets better expectations by acting on opinions rather than on reality. 17 This furnishes a rather depressing justification for the panorama one witnesses in many countries, where marketing efforts aimed at forming populations' opinions are endowed with more resources than efforts to change the objective conditions under which the State functions. Such strategies are only reinforced when perceptions about corruption (and about other themes) are overvalued and confused with the actual levels of the phenomena they purport to reflect. By taking that course, one is induced to equate "real levels" of corruption with perceptions -as the media does -, and so becoming ensnared in an imaginary world of hunches.

Other Opinions
Besides surveying information and perceptions about corruption, the GCB inquired about other topics. The questions were the same as those concerning the Petty and Grand variables, and focused on high Prices/inflation, Poverty, Environmental problems, human Rights violations, insecurity/crime/Violence/terrorism and Jobs.
It is illuminating to examine the relationships between these other opinion variables and those Effects tend to be more uniform among the former than among the latter. Table 16 summarizes the numbers for these variables, and Graph 5 depicts, as an example, the relationship between the opinions about petty corruption and human rights violations. Petty corruption. In order to verify whether or not this makes sense, we will take recourse once again to tests of dependence between the variables. Table 17 shows the results for the whole set of countries.
www.economics-ejournal.org We have thus reached the conclusion that it is likely that asking the general public about their opinions about corruption does not produce much more information than is obtained by just asking about poverty, human rights etc. What the GCB data show is that opinions are so strongly dependent on one another that probably it suffices to assess some of them to safely project the results upon the others. Since the only question about the actual experiences of respondents concerned bribery, the relationship of other opinions with personal contact with assorted social phenomena cannot be ascertained. It would hazardous to project onto these relationships the same conclusions reached about corruption variables -but these conclusions prompt questions that future surveys could strive to answer. Where do opinions about violence, security, poverty, the environment etc. come from?
Of course, for many of the "general" questions asked by the GCB, personal or household experiences are not relevant. However, this does not void the question: Why is it that people consider that their countries are confronted with grave environmental problems (say)? Are those problems actually present in people's minds as a result of personal testimony, or were they simply projected over the public's mind by the media and pressure groups? It is well known and often pointed out that the media, or interest groups, are not equivalently trustworthy across countries. The opinions they project not always are grounded in persuasive evidence. So, in many countries opinions collected about many issues would be subjected at least to doubt about their foundations.

Consequences for the Interpretation of the CPI
The findings of the present study beg similar questions about perceptions of corruption collected among transnational business representatives and institutions that have them as their primary public, which are at the heart of international indicators of perceptions of corruption. Of special interest is the most prestigious of these indicators, namely Transparency International Corruption Perceptions Index (CPI). That index is built on the basis of a number of other indicators and is computed in isolation, not including other queries 19 -and, anyhow, the primary data are not available, so tests for dependence are out of the question. In particular, there is no explicit Experience variable with which to compare the CPI. The most one can do within the present scope is to compare the CPI with the GCB averages, keeping in mind that the samples are not similar. 20 Since the CPI is an ordinal ranking and not an actual measure of a dimension of social life, the following uses the ranks of the countries arising from the GCB percentages (weighted) and from the CPI scores, in this case 19 For an explanation of the methodology, see Lambsdorff (2004). Responsibilities about the index are not totally clear. According to the press release announcing the index (which is repeated every year up to 2007), "The CPI methodology used is reviewed by a Steering Committee consisting of leading international experts in the fields of corruption, econometrics and statistics. Members of the Steering Committee make suggestions for improving the CPI, but the management of TI takes the final decisions on the methodology used." Neither the members of the Steering Committee nor the persons taking methodological decisions are identified. 20 The same analyses reported in this section were performed over the "Control of Corruption" indicator from the KK set of governance indicators Kaufmann et al. (2003), as well as over the "Corruption" component of the World Economic Forum's Growth Competitive Index (2003) (Table 19).  It thus appears that one is partially justified in using the CPI as a proxy to in-country opinions about certain types of corruption in the ensemble of richer countries (Petty, Grand), but not concerning actual bribery affecting citizens either among countries at the Top (the small correlation not being significant) or at the Bottom (significant, but small). One may speculate that citizens of Top countries tend to be more informed than citizens of Bottom countries, so among them, the opinions about Grand corruption might be informed by the Corruption Perceptions Index itself, while for Bottom countries the CPI does not influence common opinion. This would be natural considering www.economics-ejournal.org that the reach of information about the CPI, as a media feature, is affected by different levels of access to information enjoyed by citizens of rich and poor countries.
A converse speculation would be that, since the great majority of persons whose opinions are used to build the CPI are connected to transnational business, thus being either citizens of rich countries or under the influence of their outlooks and values, their opinions about their own countries would be bound to be concordant in the CPI and in the GCB.
As Andvig (2004) puts it: "[…] I will expect strong correlation and spillover effects: The experts read the same reports and gauge other experts' statements. Since the assessments are often not based on individual experience, when expert X claims corruption in A is very high, expert Z has no clear evidence to the contrary, so when knowing X's statement it may be optimal to make an assessment close to his. Informational cascades may easily develop in this context. The fact that the TI index in particular is widely published reinforces the argument. The case of information given by expatriate businessmen is somewhat different, but they are not likely to base their assessments to only on their own, independent experience either. Most will be based upon other businessmen's communication. The degree to which that will contain private information will at best depend on how much genuine information other expatriates reveal." On the basis of statistical arguments, Lambsdorff argues that the sources used in the CPI exhibit low vulnerability to cultural differences and cultural bias. He also argues that the concept of corruption the respondents probably have in mind is reasonably uniform. A similar disclaimer about possible bias acting on assessments of corruption is stated by Kaufmann et al. about the KK indicators. However, there is one peculiarity that all respondents of the CPI share (and most of them in the case of the KK), namely, they are all connected with business.
Besides observing that the lack of objective data on the extent of corruption forces one to stick to subjective assessments of corruption, Treisman (2000) argues that using them is justified by the high correlations observed both between different indices and between year-to-year editions of the same indices. The findings of the present study indeed confirm that opinions are mutually coherent, but since their relationship with the objective data represented by the experiences reported are very weak or nonexistent, such coherence casts a different light on perceptions, namely, that perhaps what they indicate is the pervasiveness of a certain type of bias.
The conclusions of the previous sections -that opinions about corruption do not likely arise from actual experience with bribery, but are more probably linked with other opinions -can be exwww.economics-ejournal.org tended to the CPI (and KK) only insofar as one keeps in mind that the universes in question are different. The GCB reports on data collected among the general population, and experience most likely means experience with (petty) bribery, while the CPI is built on the opinions of business people involved in international business transactions.
Questions about the connection of the CPI (or the KK) ranking and the actual experience of respondents with (presumably grand) corruption are certainly in line, but they cannot be answered within the present scope. However, it would be of the utmost importance for the very credibility of these indicators that efforts be made to answer the question. To simply assume that the CPI and other such indices, as the KK or the World Economic Forum's, are good indicators of actual corruption happening in countries simply because the opinions they depict come from business-related persons rather than from common citizens would unjustifiably attribute to the former special critical attributes that would allow them to better "filter" stray influences when forming their opinions. But business people are just people, and rhe evidence furnished by the GCB is that experience enters at best discreetly into people's opinion-forming mechanisms.   Table below. DKM depicts an increasing gap of theoretical GDP per capita losses due to corruption between rich and poor countries. Whereas for 1980 the minimum estimated loss was 30% (Denmark) and the maximum 52% (a number of countries, mainly in Africa), making for a ratio of about 1.7, for 1997 the minimum was 11% (Norway) and the maximum about 67% (Guinea-Bissau), a ratio of more than 6. In any case, if one is to give more weight to perceptions than to reported experience, one would still have to assume that opinions collected among the general population concerning petty corruption and the impact of bribery on life were reasonably informed by something else than experience.

Consequences for the Interpretation of the DKM Index
Clarifying that matter is likely to be impossible. Measuring the amount and especially the quality of information individuals receive would depend on external references establishing not only quantities but also the objectivity of information and of information-transforming mechanisms such as e.g.
the media. Consensually accepting such measures and using them methodologically in sample design seems far-fetched. In the absence of better information about how opinions are formed and being materially unable to directly observe and measure the actual incidence of corruption, one is forced to give weight primarily to data derived from claims of direct experiences as reported by those who hold to have been subjected to or have participated in acts of bribery. As has been argued above, failure to do this entails a high risk of producing misleading indicators, the consequences of which can be significantly negative. 25 Daniel Treisman argues 26 that a high correlation between answers about personal experience with bribery and opinions about the prevalence of corruption in any given sector is not necessarily to be expected, because bribery might affect some sectors more intensely than others.  Arndt and Oman (2006). For the reply, see Kaufmann et. al. (2006). 26 Private communication. 27 Private communication.

www.economics-ejournal.org
Of course, in order to ascertain each sector's level of actual bribery it would be necessary to actually survey the matter, by asking about bribes specifically practiced in a number of sectors. This poses a significant practical problem, because the frequency of reports of (overall) bribery is usually low, and restricting the questions to each particular sector would lead to still lower rates. This means that in order to achieve representative samples at the sub-level of each institution's users, overall samples would have to be quite numerous -and this costs a lot of money.
However, at least qualitative data is available in selected countries. A survey conducted in the city of São Paulo (Brazil) by Transparência Brasil, the World Bank and the municipal administration asked for the experience of citizens with bribery relating to fifteen different services. 28 Percentages ranged from 0.0% of actual users to 7.7%. The weighted average was 3.0%. Zero or nearzero percentages referred to services that would be improbably affected by corruption: public transportation and information-related services. Eliminating those, the minimum level was 1.3% (in nurseries). The rest turned around 4%, but actual users varied, in most cases being well below significant levels. Anyway, such qualitative results indicate that if bribery is present in an administration, then it would manifest itself in several institutions and not just a few. This is confirmed (always keeping in mind the non-representativeness of the sub-samples) by the results of the same survey about the experience with bribery in eleven administrative processes reported by private firms.
Treisman's and Uslaner' arguments would have to be applied also to perceptions about institutions. If bribery affects institutions differently, and if perceptions indeed give a better inkling of "real" corruption than experience, then this should be reflected in the correlations between the perceptual variables. However, as can be seen in Table 21, the correlations within the income groups are high practically across the board, with few exceptions. 28 Speck and Weber Abramo (2003: 42). Firms' and public officials' experiences were also surveyed.
www.economics-ejournal.org Measures of bribery and corruption are essentially policy tools. Their role is to guide effective policy formation and review. This analysis doe not junk perceptions but provides for the first time not simply a general health warning on their use (of which there is now a fairly significant literature), but also a rigorous approach to their use and so to avoid the common abuse of the apparent information in data. The approach set out above provides a coherent method to interpret what are the likely causal links between recorded data and incidence in different socio-economic and institutional settings and thus attempts to improve the targeting of policy to create both measures of the scale and scope of bribery and so to provide clearer positive incentives for reform.

Annex -Testing for Randomness
For each country and each variable, a binary sequence was built by attributing the value "1" to the event under scrutiny (e.g., all answers "Yes" given to the Experience question) and "0" other- wise. The sequences were tested for pairwise dependence by performing on each of them placeselections based on the other sequences. A place-selection is a sampling procedure defined by a recursive rule that selects positions from a sequence, with the only provision that one is barred from using the outcome of a position to determine whether or not that position will be selected. All statistical tests are based on place selections, although that is not usually made explicit. The frequencies of the studied event in the original sequence and in the subsequence defined by the selection are then compared. If the sampled frequency falls within a previously defined interval, the tested sequence is declared random relative to the place selection in question and non-random otherwise.
The interval of confidence depends on both the original and the sampled subsequence, as well as on an arbitrarily defined level (what we are willing to accept/reject). The distribution arising from the sampling procedure is hypergeometric, and the usual practice is to approximate it by the binomial distribution.
However, the fit between the hypergeometric distribution and its binomial approximation depends on the relationship between the frequency of the observed event in the original sequence and the size of the sampling produced by the test. For sampling procedures in which those numbers are of comparable orders of magnitude, the binomial approximation to the hypergeometric makes too many sequences pass as random relative to tests (see Example 4, below). An alternative criterion, developed by the author, 29 does not make use of such approximation. The interval of confidence for each test is determined by the expression n is the length of the sequence; 29 Weber Abramo (1993).
www.economics-ejournal.org f is the frequency of the studied event in the sequence; 30 r is the number of elements selected by the rule; λ π is the parameter of the chosen level of confidence, corresponding to , where ϕ is the normal distribution function. This means that, given a sequence, we are willing to consider that of all possible results of a place-selection, the sequence will be non-random relative to π of them.
The choice of a level of confidence is arbitrary. There is no compelling reason to favour a level of confidence of 95% (say) over a level of 99%. The only reason why some levels are used and others are not is practical: In statistical practice as applied to the sciences, levels of confidence of 99%, 95% and 90% function adequately vis à vis observed phenomena, depending on samples sizes, sensitivity of measurements and a host of other practical factors.
In our case, we want to be as accommodating as possible concerning the rigour of the tests we want to apply, in order not to be guilty of bias towards rejection. We will use tests to ascertain whether or not variables are interdependent. We do not want to reject too many relationships as random. Thus, we will use a level of confidence of 90% for these tests (we will accept as dependent as much as 10% of all possible outcomes of tests).
To apply a test, the absolute value δ of the distance between the sampled frequency and the frequency of the event in the original sequence is compared with ε(r). If δ > ε(r), the sequence is not random relative to the test. 31 Testing for randomness is the same thing as testing for dependence.
Two sequences that are mutually dependent (at a given confidence level) are not relatively random and conversely.
The testing can be depicted graphically. For a given sequence and all tests that pick up r positions, we plot the distribution of all possible outcomes, mark the area corresponding to the confidence interval for randomness and plot the outcome of the application of the test in question. If the outcome falls within the confidence interval, the sequences are declared mutually random at that 30 Observe that this is not the weighted frequency for the variable, but the actual frequency of the event in the sequence. 31 The margin ε (r) must not be confused with the margin of error arising from the sampling of the country's population used to collect the data. ε (r) is intrinsic to the sequences under test.
www.economics-ejournal.org level and mutually dependent otherwise. Three examples are given below (at the 90% confidence level): The abscissas correspond to the possible outcomes of the application of the test (the number of possible coincident responses between the two variables in question) and the ordinates to the probabilities of getting them. Of course, by construction, the integral of the curve bounding the shaded area corresponds to 1 -π = 90% of the solid area. As the binomial distribution is less peaked and more spread-out than the hypergeometric, using the former approximation to the latter results in the outcome being random according to it and non-random according to the hypergeometric.
Another way to express the difference of using the hypergeometric or the binomial distributions in testing procedures is to observe that, in the general case, when passing from one to the other one must adjust the confidence level: For a given confidence level, the hypergeometric distribution admits for smaller margins of confidence than the binomial. Thus, if one wants to stick with the binomial approximation to the hypergeometric distribution in testing set-ups, then one must use