WP5 JIqS
POLICY RESEARCH WVORKING PAPER 2195
Aggregating Governance With the right method,
aggregate indicators can
Indicators provide useful estimates of
basic governance concepts as
well as measures of the
Daniel Kafrfann imprecision of these
Aart Kraay aggregate estimates and their
Pablo Zoido-Lobat6n
components.
The World Bank
Development Research Group
Macroeconomics and Growth
and
World Bank Institute
Governance, Regulation, and Finance
October 1999 a
POLICY RESEARCH WORKING PAPER 2195
Summary findings
In recent years the growing interest of academics and governance than any single indicator, the standard errors
policymakers in governance has been reflected in the associated with estimates of governance are still large
proliferation of cross-country indices measuring various relative to the units in which governance is measured. In
aspects of governance. light of these margins of error, it is misleading to offer
Kaufmann, Kraay, and Zoido-Lobat6n explain how a very precise rankings of countries according to their level
simple variant of an unobserved components model can of governance: small differences in country rankings are
be used to combine the information from these different unlikely to be statistically - let alone practically -
sources into aggregate governance indicators. The main significant. Nevertheless, these aggregate governance
advantage of this method is that it allows quantification indicators are useful because they allow countries to be
of the precision of both individual sources of governance sorted into broad groupings according to levels of
data and country-specific aggregate governance governance, and they can be used to study the causes and
indicators. consequences of governance in a much larger sample of
Kaufmann, Kraay, and Zoido-Lobat6n illustrate the countries than previously used (see for example the
methodology by constructing aggregate indicators of companion paper by Kaufmann, Kraay, and Zoido-
bureaucratic quality, rule of law, and graft for a sample Lobat6n, "Governance Matters," Policy Research
of 160 countries. Although these aggregate governance Working Paper 2196).
indicators are more informative about the level of
This paper - a joint product of Macroeconomics and Growth, Development Research Group; and Governance,
Regulation, and Finance, World Bank Institute -is part of a larger effort in the Bank to study the causes and consequences
of governance for development. Copies of the paper are available free from the World Bank, 1818 H Street NW,
Washington, DC 20433. Please contact Diane Bouvet, room G2-136, telephone 202-473-5818, fax 202-334-8350,
Internet address dbouvet@worldbank.org. Policy Research Working Papers are also posted on the Web at http://
www.worldbank.org/html/dec/Publications/Workpapers/home.html. The authors may be contacted at
dkaufmann@worldbank.org, akraay@worldbank.org, or pzoidolobaton@worldbank.org. October 1999. (39 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas abot
development issues. An objective of the series is to get the findings out quickly, even if the presentationts are less than fully polisbed. The
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paper are entirely those of the authors. They do not necessarily represent the viewv of the Worid P,ank, its Execu tive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Cen1ter
Aggregating Governance Indicators
Daniel Kaufmann
Aart Kraay
Flablo Zoido-Lobat6n
The World Bank
Abstract: In recent years, the growing interest of academics and policymakers in
govemance has been reflected in the proliferation cross-country indices measuring
various aspects of governance. In this paper we explain how a simple variant of an
unobserved components model can be used to combine the information from these
different sources into aggregate govemance indicators. The main advantage of this
method is that it allows us to quantify the precision of the both individual sources of
governance data as well as the aggregate governance indicators. We illustrate the
methodology by constructing aggregate indicators of bureaucratic quality, rule of law,
and graft, for a large sample of 160 countries. Although these aggregate governance
indicators are more informative atbout the level of governance than any individual
indicator, the standard errors associated with estimates of govemance are still large
relative to the units in which governance is measured.
The World Bank, 1818 H Street N.W., Washington, D.C. 20433.
(dkaufmann(afworldbank. ora, akraavyworldbank.orq, ozoidolobatonAworldbank. ora).
The views expressed in this paper are the authors' alone, and in no way reflect those of
the World Bank, its Executive Directors, or the countries they represent. We would like
to thank without implication Craig Burnside, Brad Efron, Eduardo Engel, Gil Mehrez,
Jakob Svensson, Scott Wallsten, Shang-jin Wei, and seminar participants at the World
Bank, UNDP and Latin American Econometric Society Meetings for helpful comments.
1. Introduction
In recent years, the growing interest of academics and policymakers in the
extent, causes and consequences of governance and misgovemance has been reflected
in the proliferation of cross-country indicators of various aspects of governance. In an
accompanying paper (Kaufmann, Kraay, Zoido-Lobat6n (1999)) we present a large
database compiling several hundred cross-country indicators of various aspects of
governance, produced by thirteen clifferent organizations, and covering 178 countries.
These indicators report subjective perceptions on a wide range of issues relating to
govemance, ranging from the extent to which corruption in the political system affects
foreign investment, to the efficiency of public services delivery, to the likelihood that
citizens of a country resort to extrajudicial means to settle disputes.
In this paper, we take the view that many of these indicators serve as imperfect
proxies for one of a much smaller number of fundamental concepts of governance.
Given this view, there are considerable benefits from combining related indicators into a
small number of aggregate governance indicators. First, the aggregate indicators span
a much larger set of countries than any individual source, permitting comparisons of
govemance across a broad set of countries. Second, aggregate indicators can provide
more precise measures of governance than individual indicators. Third, it is possible to
construct quantitative measures of the precision of both the aggregate govemance
indicators and their components, allowing formal testing of hypotheses regarding cross-
country differences in governance
We realize these benefits by constructing aggregate governance indicators using
an unobserved components model. This model expresses the observed data as a linear
function of unobserved governance plus a disturbance term capturing perception errors
and/or sampling variation in each indicator. The main advantage of this method is that it
allows us to obtain estimates of the variance of this disturbance term for each indicator.
These can be interpreted as a measure of how informative each indicator is about the
broader concept of governance it measures. We then compute the mean of the
conditional distribution of govemance given the observed data for each country as a
natural point estimate of the level of governance in that country. Similarly, the variance
1
of this conditional distribution provides a natural estimate of the precision of this
aggregate governance measure for each country.
We illustrate our approach with reference to three fundamental aspects of
governance: rule of law, government effectiveness, and graft. We group 31 indicators
constructed in 1997 and/or 1998 into three clusters corresponding to these three
concepts of governance, and compute aggregate indicators spanning 166, 156 and 155
countries respectively. In our companion paper documenting the governance database,
we construct similar indices for several other aspects of governance.
Although the unobserved components methodology we use is quite standard, we
find its application to the construction of composite govemance indicators interesting.'
One of our major findings is that the aggregate governance indicators we construct are
rather imprecise, despite the high correlations observed between various sources of
governance data. In particular, a 90% confidence interval around the point estimate of
governance for a typical country spans almost the entire interquartile range of the
distribution of estimated govemance. This implies that although it is possible to robustly
identify twenty or so countries with the best and worst govemance in the world, it is
much more difficult to identify statistically significant differences in govemance among
the majority of countries.
Our results are based on three key assumptions: (1) that the measurement errors
in individual indicators of govemance are uncorrelated across indicators; (2) that the
relationship between unobserved govemance and observed indicators is linear, and (3)
that the distribution of unobserved governance across countries is normal. Relaxing the
first assumption is difficult to do in practice, simply because without this assumption we
cannot determine whether the correlation of observed scores across indicators is merely
due to correlated perception errors or whether it reflects the common concept of
governance being measured. However, under the likely altemative that perception
errors are correlated across sources, the measures of precision we report will be biased
downwards. As a result, the standard errors we report should be interpreted as a lower
bound on the precision of aggregate govemance indicators. We consider the
1Unobserved components models were pioneered in economics by Goldberger (1972), and the closely-
related hierarchical and empirical Bayes models in statistics by Efron and Morris (1971, 1972).
2
consequences of relaxing the second assumption by proposing a method which simply
aggregates the ordinal information across indicators. Although this has the advantage of
simplicity and does not require assumptions of linearity, it is also much less precise than
the unobserved components method since it discards the cardinal information in the
data. The third assumption of a normal distribution for unobserved governance implies
that our estimates of governance will be clustered around the mean of this distribution.
This raises the possibility that the! difficulty in distinguishing between countries is in part
driven by this assumption. We therefore explore the robustness of our results by
considering altematives to this assumption, and find that our conclusions are materially
unaffected by our assumptions on the shape of the distribution of unobserved
govemance.
These findings have several implications for policy and empirical research on the
causes and consequences of governance for economic development. At a basic level,
the finding that governance is imprecisely measured should warn against taking too
seriously the exact point estimates of govemance, as well as country rankings based on
these estimates. At best, it is possible to sort countries into broad categories according
to their levels of governance, and even then there is considerable uncertainty regarding
the category to which many countries should be assigned. To emphasize this point, we
avoid discussions of specific countries in this paper. Second, since available indicators
of governance are noisy measures of "true" govemance, empirical work which uses
these indicators as explanatory variables may well underestimate the impact of
-governance due to the usual attienuation bias caused by badly-measured right-hand side
variables. Since our methodology allows us to quantify the measurement errors in these
2
variables, it is possible to obtain rough measures of the extent of this attenuation bias.
Finally, our results suggest that if we want to more precisely differentiate among
countries according to their leveil of governance, we need to improve the quality and
quantity of data gathered on governance.
The remainder of this paper proceeds as follows. In Section 2, we motivate the
empirical work which follows by describing the indicators of governance we use to
2 In our companion paper we explore this idea in more detail, using cross-country regressions of per capita
income on various governance measures instrumenting for govemance using measures of the linguistic'
composition of the population - in the spirit of Hall and Jones (1999).
3
illustrate our ideas. In Section 3, we lay out and implement the unobserved components
framework for estimating governance, and present the main results in Section 4. In
Section 5, we discuss the consequences of relaxing several of the assumptions
underlying the model. We conclude with a discussion of the implications of our findings
for research and policy advice regarding governance.
4
2. Indicators of Governance
In this paper, we use data frorn 31 different indicators of governance constructed in
1997 and/or 1998. These indicators are drawn from 13 different sources and are
grouped into three clusters corresponding to rule of law, government effectiveness, and
graft. The key features of these indicators are summarized in Table 1, and a detailed
description of the sources and variables can be found in Kaufmann, Kraay and Zoido-
Lobat6n (1999). In the first two columns of Table I we identify each source of
governance data by abbreviation and by name. In the next three columns, we report the
source of information for each measure (surveys of residents or polls of experts), the
country coverage, and a measure of the extent to which the sample of countries covered
by each indicator is representative of the population of countries in the world. In the
remaining columns we report the specific concepts measured by each source in each of
the three clusters. 3
A quick look at Table 1 shows that these indicators differ along several dimensions.
First, even within clusters there is considerable variation in the particular concept
measured by each indicator. For example, questions about graft range from the
incidence of "improper practices' (WCY) to the likelihood that additional payments are
required to "get things done" (WDR). Similarly, questions regarding the rule of law range
from whether citizens can successfully sue the state to whether citizens are likely to
resolve disputes extra-judicially. Despite this heterogeneity, we take the view that within
each cluster, each of these concepts is an imperfect indicator of the corresponding
broader concept of governance.
The second respect in which these indicators differ is in the nature of the
respondents who provide the information. Slightly less than half of the indicators are
surveys of businesspeople and/or residents of a country, while the remaining indicators
are polls of experts who rate a set of countries according to various criteria. As we
discuss in more detail later in the paper, this difference between these two types of
3 For a number of these sources, we use the average of several questions relating to the corresponding
core concepts of govemance. As we discuss subsequently, we are reluctant to include individual questions
from a single source separately in our analysis, as the necessary assumption that measurement errors are
uncorrelated across indicators is much more difficult to support for the case of multiple questions from a
single source.
5
indicators has implications for how we interpret the error terms in the relationship
between observed indicator scores and the underlying concepts of governance.
The third respect in which these indicators differ is in the sample of countries they
cover. A number of indicators cover a very large and broad sample of developed and
developing countries (EIU, DRI, HFWSJ, PRS and WDR), while others cover very
narrowly-focused samples of countries (PERC for Asia, CEER and FHNT for transition
economies). Some indicators cover primarily developed countries but also include major
developing countries (WCR, GALLUP, BERI). This difference between indicators is
perhaps the most important for the empirical work which follows. There is by now
considerable evidence that govemance on average tends to be better in richer countries.
This implies that the distribution of governance is likely to be very different in indicators
which cover sets of countries with different average income levels. These differences
need to be taken into account when placing the observed data from various indicators
into common units and combining them into aggregate govemance indicators.
In order to distinguish between indicators in this dimension, we construct a simple
coverage index which measures differences between the distribution of countries across
income and regional classifications and the distribution of all countries in the world
across these categories. In particular, we divide the world into a two-way classification
by region and income, following the World Bank's 1998 World Development Report. For
each of the sources of govemance data, we report one-half of the sum of absolute
-deviations between the share of countries in each of the 45 region/income categories in
that source and in the world as a whole. By construction, this measure ranges from zero
to one, with low values indicating more representative indicators. We report this number
in the fifth column of Table 1. The five indicators covering the largest number of
countries (DRI, EIU, HF, PRS and WDR) are substantially more representative
according to this measure than the others, with a value of the coverage index of less
than 0.25. In our subsequent empirical work we will refer to these as representative
indicators, and the remainder as non-representative indicators.
Finally, we note that each of these sources of governance data uses different
units to measure governance. Most polls of experts report discrete categorical
responses (e.g. the prevalence of corruption on an integer scale from one to four), while
6
for most surveys of citizens or entrepreneurs we have the mean response across
respondents of discrete categorical scores. We re-orient data from each source so that
higher values correspond to better outcomes (i.e. stronger rule of law, more effective
govemment, and less graft). In addition, we rescale each indicator by subtracting the
minimum possible score and dividing by the difference between the maximum and
minimum scores, so that each indicator is on a possible scale from zero to one. Since
we rescale each indicator using the maximum and minimum possible scores (rather than
the maximum and minimum actual scores in the sample of countries covered by each
indicator), this is nothing more than a convenient choice of units.
In Table 2, we report the pairwise correlations among indicators within each of the
three governance clusters. The great majority of these are positive and substantial,
frequently greater than 0.6. In the empirical work which follows, we will interpret these
large correlations within clusters as reflecting the common component of govemance in
these indicators. It is interesting to note that despite the strong pairwise correlations
among these indicators, and despite the favourable interpretation that these correlations
reflect the common component of governance rather than correlated perception errors,
we nevertheless find that governance is not very precisely measured. We provide some
intuitions for this in the following section.
7
3. Estimating Governance
In this section we interpret the data as being generated by an unobserved
components or multiple-indicator model in which the observed data on governance can
be expressed as a linear function of unobserved governance plus a random error term.
We review the well-known features of this model, and propose a simple extension which
delivers consistent parameter estimates for representative as well as non-representative
indicators. We then describe how the parameters of this model can be estimated and
can be used to construct estimates of each of the three aspects of govemance in each
country.
The Model
Our data consists of clusters of indicators of three aspects of governance - rule
of law, government effectiveness, and graft. Let go) denote an unobserved index of one
of these three aspects of governance in country j, for example, graft. The observed data
on graft consists of a cluster of k=1,...,K indicators, each one providing a numerical
rating of some aspect of graft in each of the j=1,..,J(k) countries covered by that
indicator. We assume that we can write the observed score of country j on indicator k,
y(j,k), as a linear function of unobserved governance, go), and a disturbance term, eo,k),
as follows:
(1) y(j,k) = a(k) + 1(k). (g(j) + F(j,k))
where a(k) and ,B(k) are unknown parameters which map unobserved governance go)
into the observed data yo,k). We assume that go) is a random variable with mean zero
and variance one. Our objective is to summarize our knowledge about go) for each
country j using the distribution of go) conditional on the observed data yo,k), k=1,...,Ko)
for country j. The mean of this conditional distribution provides a natural estimate of the
level of govemance in country j, and the variance of this conditional distribution is a
natural measure of the precision of this indicator of governance. The assumption of a
zero mean and unit variance for governance is an innocuous choice of units required to
identify the parameters a(k) and ,B(k). Since we will allow the variance of the error term
8
to vary across indicators k, the fact that P(k) multiplies the error term is an innocuous
rescaling which slightly simplifies some of the expressions which follow.
We use this unobserved components model, which treats unobserved
govemance as a random variable rather than as a fixed parameter to be estimated, for a
pragmatic reason. We will shortly also assume that the variance of the disturbance term
e(j,k) may differ across indicators. In this case, we cannot treat the ga)s as fixed
parameters to be estimated for each country, since individual effects are not identified in
a fixed effects model with heteroskedastic disturbances.4 Moreover, it should be clear
from Equation (1) that naive aggregates such as a simple average of rescaled indicators
for each country will not result in sensible estimates of govemance, as long as the
parameters a(k) and ,3(k) differ across indicators and different countries appear in
different sets of indicators. It is also not possible to remove the dependence of the
observed data on these nuisance! parameters by standardizing (i.e. by removing the
sample mean from each indicator, and dividing by the sample standard deviation). This
is because if indicator k is non-representative, the sample mean will reflect not only a(k),
but also the mean of go) in the sample of countries covered by indicator k. Even if an
indicator is representative in the sense that the standard deviation of unobserved
governance is equal to one in the sample of countries it covers, the sample standard
deviation of observed scores will reflect not only ,8(k), but also the standard deviation of
the disturbances.
The disturbance term s(j,k) captures two sources of uncertainty in the relationship
between true governance and the observed indicators. First, the particular aspect of
governance covered by indicator k is imperfectly measured in each country, reflecting
either perception errors on the part of experts (in the case of polls of experts), or
sampling variation (in the case of surveys of citizens or entrepreneurs). Second, the
relationship between the particular concept measured by indicator k and the
corresponding broader aspect olF governance may be imperfect. For example, even if
the particular aspect of graft covered by some indicator k, (such as the prevalence of
4To see this, consider the special case! where a(k)=O and 13(k)=1 for all indicators. We can make the
likelihood function of the observed data arbitrarily large simply by estimating go) as the observed score on a
particular indicator, for example ga)=y(j.K), for every country j, and setting cr(K)=0. Kiefer (1980) provides a
detailed discussion of this point.
9
"improper practices") is perfectly measured, it may nevertheless be a noisy indicator of
graft if there are differences across countries in what "improper practices" are
considered to be.
We assume that the disturbance term has zero mean, E[Eo,k)1=O; has the same
variance across countries within a given indicator but a different variance across
indicators, E[gj,k)2]=ao(k)2; and is independent across indicators and countries,
E[E(,k)gj',k')]=O if j#j' or kk'. The variance of the error term can be interpreted as a
measure of how informative indicator k is about go), and is likely to vary across
indicators. The assumption that the errors are independent across indicators is a strong
one, but unfortunately one that is also difficult to relax. Intuitively, without this
assumption we cannot identify whether the correlation of scores between two indicators
is due to their common component of governance go), or whether it simply reflects the
correlation of errors. In contrast, this identifying assumption maintains that all of the
correlation of scores across indicators is attributable to their common estimate of
govemance. We will consider the consequences of relaxing this assumption in the
following section. For now, we simply note that this identifying assumption corresponds
to a "best case" scenario regarding the precision of govemance aggregates, since it
assumes that each indicator provides independent information on a particular aspect of
governance. As a result, we are if anything likely to overstate the precision with which
governance is measured.
The parameters c(k) and P(k) map unobserved govemance into the observed
data. Although all of our indicators (after rescaling) are nominally in the same units and
are measured on a scale from zero to one, there are nevertheless three reasons why
these parameters may differ across indicators. First, not all indicators use the entire
range of possible scores. For example, although WDR measures perceptions of graft on
a scale from one to six, the lowest observed score is only 2.36. This suggests that a(k)
on this indicator may be greater than that of an indicator such as EIU which uses the full
range of possible scores. Second, a given indicator might be 'easy" ("tough") relative to
other indicators in the sense that it tends to overestimate (underestimate) a particular
aspect of governance in countries where it is in fact low (high). This would be reflected
in a relatively high (low) value of a(k) on that indicator. Third, consider a non-
representative indicator that covers a set of countries in which the average level of a
10
particular aspect of governance is better than in the world as a whole (e.g. BERI, which
covers primarily developed countries). Suppose further that this source tends to score
countries relative to each other, so that the worst (best) country in the sample receives
the lowest (highest) possible score? of zero (one). This would be reflected in a relatively
high value of ,8(k), since relatively small differences in true govemance are magnified
into relatively large differences in observed scores.
The Conditional Distribution of Governance
Our objective is to summarize our knowledge about governance in each country j
by the distribution of governance conditional on the observed data in country j. This task
is greatly simplified by assuming that both g() and the disturbances so,k) are jointly
normally distributed. In this case, go) and y(,k), k=1,...,Ko) are jointly normal, and the
conditional distribution of g() given the data is also normal, with mean and variance
given by:.
(3) VE[(g)ly(j)] = 1y- - c
where y() is a Kj)xl vector which stacks the K(j) data points for country j, a is the
corresponding K()xl vector of a(k)s, B and , are K&)xK() diagonal matrices with the
corresponding ,B(k)s and a,(k)2s on the diagonal, and t is a K()xl vector of ones. We
refer to the conditional mean in (2) as the estimated value of that aspect of govemance
in country j. With a slight abuse of terminology, we refer to an interval from the (o/2)t
percentile to the (1-8/2)th percentile of the conditional distribution of go) as an o-percent
"confidence interval" around this estimate, and we refer to the square root of the
conditional variance in (2) as the "standard error' of this estimate.5
5 This framework has a distinctly Bayesian interpretation. The distribution of go) conditional on the observed
data yj) can be viewed a posterior distrlibution, and the mean of this distribution as an estimator of g() would
be justified as a point estimate of go) by a quadratic expected posterior loss function. Similarly, the
"confidence interval' is analogous to a Bayesian highest posterior density interval.
11
These expressions have a very natural interpretation. If the parameters a(k),
,(k) and acn(k)2 were known, a sensible way to estimate go) would be to rescale the
observed scores by subtracting a(k) and dividing by ,B(k), and then construct a weighted
average of these re-scaled scores. In particular, let 9(j,k) =1k) ( - g(j) + e(j, k)
P(k)
denote the rescaled value of y(,k). Then the conditional mean in (2) is a weighted
average of these standardized scores for country j on each of the KG) indicators in which
it appears, with weights corresponding to the inverse of the variance of the error term on
each indicator, i.e.
E[(j)jy(j)] t(k) *(j,k) The conditional variance is simply
k= 1 + E a (k) -2
k=1
( K(j)
V[g(j)ly(j)J = (1+ (k)-2 ), which is decreasing in the number of indicators
k=1
available for that country, K(), and is increasing in the variance of the error term in each
of these indicators, ue(k)2.
Estimating the Unknown Parameters
In order to implement (2) and (3), we need to first estimate the unknown
parameters a(k), P(k) and o,(k)2 for every indicator k. For the set of representative
indicators, we can use the assumption of normality of go) and so,k) to write down the
likelihood function of the observed data. Provided that we have at least three such
indicators, the model is identified and it is straighfforward to maximize this function with
respect to the a(k)s, P(k)s, and cre(k)2S to obtain estimates of the unknown parameters
for the representative indicators.6
6 Although maximum likelihood estimation of these parameters requires the assumption of normality, it is
also possible to dispense with this assumption and apply a method of moments procedure. In the just-
identified case of three indicators, these methods lead to identical parameter estimates. In the overidentified
case of more than three indicators, these methods differ only in the weights applied to the various moment
conditions, and in practice this makes little difference for the parameter estimates.
12
We cannot apply this method to non-representative indicators. To see why,
consider the maximum-likelihood estimate of a(k), which unsurprisingly is the mean
score across countries on indicator k. It is straightforward to see from Equation (1) that
the expected value of the sample imean of scores on indicator k is a(k) + ,B(k) * g(k),
where g(k) denotes the average level of governance in the sample of countries covered
by indicator k. For representative indicators, our choice of units for governance
normalizes g(k) = 0. However, for a non-representative indicator where the average
level of govemance is different from the world as a whole, g(k) 0 and the sample
mean does not provide a consistent estimate of a(k).
We can nevertheless obtain consistent estimates of the unknown parameters by
using the following simple argument. If go) were observable, we could estimate a(k),
P3(k) and aj(k) for any indicator by regressing the observed scores y(,k) on go).
Although go) is itself not observable, we do have an estimate of go) based on the
representative indicators. In partilcular, let g*() denote the mean of go) conditioning only
on the data from the representative indicators. We can decompose this conditional
mean into observed governance go) plus its deviation from the mean u0), i.e.
g*()=go)+uo) Since u0) is independent of go), we can view g*o) as measuring go) with
error, i.e. as a classic errors-in-variables problem. It is well-known that OLS estimates of
,8(k) from a regression of y(,k) on g*() will produce downward-biased estimates due to
the usual attenuation bias imparted by measurement error in g*(). In particular, the
probability limit of the OLS slope coefficient is 1,(k) - V * A WI . Since the variance
of uO) is simply the variance of the conditional mean of go) given in Equation (3), and
since V[g*0)] is observable, we can correct the OLS coefficients for this attenuation bias
to arrive at consistent estimates of the parameters of the non-representative indicators.7
7 An altemative approach to the problem of non-representative indicators would be to impute data for the
missing observations (in the spirit of Rubin (1987)). We do not pursue this approach here simply because it
is difficult to specify the key ingredient of the imputation process - the conditional distribution of the
unobserved data given the observed data - in our application.
13
It is worth noting that this estimation method urewards conformity", in the sense that
indicators that are highly correlated will have low estimated variances and hence will be
perceived as more precise. Given our assumption that the disturbance terms are
independent across indicators, it makes sense to treat highly correlated indicators in this
way. If on the other hand indicators are correlated simply because their disturbances
are correlated, this interpretation would be inappropriate. We take this issue up in more
detail in Section 4, and argue that it will result in even less precise estimates of
govemance than those we obtain here.
14
4. Results
In this section we implement the unobserved components model laid out in the
previous section for three concepts of governance: government effectiveness, rule of
law, and graft. We first present estimates of governance and associated standard errors
for each country, and then consider the consequences of these standard errors for
identifying cross-country differences in govemance. We conclude with a simple example
which relates the pairwise correlations observed among individual governance indicators
directly to the measures of precision of the aggregate indicators.
Estimates of Governance
Our main finding is that thoa available data do not permit very precise estimates of
governance. We illustrate this point in Figure 1. In each of the three panels of Figure 1,
we order countries on the horizontal axis by their estimate of governance, and on the
vertical axis we plot the corresponding point estimate of governance, i.e. the conditional
expectation of go) given the observed data for country j, and a 90-percent confidence
interval around this point estimate, i.e. the 5t and 95t percentiles of the conditional
distribution of governance for each country j. The size of these confidence intervals
varies by country, reflecting the fact that different countries appear in different numbers
of sources, and that different countries appear in different sets sources of differing
precision. To provide a sense of the dispersion in the point estimates of governance, the
three horizontal lines in each graph delineate the quartiles of the distribution of the point
estimates of governance for each cluster.
The most striking feature of Figure 1 is that these confidence intervals are large
relative to the units in which governance is measured. For example, for a typical country
the standard deviation of the conditional mean of rule of law or graft is around 0.3, so
that a typical 90% confidence interval extends 0.5 above and below the point estimate of
graft. In the case of government effectiveness, the standard deviation of the conditional
mean is on average slightly larger and equal to 0.33, so that a 90% confidence interval
extends 0.55 above and below the point estimate of rule of law. These confidence
intervals are large in the sense that they are comparable in size to the entire interquartile
range of the distribution of estimates of governance. Moreover, it should be noted that
15
these confidence intervals do not reflect the sampling variation in the point estimates of
the unknown parameters a(k), ,8(k) and a.(k). If this uncertainty were also taken into
account, the standard errors would be even larger.
The parameter estimates reported in Table 3 reveal some interesting differences
across indicators. To interpret the estimates of the a(k)s and f3(k)s, note that our
assumption of a standard normal distribution for governance implies that the vast
majority of countries wili have govemance ranging from -2 to 2. Since the observed
data range from zero to one, one might expect that a representative indicator would
have a(k)=0.5 and ,(k)=0.25. Interestingly, there are significant departures from this
benchmark. Several indicators (e.g. WDR) have estimated values of o(k) substantially
lower than this benchmark, and higher values of a(k), indicating that they do not use the
entire range of possible scores. There is also a great deal of variation in the estimates
of the standard deviation of the errors on each individual indicator, c6(k), suggesting that
the precision with which individual sources measure govemance varies widely.
Assessing Cross-Country Differences in Governance
An advantage of this methodology is that it permits straighfforward tests of
hypotheses regarding cross-country differences in govemance. However, the large size
of the confidence intervals documented in Figure 1 suggests that it will be difficult to find
statistically significant differences in govemance between many pairs of countries. We
illustrate this point with two simple exercises. Suppose first that for each of the three
aspects of governance, we want to group countries into quartiles according to their level
of govemance. A natural way to do this is to group countries according to their point
estimates of govemance, i.e. according to the mean of the conditional distribution of
govemance in each country. Moreover, a natural way to assess the confidence with
which countries are assigned to quartiles is to consider the corresponding 90%
confidence intervals shown in Figure 1. In particular, if the 90% confidence interval for a
country falls entirely within a given quartile, the probability that this country in fact
belongs in another quartile is less then 10%. For a small group of countries at each end
of the distribution of governance, we can conclude with a great deal of confidence that
these countries are in fact in the top and bottom quartiles. However, for the middle
16
quartiles the situation is much less clear, as very few countries' 90% confidence intervals
lie entirely within a given quartile, for each of the three aspects of govemance.
Clearly, the number of countries we can assign to a particular quartile using this rule
depends on the size of the confidence interval. If we instead consider shorter
confidence intervals, such as 75% or 50% intervals, we can better discriminate among
countries, albeit with lower confidence. We explore this possibility in Table 4, where we
report the proportion of all countries for which an x% confidence interval falls entirely
within the indicated quartile, for the three govemance aggregates in tum. We consider
three possibilities, x=90%, x=75% and x=50%. At all significance levels, a substantial
fraction of countries in the top and bottom quartiles can be clearly identified as belonging
in these groups. As the size of the confidence interval declines, more and more
countries can be significantly assigned to quartiles. Nevertheless, even at very low
significance levels, only one-quarter to one-half of the countries in the middle two
quartiles have confidence intervals lying entirely within their respective quartiles.
A related issue is the significance of pairwise differences in governance. In
particular, for every pair of countries in which our point estimate of governance in
country j is greater than in country j', we can investigate the hypothesis that country j in
fact has better govemance by computing the probability that g(j)>g(').8 For countries
with similar point estimates oF govemance, this probability will be close to 0.5, while for
countries far apart in the distribution of govemance, this probability will approach one.
-To illustrate this point systematically, for each country j in the sample, we compute the
probability that, conditional on the observed data for countries j and j', g(j)>g(j') for every
comparator country j'. We then compute the proportion of comparator countries for
which this probability is betwesen 5% and 95%. This is analogous to counting the
number of comparator countiries for which a conventional test at the 10% significance
level of the null hypothesis that govemance is the same in these two countries cannot be
rejected. We summarize the results of these pairwise comparisons in Figure 2. We
again order countries in ascending order according to their point estimates of
governance on the horizontail axis, and we plot this proportion of comparator countries
8 Since the ga)ly() and g(')ly(') are jointly normal and independent by assumption, this calculation involves
a straighfforward integration of the area under a bivariate normal probability density function.
17
as dark points on the vertical axis. We also repeat the exercise, but instead report the
larger proportion of countries for which this probability is between 25% and 75%, which
corresponds to a test at the 50% significance level. This proportion is shown as a light
dot in Figure 2.
Not surprisingly, at the two ends of the distribution there are significant differences
between the level of govemance in these countries and most other countries, especially
at the 50% significance level. However, there is also a strong inverted U-shaped pattem
in this graph, reflecting the fact that a large fraction of countries are clustered near the
middle of the distribution of estimated govemance, and it is relatively difficult to
distinguish among such countries. In particular, for the "typical" country around the
middle of the distribution of govemance, govemance is not significantly different from
nearly half of all other countries in the world, at conventional significance levels.
Intuitions
Our finding that governance is imprecisely measured is somewhat surprising.
After all, in Section 2 we documented that fact that the pairwise correlations among
various governance indicators are substantial, and the identifying assumption of
independent errors across indicators implies that the only source of this observed high
correlation among indicators is the unobserved common component of governance.
One might therefore easily conclude that govemance is quite well measured and that it
is straightforward to distinguish among countries' govemance using this data. We now
illustrate why this intuition is misleading, unless the correlations in the observed data are
very high indeed.
As a specific example, suppose that there are only three representative
indicators associated with a particular governance concept, i.e. K=3, and that the
pairwise correlations among the observed scores are all equal to p. It is straightforward
to show that in this case, the estimated variance of the residual will be a (k)2 =P
18
for each of the surveys k=1,2,:3.9 Inserting this into Equation (3), the variance of the
aggregate governance indicator based on this hypothetical data will be the same for
each country and is equal to V[g(j)l ( = y 1 +2 . To give an idea of the magnitude
of the corresponding 90% confidence intervals, we superimpose them on the
hypothetical distribution of governance in the upper panel of Figure 3, for various values
of p. As p increases, the confidence intervals become shorter. However, for the
correlations of around 0.75 typically observed in our governance data, this confidence
interval remains large relative to the units in which govemance is measured.
In the lower panel of Figure 3, we relate this to the significance of cross-country
comparisons. A simple summary statistic is the proportion of countries whose true level
of governance lies within the 90% confidence interval of a particular country. This
proportion will depend on the location of the reference country, and on the correlations in
the observed data. We plot tliis proportion for the median country and the country at the
first quartile of the distribution of govemance, for various values of p. For the observed
correlation of indicators of around 0.75, the 90% confidence interval around the point
estimate of govemance for the median country encompasses the true level of
governance in about half of all other countries in the world, and somewhat less for a
country at the first quartile. Only if the observed correlations are very large is it possible
to distinguish the median country from most other countries with a high degree of
confidence.
9To see this, it is only necessary to solve the system of nine equations relating the three sample means and
the six unique elements of the sample covariance matrix of the indicators to their population counterparts
and solve for the unknown parameters.
19
4. Extensions
In this section we consider how our results depend on three assumptions
underlying the unobserved components model of the previous sections: that the
disturbances are independent across indicators, that the mapping from unobserved
governance into observed data is linear, and that the distribution of unobserved
governance is normal. We find that the first two assumptions if anything overstate the
precision with which govemance is measured. Relaxing the third assumption does not
materially affect our results.
Correlated Disturbances
In the previous section we assumed that the disturbances Eo,k) were
independent across indicators. Intuitively, this assumption allowed us to attribute all of
the observed correlation of scores across indicators to the common component of
governance go), and hence permitted us to identify the portion of the variation in scores
across countries within each indicator due to measurement error. A consequence of this
assumption is that any indicator which is not very correlated with the others was
interpreted as having a large residual variance.
Although useful, the assumption that the errors are independent across
indicators may not be valid, for at least three reasons. First, in the case of polls of
experts, it is possible that the perceptions of experts who rank countries on a particular
indicator are influenced by their knowledge of countries' rankings on other indicators.
Second, the errors in surveys of residents might be correlated across countries if
residents of a particular country have a tendency to systematically overstate regulatory
and govemance obstacles, due to a broad-based predisposition to report a worse
situation than is objectively warranted.10 Finally, it is possible that perceptions of
governance from various indicators are unduly influenced by a single event, such as a
high-profile scandal which is not representative of the level of graft in that country.
10 See Kaufman and Zoido-Lobat6n (1999).
20
Although it is not possible to statistically identify the correlation of the
disturbances across sources, it is straighfforward to see the consequences of positively-
correlated errors for our results. If the errors are correlated across indicators, each
additional indicator contributes less information to our estimate of governance. This will
be reflected in the variance of the conditional distribution of governance in each country.
In particular, it is straightforwaird to show that holding constant the variance of the
residuals on each indicator, the variance of the condition al distribution of govemance is
increasing in the correlation between the errors on any two indicators.11
We illustrate the practical consequences of this observation in Table 5. For each
of the three aggregate indicators, we re-estimate the variance of the conditional
distribution of govemance, imposing a range of assumptions on the correlation of the
disturbances. For the purposes of this example, we restrict ourselves to a set of three
representative indicators (EIU, DRI and PRS), and also to the set of about 100 countries
which appear in all three indicators.12 As the assumed correlation among the errors rises
from 0 to 0.5, the aggregate govemance indicators become less precise, although the
magnitude of the effect depends on the indicator (since the estimated variances of the
disturbances change as well). In the case of government effectiveness, the standard
error of the aggregate increases only slightly, from 0.32 to 0.35. In contrast, for rule of
law the standard error doubles from 0.33 to 0.66.
It is difficult to adequately address the problem of correlated disturbances simply
because it is not possible to separately identify the correlations between the errors.
Nevertheless, it is useful to realize that the estimated standard errors associated with
point estimates of governance are likely to be substantially understated under the
assumption of independent errors. This reinforces our argument of the previous section
that cross-country comparisons of the level of governance should be made with caution.
11 If the positive correlations between the residuals differ across pairs of indicators, the relative magnitudes
of the estimated variances will also be affected. In particular, suppose that two indicators of bureaucratic
quality are highly correlated with each other, but not very correlated with the third. In the previous section
we assumed that the errors were iindependent, and so the high correlation between the first two indicators
implied that the variance of the errors was small on these indicators relative to the third. However, if we
knew that the high correlation between the first two indicators was due to correlated errors, then the
estimated variances on these indicators would be large relative to that of the third indicator. As a result, the
relative rankings of countries might also be affected.
12We do this only for simplicity, since it allows us to report just one standard error per aggregate, which is
the same for all countries.
21
Non-Linearities
In the previous section we assumed that the relationship between unobserved
governance and observed indicator scores was linear. This assumption places strong
restrictions on the units in which governance is measured in the various indicators in our
sample. For example, consider an indicator such as Gallup which asks respondents
how many cases of corruption there are among public officials, and offers the choice of
four broad categories: 'none", "a few", "many" and "a lot". Our observed data consists of
numerical scores on a scale of one to four corresponding to these categories. The
assumption of a linear mapping from unobserved graft into observed scores implies that
the difference in graft between a country with a score of 4 and one with a score of 3 (i.e.
the difference between "a lot" and umany" cases of corruption) rs the same as the
difference between two countries with scores of 3 and 2 (i.e. the difference between
"many" and 'a few"). Given the somewhat vague response categories, it is not at all
clear that the assumption of linearity is warranted. Moreover, even if these categories
were equally-spaced according to some appropriate metric, the fact that the observed
data are discrete while our unobserved govemance indicator is continuous violates the
assumption of a linear relationship between the two.13
Finally, the mere fact that indicators are non-representative may also contribute
to a non-linear relationship between governance and observed scores. A number of the
indicators in our sample cover primarily developed countries together with a few
developing countries. It is possible that the developing countries in these indicators
suffer from a "curse of inclusion" in the sense that they receive worse scores than they
might otherwise have received simply because they are implicitly being compared with
countries in which various aspects of govemance are likely to be much better.14 For
example, representative surveys such as DRI or PRS assign moderate scores of 55/100
13 The straighfforward solution to this problem would be to rely on an ordered multinomial choice model with
individual effects in the latent variable. HoWever, for such a model to be identified, it would again be
necessary to assume that the variances of the errors are identical across indicators.
14 This problem may be particularly acute for polls of experts who consider a large set of countries at once,
since in contrast to surveys of residents, experts are much more likely to be aware of relative comparisons
of countries.
22
and 3/6 to Mexico for graft, while on a much less representative survey such as BERI
which covers primarily developed countries, Mexico receives a rather poor rating of 1/7.
What can be done about these non-linearities? A very general solution to this
problem might be to combine only the ordinal information in each indicator, i.e. the
relative rankings of countries within each indicator. In particular, one can think of a given
indicator as providing a ranking of pairs of countries according to their level of
governance. The information in the relative rankings of countries from various indicators
can then be combined by noting that if several indicators consistently rank country A as
having better govemance than country B, this provides evidence that governance is in
fact better in country A than in country B. Clearly, this approach has several advantages.
First, it is computationally very simple. Second, we do not have to know the choice of
units in which governance is measured , or whether indicators are representative or not.
Third, it does not require any assumption of linearity in the relationship between
governance and observed scores. However, this method will result.in larger standard
errors for pairwise comparisons since it discards information in differences in the level of
scores across countries and indicators.15
To illustrate the relative imprecision of such an ordinal aggregate, for every pair of
countries j and j' on every indicator k, we construct an indicator variable x0j,j',k) which
takes the value 1 if country j is ranked higher than country j' with respect to the aspect of
governance covered by indicator k, and zero otherwise.16 A natural null hypothesis to
test is that governance in countries j and j' is the same, i.e. that the probability x(,j',k) is
equal to one is 0.5. Under the assumption that the errors are independent across
15 A further drawback of this method is that it is difficult to construct an aggregate ranking of countries
according to governance. One possibility would be to average the indicator variables x0,j',k) over all surveys
k and partner countries j', and rank oDuntries according to this index. However, it is difficult to put standard
errors on such a ranking, since even if the errors are independent across surveys, the x(,j',k) will not be
independent across partner countries j'. A deeper problem with this method is that there is a fundamental
result from social choice theory which places strong restrictions on the properties such an aggregate ranking
may have. According to Arrow's Impossibility Theorem, it is impossible for any aggregation of each
indicators' 'preferences" to simultaneiously satisfy three intuitive and desirable properties: (i) the aggregation
respects unanimity -- if every indicator says that A is more corrupt than B, then so should our aggregate, and
(ii) the aggregation displays the independence of irrelevant alternatives property -- the ranking of A and B
does not depend on any indicators' ranking bf A or B relative to any other country C; and (iii) the aggregation
is non-dictatorial - the aggregate ranking of A and B is not uniquely determined by a single indicators
ranking of A and B. In particular, Arrow's theorem tells us that if (i) and (ii) hold, then (iii) does not hold.
16 For those surveys which report discrete categorical scores, we discard 'ties" as uninformative about the
relative level of govemance.
23
indicators, this hypothesis can be tested using the data on the proportion of indicators in
which country j is ranked higher than country j' in a simple binomial proportions test.
We report the results of this exercise in Figure 4, which is analogous to Figure 2.
We again order countries in ascending order according to their point estimates of
govemance on the horizontal axis, and we plot the proportion of all comparator countries
for which the null hypothesis that governance in these two countries is equal cannot be
rejected at the 10% significance level as dark dots on the vertical axis. The light dots
report the same information, but at the 50% level. Comparing Figures 2 and 4, it is clear
that the ordinal aggregate allows use to identify far fewer statistically significant
differences in govemance across countries. In fact, for many countries it is impossible to
reject the null at the 10% level that govemance in this country is the same as for every
other country in the world using this method! Although this ordinal method is a useful
vehicle for making rough comparisons across countries and requires little in the way of
assumptions on the underlying data, it is much more difficult to obtain statistically
significant differences among countries.
Alternative Distributions for Governance
In Section 2 we assumed that unobserved govemance and the disturbances
were jointly normally distributed. As we noted, this assumption has a significant payoff
in terms of analytical tractibility, as it ensured that the distribution of govemance
conditional on the observed data was normal, with simple expressions for its mean and
variance. However, given the bell-shape of the normal distribution, this approach
embodies the implicit assumption that a relatively large fraction of countries in the world
have similar moderate levels of governance, and relatively few have either very good or
very bad governance. There are two reasons to question this assumption. First, it is not
at all clear a priori that this provides an accurate depiction of the true cross-country
distribution of governance. Second, it is possible that our finding that it is difficult to
statistically distinguish differences in governance between a large proportion of countries
in the world is accentuated by the assumption of normality, which forces a
disproportionate fraction of countries to be clustered near the mean of the distribution of
governance. If instead we assumed that governance was more dispersed, then it is
24
possible that it is easier to identify statistically significant differences in governance
across countries.
It is not clear how one might identify the shape of the true distribution of
governance across countries, since it is difficult to disentangle the shape of this
distribution from the shape of the distribution of the error terms. However, it is possible
to explore the robustness of the results to different choices for the distribution of
governance itself. We do this by instead assuming that unobserved governance follows
a Beta[a,b] distribution. We consider three choices of parameters corresponding to
three very different shapes of the possible distribution of govemance. These three
possibilities are illustrated in the left-hand column of Figure 5. We first consider a=b=5,
which generates a symmetric bell-shaped distribution. This case serves as a benchmark
in that it is very similar to the normal distribution we have been using so far. We also
consider the possibility that the distribution of govemance is skewed to the right (a=2,
b=5), with relatively few countries with very good governance in the right tail of the
distribution. Finally, we consicder the possibility that govemance is uniformly distributed
(a=b=1), with a similar proportion of countries at each possible level of govemance. We
continue to assume that the diistribution of the disturbances is normal.
On the right-hand side of Figure 5, we explore the consequences of these
alternative assumptions for our conclusions about the significance of cross-country
differences in govemance. As a specific example, we focus on an aggregate of the
three largest representative indicators of graft (EIU, DRI and PRS), and again restrict
ourselves to the sample of about 100 countries appearing in all three indicators. For
each country, we report the point estimates and standard errors corresponding to each
assumption on the distribution of governance.17 As the assumed shape of the
distribution of true governance changes, not surprisingly so does the distribution of point
estimates. The more important observation is that our results on the difficulty of
distinguishing between countries do not change. It is clear from Figure 5 that the
17 We compute these as follows. First, using a method of moments argument we construct estimates of the
parameters of the model corresponding to the assumed distribution of govemance (note that the mean and
variance of this beta distribution change as we vary the parameters). We then construct the joint distribution
of go) and y() as the appropriate mixture of a normal and a beta distribution, and then obtain the marginal
distribution of yj) and conditional distribution of go) given yG) by appropriate numerical integrations of this
joint distribution. We numerically evaluate the mean of this distribution, and the 5e and 95 percentiles, and
report these for each country in Figure 5.
25
number of countries with 90% confidence intervals falling entirely within particular
quartiles is essentially unchanged for each quartile, as we vary our assumptions on the
shape of the distribution of govemance.
26
5. Conclusions
In this paper, we have talken the view that the many different available indicators
of governance provide imperfect signals about a relatively small number of fundamental
aspects of governance, such as rule of law, govemment effectiveness, and graft. We
grouped the many available indicators into three clusters corresponding to these
concepts of governance, and used a linear unobserved components model to obtain
aggregate estimates of these three aspects of govemance. Despite several optimistic
assumptions, we find that govemance is not very precisely measured using these
aggregate indicators. In particular, although it is possible to identify statistically
significant differences between countries at opposite ends of the distribution of
govemance, it is much more difFicult to discriminate among the majority of countries with
any degree of confidence.
Nevertheless, we find the aggregate governance indicators to be useful for
several reasons. First, they are' based on a methodology which provides a consistent
framework for placing data from various sources into common units, taking into account
that the samples of countries included in different sources may not be representative of
the world as a whole. Second, the aggregate indicators span a much larger sample of
155 or more countries, permitting (admittedly-imprecise) comparisons across a much
larger set of countries than is possible using any single indicator. Third, although the
aggregate indicators are not as precise as one might have hoped, they are nevertheless
much more reliable than any individual indicator. Finally, we believe that it is useful to
have quantitative measures of the precision of aggregate indicators in order to caution
users of both individual and aggregate indicators of the substantial margins of error
associated with cross-country comparisons of govemance.
Empirical research on governance issues can also benefit from the aggregate
indicators presented here. Many empirical studies which use govemance indicators as
either left-hand or right-hand side variables are limited to small samples by the poor
country coverage of many indicators. This can potentially introduce a variety of sample
selection biases. In addition, the measures of precision we report can be used to correct
for the attenuation bias due to measurement error in govemance indicators used as
dependent variables.
27
In the long term, however, our results also point to the inadequacy of existing
governance measures. jt is very unsatisfying that existing data, even with favourable
assumptions, allows us to identify relatively few statistically significant differences in
governance across countries. Moreover, existing data provides at best tenuous links
between perceptions of govemance and objective policy interventions that govemments
interested in improving the quality of governance can undertake. There is therefore a
need to improve the quality and quantity of govemance data, both by improving and
extending cross-country survey work of govemance perceptions, as well as employing
country-specific in-depth govemance diagnostics.18 Many of the polls and surveys we
use suffer from deficiencies, such as poorly-worded questions about ill-defined and
excessively broad concepts. There is room to improve these instruments by asking
respondents about their direct experiences with well-defined events and using
transparent units to measure govemance. However, these are time- and resource-
intensive exercises, and intemationally-comparable high-quality data of this sort is years
away.
18 Detailed country diagnostic exercises such as those currently being piloted by the World Bank have the
potential to provide much more detailed information on the specific institutional failures which contribute to
perceptions and the reality of poor govemance. Kaufmann, Pradhan and Ryterman (1998) provide a
description of these exercises.
28
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29
Table 1: Governance Indicators
Code (Sura 6e Coe C eptls
cir Pnli (P) 12M-t
BEPI Businoss P 50 mostly 0.44 Buresauratic delays Erforceability of contracts Mewntality" regarding
Environment Risk developed corruption
Intelligenco countries
CEER Central Ewopean P 26 transition 0.84 Rule of law Effect of conotion on
Economic Review economies 'attractiveness of com"tiy
as a piace to do business'
DRN Standard and P 106 developed 0.23 Government ineffectiveness, Enforceability contracts, Comuption among pubic
Poor's DRI and developing instiutional hfaihe costs of crime officials, offectiveness of
countries antkorruption iitiativs
EIU Economist P 115developed 0.19 Insitutional efficacy, red tape Cme, corruption in Corruptionemong public
Intelligence Unit and developing bakng sector of4ciats
counties
FHNT Freedom House P 28 transiion 0.82 Quality of goverment and Rule of law Perep,tions of corrlp,tiOn
economies public administration in civil service, business
interests of polkymakers
GALLUP Galup S 44 mostly 0.50 Freqwency of "cases of
Intemational developed corruption"ramong public
countries offcials
GCS Gobal S 59 develped 0.42 Competence of pubic Cdizens can file awsuts Frequency of "kregular
Competitiveness and developing sector, polrtial pressures on against government payments" to officials and
Survey countries civi servants, time spent citizns acoept legal judiiary
with tbrreauciats e4udicln,
independence of judiciary,
costs of crime
GCSA Global S 23 African 0.73 Competence Of pblic Citiwens can file lawsuits Frequency of "iregular
Competitiveness countries servants, commitment to against goversnent, paymentsW to offiials and
Stivey, Afria polices of previous cdizens acceot legal judiciary
govefmments edudication,
independence of judiciary,
costs of mime
HF Heritage P 160 developed 0.06 Law and order tradition,
Foundation and developing prevalence of black
countries market activiies
PERC Poliical and S 12 Asian 0.83 Effect of corrupton on
Economic Risk economies busins environment for
Consultancy foreign companies
PRS Poitical Risk P 131 developed 0.10 Bureatic qulaity, policy Rule of law Corruption in the political
Services and developing stability system sa "threat to
countries foreign investment"
WCY World S 46 primarily 0.59 Efflcien implementation of Tax evasion, confidence "Improper pratices in
Competitiveness devetoped goennrert decisions in atblity o ato ties to the publi sptere
Yearbook countries political pressures on civil protect property,
servants confidence in
admrinistration of justice
WDR World S 74 developed 0.25 Efficiency of govemment in Unpredictability of the Corruption as "obstacle to
Deveopment and develoing delivenrig services, judiciary, ttheft end crime, busine, frequency of
Report countries predictabiliy of rules, time ability of state to protect "additiol payments" to
spent wih bureaucrats private propeity "get things done"
Notes: Details on these sources of governance data, and definitions of the concepts
measured, may be found in Appendix A of Kaufmann, Kraay and Zoido-Lobat6n
(1 999).
30
Table 2: Correlations Among Governance Indicators
Government Effectiveness
gee,u gedn goprs gewdr geberi geefint gegcs gogcs gswcy
gaeiu 1.00
114
gadri 0.77' 1.00
96 106
geprs o.60- 0.61 1.00
111 100 140
gewdr 0.78 * 0.68 0.36 1.00
58 57 65 74
gsberi 0.74 * 0.71 * 0.54 * 0.73 1.00
49 so 50 30 so
gent 066 * 0.71 024 0.62 - 0.67 1.00
19 24 21 20 6 28
gegcs 0.76 0.74 0.52 * 0.85 0.70 0.75 * 1.00
64 62 72 45 46 6 75
gagcsa 0.64 0.69 0.55 0.26 1.00 0.56 1.00
1 15 20 - 14 2 0 19 23
gewcy 0.55 0.53 0.48' 0.81 0.65 0.06 0.92 1.00
43 44 46 27 41 4 46 0 46
Rule of Law
ddi diu rdMf rIprs rdwdr dberi dceer Mint dges dgsa ljz dwqcy iscore
rtdi 100
106
dwiu 0.73* 1.O
96 114
Mhf 0.73 0.686 1.00
105 112 16O
rtpus 0.75 0.75* 0.62 1.00
1oo' 111 137 140
dwdr 0.58 0.75 0.76 0.59s 1.00
57 58 72 es 74
rberi 0.73 0.70* 0.82* 0.62' 0.54 1.00
so 49 50 50 30 50
de 0.69 * 0.79 * 0.90 * 0.52 * 0.51 - .0.86 1.00
24 19 25 20 20 6 27
dfhrt 0.76' 0.66' 0.86 0.33 0.394 -0.75' 0.91 * 1.00
24 19 26 21 20 6 27 28
dg3 0.70* 0.768 0.78* 0.70 0.74* 0.77* 0.96 0.78 1.00
53 se 59 59 33 46 6 6 59
dugsa 0.43 031 0.03 0.27 0.61 * -1.00 0.87 1.00
15 18 23 20 14 2 0 0 3 23
rjlkz 0.63 - 0.45 0.37 0.57 0.13 0.64 0.19 0.00 0.50 0.16 1.00
6s 73 76 74 48 44 19 20' 49 8 77
dwCy 0.63 0.73 0.77' 0.68' 0.786 0.75' 0.98' 0.94' 0.94 0.47' 1.00
44 43 46 46 27 41 4 4 46 0 40 46
drscor 1.00 0.99 0.95 0.91 0.72 0.63 0.99 0.986 0.986 . 0.37 0.96' 1.00
5 5 S 5 5 5 5 5 5 0 5 4 5
Graft
gWrd grei grpn gWwdr guSeti grow grit gupilup grgrs grgca gWperc gnucy grscore
grdri 1.00
106
greiu 0.80 100
97 115
guprs 0.65 0.64 1.00
100 112 140
grwdr 0.69e 0.80* 0.46 100
57 5s 65 74
gubiei 0.57 0.58 0.48 0.78 1.00
50 50 50 30 50
gnroer 0.91 0.76 0.68 0.56' 0.38 100
24 19 20 20 6 26
grntd 0.79 o 0.60 0.72n 0.58 0.40 0.92' 100
23 19 21 20 6 25 28
grgalkp 0.63 0.78- 0.62 0.81 0.46 - 0.71 0.69 1.00
42 42 44 26 29 9 9 44
grgcs 0.77' 0.88' 0.57 0.87 0.73' 0.98 0.80 * 0.60 1.0o
53 57 59 33 46 6 7 35 59
grgcsa 0.59 0.53 * 0.45 0.61' 1.00 . . 0.9 0.79 1.00
15 18 20 14 2 0 0 3 3 23
grperc 0.58 0.95' 0.33 0.96' 0.76' . . 0.84' 0.89 * 1.00
12 12 12 6 11 0 0 5 12 0 12
gr*cy 0.69 0.-84 0.65' 0.93 0.62 -0.32 -0.51 0.67' 0.856 . 0.93 100
44 44 46 27 41 4 4 31 46 0 11 46
grscere 0.91 0.92' 0.82' 0.869 0.74' 0.89' 0.67' 0.73 0.82 0.64 0.82- 0.82' 1.0o
51 51 51 51 30 13 13 25 33 11 6 27 51
This table reports pairwise correlations between govemance indicators within each
govemance cluster. The numbers below the correlation coefficients indicate the
number of countries common to each pair of indicators. * indicates significance at the
90% level.
31
Table 3: Parameter Estimates
Govemment Effectiveness Rule of Law Graft
cx(k) Om oe) a( kfk S a(k) a (k) _s(k)
Representative Indicators
DRI 0.539 0.239 0.588 0.668 0.179 0.583 0.539 0.221 0.618
EIU 0.432 0.226 0.396 0.442 0.285 0.445 0.312 0.309 0.322
HF 0.466 0.247 0.751
PRS 0.789 0.109 1.222 0.606 0.220 0.656 0.506 0.142 1.129
WDR 0.473 0.097 0.685 0.354 0.135 0.681 0.465 0.150 0.636
Non-Representative Indicators
BERI 0.406 0.133 0.707 0.404 0.136 0.687 0.483 0.173 1.226
CEER 0.604 0.380 0.303 0.615 0.359 0.356
FHNT 0.624 0.396 0.440 0.566 0.397 0.454 0.561 0.513 0.511
GALLUP 0.470 0.149 0.709
GCS 0.398 0.151 0.600 0.526 0.148 0.594 0.493 0.247 0.457
GCSA 0.470 0.112 0.450 0.499 0.041 1.695 0.498 0.297 0.406
PERC 0.302 0.299 0.270
WCY 0.307 0.120 0.906 0.382 0.156 0.580 0.212 0.284 0.498
32
Table? 4: Assigning Countries to Quartiles
Proportion of Countries for Which an x% Confidence
Interval Lies Entirely in the Indicated Quartile
x=90% x=75% x=50%
Government Effectiveness
First Quairtile 0.31 0.54 0.72
Second Quartile 0.00 0.00 0.26
Third Quartile 0.00 0.13 0.31
Fourth Quartile 0.59 0.69 0.79
Rule of Law
First Quartile 0.31 0.43 0.65
Second Quartile 0.00 0.05 0.39
Third Quartile 0.12 0.24 0.55
Fourth Quartile 0.55 0.63 0.84
Graft
First Quartile 0.13 0.23 0.49
Second Quartile 0.00 0.03 0.26
Third Quartile 0.08 0.21 0.36
Fourth Quartile 0.65 0.72 0.80
This table reports the fraction of all countries whose point estimate of govemance
falls in the indicated quartile for which the corresponding x%/o confidence interval
also falls entirely within that quartile, for each of the three govemance aggregates
and for a range of values of x.
Table 5: Consequences of Correlated Disturbances
Average Standard Error of Govemance Aggregate
Based on Representative Indicators
Assumed Error Correlation:
p=0 p=0.25 p=0.5
Government Effectiveness 0.32 0.31 0.35
Rule of Law 0.33 0.47 0.66
Graft 0.31 0.42 0.44
This table reports the standard error of an aggregate indicator (based on a
balariced panel of three sources), under altemative assumptions regarding the
correlation of the disturbances.
34
Figure 1: Estimates of Governance
Go.,m.t EfIhws.
zT I TTT I
T4S i R L*.
. < ~~~~~~~~t. i:.1 U._ ._
2Z5
2o5
Countries are ordered on the horizontal axis in ascending order according to their
point estimates of governance, and their point estimates and 90% confidence
intervals are indicated on the vertical axis. The horizontal lines delineate the
quartiles of the distribution of governance estimates. For reasons of space,
country names are indicated onily for every fifth country.
35
Figure 2: Significance of Pairwise Governance Comparisons
I Govenment Effectvenes
0.9
Z0.
a - 10% Significance Level
1 07
X0.3
. 10% SignMcanc Le* l
. Ol
1 GaL f Lo
0.9
0.03**8
_! 02 80% S10%ne Levelfic Sn ev
'2E0 * .
0. 6 - *
c 0.4
0.
&0.29-
w~~~~~~~~~~~~
e . O t Sis gnificance L e< >*E<,, .+
O
0.8
. B 0.7 -
point estimates of governance. For e1achScountr c,nwe Lpvloto h etclaih
c 0.e are indc tevel
E0.3
0-
between 5%and 95% (ark dots) 1ri0eten2% Sglandc70e L (vligtdt) o
reasons of space,0 conr nm sae niatd0.7freer itcuty
gO S~~~3
Figure 3: Precision of Governance Aggregates
as a Function of Patirwise Correlations of Observed Data
90% Confidence interval for
median country if
correlation of observed data is:
p=0.75
p=O.90 \
Distribution of Actual
Govemance
-3 -2 -1 0 1 2 3
Govemance Index
0.7 -
5 0.6
0.5
0.5 = O S \ S , Country at Median
ou S0Country at F rst Quartile
0.3 -
o Z% 0.2-
~E
-n
to
0.
0.5 0.6 0.7 0.8 0.9 1
Pairwise Correlation Among Observed Data
37
Figure 4: Significance of Pairwise Governance Comparisons
Based on Ordinal Method
Govemment Effectivenea
Oa 01 * . . s. S *,-a -
0.7 *
0.7
}07~~~~~ *-a *-,'g @ "
0. 1~50% Sigrificance Level
0.3,
IL L
Rule of Law
0.9 - -t* -
S}: :*: *. * *'- 't :':'a
m 0.6 ,
j 0.4 - #N 5
0.4 -aU ~ a55
03 so%SJgnmcae50%SignificanceLevel
0.2
0
Grt
-V.
i 0.9
6]107~~ * . U **a. *
10.8 U** .
&; 0.7 r >; . 10% Significance Level.
i 0 5 g * g , a.
li~~~~~~
0C3 a
16 ~~~~~~50% Significance Level
0.2-
0.1
*- 0
Countries are ordered on the horizontal axis in ascending order according to their
point estimates of governance. Fpr each country, we plot on the vertical axis the
proportion of all comparator countries for which the probability that govemance in
the reference country is greater than that in the comparator country is either
between 5% and 95% (dark dots), or is between 25% and 75%. For reasons of
space, country names are indicated only for every fifth country.
38
Figure 5: Alternative Distributions for Governance
Assumed Distribution of Governance Distribution of Governance Estimates
e025 1
0.a
0.02 .
0.015
0.01 05-nMTE 9
0000~~~~~~~~~~~~~~WI
0.1
0 0.2 0.4 0.6 0.8 1 s
0.020
0.02 A >.
0.0210.
0.015
0000~~~~~~~~~~~~~~~~~~~~~~~~~.
02
o 0.2 04 0.a 08 1 0
0.0Th 1
0.02~~~~~~~~~~~~~~~~~~~~~~~~'
0.018~~~~~~~~~~~~~~~~~~~~~~~~~~~~.
coum we2 s oA the shap of thsdsrbto.I0 h ih oun eso h
0.015
0005
0.2
0.1
0 0.2 0.4 0.6 06 1 ~~~~~~~~~~~~~~~02
The rows of thi s figure correspond to the assumptions that unobserved
governance follows a Beta(5,5), Beta(2,5) and a Beta(1 ,1) distribution. In the left
column we show the shape of this distribution. In the right column, we show the
corresponding analog to Figure 1, for a governance aggregate constructed using
a balanced panel of three indicators of graft.
39
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