Corruption Perceptions Index 2017 Statistical

2 CPI — Sources and methodologyThe measurement of the perceived level of corruption by Transparency International hasbeen an evolving project since 1995. Every year, such measurement builds uponprevious editions while refined with newly available data. The CPI 2017 is calculatedfor 180 countries around the world, and it is based on 13 sources that collect theassessment of experts and business executives on some specific corrupt behaviour in thepublic sector (i.e. bribery, diversion of public funds, use of public office for private gain,nepotism in the civil service and state capture). The sources of information used to buildthe CPI are listed in Table 1. The sources differ in the number of countries covered, rangingfrom 15 countries covered in the Political and Economic Risk Consultancy AsianIntelligence to 180 countries included in the Global Insight Country Risk Ratings. The sourceVarieties of Democracy was included for the first time in 2016, to the detriment ofthe source Transparency International Bribe Payers Survey. More detailed information onthe sources and the rationale for inclusion of each source is offered in the main report ofthe CPI 2017.The most recently released country scores from those 13 sources were used in thedevelopment of the CPI 2017. Countries were included if they were evaluated by at leastthree sources; this was the case for 13 countries (e.g. Barbados, Bahamas, Grenada).The maximum number of sources based on which a country was evaluated was 10; thiswas the case for nine countries (i.e. Bulgaria, Croatia, Czechia, Estonia, Hungary, Poland,Romania, Slovenia and South Korea). Most countries were evaluated using seven(35countries) and eight sources (38 countries).For simplicity in communication and to allow comparisons over time, the CPI 2017 iscalculated using a simple average of standardised scores. More specifically, all 13 sourcesare standardised by subtracting the mean of the data and dividing by the standarddeviation (z-scores) and then rescaled to have a mean 45 and standard deviation 20.The standardization is: xi mean( x) sign 20 45std ( x)The direction of the effect of the source is taken into account at this stage. For sources,for which the lower the value of the source, the less the perceived level of corruption, anegative sign is used. This is done for four sources: Economist Intelligence Unit CountryRisk Ratings, Freedom House Nations in Transit, Political and Economic Risk ConsultancyAsian Intelligence, and Varieties of Democracy Project’s Political Corruption Index.8

After the standardisation, any values beyond the 0-100 scale are capped. For thenormalised scores to be comparable between the 13 sources, the mean and standarddeviation need to be defined as global parameters. In other words, what would the meanand standard deviation of each source have been if all 180 countries had been evaluatedby each source? As in previous editions, the CPI 2017 uses the ‘ impute’ command inthe statistical software package STATA in order to impute scores for all those countriesthat are missing data in each source. The mean and standard deviation for each sourceacross the 180 countries are then calculated and used as the parameters to standardisethe sources during the normalisation. An important remark is that the imputed valuesare used only during the calculation of the ‘global mean and standard deviation’ but notfor the calculation of CPI country scores, which are subsequently calculated as simpleaverages of the normalised scores across the available sources only. The CPI scores are inthe range 0 to 100 (0 being the lowest level of perceived corruption).9

Table 1. 2017 CPI Sources of information and number of countries in common with theCPISourceNumber ofcountries1. African Development Bank Governance Ratings (AFDB) 2016382. Bertelsmann Stiftung Governance Indicators (BF-SGI) 2017413. Bertelsmann Stiftung Transformation Index 2017-2018 (BF-BTI)1294. Economist Intelligence Unit Country Risk Service (EIU) 20171315. Freedom House Nations in Transit (FH) 20176. Global Insight Country Risk Ratings (GI) 2016291807. IMD World Competitiveness Center World Competitiveness YearbookExecutive Opinion Survey (IMD) 2017638. Political and Economic Risk Consultancy Asian Intelligence (PERC)1520179. The PRS Group International Country Risk Guide (ICRG) 201710. World Bank — Country Performance and Institutional14067Assessment (WB) 201711. World Economic Forum Executive Opinion Survey (WEF) 201713312. World Justice Project Rule of Law Index Expert Survey (WJP) 2017-110201813. Varieties of Democracy Project’s Political Corruption Index (V-Dem)1692017Source: Corruption Perceptions Index 2017.10

3Conceptual and statistical coherence in the CPIEach of the 13 sources included in the CPI measures the overall extent of corruption(frequency and/or size of corrupt transactions) in the public and political sectors andprovides a ranking of countries that reflects the ‘perception of corruption’ in the countriescovered by each source. The aim of the CPI is to provide a more reliable picture of theperceived level of corruption around the world than would any of the 13 sources takenindependently.Assessing potential redundancy of information in the CPIThe country rankings from the 13 different sources tend to correlate well with each other.There is also a high correlation between the CPI ranking and each of the sources, rangingfrom 0.87 to 0.95 (see Table 3). These high correlations were expected, given that allsources attempt to measure the same phenomenon, which is the perceived level ofcorruption in the public sector. Despite the high correlations among the CPI sources, theinformation offered by the CPI is not redundant. In fact, the 13 sources cover differentcountries — from 15 countries for the Political and Economic Risk Consultancy AsianIntelligence to 180 countries for the Global Insight Country Risk Ratings. Hence, combiningthe information on the perceived level of corruption from these different sources, asdone in the CPI, may be more reliable than each source taken separately. The CPI canefficiently differentiate the level of corruption between countries,unlike some sourceswhere a large number of countries is assessed to have the same perceived level ofcorruption (e.g. while the Global Insight Country Risk Ratings only has seven differentscores for 180 countries, the CPI presents 66 different scores for the same number ofcountries). One more feature of the CPI is that it reconciles different viewpoints on theissue of corruption. If the countries’ classifications in the 13 sources were to be taken atface value, it is found that no country is classified as better off than another country on allcommon sources. This is an important remark which adds to the contribution of the CPIin the measurement of perceived corruption at national level worldwide.11

Principal Component Analysis was applied to the six sources with the widest countrycoverage, namely WEF, GI, BF-BTI, PRS, VDEM and EIU (78 countries are common to allsources) ( 2). The first latent dimension accounts for 80 % of the total variability in the sixsources (see Table 2). Furthermore, the six sources have nearly equal weights andloadings ( 3) on the first latent dimension. These results suggest that assuming equalweights and an arithmetic average to aggregate the six sources are statistically supportedby the data. In more practical terms, however, equal weights in the case of the CPI maybe justified on the premise that all these sources are very important and that there is no apriori rationale for giving a higher weight to one source than to another.Table 2. Principal Component Analysis on six CPI sourcesPCEigenvalueVarianceexplained(% total)SourceLoadings onthe first rce: Own elaboration.(2) PCA could not be applied to the entire set of 13 sources because no single country is covered by all sources.(3) A loading in principal component analysis is the correlation coefficient between a variable and the PrincipalComponent (latent dimension).12

Table 3. Spearman rank correlations and Gamma statistics for the CPI H0.81PERC0.85WB0.87(n �WEF0.84(n 133)0.39(n 66(n 67)0.72(n 52)0.75(n 133)0.46(n I0.92(n 180)0.86(n 129)0.74(n n 38)0.82(n 37)0.45(n 25)0.44(n 38)0.76(n 33)---0.590.620.340.57--IMD0.91(n 63)(n 1)0.95(n 62)0.79(n 63)0.37(n 37)(n 0)-0.720.730.770.650.830.440.79BF-SGI0.88(n 41)(n 0)0.74(n 40)0.80(n 41)0.84(n 15)(n 0)0.80(n 40)—0.830.760.790.750.95—0.74(n 33)0.68(n 37)0.80(n 93)0.80(n 115)0.88(n 110)0.84(n 140)0.68(n 81)0.76(n 105)0.72(n 16)0.66(n 26)0.88(n 51)0.89(n 63)0.88(n 31)0.80(n 41)-0.710.730.820.560.89ICRG0.94(n 110)0.94(n 140)0.80(n 97)-0.750.910.910.66V-DEM0.91(n 169)0.65(n 63)0.68(n 128)0.81(n 169)0.70(n 127)0.47(n 38)0.80(n 60)0.82(n 39)0.88(n )1030.86(n 130)-0.820.770.78EIU0.93(n 131)0.43(n 28)0.79(n 111)0.87(n 131)0.76(n 100)0.52(n 16)0.86(n 63)0.72(n 41)0.83(n 95)0.88(n 123)0.83(n 126)-0.760.89FH0.92(n 29)(n 5)0.43(n 23)0.80(n 29)0.96(n 29)(n 0)0.53(n 14)0.93(n 11)0.69(n 20)0.92(n 20)0.89(n 29)0.74(n 23)--PERC0.95(n 15)(n 2)0.90(n 15)0.95(n 15)0.82(n 11)(n 0)0.92(n 13)(n 4)0.96(n 14)0.78(n 14)0.91(n 14)0.92(n 15)(n 0)-GIWJPSource: Own elaboration.NB: Low diagonal: Spearman rank correlation coefficients (significant at 5 % level). Number of countries that are common to each pair of sources is given in theparenthesis. Upper diagonal: Gamma statistic (significant at the 5 % level), which is to be preferred over the Spearman rank correlation for sources with tied values. Allcoefficients are positive because sources where lower scores represent lower levels of corruption were reversed by multiplying every score in the data by – 1.10

Assessing potential bias introduced in the CPIA legitimate question is whether the CPI scores or the standard errors associated withthem are biased with respect to the number of sources that were used to evaluate eachcountry (ranging from three sources that were used to evaluate 13 countries, up to 10sources that were used to evaluate nine countries, see Figure 1(a)). A multiple comparisontest after Bonferroni correction ( 4) was used for the comparison of the means of the CPIcountry scores grouped per number of sources. The results suggest that there is nopattern between the CPI score and the number of sources that were used to evaluate acountry. In fact, the eight group means of the CPI scores for three, four, up to 10 sources,are not different from each other at the 5 % level. Hence, the CPI scores are not biased tothe number of sources that were used to evaluate each country.Figure 1. Impact of number of sources on the CPI scores and standard errors(a) Impact on the CPI scores(b) Impact on the standard errorsSource: Own elaboration.Before discussing whether there is a pattern between the standard errors associated tothe CPI scores and the number of sources used to evaluate each country, we should addan important remark on the calculation of the standard error of the mean, which oftengoes unnoticed in the relevant literature. The standard error of the mean is oftencalculated as the ratio of the standard deviation over the square root of the sample size:Σ σnfor very big population sizes (1)However, this formula assumes that the populationN is very great and that the n / N isvery small. In the CPI, if one accepts that the population size is just 13, that is the maximumnumber of sources that could have been used to evaluate a country, then the assumptions(4) When performing a simple t-test of one group mean against another, one needs to specify a significance levelthat determines the cutoff value of the t-statistic. For example, one can specify the value alpha 0.05 toensure that when there is no real difference, one will incorrectly find a significant difference no more than 5 %of the time. When there are many group means, there are also many pairs to compare. If one applied an ordinaryt-test in this situation, the alpha value would apply to each comparison, so the chance of incorrectly finding asignificant difference would increase with the number of comparisons. Multiple comparison procedures aredesigned to provide an upper bound on the probability that any comparison will be incorrectly found significant(Hochberg and Tamhane, 1987).14

for the formula of the standard error above do not hold. Instead, the correct formula to beused can be found in the seminal work of Isserlis (1918), where the standard error of themean is:Σ N n σfor small population sizes (2)N 1 nHence, we recommend that the standard errors for the CPI scores are calculated usingthe formula for small population sizes. Figure 2 compares the standard errors calculatedaccording to the formula (1), and the correction calculated with formula (2). The correctedstandard errors show lowest values regardless of the number of sources. In fact, thecorrected standard errors are 9 % less than the standard errors obtained with theformula (1) for countries that were evaluated by three sources, up to 50 % less forcountries that were evaluated by 10 sources.Figure 2. Comparison between the standard errors and the corrected standard errorsgrouped by r of SourcesStandard ErrorsCorrected Standard ErrorsSource: Own elaboration.After these considerations, we assess whether there is a pattern between the standarderrors associated with the CPI scores and the number of sources that were used toevaluate a country. Figures 1(b) and 2 also suggest that overall there is a negativeassociation between the standard errors and the number of sources, implying thatstandard errors calculated over a small number of sources are greater (on average) thanstandard errors calculated over many sources. Additionally, Table 4 presents the results ofthe multiple comparison tests after Bonferroni correction for the group means of the15

standard errors calculated using the formula (2) above for small population sizes. To bemore specific, standard errors calculated over three sources are not different (on average)from those calculated over four sources; but the standard errors associated to both sourcesare significantly greater than those calculated over five or more sources. This resultsuggests the criterion for a country’s inclusion to the CPI could have been more conservative,from three sources (currently) to five, in order to avoid potential criticism that countriesevaluated on three and four sources have more uncertain CPI scores. Yet, introducing sucha conservative criterion would imply leaving 22 countries outside the CPI.Table 4. Multiple comparison: means of CPI standard errors grouped by the number ofsources.Number of e: Own elaboration.NB: A multiple comparison test after Bonferroni correction was applied. Reading: For the comparison 3-4, ‘NO’implies that the group mean of standard errors for countries evaluated on three sources is notsignificantly different (at 5 % level) from the group mean of standard errors for countries evaluated on foursources.16

4 Interpreting the CPI rankings: effect sizeThe CPI 2017 scores are reported at two digits and are accompanied by a standard error ofestimate and the 90 % confidence interval. The highest perceived levels of corruption areregistered for Somalia (9 points), Sudan (12 points), Syria (14 points) and Afghanistan(15 points). Conversely, the lowest levels of perceived corruption among the180 countries analysed are for New Zealand (89 points), Denmark (88) and Finland,Norway and Switzerland (the latter countries with 85 points each). Yet, is the level ofperceived corruption different in countries with one or two points difference in their CPIscores? To interpret the difference between two countries’ scores, we employ the effectsize. The effect size is a simple way to quantify the difference between two countrieswithout confounding the interpretation with the sample size, as is the case in thestatistical significance. There is a wide array of formulas used to measure effect size. Weused Cohen’s d formula (Cohen, 1988; Hartung et al., 2008; Hedges, 1981) for twocountries:effect size (M 1 M 2 )( N 1 1) SD12 ( N 2 1) SD22N1 N 2 2(3)M1 and M2 refer to the CPI country scores, N1 and N2 are the number of sources availablefor each country, SD1 and SD2 are the standard deviations across the sources that wereused to evaluate each country. Country 1 is the highest ranked country in the comparison.The denominator in the equation above is a so-called ‘pooled’ estimate of the standarddeviation for both countries. Essentially this estimate is an average of both standarddeviations ( 5). Cohen (1988) hesitantly defined effect sizes as ‘ small, threshold 0.2’,‘ medium, threshold 0.5’, and ‘ large, threshold 0.8’ ( 6). These effect sizes correspondrespectively to a non-overlap of 14.7 %, 33.0 % and 47.4 % in the two distributions.Effect sizes smaller than 0.2 suggest that there may be no difference in the average c

The Corruption Perceptions Index (CPI) has been developed since 1995by Transparency International as a composite indicator that measures perceptions of corruption in the public sector in different countries around the world. It does so by aggregating different sources of corruption-related d