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The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the Brookings Institution, 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. The Worldwide Governance Indicators (WGI) are not used by the World Bank for resource allocation. Financial support from the World Bank’s Knowledge for Change trust fund, and the Hewlett Foundation is gratefully acknowledged. We would like to thank, Particular thanks is due to Arseny Malov for his work in designing and maintaining the WGI website at
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The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the Brookings Institution, 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. The Worldwide Governance Indicators (WGI) are not used by the World Bank for resource allocation. Financial support from the World Bank’s Knowledge for Change trust fund, and the Hewlett Foundation is gratefully acknowledged. We would like to thank S. Rose, S. Radelet, C. Logan, M. Neumann, N. Meisel, J. Ould-Auodia, R. Fullenbaum, M. Seligson, F. Marzo, C. Walker, P. Wongwan, V. Hollingsworth, S. Hatipoglu, D. Cingranelli, D. Richards, M. Lagos, R. Coutinho, S. Mannan, Z. Tabernacki, J. Auger, L. Mootz, N. Heller, G. Kisunko, J. Rodriguez Mesa, J. Riano, V. Penciakova, and D. Cieslikowsky For providing data and comments, and answering our numerous questions. Particular thanks is due to Arseny Malov for his work in designing and maintaining the WGI website at www.govindicators.org.
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For Providing Data and Comments, and Answering Our Numerous Questions
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Rose, S.1
Radelet, S.2
Logan, C.3
Neumann, M.4
Meisel, N.5
Ould-Auodia, J.6
Fullenbaum, R.7
Seligson, M.8
Marzo, F.9
Walker, C.10
Wongwan, P.11
Hollingsworth, V.12
Hatipoglu, S.13
Cingranelli, D.14
Richards, D.15
Lagos, M.16
Coutinho, R.17
Mannan, S.18
Tabernacki, Z.19
Auger, J.20
Mootz, L.21
Heller, N.22
Kisunko, G.23
Rodriguez Mesa, J.24
Riano, J.25
Penciakova, V.26
Cieslikowsky, D.27
more..
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2
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84941101695
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Sensitivity Analysis of the WJP Rule of Law Index
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The only exceptions we are aware of are: (a) the Transparency International Corruption Perceptions Index began reporting margins of error in the mid-2000s; (b) more recently the Global Integrity Index has begun reporting measures of inter-respondent disagreement on their expert assessments of integrity mechanisms; and (c) Th e World Justice Project Rule of Law Index has calculated confi dence intervals for its rankings in a supplementary publication, Paper No. 2
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The only exceptions we are aware of are: (a) the Transparency International Corruption Perceptions Index began reporting margins of error in the mid-2000s; (b) more recently the Global Integrity Index has begun reporting measures of inter-respondent disagreement on their expert assessments of integrity mechanisms; and (c) Th e World Justice Project Rule of Law Index has calculated confi dence intervals for its rankings in a supplementary publication: M. Saisana and A. Saltelli, ‘Sensitivity Analysis of the WJP Rule of Law Index’, WJP Working Paper No. 2, available online at www.worldjusticeproject.org, 2010.
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(2010)
WJP Working
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Saisana, M.1
Saltelli, A.2
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3
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0003054754
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Maximum Likelihood Estimation of Regressions Containing Unobservable Independent Variables
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Unobserved components models were pioneered in economics by Arnold Goldberger, and the closely-related hierarchical and empirical Bayes models in statistics by
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Unobserved components models were pioneered in economics by Arnold Goldberger, ‘Maximum Likelihood Estimation of Regressions Containing Unobservable Independent Variables’, in: 13 International Economic Review (1972), p. 1 and the closely-related hierarchical and empirical Bayes models in statistics by
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(1972)
13 International Economic Review
, pp. 1
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4
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0001398623
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Limiting the Risk of Bayes and Empirical Bayes Estimators – Part 1: Th e Bayes Case
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as well as
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Bradley Efron and Carl Morris, ‘Limiting the Risk of Bayes and Empirical Bayes Estimators – Part 1: Th e Bayes Case’, in: 66 Journal of the American Statistical Association (1971), p. 807, as well as
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(1971)
66 Journal of the American Statistical Association
, pp. 807
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Efron, B.1
Morris, C.2
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5
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0000310469
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Limiting the Risk of Bayes and Empirical Bayes Estimators – Part 1: Th e Empirical Bayes Case
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Bradley Efron and Carl Morris, ‘Limiting the Risk of Bayes and Empirical Bayes Estimators – Part 1: Th e Empirical Bayes Case’, in: 67 Journal of the American Statistical Association (1972), p. 130.
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(1972)
67 Journal of the American Statistical Association
, pp. 130
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Efron, B.1
Morris, C.2
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6
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0003834555
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World Bank Policy Research Working Paper No. 2195, Washington, DC, 1999, for a discussion of alternative choices of units for governance
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See Daniel Kaufmann et al., ‘Aggregating Governance Indicators’, World Bank Policy Research Working Paper No. 2195, Washington, DC, 1999, for a discussion of alternative choices of units for governance.
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Aggregating Governance Indicators
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Kaufmann, D.1
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8
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84941126889
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Note that when we present the data in percentile rank form on the governance indicators website, we also show 90 percent confi dence intervals converted into percentile rank form. In particular, the upper (lower) end of the confi dence intervals in percentile rank terms is computed by calculating the percentile rank among all country scores of the upper (lower) bound of the confidence interval in standard normal units
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Note that when we present the data in percentile rank form on the governance indicators website, we also show 90 percent confi dence intervals converted into percentile rank form. In particular, the upper (lower) end of the confi dence intervals in percentile rank terms is computed by calculating the percentile rank among all country scores of the upper (lower) bound of the confidence interval in standard normal units.
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9
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84941105856
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As discussed further in Appendix A, a refi nement is required when the data come from sources that cover diff erent samples of countries. For example, obtaining the top rank in a sample of developing countries may not correspond to the same level of governance performance as obtaining top rank in a sample of industrialized countries. In this case a slightly modifi ed ranking procedure such as percentile matching is required, as for example is done by Transparency International. When all the individual sources cover the same set of countries, it is also possible to simply average the country ranks, rather than percentile ranks). This is done by Doing Business
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As discussed further in Appendix A, a refi nement is required when the data come from sources that cover diff erent samples of countries. For example, obtaining the top rank in a sample of developing countries may not correspond to the same level of governance performance as obtaining top rank in a sample of industrialized countries. In this case a slightly modifi ed ranking procedure such as percentile matching is required, as for example is done by Transparency International. When all the individual sources cover the same set of countries, it is also possible to simply average the country ranks, rather than percentile ranks). This is done by Doing Business.
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10
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40249113323
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For details on this point refer to, World Bank Policy Research Working Paper No. 4149, Washington, DC
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For details on this point refer to Daniel Kaufmann et al., ‘The Worldwide Governance Indicators Project: Answering the Critics’, World Bank Policy Research Working Paper No. 4149, Washington, DC, 2007.
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(2007)
The Worldwide Governance Indicators Project: Answering the Critics
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Kaufmann, D.1
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11
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34247108825
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See for example the discussion around Table 5 in, World Bank Policy Research Working Paper No. 4978, Washington, DC, 2009 and the same discussion in previous updates of the WGI. See also the discussion around Critique 2 in
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See for example the discussion around Table 5 in Daniel Kaufmann et al., ‘Governance Matters VIII: Aggregate and Individual Governance Indicators for 1996-2008’, World Bank Policy Research Working Paper No. 4978, Washington, DC, 2009 and the same discussion in previous updates of the WGI. See also the discussion around Critique 2 in
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Governance Matters VIII: Aggregate and Individual Governance Indicators for 1996-2008
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Kaufmann, D.1
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17
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34247170761
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Growth and Governance: A Reply/Rejoinder
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Daniel Kaufmann et al., ‘Growth and Governance: A Reply/Rejoinder’, in: 69 Journal of Politics (2007), p. 555.
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(2007)
69 Journal of Politics
, pp. 555
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Kaufmann, D.1
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18
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4644297202
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Governance Matters III: Governance Indicators for 1996, 1998, 2000, and 2002
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Daniel Kaufmann et al., ‘Governance Matters III: Governance Indicators for 1996, 1998, 2000, and 2002’, in: 18 World Bank Economic Review (2004), p. 253.
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(2004)
18 World Bank Economic Review
, pp. 253
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Kaufmann, D.1
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20
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84941026683
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And of course, the estimated standard errors would be larger as well since each data source would be less informative about governance
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And of course, the estimated standard errors would be larger as well since each data source would be less informative about governance. See Daniel Kaufmann et al., ‘Aggregating Governance Indicators’ for further discussion.
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Aggregating Governance Indicators for Further Discussion
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Kaufmann, D.1
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84941123980
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T is the number of countries with data in period T and(Formula presented.) is the average score of the additional countries in period T. Th e higher is the average score of the new entrants and/or the more new entrants there are, the more we lower the mean in the previous period. Th is ensures that a hypothetical sample consisting of our year T–1 adjusted scores for all countries combined with the year T scores for the countries added in year T relative to T–1 would have a mean of zero and standard deviation of one. We also adjust the standard deviation of the year T scores to ensure that the standard deviation of this hypothetical sample would be one. We do this by multiplying the scores (and the standard errors) for each country in year T– 1 by a factor of(Formula presented.), where VT is the variance across countries in our estimates of governance in year T for the new entrants to the sample in period T–1. Th e greater is the dispersion in the scores of new entrants, the more we need to reduce the dispersion of scores in the previous years.
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T is the number of countries with data in period T and(Formula presented.) is the average score of the additional countries in period T. Th e higher is the average score of the new entrants and/or the more new entrants there are, the more we lower the mean in the previous period. Th is ensures that a hypothetical sample consisting of our year T–1 adjusted scores for all countries combined with the year T scores for the countries added in year T relative to T–1 would have a mean of zero and standard deviation of one. We also adjust the standard deviation of the year T scores to ensure that the standard deviation of this hypothetical sample would be one. We do this by multiplying the scores (and the standard errors) for each country in year T– 1 by a factor of(Formula presented.), where VT is the variance across countries in our estimates of governance in year T for the new entrants to the sample in period T–1. Th e greater is the dispersion in the scores of new entrants, the more we need to reduce the dispersion of scores in the previous years.
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