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Policy Research Working Paper 8586
Efficiency of Public Spending in Education, Health, and Infrastructure
An International Benchmarking Exercise
Santiago HerreraAbdoulaye Ouedraogo
Macroeconomics, Trade and Investment Global Practice September 2018
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Produced by the Research Support Team
Abstract
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Policy Research Working Paper 8586
Governments of developing countries typically spend between 20 and 30 percent of gross domestic product. Hence, small changes in the efficiency of public spending could have a major impact on aggregate productivity growth and gross domestic product levels. Therefore, measuring efficiency and comparing input-output combinations of different decision-making units becomes a central chal-lenge. This paper gauges efficiency as the distance between observed input-output combinations and an efficiency frontier estimated by means of the Free Disposal Hull and Data Envelopment Analysis techniques. Input-inefficiency (excess input consumption to achieve a level of output) and output-inefficiency (output shortfall for a given level of inputs) are scored in a sample of 175 countries using
data from 2006–16 on education, health, and infra-structure. The paper verifies empirical regularities of the cross-country variation in efficiency, showing a negative association between efficiency and spending levels and the ratio of public-to-private financing of the service provision. Other variables, such as inequality, urbanization, and aid dependency, show mixed results. The efficiency of capi-tal spending is correlated with the quality of governance indicators, especially regulatory quality (positively) and per-ception of corruption (negatively). Although no causality may be inferred from this exercise, it points at different factors to understand why some countries might need more resources than others to achieve similar education, health, and infrastructure outcomes.
This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at sherrera@worldbank.org and aouedrago3@worldbank.org.
Efficiency of Public Spending in Education, Health, and Infrastructure: An International Benchmarking Exercise1
Santiago Herrera Abdoulaye Ouedraogo
JEL Classification: C14, H5, H51, H52, H54, I1, I2, E62
Keywords: efficiency frontiers, efficiency of public spending, education expenditure, health expenditure, infrastructure spending.
1 The paper carries the names of the authors and should be cited accordingly. It follows closely the presentation of Herrera-Pang (2005) and uses the data and STATA codes available in the WPS website. The findings, interpretations and conclusions are the authors’ responsibility and do not necessarily represent the view of the World Bank or its Executive Directors.
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I. Introduction
Governments of developing countries typically spend resources equivalent to between 15 and 30 percent of GDP. Hence, small changes in the efficiency of public spending could have a significant impact on GDP and on the attainment of the government’s objectives. The first challenge faced by stakeholders is measuring efficiency. This paper attempts such quantification and verifies empirical regularities in the cross country-variation in the efficiency scores. The paper has four chapters. The first one presents the methodology that defines efficiency as the distance from the observed input-output combinations to an efficient frontier. This unobservable frontier is estimated using the Free Disposable Hull (FDH) and Data Envelopment Analysis (DEA) techniques. The exercise focuses on health and education expenditure because they absorb the largest share of most countries’ budgets, and because it facilitates comparison of results with existing literature.2 We extend the analysis by measuring efficiency of capital spending in achieving several infrastructure output indicators. The second chapter estimates the efficiency frontiers for 14 education output indicators and seven health output indicators, based on a sample of data for 175 countries for the period 2006-2016, and six infrastructure output indicators based on a sample of 150 countries using 2007-2015 data. Both input-efficiency (excess input consumption to achieve a level of output) and output-efficiency (output shortfall for a given level of inputs) are scored. The chapter presents both the single input-single-output and the multiple-inputs multiple-outputs frameworks. The third chapter explores empirical regularities in the cross-country variation in the efficiency scores. Using a Tobit panel approach, this chapter explores the relationship between efficiency scores and expenditure levels, the wage bill as a share of the total budget, the degree of urbanization, and aid-dependency. The fourth and last chapter summarizes the conclusions. II. Measuring Efficiency: Methodologies and Overview of the Literature This chapter describes the empirical methods used in this paper to measure efficiency and surveys the literature more directly related to the analysis of public expenditure efficiency. Empirical and theoretical measures of efficiency are based on ratios of observed output levels to the maximum that could have been obtained given the inputs utilized. This maximum constitutes the efficient frontier which will be the benchmark for gauging the relative efficiency of the observations. There are multiple techniques to estimate this frontier and they have been applied to examine the efficiency of public spending in different contexts. These are the topics of the next two sections. 2 This paper follows closely the Herrera-Pang (2005) presentation to facilitate intertemporal comparisons.
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II.1. Methods for Measuring Efficiency
The origin of the discussion of efficiency measurement dates to Farell (1957), who identified two different ways in which productive agents could be inefficient: one, they could use more inputs than technically required to obtain a given level of output, or two, they could use a sub-optimal input combination given the input prices and their marginal productivities. The first type of inefficiency is termed technical inefficiency while the second one is known as allocative inefficiency. These two types of inefficiency can be represented graphically by means of the unit isoquant curve in Figure 1. The set of minimum inputs required for a unit of output lies on the isoquant curve YY’. An agent’s input-output combination defined by bundle P produces one unit of output using input quantities X1 and X2. Since the same output can be achieved by consuming less of both inputs along the radial back to bundle R, the segment RP represents the inefficiency in resource utilization. The technical efficiency (TE), input-oriented, is therefore defined as TE = OR/OP. Furthermore, the producer could achieve additional cost reduction by choosing a different input combination. The least cost combination of inputs that produces one unit of output is given by point T, where the marginal rate of technical substitution is equal to the input price ratio. To achieve this cost level implicit in the optimal combination of inputs, input use needs to be contracted to bundle S. The input allocative efficiency (AE) is defined as AE = OS/OR.
Figure 1 Technical and Allocative Inefficiency
This paper focuses on technical efficiency, due to the lack of comparable input prices across the countries. This concept of efficiency is narrower than the one implicit in social welfare analysis. That is, countries may be producing the wrong output very efficiently (at low cost). We abstract from this consideration (discussed by Tanzi 2004), focusing on the narrow concept of efficiency.
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Numerous techniques have been developed to estimate the unobservable efficient frontier (in this case the isoquant YY”). These may be classified using several taxonomies. The two most widely used catalog methods into parametric or non-parametric, and into stochastic or deterministic. The parametric approach assumes a specific functional form for the relationship between the inputs and the outputs as well as for the inefficiency term incorporated in the deviation of the observed values from the frontier. The non-parametric approach calculates the frontier directly from the data without imposing specific functional restrictions. The first approach is based on econometric methods, while the second one uses mathematical programming techniques. The deterministic approach considers all deviations from the frontier explained by inefficiency, while the stochastic focus considers those deviations a combination of inefficiency and random shocks outside the control of the decision maker.
This paper uses non-parametric methods to avoid assuming specific functional forms for the relationship between inputs and outputs or for the inefficiency terms. Other papers use the parametric approach (Greene (2003) Grigio (2013, 2014). The remainder of the section briefly describes the two methods: Free Disposable Hull (FDH) and Data Envelopment Analysis (DEA). The FDH method imposes the least amount of restrictions on the data, as it only assumes free-disposability of resources. Figure 2 illustrates the single-input single-output case of the FDH production possibility frontier. Countries A and B use inputs XA and XB to produce outputs YA and YB, respectively. The input efficiency score for country B is defined as the quotient XA/XB. The output efficiency score is given by the quotient YB/YA. A score of one implies that the country is on the frontier. An input efficiency score of 0.75 indicates that this country uses inputs in excess of the most efficient producer to achieve the same output level. An output efficiency score of 0.75 indicates that the inefficient producer attains 75 percent of the output obtained by the most efficient producer with the same input intake. Multiple input and output efficiency tests can be defined in an analogous way.
Figure 2 Free Disposal Hull (FDH) production possibility frontier
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The second approach, Data Envelopment Analysis (DEA), assumes that linear combinations of the observed input-output bundles are feasible. Hence it assumes convexity of the production set to construct an envelope around the observed combinations. Figure 3 illustrates the single input-single output DEA production possibility frontier. In contrast to the vertical step-ups of the FDH frontier, the DEA frontier is a piecewise linear locus connecting all the efficient decision-making units (DMU). The feasibility assumption, displayed by the piecewise linearity, implies that the efficiency of C, for instance, is not only ranked against the real performers A and D, called the peers of C in the literature, but also evaluated with a virtual decision maker, V, which employs a weighted collection of A and D inputs to yield a virtual output. DMU C, which would have been efficient by FDH, now lies below the variable returns to scale (VRS, further defined below) efficiency frontier, XADF, by DEA ranking. This example shows that FDH efficiency scores are higher than DEA ones. The input-oriented technical efficiency of C is now defined by TE = YV/YC.
Figure 3 DEA production possibility frontier
If constant returns to scale (CRS) characterize the production set, the frontier may be represented by a ray extending from the origin through the efficient DMU (ray OA). By this standard, only A would be rated efficient. The important feature of the XADF frontier is that this frontier reflects variable returns to scale. The segment XA reflects locally increasing returns to scale (IRS), that is, an increase in the inputs results in a greater than proportionate increase in output. Segments AD and DF reflect decreasing returns to scale. It is worth noticing that constant returns to scale technical efficiency (CRSTE) is equal to the product of variable returns to scale technical efficiency (VRSTE) and scale efficiency (SE). Accordingly, DMU D is technically efficient but scale inefficient, while DMU C is neither technically efficient nor scale efficient. The scale efficiency of C is calculated as YN/YV. For more detailed exploration of returns to scale, readers are referred to Charnes, Cooper, and Rhodes (1978) and Banker, Charnes, and Cooper (1984), among others.
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The limitations of the non-parametric method derive mostly from the sensitivity of the results to sampling variability, to the quality of the data and to the presence of outliers. This led the literature to explore the relationship between statistical analysis and non-parametric methods (Simar and Wilson, 2000) and propose solutions like constructing confidence intervals for the efficiency scores using asymptotic theory in the single input case (for input-efficiency estimators) or single-output (in the output efficiency) case, given these are shown to be maximum likelihood estimators (Banker, 1993 and Goskpoff, 1996). For multiple input-output cases the distribution of the efficiency estimators is unknown or quite complicated and analysts recommend constructing the empirical distribution of the scores by means of bootstrapping methods (Simar and Wilson, 2000). Other solutions to the outlier or noisy data consist in constructing a frontier that does not envelop all the data points, building an expected minimum input function or expected maximum output functions (Cazals, Florens and Simar, 2002, and Wheelock and Wilson, 2003). Another limitation of the method, at least in the context of this paper, is the inadequate treatment of dynamics, given the lag between input consumption (public expenditure) and output production (health and education outcomes). II.2. Overview of Precursor Papers There is abundant literature measuring productive efficiency of diverse types of decision-making units. For instance, there are papers measuring efficiency of museums (Bishop and Brand, 2003), container terminals (Cullinane and Song, 2003; Herrera-Pang 2006), electric generation plants (Cherchye and Post 2001), banks (Wheelock and Wilson, 2003), schools (Worthington, 2001) and hospitals (Bergess and Wilson, 1998), among others. Few papers, however, analyze aggregate public-sector spending efficiency using cross-country data. These are the direct precursors of this paper and have been surveyed elsewhere.3 The more recent directly related papers are Herrera-Pang (2005), which use non-parametric methods (FDH and DEA) to gauge efficiency for numerous health and education output indicators. Using a large set of developing countries for the period 1996-2002, the paper estimates efficiency scores in a first stage and in a second stage they use panel methods to explore the correlates of efficiency variation across countries. One of the common results of that paper and previous literature is that countries with low attainment in results in health or education show up with high efficiency scores. The apparently counterintuitive result is due to some countries’ low spending levels and low education attainment results, which are considered as the “origin” of the efficiency frontier: though the country appears as efficient because the peer countries spend more (in the OECD context), its output levels are also higher and probably more desirable from a broader perspective. The next chapters discuss this topic and report similar results for other countries.
3 Gupta and Verhoeven (2001), Evans and Tandon (2000), Jarasuriya and Woodon (2002) Greene (2003a), Afonso, Schuknecht and Tanzi (2003), Afonso and St. Aubyn (2004) were surveyed in Herrera-Pang (2005).
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Afonso, Romero and Monsalve (2013) focus exclusively on Latin American and Caribbean countries, and define aggregate measures of public sector output, which include education, health infrastructure, macro stability, and economic performance. The aggregations are weighted and unweighted. Given the complexity of the aggregations, their results are not directly comparable to Herrera-Pang or Grigoli’s results described below. But their findings in general show output efficiency scores higher than input efficiency scores, like the Herrera-Pang results for LAC, especially in health. Grigoli and Kapsoli (2013) use stochastic frontier analysis (SFA) to examine efficiency in health spending in a sample of 80 countries. Using a single indicator for health outcomes, the health adjusted life expectancy (HALE) average for 2006-2010, and lagged values of spending and other correlates (average of 2001-2005), the authors compute efficiency scores. This is an innovative way to capture the dynamics in the relationship between spending and health outcomes, but still imposes restrictions on the data. The reported scores are high, and the authors acknowledge the fact when reporting average efficiency scores of .94 compared to significantly lower scores of .81 of other studies. That average also seems high compared to results presented in this paper. The efficiency rankings of Grigoli and Kapsoli (2013) are also strange, as the efficiency scores of Trinidad and Tobago, for instance, ranked within the most efficient group in Herrera-Pang (2005) and Afonso et.al (2013), show up in the third quartile of the efficiency distribution. Grigoli (2014) uses an envelopment methodology, variant of the DEA, designed by Wagstaff and Wang (2011), to examine efficiency of education spending. One of the advantages of this approach is that it allows dealing with heterogeneity across groups, as different frontiers are constructed for different groups of countries. It also uses a LOWESS method, which helps dealing with the measurement error, data outliers, and stochastic nature of the problem at hand. The added complexity comes at a cost, as the study uses only one education outcome variable, net secondary enrollment. The efficiency scores have a larger dispersion and little information is given on the distribution of the scores, but many countries about 15% of the total, are on the efficiency frontier. Perelman et al. (2017) use two concepts, performance and productivity, to compare Latin American countries’ efficiency in education and health spending. The performance concept compares outcomes without considering resource constraints. Their concept of productivity links the outcomes to the resources, like the efficiency concept used in this paper and other literature in this review. For education outcomes, the authors use the PISA scores exclusively, while the health outcome is a human development index which is an aggregation of several health outcomes.4 The education efficiency scores of the Perelman et al. study are, on average, .63 for input-efficiency and .75 for output-
4 The education outcome considers only six LAC countries. The health outcomes used to compute the human development index are Disability-Adjusted Life Years (DALY), the probability of dying between 30 and 70 years old from cardiovascular, cancer, diabetes, or chronic respiratory diseases (PROB); the percentage of out-of-pocket expenditure in total health expenditure as an indicator of financial protection (FIPR); and an indicator of equity in health EQTY.
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efficiency. In health, the average input-efficiency is .59 and output-efficiency is .90. These results match the pattern found in other studies, including the present one, of output-efficiency exceeding input-efficiency, and that of health efficiency tending to be higher than education, especially on the output measure.5 III. Empirical Results
III.1. Input and Output Indicators: Description, Assumptions and Limitations Cross-country comparisons assume some homogeneity across the world in the production technology of health, education, and infrastructure.6 There are two particular aspects in which the homogeneity assumption is important. First, the comparison assumes that there is a small number of factors of production that are the same across countries. Any omission of an important factor will yield as a result a high efficiency ranking of the country that uses more of the omitted input. Second, the comparison requires that the quality of the inputs is the same, with the efficiency scores biased in favor of countries where the quality is of higher grade. Factor heterogeneity will not be a problem if it is evenly distributed across countries. It will be problematic if there are differences between countries in the average quality of a factor (Farrell, 1957). The exercise that we present suffers from this limitation, given that the main input in both production technologies is used more intensively in richer countries (with higher per-capita GDP). The main input is public spending per capita on education, health and infrastructure, and it shows a clear positive association with per-capita GDP (Figures 4A, 4B and 4C).7 This positive association may be explained by several factors. One of them is the Balassa-Samuelson effect, according to which price levels in wealthier countries tend to be higher than in poorer countries.8 This applies to both final goods and factor prices. Thus, the price of the same service (health or education, for instance) will be higher in the country with higher GDP. Similarly, wages in the relatively richer counties are higher, given the higher marginal productivity of labor, which will tend to increase costs, especially in labor-intensive activities such as health and education. 5 Averages of Perelman scores come from Tables 6 and 19. The order of magnitude of the averages is very similar to those reported in this study for the PISA scores of the same LAC country sample. The average reported in this study for education input efficiency is 0.67 and the output efficiency is .80. The LAC region health input efficiency score is .48 and output efficiency is .95, presented in tables in the next section. 6 See Table A.9 in Appendix A for the list of countries included in the study. 7 Education and health spending are measured in constant 2011 US dollars in PPP terms, and is an update of the figures presented in Herrera-Pang (2005), and the source is WDI from the World Bank. Capital spending comes from a different source, namely the IMF WEO. 8 The Balassa-Samuelson effect refers to the fact that price levels are higher in richer countries than in poorer countries. It can be shown that relative wages and relative prices are a function of the marginal productivity of labor in the traded goods. Given higher capital abundance in the richer countries, the productivity of labor tends to be higher in these countries, and hence will be wages and prices.
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The positive association (Figures 4A, 4B and 4C) can also be interpreted as evidence of the validity of Wagner’s hypothesis at the cross-country level. This hypothesis, postulates that there is a tendency for governments to increase their activities as economic activity increases. Since 1890 Wagner postulated that economic development implied rising complexities that required more governmental activity, or that the elasticity of demand for publicly provided services, in particular education, was greater than one. This hypothesis has been tested econometrically (Chang, 2002; Afonso et. al. 2017) in time series and cross-country settings, showing that this is not particular to the series used for the present study.
Figure 4. Public Expenditure on Education, Health and Capital and GDP (all per capita and in logs) 2009-2015
Figure 4A. Public Expenditure on Education and
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Figure 4C. Public Capital Spending and GDP 2007-2015
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Previous studies that measured the efficiency of public spending recognized the positive association and suggested alternative solutions. One possibility is to split the sample by groups of countries (Gupta and Verhoeven, 2001). We may partially control for this factor by excluding the industrialized nations from the sample, or by presenting the results clustered regionally (Africa (AFR), East Asia and Pacific (EAP), Eastern Europe and Central Asia (ECA), Latin America and Caribbean (LAC), Middle-East and North Africa (MNA) and South Asia (SAS)). A second alternative incorporates directly the per-capita GDP as a factor of production, jointly with expenditure and other inputs (Jarasuriya and Woodon 2002). The problem with this approach is that it combines variables derived from a production function approach, and hence with clear interpretation, with others (GDP per capita) that are difficult to interpret from any viewpoint. When the two types of variables are combined, their effects cannot be disentangled. We attempt to control for this factor by including GDP per capita as an explanatory variable in the “second stage” regressions presented in the last section. A third option consists in using as an input the orthogonal component of public expenditure to GDP.9 We estimated the efficiency scores using as input both the original and the orthogonalized variables. The goodness-of-fit of each model was gauged based 9 The orthogonalized expenditure variable is the residual of the linear regression between pubic expenditure and GDP per capita. Since residuals may take positive and negative values, the variable was right-shifted to avoid negative values to facilitate graphical presentation of the frontiers. The orthogonalization of capital spending was done using a log-log regression, as this transformation of the variables resulted in a distribution of the efficiency scores that produced a better fitness observed by comparing Fig. 5B (log-log) and the figure reported in the Appendix without the log transformation.
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on the frequency distribution of the inefficiency measures, as suggested by Farrell (1957) and Varian (1990). Comparing the distributions of the efficiency scores computed alternatively with the public expenditure or the orthogonalized value (Figures 5A and 5B), we see that the orthogonalization reduces the bias towards inefficiency (in the case of education, Fig. 5A) or towards efficiency (capital spending, Fig. 5B).10 Given this mitigation of the skewedness, the remainder of the paper considers the orthogonal component of expenditure as the input in all the efficiency score calculations.
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Figure 5B. Density of Efficiency Scores – Capital Spending-Overall Quality of Infrastructure
10 The efficiency scores depicted in Figs. 5A and 5B are FDH efficiency scores, one for input efficiency (5A) and the other for output efficiency (5B).
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This paper uses 14 indicators of education output, seven indicators of health output, and six indicators of infrastructure output.11 The education indicators are: primary school enrollment (gross and net), secondary school enrollment (gross and net), gross tertiary school enrollment, literacy of youth, average years of school, second level complete, PISA learning scores for math, reading and science and the WEF Indices for Quality of Match and Science Education, Quality of Primary Education, and Quality of the education system. Though the PISA country sample is limited, it is a numerical score. The WEF indices are computed for a significantly larger sample but have a limited range from 1-7. The correlation between the PISA learning scores and other output variables is high (.80 with average years of school and .78 with net primary school enrollment), as shown in Figure 6.12 The health output indicators are: life expectancy at birth, immunization (DPT13 and measles), and the disability-adjusted life expectancy (DALE), maternal survival rate, infant survival rates and Tuberculosis Free Population.14 For infrastructure output, we considered six indexes produced by the World Economic Forum: quality of overall infrastructure, quality of roads, quality of railroad infrastructure, quality of port infrastructure, quality of transport infrastructure, and quality of electricity supply. The cross-country comparisons with this set of indicators assume some form of data homogeneity, which might be problematic given the diversity of countries in the sample considered. Even for a more homogeneous group of countries, such as the OECD, there is call for caution when comparing expenditure levels in member countries (Jounard, et al. 2003). There is very little to do to overcome this limitation, except subdivide the sample into different groups. Probably a regional aggregation can be useful, but even at that level there may be extreme heterogeneity.
11 The data sources are: The World Bank World Development Indicators (WDI), Barro-Lee database, and Crouch and Fasih (2004), PISA, and the World Health Organization (Mathers et al, 2000). A complete list of variables and data sources can be found in Table A.10 of Appendix A. For capital spending the source is the WEO data base from the IMF and the infrastructure output indicators come from the World Economic Forum (WEF). 12 The correlation coefficients and Figure 6 exclude developed nations for the Crouch and Fasih (2004) sample. 13 DPT is Diphtheria-Pertussis and Tetanus 14 Maternal survival rates and infant survival rates are transformations of the mortality rates as follows: Maternal Survival Rate= (100000-Maternal Mortality Rate)/100000. The infant survival rate (ISR)=1000-Infant Mortality rate)/1000. Tuberculosis free population is a transformation of the incidence of tuberculosis variable (per 100,000 inhabitants).
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ARE
ARG
AUS
AZE
BGR
BRA
CAN
CHE
CHL
CHN
COL
CRI
CYP
DEU
DNK
DOM
DZA
ERI
ESP
FIN
FRA
GBR
GEO
GRC
HRVHUN
IDN
ISLITA
JOR
KAZ
KGZ
KOR
LBN
LTULUXLVA
MDA
MEX
MKD
NLD
NOR
NZL
PANPER
POL
ROM
RUS
SVN
SWE
THATTO
TUN
TURURY
USA
VNM
350
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500
550
PIS
A S
cien
ce S
core
s
40 60 80 100Net Primary Enrollment
Data Source: World Bank Indicators
Correlation: PISA Science Scores and Net Primary Enrollment
ALB
ARE
ARG
AUS
AUT
BGR
BRA
CAN
CHE
CHL
CHN
COL
CRI
CYP
CZE
DEU
DNK
DOM
DZA
ESP
FIN
FRA
GBR
GRC
HRVHUN
IDN
ISLITA
JOR
KAZ
KGZ
KOR
LTULUXLVA
MDA
MEX
NLD
NOR
NZL
PANPER
POL
ROM
RUSSVK
SVN
SWE
THATTO
TUN
TURURY
USA
VNM
350
400
450
500
550
PIS
A S
cien
ce S
core
s
0 5 10 15Average Years of School
Data Source: World Bank Indicators & Barro Lee
Correlation: PISA Science and Average Years of School
Figure 6. Correlation between Learning Scores and Other Education Indicators
There are four other limitations arising from the variables and data selected for the analysis. The first one refers to the level of aggregation. While the exercises use aggregate public spending on health, education and capital spending as inputs, they use disaggregate measures of output, such as primary enrollment or secondary enrollment. Ideally, the input should have differentiated between primary and secondary education expenditures. Similarly, health care spending could be disaggregated into primary care level care and secondary level. The data can be disaggregated even further, by analyzing efficiency at the school or hospital levels. Second, there are omitted factors of production. This is especially true in education, as the paper did not consider private spending due to data constraints for developing nations. If this factor were used more intensively in a group of countries, then the efficiency scores (reported in the next section) would be biased favoring efficiency in that group. The third limitation arising from the data is the combination of monetary and non-monetary factors of production and outputs. The paper uses together with public expenditure, other non-monetary factors of production such as the ratio of teachers to students, in the case of education, or literacy of adults in the case of health and education. Other factors of production that could have been used were the physical number of teaching hours (in education) or the number of doctors or in-patient beds, as Afonso and St. Aubyn did for the OECD countries. However, inexistent data for many developing countries constrained the options. In the case of infrastructure output, the physical measures such as those used in Herrera-Pang for container ports are not available, hence we are limited to using indexes. A fourth limitation arising from the selected indicators is that these do not allow for a good differentiation between outputs and outcomes. For instance, most of the indicators of education, such as completion and enrollment rates, do not measure how much learning is taking place in a country. In education, this paper advances by considering the learning scores as one of the indicators. In health, other outcomes such as the number of sick-day leaves or the number of missed-school days because of health-related causes
14
could be better reflections of outcomes. Two of the selected health output indicators, DPT and measles immunization, are delivered in vertical programs, that is, in campaigns that are relatively independent of basic health systems and therefore may not be good indicators of the actual quality of the health system. Additionally, in most countries, these two activities (immunization) account for very small fractions of the health budgets. Finally, the fact that life expectancy is influenced by diet, lifestyle, and a clean environment, that to the extent that are not included as factors of production may bias the efficiency scores. III.2. Single Input-Output Results
III.2.1. FDH and DEA Education Frontiers Figures 7a-d show both FDH and DEA efficiency frontiers for four of the 14 output indicators: gross primary school enrollment, secondary gross enrollment, quality of math and science education index (from WEF) and the PISA Science scores. Individual country efficiency scores for the four indicators are reported in Table A.1-2 of Appendix A.15 The graphical efficiency frontiers for other output indicators can be found in Appendix A (Figure A.1). Several results may be highlighted:
a. The input efficiency rankings (education) are robust to the output indicator selected, as implied by the Spearman rank-correlation coefficient (see Tables A.1 and A.3 in Appendix A), which is positive, significant and high. The range oscillates between .35 and .97. This result implies that countries ranked as efficient (or inefficient) per one indicator, are ranked similarly when other output indicators are used.
b. Despite the orthogonalization by GDP, the relatively rich countries tend to be in the more efficient group, especially when output efficiency is considered.
c. In general, output efficiency scores are higher than input efficiency scores.
15 The efficiency scores of all the indicators can be found at the MFM website indicated in footnote 1.
15
Free Disposable Hull (FDH)
Data Envelopment Analysis (DEA)
AGO
ALB
ARG
ARMATG
AUS
AUTAZE
BDI
BEN
BFA
BGD
BGR BLR
BLZ
BOL
BRA
BRB
BWA
CAF
CAN
CHECHL
CHN
CIV
CMRCOG
COL
COM
CPVCRI
CYPCZEDEU
DJI
DNK
DOM
ECU
EGYESP
EST
ETH
FIN
FJIFRAGBR
GEO
GHA
GINGMB
GNBGTM
GUY
HND
HRV
HUN
IDNINDIRN
ISLITA
KAZ
KEN
KGZ
KHM
KNA
KOR
LAO
LBN LKA
LSO
LTULVA
MAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN PER
PHL
POL
PRY
ROM
RUS
RWA
SAU
SDN
SEN
SLB
SLE
SLV
SVKSVN
SWE
SWZ
TCD
TGO
THA TJK
TKM
TTOTUN
TUR
TZA
UGA
UKR
URY
USA
VCTVEN
VNM
VUT
ZAFZARZWE
6080
100
120
140
Gro
ss P
rimar
y S
choo
l Enr
ollm
ent
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI
Gross Primary Enrollment vs Education Expenditure
AGO
ALB
ARG
ARMATG
AUS
AUTAZE
BDI
BEN
BFA
BGD
BGR BLR
BLZ
BOL
BRA
BRB
BWA
CAF
CAN
CHECHL
CHN
CIV
CMRCOG
COL
COM
CPVCRI
CYPCZEDEU
DJI
DNK
DOM
ECU
EGYESP
EST
ETH
FIN
FJIFRAGBR
GEO
GHA
GINGMB
GNBGTM
GUY
HND
HRV
HUN
IDNINDIRN
ISLITA
KAZ
KEN
KGZ
KHM
KNA
KOR
LAO
LBN LKA
LSO
LTULVA
MAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN PER
PHL
POL
PRY
ROM
RUS
RWA
SAU
SDN
SEN
SLB
SLE
SLV
SVKSVN
SWE
SWZ
TCD
TGO
THA TJK
TKM
TTOTUN
TUR
TZA
UGA
UKR
URY
USA
VCTVEN
VNM
VUT
ZAFZARZWE
6080
100
120
140
Gro
ss P
rimary
Sch
ool E
nrollm
ent
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI
Gross Primary Enrollment vs Education Expenditure
(a.1) (a.2)
AGO
ALB ARGARM
ATGAUS
BDI
BEN
BFA
BGD
BGR
BLR
BLZ
BOL
BRA
BRB
CAF
CHE
CHL
CHN
CMR
COL
COM
CPV
CRI
CYPDNK
DOM
ECUEGY
ESPEST
ETH
FIN
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FRA
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GHA
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GTM
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IND
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KOR
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LVA
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MYS
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NLD
NOR
NPL
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OMN
PAK
PAN
PER
PHL
POL
PRY
ROM
RWA
SAU
SLV
SVN SWE
SWZ
THATJKTUR
UKR
URY
USAVCT
VEN
VUT
ZWE
2040
6080
100
Gro
ss S
econd
ary
Sch
ool E
nro
llmen
t
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI
Gross Secondary Enrollment vs Education Expenditure
AGO
ALB ARGARM
ATGAUS
BDI
BEN
BFA
BGD
BGR
BLR
BLZ
BOL
BRA
BRB
CAF
CHE
CHL
CHN
CMR
COL
COM
CPV
CRI
CYPDNK
DOM
ECUEGY
ESPEST
ETH
FIN
FJI
FRA
GBR
GEO
GHA
GIN
GTM
GUY
HND
HRVHUN
IDN
IND
IRN
ISL
ITA
JAM
KAZ
KEN
KGZKNA
KOR
LAO
LBN
LCALKA
LSO
LTU
LVA
MAR
MDA
MDG
MEX
MLI
MOZ
MRT
MUS
MWI
MYS
NER
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRY
ROM
RWA
SAU
SLV
SVN SWE
SWZ
THATJKTUR
UKR
URY
USAVCT
VEN
VUT
ZWE
2040
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100
Gro
ss S
econ
dary
Sch
ool E
nrol
lme
nt
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI
Gross Secondary Enrollment vs Education Expenditure
(b.1) (b.2)
AGO
ALB
ARG
ARM
AUS
AUT
AZE BDI
BEN
BFA
BGD
BGR
BLZBOL
BRA
BRB
BWA
CAN
CHE
CHL
CHN
CIV
CMR
COL
CPV
CRI
CYP
CZE
DEU DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FRA
GAB
GBR
GEO
GHA
GIN
GMB
GTM
GUY
HND
HRV
HTI
HUNIDNINDIRN
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ITA
JAM
KAZKEN
KGZKHM
KOR
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LBN
LKA
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LTU
LVA
MARMDA
MDG
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MKD
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MRT
MUS
MWI
MYS
NAM
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NIC
NLD
NOR
NPL
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OMN
PAK
PAN
PER
PHL
POL
PRY
ROMRUS
RWASAU
SEN
SLE
SLV
SVK
SVN
SWE
SWZ
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TTO
TUN
TUR
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UGA
UKR
URY
USA
VEN
VNM
ZAF
ZWE
23
45
6Q
ualit
y of
mat
h a
nd s
cien
ce
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/World Economic Forum
Quality of math and science vs Education Expenditure
AGO
ALB
ARG
ARM
AUS
AUT
AZE BDI
BEN
BFA
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BGR
BLZBOL
BRA
BRB
BWA
CAN
CHE
CHL
CHN
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CMR
COL
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CRI
CYP
CZE
DEU DNK
DOM
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EGY
ESP
EST
ETH
FIN
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GBR
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GIN
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HTI
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ITA
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KOR
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MYS
NAM
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PER
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POL
PRY
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SLE
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ZWE
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ua
lity
of m
ath
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ienc
e
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/World Economic Forum
Quality of math and science vs Education Expenditure
(c.1) (c.2)
16
ALB
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AUT
AZE
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CAN
CHE
CHL
CHN
COL
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CYP
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DEU
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KOR
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TURURY
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a S
cience
Lite
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re
1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/NCES
Pisa Science Literacy score vs Education Expenditure
ALB
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AUT
AZE
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CAN
CHE
CHL
CHN
COL
CRI
CYP
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DEU
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KOR
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a S
cien
ce L
itera
cy s
core
1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/NCES
Pisa Science Literacy score vs Education Expenditure
(d.1) (d.2)
Figure 7 Education Efficiency Frontier: Single Input and Single Output
d. Output-efficiency rankings also vary with the selected output indicators. The Spearman correlation coefficient of the output-efficiency scores (see Tables A.2 and A.4 in Appendix) show that these are robust to the selected indicator, though the range is higher (.16 to .90).
e. To grasp the order of magnitudes of the deviations from the efficiency frontier, and the disparity in efficiency across countries, we computed an average for all indicators for the groups of more efficient and least efficient countries (Table 1).16 The input-efficiency estimations indicate that a country in the bottom of the distribution could reach the same educational attainment levels by spending approximately 50 percent less. The output efficiency estimators indicate that, on average, with the prevailing expenditure level a typical country of this group could reach educational attainment levels more than twice as high (Table 1A).
Table 1. Education Attainment: Single Input, Single Output Country Clustering
Input-Efficient Output Efficient More efficient Italy, Kazakhstan, Lebanon,
Czech Republic, Slovak Republic, China, Republic of Korea
Austria, Finland, Kazakhstan, Italy, Canada, Lebanon, Czech Republic, Great Britain, Sweden, Republic of Korea
Least efficient Denmark, Norway, Sweden, Saudi Arabia, Namibia, Botswana, Moldova, Costa Rica
Angola, Mozambique, Burundi, Mauritania, Tanzania, Peru
16 These are simple averages of the top 10 and bottom 10 countries in each ranking.
17
Table 1A. Education Attainment: Single Input, Single Output Efficiency Scores
Input-Efficient Output Efficient More efficient .89 .92 Least efficient .47 .39 f. This clustering exercise reveals (Table 1) that several developed economies, such
as Denmark, Norway and Sweden, appear within the least input-efficient category. This is due to the amount of spending these countries do. Resource-rich countries also appear in the inefficient group, such as Saudi Arabia, Botswana, Angola, and Mozambique. Mostly African countries populate this group. Among the more efficient group, Lebanon, Republic of Korea, China, Czech Republic, and Kazakhstan appear as both input and output efficient. Curiously, Sweden appears within the most output-efficient category. Explaining why these countries appear in each cluster requires more in-depth analysis, undertaken in the last section, which explores the association of efficiency scores with other variables.
g. It is critical to note that even if a country appears as efficient, there might still be a significant discrepancy between the observed output level and the desired or target output level. For instance, Azerbaijan, Lebanon and Romania appear as efficient countries on the FDH efficiency frontier or very close to it (Figure 7 a.1) because they spend relatively little on education; they are close to the origin of the frontier with low spending and low learning levels. But their PISA scores are far below those of countries that spend similar amounts but have significantly higher PISA scores, such as Italy or the Czech Republic. Within the LAC countries, Panama and Chile have the highest input efficiency scores, though Panama’s case is due to the low spending level effect discussed above. The important point is that the country moves along the efficiency frontier to the higher target output level. Countries can even improve efficiency by exploiting scale economies if they are operating in the increasing returns to scale zone of the production possibility frontier (output levels smaller than that of point A, Figure 3).
h. The regional aggregation of the efficiency scores shows that input-oriented scores (Table 2A) are lower than output-oriented scores (Table 2B).17 This is especially true in ECA, EAP, and MNA. In general, scores are higher for primary enrollment and decrease with the level of education (secondary enrollment), especially when output-oriented measures are considered. Across regions, ECA, EAP, and MENA have similar levels of input-inefficiency of about 65-70 percent, while LAC and SAS average around 60 percent, and AFR about 55 percent.
17 The regional aggregate is the simple average of the individual country scores obtained for the whole sample. The scores were not computed by constructing separate efficiency frontiers for each region. The regional classification exercise excludes the developed economies in all the regional aggregation exercises.
18
i. Output efficiency in ECA and EAP is in the range of 75 to 80 percent, in LAC and MNA around 70 percent, in SAS about 60 percent and in AFR 50 percent.18 In EAP, ECA, and LAC the output efficiency scores are about 15 percent higher than the input efficiency, while in SAS they are about the same and in AFR 7 percent lower. This indicates that the first three regions are closer to the frontier on the output side than on the input (spending) side.
Table 2A. Educational Attainment: Input-Efficiency scores by regions across the world
- Single Input, Single Output
AFR EAP ECA LAC MNA SAS Gross primary enrollment .61 .65 .67 .65 .65 .70 Net primary enrollment .58 .72 .73 .70 .75 .69 Gross Secondary enrollment .57 .68 .66 .63 .70 .63 Net secondary enrollment .56 .61 .66 .63 .65 .62 Average years of school .56 .64 .69 .60 .59 .63 Second level complete .56 .63 .68 .60 .59 .63 PISA Science .82 .79 .68 .74 PISA Reading .78 .78 .68 .74 PISA Math .80 .79 .67 .74 Quality of Math and Science .57 .64 .69 .60 .69 .64
Table 2B. Educational Attainment: Output-Efficiency scores by regions across the world
- Single Input-Single Output
AFR EAP ECA LAC MNA SAS Gross primary enrollment .72 .79 .75 .77 .76 .79 Net primary enrollment .81 .93 .94 .94 .92 .90 Gross Secondary enrollment .34 .73 .89 .74 .77 .59 Net secondary enrollment .33 .59 .75 .68 .63 .49 Average years of school .42 .65 .86 .65 .59 .51 Second level complete .20 .39 .76 .41 .35 .32 PISA Science .90 .87 .77 .79 PISA Reading .88 .85 .79 .74 PISA Math .88 .86 .74 .78 Quality of Math and Science .57 .72 .72 .53 .73 .66 j. Two groups of indicators capture the quality of educational attainment: the PISA
scores (Math, Science and Reading) and the World Economic Forum (WEF) various indicators, of which we focus on one, the Quality of Math and Science
18 These are simple averages of the indicators by region. In output efficiency the primary and secondary level completed indicators were omitted due to problems with the data.
19
education. Both variables have limitations: the PISA country sample is smaller and with relatively greater weight of developed nations, while the WEF variable is an index constructed to reflect the quality in a large sample of countries.
III.2.2. FDH and DEA Health Frontiers This section presents the single input (public expenditure on health per capita in PPP terms)-single output efficiency frontiers using both the FDH and DEA methodologies; seven alternative output indicators are used: life expectancy at birth, the disability adjusted life expectancy (DALE), DPT immunization, measles immunization, tuberculosis free population, maternal survival, and infant survival rates.19 Figures 8a-d show the FDH and DEA efficiency frontiers for four indicators. The specific country rankings for four of the health indicators are listed in Table A.4-5 of Appendix A. The graphical efficiency frontiers for other output indicators can be found in Appendix A (Figure A.2).
Free Disposable Hull (FDH) Data Envelopment
AGO
ALBARGARM AUS AUTAZE
BDI
BENBFA
BGD
BGRBHR
BHS
BLR BLZ
BOL
BRABRB
BWA
CAF
CANCHECHL CHN
CIVCMR
COG
COL
COM
CPV CRICYP CZE DEU
DJI
DNK
DOMDZA
ECUEGY
ERI
ESPEST
ETH
FINFJI FRA
GAB
GBRGEO
GHA
GINGMB
GNB
GRCGRDGTM
GUY
HND
HRV
HTI
HUN
IDNIND
IRN ISLITA
JAMJOR
KAZ
KEN
KGZ
KHM
KOR
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LBNLCALKA
LSO
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MAR
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MDG
MEXMKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLDNOR
NPL
NZLOMN
PAK
PANPER
PHL
PNG
POL
PRY
ROMRUS
RWA
SAU
SDNSEN
SLB
SLE
SLVSVK SVN SWE
SWZ
TCD
TGO
THA TJKTKM
TONTTO TUN
TUR
TZAUGA
UKRURY USAUZBVCTVEN
VNMVUTWSM
ZAF
ZAR
ZMB
ZWE
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000
Mat
ern
al S
urv
ival R
ate
1000 2000 3000 4000 5000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI, World Health Organization
Maternal Survival Rate vs Health Expenditure
AGO
ALBARGARM AUS AUTAZE
BDI
BENBFA
BGD
BGRBHR
BHS
BLR BLZ
BOL
BRABRB
BWA
CAF
CANCHECHL CHN
CIVCMR
COG
COL
COM
CPV CRICYP CZE DEU
DJI
DNK
DOMDZA
ECUEGY
ERI
ESPEST
ETH
FINFJI FRA
GAB
GBRGEO
GHA
GINGMB
GNB
GRCGRDGTM
GUY
HND
HRV
HTI
HUN
IDNIND
IRN ISLITA
JAMJOR
KAZ
KEN
KGZ
KHM
KOR
LAO
LBNLCALKA
LSO
LTU LUXLVA
MAR
MDA
MDG
MEXMKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLDNOR
NPL
NZLOMN
PAK
PANPER
PHL
PNG
POL
PRY
ROMRUS
RWA
SAU
SDNSEN
SLB
SLE
SLVSVK SVN SWE
SWZ
TCD
TGO
THA TJKTKM
TONTTO TUN
TUR
TZAUGA
UKRURY USAUZBVCTVEN
VNMVUTWSM
ZAF
ZAR
ZMB
ZWE
9850
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099
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00M
ate
rnal S
urv
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ate
1000 2000 3000 4000 5000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI, World Health Organization
Maternal Survival Rate vs Health Expenditure
(a.1) (a.2)
19 Tuberculosis free, maternal survival rates, and infant survival rates are transformations of the original variables, tuberculosis incidence, maternal mortality, and infant mortality, respectively. Transformations are described in footnote 15.
20
AGO
ALBARG
ARM
ATGAUS AUT
AZE
BDI
BEN
BFA
BGD
BGRBHRBHS
BLR
BLZ
BOL
BRABRB
BWA
CAF
CANCHECHL
CHN
CIV
CMR
COG
COL
COM
CPV
CRI
CYP CZE DEU
DJI
DMA
D
DOM
DZAECU
EGY
ERI
ESPEST
ETH
FIN
FJI
FRA
GAB
GBR
GEO
GHA
GIN
GMB
GNB
GRC
GRD
GTMGUY
HND
HRV
HTI
HUN
IDN
IND
IRN
ISLITA
JAMJORKAZ
KEN
KGZ
KHM
KNA
KOR
LAO
LBN
LCALKA
LSO
LTULUX
LVA
MAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLNOR
NPL
NZL
OMN
PAK
PANPER
PHL
PNG
POL
PRY
ROMRUS
RWA
SAU
SDN
SEN
SLB
SLE
SLV
SVKSVN SWE
SWZ
TCD
TGO
THA
TJK
TKM
TONTTO
TUNTUR
TZAUGA
UKRURYUSA
UZB
VCTVEN
VNM
VUT
WSM
YEM
ZAF
ZAR
ZMBZWE
.9.9
2.9
4.9
6.9
81
Infa
nt S
urv
iva
l Ra
te
1000 2000 3000 4000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI, World Health Organization
Infant Survival Rate vs Health Expenditure
AGO
ALBARG
ARM
ATGAUS AUT
AZE
BDI
BEN
BFA
BGD
BGRBHRBHS
BLR
BLZ
BOL
BRABRB
BWA
CAF
CANCHECHL
CHN
CIV
CMR
COG
COL
COM
CPV
CRI
CYP CZE DEU
DJI
DMA
DNK
DOM
DZAECU
EGY
ERI
ESPEST
ETH
FIN
FJI
FRA
GAB
GBR
GEO
GHA
GIN
GMB
GNB
GRC
GRD
GTMGUY
HND
HRV
HTI
HUN
IDN
IND
IRN
ISLITA
JAMJORKAZ
KEN
KGZ
KHM
KNA
KOR
LAO
LBN
LCALKA
LSO
LTULUX
LVA
MAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLDNOR
NPL
NZL
OMN
PAK
PANPER
PHL
PNG
POL
PRY
ROMRUS
RWA
SAU
SDN
SEN
SLB
SLE
SLV
SVKSVN SWE
SWZ
TCD
TGO
THA
TJK
TKM
TONTTO
TUNTUR
TZAUGA
UKRURYUSA
UZB
VCTVEN
VNM
VUT
WSM
YEM
ZAF
ZAR
ZMBZWE
.9.9
2.9
4.9
6.9
81
Infa
nt S
urv
iva
l Ra
te
1000 2000 3000 4000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI, World Health Organization
Infant Survival Rate vs Health Expenditure
(b.1) (b.2)
AGO
ALBARGARM
AUS AUT
AZE
BDI
BENBFA
BGD
BGRBHR BLZ
BOL
BRABRB
BWA
CANCHECHL
CHN
CIVCMR
COL
CPV
CRICYP CZE DEU DNKDOM DZAECUEGY ESPEST
ETH
FIN FRA
GAB
GBR
GEO GHA
GINGMB
GRCGTM
GUYHND
HRV
HTI
HUN
IDN IND
IRN ISLITAJAM JOR
KAZ
KEN
KGZ
KHM
KOR
LAO
LBNLKA
LSO
LTULUX
LVAMAR
MDA
MDG
MEX MKD
MLIMNG
MOZ
MRT
MUS
MWI
MYS
NAM
NGA
NICNLDNOR
NPL
NZLOMN
PAK
PAN
PER
PHL
POL PRYROMRUS
RWA
SAU
SEN
SLE
SLVSVK SVN SWE
SWZ
TCD
THATJK
TTO TUNTUR
TZAUGA
UKR
URY USAVEN
VNM
YEM
ZAF
ZMB
ZWE
.985
.99
.995
1F
ree
Tu
be
rcu
losi
s
1000 2000 3000 4000 500Orthogonalized Public Expditure on Health
Data Source: World Bank WDI, World Health Organization
Free Tuberculosis vs Health Expenditure
AGO
ALBARGARM
AUS AUT
AZE
BDI
BENBFA
BGD
BGRBHR BLZ
BOL
BRABRB
BWA
CANCHECHL
CHN
CIV
CMR
COL
CPV
CRICYP CZE DEU DNKDOM DZAECUEGY ESPEST
ETH
FIN FRA
GAB
GBR
GEO GHA
GINGMB
GRCGTM
GUYHND
HRV
HTI
HUN
IDN IND
IRN ISLITAJAM JOR
KAZ
KEN
KGZ
KHM
KOR
LAO
LBNLKA
LSO
LTULUX
LVAMAR
MDA
MDG
MEX MKD
MLIMNG
MOZ
MRT
MUS
MWI
MYS
NAM
NGA
NICNLDNOR
NPL
NZLOMN
PAK
PAN
PER
PHL
POL PRYROMRUS
RWA
SAU
SEN
SLE
SLVSVK SVN SWE
SWZ
TCD
THATJK
TTO TUNTUR
TZAUGA
UKR
URY USAVEN
VNM
YEM
ZAF
ZMB
ZWE
.985
.99
.995
1F
ree
Tu
be
rcu
losi
s
1000 2000 3000 4000 5000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI, World Health Organization
Free Tuberculosis vs Health Expenditure
(c.1) (c.2)
AGO
ALBARG
ARM
ATG
AUSAUT
AZE
BDI
BEN
BFA
BGD
BGRBHR
BHS
BLRBLZBOL
BRA
BRB
BWA
CAF
CANCHE
CHL
CHN
CIVCMR
COG
COL
COM
CPV
CRICYP
CZE
DEU
DJI
DMA
DNK
DOM
DZAECU
EGY
ERI
ESP
EST
ETH
FIN
FJI
FRA
GAB
GBR
GEO
GHA
GIN
GMB
GNB
GRC
GRDGTM
GUY
HND
HRV
HTI
HUN
IDN
IND
IRN
ISLITA
JAM JOR
KAZ
KEN
KGZ
KHM
KOR
LAO
LBN
LCALKA
LSO
LTU
LUX
LVAMAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAMNER
NGA
NIC
NLDNOR
NPL
NZL
OMN
PAK
PANPER
PHL
PNG
POL
PRYROM
RUS
RWA
SAU
SDN
SEN
SLB
SLE
SLVSVK
SVN
SWE
SWZ
TCD
TGO
THA
TJK
TKM
TON
TTO
TUNTUR
TZA
UGA
UKR
URY
USA
UZB
VCT
VEN
VNM
VUT
WSM
YEM
ZAF
ZAR
ZMBZWE
5060
7080
Dis
ab
ility
Ad
just
ed
Life
Exp
ect
an
cy
1000 2000 3000 4000 500Orthogonalized Public Expditure on Health
Data Source: World Bank WDI, Institute for Health Metrics and Evaluation (IHME)
Disability Adjusted Life Expectancy vs Health Expenditure
AGO
ALBARG
ARM
ATG
AUSAUT
AZE
BDI
BEN
BFA
BGD
BGRBHR
BHS
BLRBLZBOL
BRA
BRB
BWA
CAF
CANCHE
CHL
CHN
CIVCMR
COG
COL
COM
CPV
CRICYP
CZE
DEU
DJI
DMA
DNK
DOM
DZAECU
EGY
ERI
ESP
EST
ETH
FIN
FJI
FRA
GAB
GBR
GEO
GHA
GIN
GMB
GNB
GRC
GRDGTM
GUY
HND
HRV
HTI
HUN
IDN
IND
IRN
ISLITA
JAM JOR
KAZ
KEN
KGZ
KHM
KOR
LAO
LBN
LCALKA
LSO
LTU
LUX
LVAMAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAMNER
NGA
NIC
NLDNOR
NPL
NZL
OMN
PAK
PANPER
PHL
PNG
POL
PRYROM
RUS
RWA
SAU
SDN
SEN
SLB
SLE
SLVSVK
SVN
SWE
SWZ
TCD
TGO
THA
TJK
TKM
TON
TTO
TUNTUR
TZA
UGA
UKR
URY
USA
UZB
VCT
VEN
VNM
VUT
WSM
YEM
ZAF
ZAR
ZMBZWE
5060
7080
Dis
ab
ility
Ad
just
ed
Life
Exp
ect
an
cy
1000 2000 3000 4000 5000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI, Institute for Health Metrics and Evaluation (IHME)
Disability Adjusted Life Expectancy vs Health Expenditure
(d.1) (d.2)
Figure 8: Health Efficiency Frontiers Single Input-Single Output
21
Several results may be highlighted:
a. The input-efficiency rankings of the health indicators are positively and significantly correlated, with the Spearman rank correlation coefficient oscillating between .19 and .93 (see Tables A.1 and A.3 in Appendix A). This indicates that the efficiency ranking is similar regardless of the output indicator being used.
b. Despite the orthogonalization by GDP, the richer countries tend to be more efficient (Table 3). The inefficient group has two types of countries: one small group of rich countries like the USA, Great Britain, and Switzerland which have high expenditure levels and not extremely high output (input inefficiency) and another much larger group of countries with relatively low spending but their output indicators could be substantially larger, like Lesotho, Malawi, and Sierra Leone. Other large African countries, Nigeria and Mozambique, appear in this group as well.
Table 3. Health Attainment: Single Input, Single Output
Input-Efficient Output Efficient More efficient Bahrain, Saudi Arabia, Oman,
Luxembourg, Trinidad and Tobago, Republic of Korea, Australia
Oman, Saudi Arabia, Bahrain, Luxembourg, Switzerland, Czech Republic, Finland, Italy
Least efficient Burundi, Mozambique, Democratic republic of Congo, Lesotho, Malawi, Switzerland, United States, Great Britain
Central African Republic, Sierra Leone, Nigeria, Lesotho, Malawi, Mozambique, Democratic Republic of Congo, Zimbabwe
Table 3A. Health Attainment: Single Input, Single Output Efficiency Scores
Input-Efficient Output Efficient More efficient .85 1.0 Least efficient .38 .77
c. The health efficiency rankings are closely correlated: the Spearman coefficient of output-efficiency ranking is .34 and the output one is .93 (see Tables A.2 and A.4 in Appendix A).
d. To examine the efficiency differences across groups of countries and the potential efficiency gains of moving closer to the frontier, countries were clustered into the least and most efficient (Tables 3 and 3A). The typical country of the least efficient group could maintain the same output levels with about 50% of the expenditure level. Or on the output side, the least efficient group could increase output levels by 35% for a given expenditure level (Table 3A) The divergence
22
between least and most efficient groups in output-efficiency is not as large as in education.
e. Output-efficiency scores are notoriously higher than the input-efficiency ones (Tables 4A and 4B). While the input-efficiency regional average oscillates between 40 and 50 percent, the output-efficiency average fluctuates between 90 and 95 percent, except in AFR where it is 85 percent. The large difference between the health input and output efficiency did not happen in the case of education, nor in previous studies based on data from the early 2000s. Comparing these results with efficiency scores of the early 2000s (Herrera-Pang, 2005), there seems to be a stagnation of input efficiency while output efficiency increased significantly, especially in AFR and SAS, which had the lowest achievement levels in the earlier studies.
Table 4A. Health Input-Efficiency scores by regions across the world
- Single Input, Single Output
AFR EAP ECA LAC MNA SAS Immunization, measles .42 .46 .46 .46 .58 .44 Immunization .42 .55 .50 .47 .63 .47 Life Expectancy at birth .42 .48 .48 .48 .60 .44 DALE .49 .54 .54 .56 .65 .50 Free Tuberculosis Cases .42 .48 .48 .48 .61 .44 Infant Survival Rate .42 .48 .56 .47 .59 .44 Maternal Survival Rate .42 .46 .46 .46 .59 .44
Table 4B. Health Output-Efficiency scores by regions across the world
- Single Input-Single Output
AFR EAP ECA LAC MNA SAS Life Expectancy at birth .72 .87 .90 .90 .91 .85 Immunization DPT .82 .87 .95 .93 .94 .89 Immunization Measles .80 .87 .96 .93 .93 .85 DALE .73 .85 .90 .91 .92 .85 Tuberculosis free .99 1.0 1.0 1.0 1.0 1.0 Infant survival rate .95 .98 .99 .98 .98 .96 Maternal Survival rate 1.0 1.0 1.0 1.0 1.0 1.0
23
III.2.3. FDH and DEA Infrastructure Efficiency frontiers This section presents the single input (public capital expenditure per capita)- single output frontiers, using both the FDH and DEA methodologies, with six alternative output indicators: quality of overall infrastructure, quality of roads, quality of railroad infrastructure, quality of port infrastructure, quality of transport infrastructure, and quality of electricity supply. Figures 9a-c show the FDH efficiency frontier for three indicators. The specific country scores for all the infrastructure indicators and the DEA frontiers are can be found in Appendix A.7.
Free Disposable Hull (FDH) Data Envelopment
AGO
ALB
ARE
ARG
ARM
AUS
AUT
AZE
BDI
BEL
BEN
BFABGD
BGR
BHR
BIH
BLZ
BOL
BRA
BRB
BTNBWA
CAN
CHE
CHL
CIV
CMR
COL
CPV
CRI
CZE
DEU
DOM DZAECU
EGY
EST
ETH
FINFRA
GAB
GBR
GEO
GHA
GIN
GMBGRC
GTM
GUYHND
HRV
HTI
IDN IND
IRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KENKHM
KOR
KWTLKA
LSO
LTU
LUX
LVA
MAR
MDA
MDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZL
OMN
PAK
PAN
PERPHL
POL
PRT
PRY
ROM
RUS
RWA
SAU
SEN
SGP
SLE
SLV
SRB
SURSVK SWZ
SYC
TCD
THA
TJK
TTO
TUNTUR
TZA
UGA
UKRURY
USA
VEN
VNM
YEM
ZAF
ZMBZWE
AGO
ALB
ARE
ARG
ARM
AUS
AUT
AZE
BDI
BEL
BEN
BFABGD
BGR
BHR
BIH
BLZ
BOL
BRA
BRB
BTNBWA
CAN
CHE
CHL
CIV
CMR
COL
CPV
CRI
CZE
DEU
DOM DZAECU
EGY
EST
ETH
FINFRA
GAB
GBR
GEO
GHA
GIN
GMBGRC
GTM
GUYHND
HRV
HTI
IDN IND
IRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KENKHM
KOR
KWTLKA
LSO
LTU
LUX
LVA
MAR
MDA
MDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZL
OMN
PAK
PAN
PERPHL
POL
PRT
PRY
ROM
RUS
RWA
SAU
SEN
SGP
SLE
SLV
SRB
SURSVK SWZ
SYC
TCD
THA
TJK
TTO
TUNTUR
TZA
UGA
UKRURY
USA
VEN
VNM
YEM
ZAF
ZMBZWE
23
45
67
Qualit
y of O
vera
ll In
frast
ruct
ure
0 .5 1 1.5 2 2.5Log-Log Form: Orthogonalized Public Investment Per Capita
Data Source: World Economic Outlook-IMF/World Economic Forum
Quality of Overall Infrastructure vs Public Investment
AGO
ALB
ARE
ARG
ARM
AUS
AUT
AZE
BDI
BEL
BEN
BFABGD
BGR
BHR
BIH
BLZ
BOL
BRA
BRB
BTNBWA
CAN
CHE
CHL
CIV
CMR
COL
CPV
CRI
CZE
DEU
DOM DZAECU
EGY
EST
ETH
FINFRA
GAB
GBR
GEO
GHA
GIN
GMBGRC
GTM
GUYHND
HRV
HTI
IDN IND
IRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KENKHM
KOR
KWTLKA
LSO
LTU
LUX
LVA
MAR
MDA
MDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZL
OMN
PAK
PAN
PERPHL
POL
PRT
PRY
ROM
RUS
RWA
SAU
SEN
SGP
SLE
SLV
SRB
SURSVK SWZ
SYC
TCD
THA
TJK
TTO
TUNTUR
TZA
UGA
UKRURY
USA
VEN
VNM
YEM
ZAF
ZMBZWE
AGO
ALB
ARE
ARG
ARM
AUS
AUT
AZE
BDI
BEL
BEN
BFABGD
BGR
BHR
BIH
BLZ
BOL
BRA
BRB
BTNBWA
CAN
CHE
CHL
CIV
CMR
COL
CPV
CRI
CZE
DEU
DOM DZAECU
EGY
EST
ETH
FINFRA
GAB
GBR
GEO
GHA
GIN
GMBGRC
GTM
GUYHND
HRV
HTI
IDN IND
IRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KENKHM
KOR
KWTLKA
LSO
LTU
LUX
LVA
MAR
MDA
MDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZL
OMN
PAK
PAN
PERPHL
POL
PRT
PRY
ROM
RUS
RWA
SAU
SEN
SGP
SLE
SLV
SRB
SURSVK SWZ
SYC
TCD
THA
TJK
TTO
TUNTUR
TZA
UGA
UKRURY
USA
VEN
VNM
YEM
ZAF
ZMBZWE
23
45
67
Qualit
y of O
vera
ll In
frast
ruct
ure
0 .5 1 1.5 2 2.5Log-Log Form: Orthogonalized Public Investment Per Capita
Data Source: World Economic Outlook-IMF/World Economic Forum
Quality of Overall Infrastructure vs Public Investment
(a.1) (a.2)
AGO
ALB
ARE
ARGARM
AUS
AUT
AZE
BDI
BEL
BENBFA
BGD
BGR
BHR
BIH
BLZ
BOL
BRA
BRB
BTN
BWA
CANCHE
CHL
CIV
CMRCOL
CPV
CRI
CZE
DEU
DOM
DZA
ECUEGY
EST
ETH
FIN
FRA
GAB
GBR
GEO
GHA
GIN
GMBGRC
GTM
GUYHND
HRV
HTI
IDN
INDIRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KEN
KHM
KOR
KWTLKA
LSO
LTU
LUX
LVAMAR
MDAMDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZLOMN
PAK
PAN
PERPHL POL
PRT
PRY
ROM
RUS
RWA
SAU
SEN
SGP
SLE
SLV
SRB
SURSVK SWZ
SYC
TCD
THA
TJK
TTOTUN
TUR
TZA UGA
UKR URY
USA
VEN
VNM
YEM
ZAF
ZMBZWE
AGO
ALB
ARE
ARGARM
AUS
AUT
AZE
BDI
BEL
BENBFA
BGD
BGR
BHR
BIH
BLZ
BOL
BRA
BRB
BTN
BWA
CANCHE
CHL
CIV
CMRCOL
CPV
CRI
CZE
DEU
DOM
DZA
ECUEGY
EST
ETH
FIN
FRA
GAB
GBR
GEO
GHA
GIN
GMBGRC
GTM
GUYHND
HRV
HTI
IDN
INDIRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KEN
KHM
KOR
KWTLKA
LSO
LTU
LUX
LVAMAR
MDAMDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZLOMN
PAK
PAN
PERPHL POL
PRT
PRY
ROM
RUS
RWA
SAU
SEN
SGP
SLE
SLV
SRB
SURSVK SWZ
SYC
TCD
THA
TJK
TTOTUN
TUR
TZA UGA
UKR URY
USA
VEN
VNM
YEM
ZAF
ZMBZWE
23
45
67
Tra
nsp
ort
Infr
ast
ruct
ure
0 .5 1 1.5 2 2.5Log-Log Form: Orthogonalized Public Investment Per Capita
Data Source: World Economic Outlook-IMF/World Economic Forum
Transport Infrastructure vs Public Investment
AGO
ALB
ARE
ARGARM
AUS
AUT
AZE
BDI
BEL
BENBFA
BGD
BGR
BHR
BIH
BLZ
BOL
BRA
BRB
BTN
BWA
CANCHE
CHL
CIV
CMRCOL
CPV
CRI
CZE
DEU
DOM
DZA
ECUEGY
EST
ETH
FIN
FRA
GAB
GBR
GEO
GHA
GIN
GMBGRC
GTM
GUYHND
HRV
HTI
IDN
INDIRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KEN
KHM
KOR
KWTLKA
LSO
LTU
LUX
LVAMAR
MDAMDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZLOMN
PAK
PAN
PERPHL POL
PRT
PRY
ROM
RUS
RWA
SAU
SEN
SGP
SLE
SLV
SRB
SURSVK SWZ
SYC
TCD
THA
TJK
TTOTUN
TUR
TZA UGA
UKR URY
USA
VEN
VNM
YEM
ZAF
ZMBZWE
AGO
ALB
ARE
ARGARM
AUS
AUT
AZE
BDI
BEL
BENBFA
BGD
BGR
BHR
BIH
BLZ
BOL
BRA
BRB
BTN
BWA
CANCHE
CHL
CIV
CMRCOL
CPV
CRI
CZE
DEU
DOM
DZA
ECUEGY
EST
ETH
FIN
FRA
GAB
GBR
GEO
GHA
GIN
GMBGRC
GTM
GUYHND
HRV
HTI
IDN
INDIRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KEN
KHM
KOR
KWTLKA
LSO
LTU
LUX
LVAMAR
MDAMDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZLOMN
PAK
PAN
PERPHL POL
PRT
PRY
ROM
RUS
RWA
SAU
SEN
SGP
SLE
SLV
SRB
SURSVK SWZ
SYC
TCD
THA
TJK
TTOTUN
TUR
TZA UGA
UKR URY
USA
VEN
VNM
YEM
ZAF
ZMBZWE
23
45
67
Tra
nspo
rt In
fra
stru
ctur
e
0 .5 1 1.5 2 2.5Log-Log Form: Orthogonalized Public Investment Per Capita
Data Source: World Economic Outlook-IMF/World Economic Forum
Transport Infrastructure vs Public Investment
(b.1) (b.2)
24
AGO
ALB
ARE
ARG
ARM
AUS
AUT
AZE
BDI
BEL
BEN BFA
BGD
BGR
BHR
BIH
BLZBOL
BRA
BRBBTN
BWA
CANCHE
CHL
CIV
CMR
COL
CPV
CRI
CZEDEU
DOM
DZA
ECU
EGY
EST
ETH
FINFRA
GAB
GBR
GEO
GHA
GIN
GMB
GRCGTM
GUY
HND
HRV
HTI
IDN
IND
IRL
IRN
ISL
ISRITA JOR
JPN
KAZ
KEN
KHM
KOR
KWTLKA
LSO
LTU
LUX
LVAMAR
MDA
MDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRT
PRY
ROMRUS
RWA
SAU
SEN
SGP
SLE
SLVSRB
SUR
SVK
SWZ
SYC
TCD
THA
TJK
TTOTUN
TUR
TZA UGA
UKR
URY
USA
VEN
VNM
YEM
ZAFZMB
ZWEAGO
ALB
ARE
ARG
ARM
AUS
AUT
AZE
BDI
BEL
BEN BFA
BGD
BGR
BHR
BIH
BLZBOL
BRA
BRBBTN
BWA
CANCHE
CHL
CIV
CMR
COL
CPV
CRI
CZEDEU
DOM
DZA
ECU
EGY
EST
ETH
FINFRA
GAB
GBR
GEO
GHA
GIN
GMB
GRCGTM
GUY
HND
HRV
HTI
IDN
IND
IRL
IRN
ISL
ISRITA JOR
JPN
KAZ
KEN
KHM
KOR
KWTLKA
LSO
LTU
LUX
LVAMAR
MDA
MDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRT
PRY
ROMRUS
RWA
SAU
SEN
SGP
SLE
SLVSRB
SUR
SVK
SWZ
SYC
TCD
THA
TJK
TTOTUN
TUR
TZA UGA
UKR
URY
USA
VEN
VNM
YEM
ZAFZMB
ZWE
02
46
8Q
ualit
y of
Ele
ctric
ity S
upp
ly
0 .5 1 1.5 2 2.5Log-Log Form: Orthogonalized Public Investment Per Capita
Data Source: World Economic Outlook-IMF/World Economic Forum
Quality of Electricity Supply vs Public Investment
AGO
ALB
ARE
ARG
ARM
AUS
AUT
AZE
BDI
BEL
BEN BFA
BGD
BGR
BHR
BIH
BLZBOL
BRA
BRBBTN
BWA
CANCHE
CHL
CIV
CMR
COL
CPV
CRI
CZEDEU
DOM
DZA
ECU
EGY
EST
ETH
FINFRA
GAB
GBR
GEO
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GIN
GMB
GRCGTM
GUY
HND
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IDN
IND
IRL
IRN
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JPN
KAZ
KEN
KHM
KOR
KWTLKA
LSO
LTU
LUX
LVAMAR
MDA
MDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRT
PRY
ROMRUS
RWA
SAU
SEN
SGP
SLE
SLVSRB
SUR
SVK
SWZ
SYC
TCD
THA
TJK
TTOTUN
TUR
TZA UGA
UKR
URY
USA
VEN
VNM
YEM
ZAFZMB
ZWEAGO
ALB
ARE
ARG
ARM
AUS
AUT
AZE
BDI
BEL
BEN BFA
BGD
BGR
BHR
BIH
BLZBOL
BRA
BRBBTN
BWA
CANCHE
CHL
CIV
CMR
COL
CPV
CRI
CZEDEU
DOM
DZA
ECU
EGY
EST
ETH
FINFRA
GAB
GBR
GEO
GHA
GIN
GMB
GRCGTM
GUY
HND
HRV
HTI
IDN
IND
IRL
IRN
ISL
ISRITA JOR
JPN
KAZ
KEN
KHM
KOR
KWTLKA
LSO
LTU
LUX
LVAMAR
MDA
MDG
MEX
MLI
MMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRT
PRY
ROMRUS
RWA
SAU
SEN
SGP
SLE
SLVSRB
SUR
SVK
SWZ
SYC
TCD
THA
TJK
TTOTUN
TUR
TZA UGA
UKR
URY
USA
VEN
VNM
YEM
ZAFZMB
ZWE
02
46
8Q
ua
lity
of E
lect
rici
ty S
up
ply
0 .5 1 1.5 2 2.5Log-Log Form: Orthogonalized Public Investment Per Capita
Data Source: World Economic Outlook-IMF/World Economic Forum
Quality of Electricity Supply vs Public Investment
(c.1) (c.2)
Figure 9: Infrastructure Frontiers Single Input-Single Output
As in previous cases, countries were clustered into the more efficient and least efficient groups (Table 5). The more efficient countries are the richer economies, with Chile included in that group. Within the inefficient group we find mostly African countries and a few LAC countries like Ecuador and Trinidad and Tobago. The discrepancy in efficiency between both groups is extraordinary (Table 5A) and much larger than in education or health.
Table 5. Infrastructure Single Input, Single Output)
Input-Efficient Output Efficient More efficient Germany, Belgium,
Switzerland, Singapore, United Kingdom, Austria, Chile, Finland, France.
Israel, United Araba Emirates, Germany, Slovenia, Switzerland, Netherlands, Great Britain, Iceland.
Least efficient Ecuador, Etiopia, Lesotho, Venezuela RB, Trinidad and Tobago, Angola, Botswana
Haiti, Tchad, Gabon, Uganda, Romania, Vietnam
Table 5A. Infrastructure Single Input, Single Output Efficiency Scores
Input-Efficient Output Efficient More efficient .68 .96 Least efficient .10 .32
Input-efficiency is extremely low, with the average regional input-efficiency score between 18% and 30% (Table 6A); AFR is the lower bound at 18% and EAP at 29%. Output-efficiency is significantly higher (Table 5B), indicating that capital spending
25
deviation from the frontier is larger than the output deviation from the frontier. This result could be explained due to the index of quality being used as output indicator (which is limited by nature of the construction from 1-7). Also, the computation of the frontiers including both developed and developing countries could be biasing the results, though when other inputs are included the problem is mitigated significantly. The efficiency scores are closely correlated with indicators of the regulatory quality, or the effectiveness of government (Table 7). This is especially true when output- efficiency indicators are used.20 These relationships are explored econometrically in the last section, when other factors are controlled for.
Table 6A Infrastructure: Input-Efficiency scores by regions across the world
- Single Input, Single Output
AFR EAP ECA LAC MNA SAS
Quality of electricity supply 0.17 0.24 0.19 0.18 0.20 0.19
Transport infrastructure 0.17 0.33 0.18 0.19 0.25 0.20
Quality of air transport infrastructure 0.18 0.31 0.17 0.20 0.22 0.19
Quality of port infrastructure 0.19 0.32 0.19 0.22 0.24 0.20
Quality of railroad infrastructure 0.20 0.25 0.23 0.19 0.24 0.28
Quality of roads 0.18 0.30 0.18 0.20 0.24 0.19
Quality of overall infrastructure 0.17 0.26 0.18 0.19 0.22 0.19
Table 6B Infrastructure: Output-Efficiency scores by regions across the world
- Single Input, Single Output
AFR EAP ECA LAC MNA SAS
Quality of electricity supply 0.44 0.68 0.70 0.63 0.75 0.49
Transport infrastructure 0.48 0.67 0.53 0.54 0.63 0.54
Quality of air transport infrastructure 0.57 0.71 0.62 0.66 0.71 0.60
Quality of port infrastructure 0.56 0.65 0.55 0.60 0.67 0.53
Quality of railroad infrastructure 0.35 0.52 0.51 0.30 0.48 0.47
Quality of roads 0.52 0.66 0.51 0.57 0.70 0.56
Quality of overall infrastructure 0.52 0.65 0.59 0.57 0.69 0.54
20 The overall infrastructure index is weakly correlated with ranking on the quality of the public investment management systems (Dabla-Norris, et. al.), probably due to the limited sample in the PIMS study.
26
Table 7 Correlation of Efficiency Rankings and Governance indicators.
III.3. Multiple Inputs and Multiple Outputs Education, health, and infrastructure attainment are not solely determined by public spending. Other inputs, such as private spending also affect the output indicators. For both health and capital spending, we could get data on private spending, but not for education.21 Hence the education production technology will have multiple indicators of educational attainment, and three possible inputs (public spending, teachers per pupil, and adult literacy rate). In health, besides public spending, three other inputs were included: private spending, improved sanitation condition, gross secondary school enrollment and the literacy of adults. The analysis was limited to include up to two inputs and two outputs to avoid the curse of dimensionality: increasing the number of output or input indicators biases efficiency scores towards one, increases the variance of the estimators, and reduces the speed of convergence to the true efficiency estimators (Simar and Wilson, 2000; Groskopff, 1996). III.3.1. DEA Education Frontiers The multi-input multi-output efficiency scores produce a ranking of countries like the single input-single output case (Table 8). Lebanon and Kazakhstan appear as efficient countries, close to the origin due to their low spending levels but low attainment levels. However, new countries appear within the more efficient group, such as Finland, the Islamic Republic of Iran and Spain. Within the least efficient countries, Norway appears as input-inefficient, as well as Brazil and Saudi Arabia. The least output efficient countries are mostly African counties, with Pakistan and Peru. The discrepancy in efficiency between the more efficient group and least efficient is lower than in the single input case, but still the typical country of the least efficient group could achieve the same output with 40% lower spending.
21 The source of health data is the WDI while for capital spending it is WEO.
Spearman Rank Correlation
Control of Corruption
Government Effectiveness
Political Stability and Absence of
Violence/Terrorism
Regulatory Quality
Rule of Law
Voice and Accountability
Input Efficiency
0.358*** (113)
0.374*** (113)
0.291*** (113)
0.439*** (113)
0.381*** (113)
0.378*** (113)
Output Efficiency
0.678*** (113)
0.752*** (113)
0.488*** (113)
0.720*** (113)
0.686*** (113)
0.420*** (113)
27
Table 8. Educational Attainment: Multiple Inputs, Multiple Outputs sample countries
Input-Efficient Output Efficient More efficient Lebanon, Panama, Bahrain,
Kazakhstan, Finland, China, Spain, Islamic Republic of Iran
Kazakhstan, Spain, Islamic Republic of Iran, Switzerland, Bahrain, Lebanon, Russian Federation
Least efficient Cyprus, Costa Rica, Norway, Iceland, Moldova, Brazil, Saudi Arabia
Mali, Senegal, Dominican Republic, Côte d’Ivoire, Angola, Mozambique, Sierra Leone, Pakistan, Peru.
Table 8A. Educational Attainment: Multiple Inputs, Multiple Outputs efficiency scores
Input-Efficient Output Efficient More efficient .99 .99 Least efficient .61 .56
When multiple inputs are considered, efficiency scores tend to rise. The regional aggregation for input and output efficiency scores shows (Tables 9A and 9B) that, as the model becomes more complex (adding inputs or outputs), scores rise due to the increasing uniqueness of the input-output bundle, and the relatively higher difficulty of finding peers. The first four rows of Table 8A allow gauging the impact on efficiency of adding literacy of adults as an additional input, by comparing scores with the single input case (Table 2A). In Africa and SAS, the change is dramatic, increasing from around 60 percent to the low 80s in AFR and low 90s in SAS. In EAP, ECA and MNA changes are of relatively lower importance, and in LAC the addition of the input is insignificant. This differential response to the inclusion of the additional input is due to the low levels of adult literacy in AFR and SAS, which yield gains in efficiency. In output efficiency there is no change in EAP and ECA, but in MENA and LAC the change is relevant with MNA being on the efficiency frontier (Table 8B, row 1 and Table 2B row 8). Individual country efficiency scores for the multiple inputs for education are reported in Table A.3 of Appendix A.
Table 9A. Education Attainment: Input-Efficiency scores by regions across the world
- Multiple Inputs, Multiple Outputs
AFR EAP ECA LAC MNA SAS 2 inputs (public expenditure, literacy of adult) – 1 outputs (Net primary enroll.)
0.84 0.83 0.78 0.76 0.82 0.91
2 inputs (public expenditure, literacy of adult) – 1 outputs (Net Secondary enroll.)
0.84 0.81 0.83 0.82 0.88 0.91
2 inputs (public expenditure, literacy of adult) – 1 outputs (Average Year of Schooling)
0.83 0.82 0.92 0.78 0.81 0.90
2 inputs (public expenditure, literacy of adult) – 1 outputs (Pisa Science)
0.96 0.91 0.91 1.00
2 inputs (public expenditure, teachers per pupil) – 2 outputs (Pisa Science & net primary enroll.)
0.92 0.86 0.89 0.88
28
Table 9B. Education Attainment: Output-Efficiency scores by regions across the world
- Multiple Inputs, Multiple Outputs
AFR EAP ECA LAC MNA SAS 2 inputs (public expenditure, literacy of adult) – 1 outputs (Pisa Science)
0.91 0.87 0.80 1.00
2 inputs (public expenditure, literacy of adult) – 1 outputs (Net primary enroll.)
0.85 0.96 0.95 0.93 0.98 0.91
2 inputs (public expenditure, literacy of adult) – 1 outputs (Net Secondary enroll.)
0.57 0.71 0.81 0.74 0.81 0.76
2 inputs (public expenditure, literacy of adult) – 1 outputs (Average Year of Schooling)
0.69 0.73 0.92 0.74 0.79 0.82
2 inputs (public expenditure, teachers per pupil) – 2 outputs (Pisa Science & net primary enroll.)
0.98 0.95 0.96 0.98
III.3.2. DEA Health Multi Input-Output In health there are multiple possible combinations of inputs (public expenditure, private expenditure, and literacy of adults) and outputs (life expectancy at birth, immunization DPT, immunization measles, and Disability Adjusted life expectancy (DALE)). Of the additional inputs, private sector health spending deserves special attention given its magnitude and pattern of use across countries. In many countries, private spending in health is larger than public spending, with the ratio of private to public spending being larger than one and decreasing with the level of GDP per capita (Fig 10). Hence, richer countries use this input less intensively than poorer countries, or, that poorer countries use more public financing relative to private to achieve health outcomes. There is a clear positive relationship between private spending in health and GDP per capita (Fig. 11), like the one displayed by public spending. Hence, we will use the orthogonalized component in the inputs.
29
AGO
ALB
ARE
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ARM
AUSAUT
AZE
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CAF
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COG COL
COM
CPV CRI
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CZEDEU
DJI
DNK
DOM
DZA
ECU
EGY
ERI
ESPEST
ETH
FINFJI
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GIN
GMB
GNB
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GRD
GTM
GUY
HND
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HTI
HUN
IDN
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IRN
ISLITA
JAM
JOR
KAZKEN
KGZ
KHM
KOR
LAOLBN
LCALKA
LSOLTU
LUX
LVA
MAR
MDA
MDGMEX
MKD
MLI
MNGMOZ
MRT MUS
MWI MYSNAM
NER
NGA
NIC
NLD NOR
NPL
OMN
PAK
PAN
PER
PHL
PNGPOL
PRY
ROM
RUS
RWA
SAU
SEN
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SLE
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SWESWZ
TCD
TGO
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TJK
TON
TUN
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TZA
UGA
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URY
USAUZB
VEN
VNM
VUT WSM
ZAF
ZAR
ZMB
ZWE
ATGDMA
KNA
KWTNZL
SDN
TKMVCT
YEM
TTO
01
23
45
share
priva
tepublic
gdp /L
inear pre
dic
tion
6 8 10 12 Log GDP Per Capita PPP 2011
Data Source: World Bank Indicators
Ratio of Private to Public Health Spending as a Share of GDP vs GDP Per Capita
Figure 10 Ratio of Private to Public Health Spending and GDP per Capita
SLB
VUT
OMN
KWT
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TKM
PNG
TONCOG
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GABROM
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ZWE
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UKRNAM
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KNA
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ECU
GNB
MAR
CIV
CAN
TJK
RWA
YEMKHM
GTM
LCA
HND
CHL
LBN
BHS
AZE
CYP
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IRN
CHE
BRA
UGA
MDASDN
PRY
HTI
GEO
SLE
USA
TTO
24
68
lhea/
Lin
ear pre
dic
tion
6 8 10 12 Log GDP Per Capita PPP 2011
Data Source: World Bank Indicators
Private Health Spending vs GDP Per Capita
Figure 11 Private Health Spending and GDP per Capita
30
Table 10. Health Attainment Country Clusters: Multiple Inputs-Multiple Outputs Sample of countries
Input-Efficient Output Efficient More efficient Oman, Bahrain, Cyprus,
Luxembourg, Saudi Arabia, Lebanon
Oman, Luxembourg, Cyprus, Iceland, Norway, Saudi Arabia, Bangladesh, Bahrain
Least efficient South Africa, Brazil, Georgia, Paraguay, Namibia, St. Lucia
South Africa, Lesotho, Zimbabwe, Angola, Sierra Leone
Table 10A. Health Attainment Country Clusters: Multiple Inputs-Multiple Outputs Efficiency scores
Input-Efficient Output Efficient More efficient 1.0 1.0 Least efficient .64 .84
As in previous cases, the countries were clustered into the most efficient and least efficient groups. In this more complex model, the more efficient group is directly on the frontier (score of 1) while the least efficient group on average scores .64 and .84 in input and output efficiency, respectively. The discrepancy between the groups narrows, but still the scope for expenditure reduction is about 30%. This is lower than in the education case.
31
Table 11A. Health Attainment: Input-Efficiency scores by regions across the world
- Multiple Inputs-Multiple Outputs
AFR EAP ECA LAC MNA SAS 2 inputs (public expenditure, Private expenditure) – 1 output (Immunization DPT)
0.41 0.52 0.46 0.40 0.59 0.44
2 inputs (public expenditure, Private expenditure) – 1 output (Maternal Survival Rate)
0.41 0.43 0.47 0.39 0.53 0.42
2 inputs (public expenditure, Private expenditure) – 1 output (Dale)
0.45 0.51 0.48 0.49 0.59 0.46
2 inputs (public expenditure, Improved Sanitation) – 1 output (Maternal Survival Rate)
0.85 0.83 0.83 0.82 0.90 0.84
2 inputs (public expenditure, Improved Sanitation) – 1 output (Dale)
0.86 0.79 0.72 0.82 0.88 0.80
2 inputs (public expenditure, Adult Literacy Rate) – 1 output (Immunization DPT)
0.80 0.76 0.65 0.64 0.83 0.86
2 inputs (public expenditure, Adult Literacy Rate) – 1 output (Maternal Survival Rate)
0.78 0.79 0.86 0.76 0.94 0.89
2 inputs (public expenditure, Adult Literacy Rate) – 1 output (Dale)
0.81 0.75 0.70 0.82 0.92 0.87
2 inputs (public expenditure, Improved Sanitation) – 2 outputs (Dale, Maternal Survival Rate)
0.88 0.86 0.89 0.85 0.86 0.84
2 inputs (public expenditure, Improved Sanitation) – 2 outputs (Dale, Infant Survival Rate)
0.87 0.82 0.84 0.84 0.84 0.83
2 inputs (public expenditure, Adult Literacy Rate) – 2 outputs (Dale, Maternal Survival Rate)
0.82 0.81 0.86 0.85 0.97 0.93
2 inputs (public expenditure, private expenditure) – 2 outputs (Dale, Infant Survival Rate)
0.94 0.98 0.99 0.98 0.98 0.96
Table 11B. Health Attainment: Output-Efficiency scores by regions across the world
- Multiple Inputs, Multiple Outputs
AFR EAP ECA LAC MNA SAS 2 inputs (public expenditure, Private expenditure) – 1 outputs (Immunization, DPT)
0.81 0.87 0.95 .093 0.94 0.88
2 inputs (public expenditure, Improved Sanitation) – 1 outputs (Life Expectancy at Birth)
0.86 0.93 0.91 0.93 0.94 0.93
2 inputs (public expenditure, Improved Sanitation) – 1 outputs (Immunization, DPT)
0.86 0.88 0.95 0.92 0.97 0.90
2 inputs (public expenditure, Improved Sanitation) – 1 outputs (Dale)
0.88 0.91 0.91 0.94 0.95 0.93
2 inputs (public expenditure, Adult Literacy Rate) – 1 outputs (Immunization, DPT)
0.85 0.88 0.93 0.92 0.97 0.90
2 inputs (public expenditure, Adult Literacy Rate) – 1 outputs (Maternal Survival Rate)
1.0 1.0 1.0 1.0 1.0 1.0
2 inputs (public expenditure, Adult Literacy Rate) – 1 outputs (Dale)
0.84 0.90 0.91 0.95 0.98 0.94
2 inputs (public expenditure, Improved Sanitation) – 2 outputs (Dale, Maternal Survival Rate)
1.0 1.0 1.0 1.0 1.0 1.0
2 inputs (public expenditure, Adult Literacy Rate) – 2 outputs (Dale, Infant Survival Rate)
0.97 0.99 0.99 0.99 1.0 0.99
2 inputs (public expenditure, private expenditure) – 2 outputs (Dale, Infant Survival Rate)
0.94 0.98 0.99 0.98 0.98 0.96
32
The impact of private spending on efficiency scores is puzzling. The input efficiency scores remain unchanged (Table 11A, rows 1-3) compared to the single output case (Table 4A), though output efficiency increases (Tables 11B vs. 4B). But all the other combinations of inputs increase efficiency. For instance, when the adult literacy rate is included as an input, the AFR DALE efficiency increases from .49 to .81 and MNA efficiency increases from .65 to .92. Output efficiency increase as well, though not in the same proportion; from .73 to .84 in AFR and from .92 to .98 in MNA. Other additional inputs, such as improved sanitation conditions, have similar effects on efficiency measures. Similar results are obtained when the two input-two output models are considered, but efficiency scores increase when private health spending is considered. Table 11B shows that, on average, developing nations score between .84 and .89 in output efficiency in the multiple input-output framework. These figures imply that developing countries could raise their output levels by an average of 15 percent with the same input consumption, if they were as efficient as the comparable benchmark countries. This figure is simply indicative, as the estimate varies with the country and with the selected indicator and has a large variance across countries: for instance, the bottom decile of (input) efficiency scores is about .64, implying that the scope for increasing health and education attainment levels is between 3 or 4 times higher than for the whole sample average. Individual country efficiency scores for the multiple inputs for health are reported in Table A.6 of Appendix A. III.3.3. DEA Infrastructure Multi Input-Output In infrastructure we will focus on adding private capital spending as an input.to the existing production function of one input (quality of overall infrastructure). The private spending is generally larger than public capital spending, with the ratio being larger than one (Figure 12). However, there are cases where private spending is extremely low compared with public capital spending, such as Trinidad and Tobago, Venezuela, and Mozambique. The trend is for the ratio to increase with the level of GDP. Private capital spending is also positively correlated with GDP (Fig. 13). Hence, we will use the orthogonalized component. Countries were clustered into the most and least efficient (Table 12) and the efficiency scores of both groups show a marked increase in efficiency (Table 12A). The most efficient group lies on the frontier, while the least efficient group averages .28.
33
AGO
ALB
ARE
ARG
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AUT
AZEBDI
BEL
BEN
BFA
BGD BGR BHR
BIHBLZ
BOL
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BRB
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CMR COLCPV
CRI CZE
DEU
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JOR JPNKAZ
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LBN
LKA
LSO
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MDA
MDGMEX
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MNE
MOZ
MUS
MWI MYS
NAM
NGANICNLD
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRT
PRY
ROM
RUS
RWA SAU
SEN
SGP
SLE
SLV SRB
SUR
SVK
SWZ
SYC
TCD
THA
TJKTTO
TUN
TURTZA
UGA
UKR
URYUSA
VEN
VNMYEM
ZAF
ZAR
ZMB
ZWE
05
1015
privp
ub10 /L
inear
pre
dic
tion
6 8 10 12lgdp
Data Source: World Economic Outlook-IMF
Ratio of Private to Public Investment Spending vs GDP per Capita
Figure 12 Ratio of Private to Public Capital Spending
AGO
ALB
ARE
ARG
ARM
AUSAUT
AZE
BDI
BEL
BEN
BFA
BGD
BGR
BHR
BIHBLZ
BOL
BRA BRB
BTN
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COLCPV
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HRV
HTI
IDN
IND
IRL
IRN
ISLISR
ITA
JOR
JPN
KAZ
KEN
KHM
KORKWT
LBN
LKA
LSO
LTU
LUX
LVA
MAR
MDA
MDG
MEX
MLIMMR
MNE
MOZ
MUS
MWI
MYS
NAM
NGANIC
NLD
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRT
PRY
ROMRUS
RWA
SAU
SEN
SGP
SLE
SLV
SRB
SUR SVK
SWZ
SYC
TCD
THA
TJK
TTOTUN
TUR
TZAUGA
UKR
URY
USA
VEN
VNM
YEM
ZAF
ZAR
ZMB
ZWE
24
68
10Priva
te In
vest
ment S
pen
din
g P
er C
api
ta
4 6 8 10 12lgdp
Data Source: World Economic Outlook-IMF
Private Investment Spending vs GDP per Capita
Figure 13 Private Capital Spending per capita and GDP per capita
The regional aggregation shows that MNA and EAP have the highest efficiency scores, both input and output oriented (Table 13). Individual country efficiency scores for the multiple inputs for infrastructure are reported in Table A.8 of Appendix A.
34
Table 12. Capital Spending Multiple Inputs, Multiple Outputs
Input-Efficient Output Efficient More efficient Germany, Israel, Singapore,
Belgium, Switzerland, France, Finland, United Arab Emirates
Germany, Israel, United Arab Emirates, Barbados, Switzerland, Netherlands, Singapore
Least efficient Haiti, Bosnia-Herzegovina, Myanmar, Paraguay, Angola, Burundi, Sierra Leone, Venezuela RB
Haiti, Chad, Myanmar, Bosnia-Herzegovina, Paraguay, Bangladesh, Nigeria, Moldova, Lesotho
Table 12A. Capital Spending Multiple Inputs, Multiple Outputs
Input-Efficient Output Efficient More efficient .99 1.0 Least efficient .28 0.33
Table 13A. Infrastructure: Input-Efficiency scores by regions across the world
- Multiple Inputs-Multiple Outputs
AFR EAP ECA LAC MNA SAS
Quality of electricity supply 0.52 0.57 0.61 0.61 0.69 0.47
Transport infrastructure 0.48 0.59 0.48 0.52 0.59 0.47
Quality of air transport infrastructure
0.49 0.57 0.49 0.56 0.60 0.46
Quality of port infrastructure 0.47 0.54 0.43 0.51 0.58 0.43
Quality of railroad infrastructure 0.46 0.55 0.56 0.46 0.50 0.54
Quality of roads 0.54 0.58 0.47 0.55 0.67 0.49
Quality of overall infrastructure 0.52 0.56 0.53 0.55 0.66 0.47
35
Table 13B. Infrastructure: Output-Efficiency scores by regions across the world
- Multiple Inputs-Multiple Outputs
AFR EAP ECA LAC MNA SAS
Quality of electricity supply 0.50 0.68 0.71 0.66 0.78 0.49
Transport infrastructure 0.54 0.67 0.55 0.58 0.66 0.55
Quality of air transport infrastructure
0.63 0.71 0.64 0.69 0.75 0.61
Quality of port infrastructure 0.62 0.66 0.56 0.63 0.71 0.54
Quality of railroad infrastructure 0.42 0.54 0.55 0.36 0.49 0.47
Quality of roads 0.59 0.66 0.52 0.60 0.74 0.57
Quality of overall infrastructure 0.58 0.65 0.61 0.61 0.74 0.55
IV. Covariates of Inefficiency Variation across Countries This chapter seeks to identify correlates of efficiency variation across countries. Efficiency scores were obtained in the first stage described up to this section. This two-stage approach seeks to identify statistically significant regularities common to efficient or inefficient countries. This exercise does not try to identify supply or demand factors that affect health and education outcomes, such as those described by Filmer (2003). The scope is limited to verifying statistical association between the efficiency scores and environmental variables, as done in Herrera and Pang (2005). IV.1. Method, Variables and Data Description The cross-section consists of many countries (varying from 19 to 69 depending on the output indicator) and a single period, as we collapsed the 2009-2015 information into a period average for each variable. The dependent variable is the input efficiency score calculated by the DEA method in the first stage. Given that the dependent variable (the efficiency score) is continuous and distributed over a limited interval (between zero and one), it is appropriate to use a censored (Tobit) regression model to analyze the relationships with other variables. The input-oriented estimator reflects the consideration that input choices are more under the policy maker’s control. The independent variables reflect environmental effects included in precursor papers, as well as suggested by others recently. We included the following independent variables.22 a. The size of government expenditure. Most of the papers surveyed in the previous section explore the relationship between the size of the government (or expenditure as a percentage of GDP) and efficiency levels. The objective is to verify if additional pubic spending is associated with better education and health outcomes. While some papers have found a negative association between efficiency and expenditure levels (Gupta-Verhoeven 2001, Jarasuriya-Woodon 2003, and Afonso et.al. 2003 Herrera-Pang, 2005),
22 The precise definition and sources can be found in Appendix A, Table A.10.
36
others have found a positive association (Evans et.al. 2003) and others have found no significant impact (Filmer and Pritchett, 1999). b. A government budget composition variable. Given that both education and health are labor-intensive activities, the government’s labor policies will determine the efficiency with which outputs are delivered. We chose a budget composition indicator to reflect this, in particular, the ratio of the wage bill to the total budget. A higher ratio is expected to be negatively correlated with efficiency. c. Per-capita GDP. We included the per-capita GDP to control for the Balassa-Samuleson effect in comparing across countries. If richer countries tend to be more inefficient (given higher wages in these countries), a negative sign is expected. However, it must be recalled that to obtain the efficiency scores in the “first stage” we constructed an auxiliary variable (the orthogonalized public expenditure). Hence the inclusion of this variable in the second stage is an attempt to control for any remaining Balassa- Samuleson effects. d. Urbanization. The clustering of agents makes it cheaper to provide services in urbanized areas rather than in rural. Higher degree of urbanization should reflect in higher efficiency, making positive as the expected sign of the coefficient on this variable. e. Prevalence of HIV/AIDS. Based on WHO mappings of the disease, we included a dummy variable in the most severely affected countries to control for the role of this epidemic in the poor health outcomes. Evans et al. (2000) report that AIDS lowers the disability adjusted life expectancy (DALE) by 15 years or more. AIDS also affects education outcomes both directly and indirectly (Drake, et al. 2003): directly because school-age children are affected: UNAIDS estimates that almost 4 million children have been infected since the epidemic began, and two-thirds have died. However, the indirect channel is relatively more important: AIDS leaves orphaned children who are more likely to drop-out of school or repeat. All these factors reflect how AIDS affects the demand for education. But the supply is also affected by the decreasing teacher labor force due to illness or death, or the need to care for family (Pigozzi, 2004). Prevalence of HIV/AIDS should be negatively associated with education and health outcomes. Consequently, efficiency scores should be negatively associated with the dummy variable. f. Income distribution inequality. Ravallion (2003) argues that, besides the mean income, its distribution affects social indicators because their attainment is mostly determined by the income of the poor. Hence, we controlled for the distribution of income by including the Gini coefficient as an explanatory variable. Higher inequality is expected to be associated with lower educational and health attainments, making negative the expected sign of this variable. g. Share of public sector in the provision of service. Services can be provided by both the public and private sectors, and efficiency indicators will differ across countries depending on the relative productivities of both sectors. Previous studies have included this variable to explain differences in outcomes (Le Grand, 1987; Berger and Messer,
37
2002) or efficiency scores (Greene, 2003a). The specific variable we included was the ratio of publicly financed service over the total spending (sum of private and public spending). h. External aid. To the extent that countries do not have to incur the burden of taxation, they may not have the incentive to use resources in the most cost-effective way. Another channel through which aid-financing may affect efficiency is through the volatility and unpredictability of its flows. Given that this financing source is more volatile than other types of fiscal revenue (Bulir and Hamann, 2000), it is difficult to undertake medium-term planning within activities funded with aid resources. If this is the case, we would expect a negative association between aid-dependence and efficiency in those activities funded with aid, mostly health services. To our knowledge there are no previous attempts to establish a relationship between efficiency and the degree to which activities are financed by external aid. There is, however, recent evidence of a negative association between donor financing and some health outcomes (Bokhari, Gottret, and Gai, 2005). i. Institutional Variables. Countries with better institutions, more transparency, and less corruption are expected to have higher efficiency scores. Similarly, countries that have suffered wars or state failures are expected to register lower efficiency scores. To capture these effects, we included the World Bank Governance Indicators. The data on educational and health indicators are not available on a continuous annual basis for many countries. Thus, averages of the variables were computed over the 2009-2016 period for all variables. IV.2. Results The Tobit estimation on panel data is defined as follows.
),,,,,,
,,,(
CONSINSTEXTAIDGINIAIDSURBANGDPPC
PUBTOTGOVEXPWAGEfVRSTE
itititititit
itititit
where itVRSTE = Variable returns to scale DEA input or output efficiency scores.
itWAGE = Wages and salaries (% of total public expenditure)
itGOVEXP = Total government consumption expenditure (% of GDP)
itPUBTOT = Share of expenditures publicly financed (public/total)
itGDPPC = GDP per capita in constant 1995 US dollars
itURBAN = Urban population (% of total)
itAIDS = Dummy variable for HIV/AIDS
itGINI = Gini Coefficient
itEXTAID = External aid (% of fiscal revenue)
itINST = Institutional indicators WB Governance Indicators.
CONS = Constant
38
Tables 14, 15, and 16 show the results for the single-input single-output education, health and infrastructure scores, with input efficiency scores (a) as dependent variable and output efficiency scores (b), respectively. The findings show:
a. Government expenditure (GOVEXP) is negatively associated with efficiency scores in education (Tables 14 a and b). This result is robust to changes in the output indicator selected. In the output efficiency case, the impact is ambiguous specially when the PISA Math and Science scores are the output indicators (Table 14 b). In health (Tables 15 a and b), the negative association is present in both input and output efficiency. In infrastructure, the expenditure variables (GOVEXP and PUBGFC10PC) are negative in the six output indicators that are used (Table 16a).23 There is a robust trade-off between size of expenditure and efficiency.
b. The wage bill within total expenditure (WAGE) and efficiency is ambiguous in
education; it is positive and significant when the enrollment indicators (Table 14 a) are considered, but negative when the PISA scores are considered (Table 14b). WAGE is insignificant in health and positive in infrastructure.
c. The share of public financing within the total (sum of public and private) is
robustly associated with lower efficiency scores. In the case of education (EDUCPUBTOT) it is negatively associated when input efficiency is considered (Table 14a) and a similar result is obtained in health (HEAPUBTOT, Table 15a). In health, the share of public financing is positively associated with output efficiency, rendering this impact as ambiguous in health. Further research would be needed to explain why this is the case in health services. In infrastructure it is negative (Table 16A).
d. GDP per capita is positively associated with efficiency scores, indicating that efficiency scores are higher in richer countries despite the orthogonalization procedure (Tables 14a, 15a, 16a).
e. Urbanization is negatively associated with efficiency scores in education (Tables 13a and b), while it is positively associated in health. However, scores are unrelated to this variable.
f. The effect of HIV/AIDS is negative on both education and health (Tables 13b and 14b).
g. Income distribution (GINI) is negatively associated with efficiency in education
(table 14a) and health (Table 15b). However, there are cases of sign reversals that
23 The govexp variable is total consumption expenditure while PUBGFC10PC is capital spending per capita. Hence the infrastructure equations include both types of spending.
39
are puzzling, with the primary enrollment output efficiency scores being positively associated with GINI (Table 14b); in Health, GINI is positively associated with input efficiency in Measles Immunization and Maternal Survival (Table 15a) but negatively related with the output efficiency measures (Table 15b).
h. The external aid dependency ratio (EXTAID) is negatively associated with
efficiency in most education indicators, except with PISA output efficiency (Table 14b) where it is positive. In the case of health there is a negative association (Table 15b). Though no causality relationship can be inferred from the exercise, this is one of the results that merit more detailed research. This result might be explained by the volatility of aid as a funding source that limits medium term planning and effective budgeting.
Interpretation of these results requires caution due to several limitations. First, education and health outcomes are explained by multiple supply and demand factors (Filmer, 2003) which are not included here. The omission of one of these factors in the health or education production functions in the previous stage could explain some of the cross-country co-variation of the efficiency results (Ravallion, 2003). The goodness-of-fit analysis of the first stage indicated that no important factor seemed to be omitted. Of course, there can always be additional factors that could be included but the curse of dimensionality24 is particularly pressing in non-parametric statistical methods (even if the data were available). The second limitation derives from the intuitive question why the set of explanatory variables used in the second stage were not included in the first stage. The answer lies in that most of these variables are environmental and outside the control of the decision-making unit. The inclusion of these environmental variables would have had little justification from the production function perspective. Additionally, by maintaining the production function as simple as possible the dimensionality curse is avoided. Finally, the third limitation arises from the fact that if the variables used in the first stage to obtain the efficiency estimator are correlated with the second stage explanatory variables, the coefficients will be inconsistent and biased (Simar and Wilson, 2004; Grosskopf, 1996; Ravallion, 2003). To examine the extent of this potential problem, we calculated correlation coefficients between the “first-stage” inputs and the second-stage explanatory variables. The largest correlation coefficients were between GDP per capita and the teachers per pupil ratio and the literacy rate of adults. To examine the sensitivity of the results to the inclusion of GDP per capita, all the estimations were performed without this variable and none of the results changed.
24 As the number of outputs increases, the number of observations must increase exponentially to maintain a given mean-square error of the estimator. See Simar and Wilson (2000).
40
V. Concluding Remarks and Directions for Future Work The paper presented an application of non-parametric methods to analyze the efficiency of public spending. Based on a sample of more than 140 countries, the paper estimated efficiency scores for 14 education output indicators, seven health output indicators, and seven infrastructure attainment indicators. Our results show that countries could achieve substantially higher education, health, and infrastructure quality levels: on average, developing countries reached output efficiency of about .6 in infrastructure, .8 in education, and .9 in health. That means that, for the same spending levels, peer countries achieve significantly higher outputs, with infrastructure being the area with more room for improvement. On the input side, efficiency is lower. Input efficiency scored .53, .75, and .86, for infrastructure, health, and education, respectively. These results indicate that developing countries deviate more from the frontier on the input (spending) side than on the output dimension. This is just an indicative figure, as the figures vary across countries and with the selected output indicator. It is crucial to identify what are the institutional or economic factors that cause some countries to be more efficient than others in service delivery. In terms of policy implications, it is vital to differentiate between the technically efficient level and the optimal or desired spending level. Even if a country is identified as an “efficient” benchmark country, it may very well still need to expand its public spending levels to achieve a target level of education or health attainment indicators. Such is the case of countries with low spending levels and low attainment indicators, close to the origin of the efficient frontier. The important thing is that countries expand their scale of operation along the efficient frontier. The methods used in the paper can be interpreted as tools to identify extreme cases of efficient countries and inefficient ones. Once the cases have been identified, more in-depth analysis is required to explain departures from the benchmark, as proposed and done by Sen (1981). Given that the methods are based on estimating the frontier directly from observed input-output combinations, they are subject to sampling variability and are sensitive to the presence of outliers. In a “second stage” the paper verified statistical association between the efficiency scores and environmental variables that are not under the control of the decision-making units. The Tobit regressions showed that the variables, which are negatively associated with efficiency scores, include the size of public expenditure, the proportion of the service that is publicly financed, the prevalence of the HIV/AIDS epidemic on health efficiency scores, income inequality on education efficiency scores, and external aid-financing on some of the efficiency scores.
41
Table 14A. Correlates of Cross-Country variation in Education Input efficiency
Note: ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
VARIABLES Net Primary Enrollment
Gross Primary Enrollment
Gross Secondary Enrollment
Net Secondary Enrollment
Average Years of School
Literacy of Youth
First Level Complete
Secondary Level Complete
Math PISA Scores
Science PISA Scores
wage 0.30** 0.35** 0.21** 0.16** 0.12 0.344* 0.12 0.10 -0.037 0.14 govexp -1.502*** -1.534*** -0.619*** -0.733*** -1.172*** 1.043* -1.383*** -0.934*** -1.317 -1.591* educpubtot -0.434 -0.922** -0.968*** -0.630*** -0.24 -1.871*** -0.416 -0.238 -0.717 -0.692 gdppc 8.1e-06* 2.6e-05*** 1.6e-05*** 1.2e-05*** 9.5e-06** -7.8E-06 1.93e-05*** 1.27e-05*** 9.7E-06 8.7E-06 urban -0.002 -0.0035** -0.0001 -0.0012 -0.0025** 0.0056** -0.0041*** -0.0024*** 0.00013 0.0022 aids 0.00491 0.068 0.0238 0.0339 0.0404 0.220*** 0.0554 0.0306 gini -0.0028 7.5E-05 -0.003* -0.003** -0.007*** -0.01*** -0.001 -0.0046*** 0.002 -0.0002 aid 0.000256 0.00428 -0.0203** -0.00687** -0.00738*** -0.00505 -0.00648 -0.00642*** 0.407* 0.362* Constant 0.999*** 0.550** 0.676*** 0.788*** 1.049*** 0.347 0.877*** 0.871*** 0.636 0.482
Observations 56 45 46 57 42 54 53 53 19 19
42
Table 14B. Correlates of Cross-Country variation in Education Output efficiency
Note: ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
VARIABLES Net Primary Enrollment
Gross Primary Enrollment
Net Secondary Enrollment
Gross Secondary Enrollment
Average Years of School
Literacy of Youth
First Level Complete
Second Level Complete
Math PISA Scores
Science PISA Scores
wage ‐0.121 ‐0.0124 ‐0.133 ‐0.0687 ‐0.219 ‐0.19 ‐0.00286 ‐0.304 ‐0.388*** ‐0.333***
govexp ‐0.251 ‐0.633** 0.475 0.610* 0.596* 0.509 ‐0.0435 1.091* 0.609** 0.439*
educpubtot ‐0.184 ‐0.556* 0.0138 ‐0.507 ‐0.216 ‐0.182 ‐0.21 ‐0.534 0.653* 0.331
gdppc 1.91E‐07 3.43E‐06 1.80e‐05*** 1.32e‐05*** 1.22e‐05** 1.12e‐05** ‐1.73E‐07 1.19E‐05 1.96e‐05*** 1.49e‐05***
urban ‐0.00017 ‐0.00188* ‐0.00035 0.000197 0.000425 ‐0.00091 ‐0.00245 0.000623 ‐0.00330** ‐0.00244*
aids ‐0.0890*** ‐0.0644* ‐0.145*** ‐0.173*** ‐0.0867* ‐0.142*** ‐0.0923 ‐0.041
gini 0.00351*** 0.00474*** ‐0.00153 ‐0.00664*** ‐0.00276 0.00415** 0.0066 ‐0.00779** ‐0.00218 ‐0.00058
aid 0.00700** 0.00438 ‐0.00362 ‐0.0340*** ‐0.0068 ‐0.0047 0.00173 ‐0.0103 0.376*** 0.283**
Constant 0.916*** 0.856*** 0.490*** 0.870*** 0.624*** 0.722*** 0.267 0.597*** 0.688*** 0.739***
Observations 58 61 59 48 54 55 54 54 19 19
43
Table 15A. Correlates of Cross-Country variation in HEALTH INPUT efficiency
VARIABLES Life Expectancy
Disability Adjusted Life Expectancy
Immunization DPT
Immunization Measles
Free Tuberculosis
Infant Survival Rate
Maternal Survival Rate
wage 0.0455 0.0684 0.0329 -0.0239 0.0406 -0.0794* -0.0226 govexp -0.436*** -0.421** -0.107 -0.231*** -0.0885 -0.190* -0.209*** heapubtot -0.105 0.106 -0.333 -0.296*** -0.160* -0.213** -0.312*** gdppc 6.50e-06*** 5.60e-06* 5.4E-06 6.44e-06*** 4.75e-06*** 1.14e-05*** 6.26e-06*** urban 0.000567 0.000925 -0.00054 -3.9E-05 0.00186*** 0.000492 9.09E-06 aids 0.0114 -0.00872 -0.0424 0.00163 -0.00517 0.000387 0.000924 gini -0.00053 0.000577 0.00129 0.000763* 0.000273 8.77E-05 0.000801** aid -0.00033 -4.2E-05 -0.0012 -0.00088 -0.00149 -0.00162 -0.00078 Constant 0.458*** 0.449*** 0.473*** 0.415*** 0.300*** 0.356*** 0.407***
Observations 67 67 67 67 62 64 67
Note: ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
44
Table 15B. Correlates of Cross-Country variation in HEALTH OUTPUTefficiency
Note: ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
VARIABLES Life Expectancy
Disability Adjusted Life Expectancy
Immunization DPT
Immunization Measles
Free Tuberculosis
Infant Survival Rate
Maternal Survival Rate
wage 0.0189 0.0814** ‐0.0125 ‐0.08 0.00275 ‐0.0134 ‐0.00143
govexp ‐0.262*** ‐0.402*** 0.352 0.369 ‐0.00890** ‐0.0144 0.000172
heapubtot 0.294*** 0.266** 0.0612 0.29 0.00444 0.0918*** 0.000682
gdppc 9.48E‐07 1.68E‐06 5.11E‐06 5.56E‐06 ‐9.50E‐08 4.97E‐07 1.03E‐08
urban 0.000585 0.00131*** ‐0.00126 ‐0.00091 3.91e‐05** 6.34E‐05 8.60E‐07
aids ‐0.111*** ‐0.0948*** ‐0.0788** ‐0.0689* ‐0.00128* ‐0.0209*** ‐0.00261***
gini ‐0.00158** ‐0.00226*** 0.000412 ‐0.00029 ‐0.000121*** ‐0.00027 ‐4.73E‐06
aid ‐0.00422*** ‐0.00172 0.00246 0.00109 ‐0.0001 ‐0.00165*** ‐0.000342***
Constant 0.912*** 0.892*** 0.883*** 0.859*** 1.003*** 0.982*** 1.000***
Observations 69 69 69 69 63 69 69
45
Table 16A Correlates of cross-country variation in Capital Spending Input efficiency
Note: ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
VARIABLES Quality of overall infrastructure
Quality of roads Quality of railroad infrastructure
Quality of port infrastructure
Quality of air transport infrastructure
Quality of electricity supply
wage 18.55* 19.21* 5.137 25.25** 11.31 16.74**
govexp ‐39.17* ‐39.59 ‐37.47* ‐45.27* ‐26.91 ‐35.98**
pubshare ‐0.183* ‐0.163 ‐0.308*** ‐0.168 ‐0.191* ‐0.235***
pubgfcp10pc ‐0.000353*** ‐0.000419*** ‐0.000202* ‐0.000461*** ‐0.000396*** ‐0.000291***
gdppc10 1.73e‐05** 2.86e‐05*** 9.76E‐06 2.42e‐05*** 1.89e‐05** 1.38e‐05**
urban 0.000526 ‐0.0002 ‐0.00011 0.000439 0.000532 0.000109
gini 0.00218 0.00247 0.00258* 0.00329** 0.00438*** 0.00155
aid 0.00155 0.00197 0.00161 0.00158 0.00285 0.000551
Voice and Accountability ‐0.0191 ‐0.0185 ‐0.0242 ‐0.0228 ‐0.0161 ‐0.00367
Rule of law 0.129** 0.131 0.115* 0.137* 0.149** 0.072
Regulatory Quality ‐0.0137 ‐0.00223 ‐0.0318 ‐0.00663 ‐0.0251 ‐0.0175
Political Stability and Absence of Violence
‐0.0272 ‐0.0296 ‐0.0115 ‐0.0322 ‐0.0311 ‐0.0227
Government Effectiveness
0.00553 0.00565 ‐0.0125 0.0246 0.0378 0.00317
Control of Corruption ‐0.0627 ‐0.0605 ‐0.0463 ‐0.0696 ‐0.109** ‐0.0407
Constant 0.140* 0.142 0.248*** 0.0971 0.054 0.190***
Observations 58 58 53 58 58 58
46
Table 16B. Correlates of cross-country variation in Capital Spending Output efficiency
Note: ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
VARIABLES Quality of overall infrastructure
Quality of roads Quality of railroad infrastructure
Quality of port infrastructure
Quality of air transport infrastructure
Quality of electricity supply
wage 1.797 20.85* ‐42.68** 21.80* 10.26 10.96
govexp 4.265 ‐39.83 49.14 ‐28.22 ‐54.46** 53.28*
pubshare ‐0.291*** ‐0.220* ‐0.412** ‐0.191 ‐0.0434 ‐0.155
pubgfcp10pc 5.01E‐05 4.85E‐05 0.000317 ‐5.75E‐05 ‐0.00017 ‐0.0002
gdppc10 ‐1.82E‐06 5.84E‐06 ‐1.81E‐05 2.70E‐06 1.87E‐06 1.23E‐05
urban 0.000218 ‐0.00131 0.000193 0.000241 0.00111 0.00224**
gini 4.27E‐05 0.00165 ‐0.00014 0.00165 0.000841 ‐0.00282
aid 0.00145 0.0037 ‐0.00112 0.000419 ‐0.00536 ‐0.00082
Voice and Accountability ‐0.100*** ‐0.0914*** ‐0.0708* ‐0.0331 ‐0.0619** ‐0.123***
Rule of law ‐0.0581 ‐0.113 0.0839 0.00519 0.0229 ‐0.126
Regulatory Quality 0.0491 0.019 ‐0.0954* 0.0164 0.113*** 0.0905*
Political Stability and Absence of Violence
0.0222 0.00201 0.0376 ‐0.0162 ‐0.0152 0.0107
Government Effectiveness
0.146** 0.229*** 0.141 0.112 0.135* 0.218**
Control of Corruption 0.056 0.0948 ‐0.0865 ‐0.00461 ‐0.0629 0.085
Constant 0.654*** 0.624*** 0.577*** 0.544*** 0.652*** 0.546***
Observations 63 63 59 63 63 63
47
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51
Appendix A. International Benchmarking Exercise
Table A.1 Efficiency Score for Selected Education Indicators (Single Input - Output)
PISA Math Score PISA Science Score
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
ALB 0.678 0.678 0.738 0.738 0.773 0.688 0.774 0.774
ARG 0.697 0.629 0.789 0.789 0.697 0.650 0.829 0.824
AUS 0.878 0.825 0.942 0.942 0.947 0.910 0.984 0.981
AUT 0.765 0.703 0.928 0.928 0.715 0.710 0.936 0.929
AZE 0.999 0.915 0.886 0.885 0.876 0.876 0.769 0.769
BGR 0.831 0.766 0.824 0.813 0.831 0.780 0.860 0.841
BRA 0.579 0.579 0.713 0.713 0.660 0.582 0.762 0.756
CAN 0.877 0.862 0.974 0.974 1.000 1.000 1.000 1.000
CHE 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
CHL 0.798 0.720 0.788 0.788 0.798 0.754 0.848 0.847
CHN 0.959 0.924 0.993 0.993 0.959 0.918 0.983 0.981
COL 0.633 0.633 0.720 0.720 0.721 0.642 0.774 0.771
CRI 0.530 0.530 0.748 0.748 0.604 0.547 0.794 0.783
CYP 0.548 0.507 0.817 0.817 0.548 0.506 0.819 0.802
CZE 1.000 0.973 1.000 0.981 1.000 1.000 1.000 1.000
DEU 0.973 0.927 0.966 0.961 1.000 0.989 1.000 0.996
DNK 0.420 0.398 0.948 0.948 0.420 0.400 0.923 0.923
DOM 0.745 0.745 0.621 0.615 0.745 0.745 0.644 0.636
ESP 0.870 0.868 0.918 0.914 0.910 0.889 0.959 0.949
FIN 0.567 0.565 0.983 0.983 1.000 1.000 1.000 1.000
FRA 0.768 0.704 0.925 0.925 0.768 0.719 0.940 0.933
GBR 0.706 0.686 0.920 0.920 0.776 0.756 0.968 0.961
GEO 0.699 0.699 0.755 0.755 0.797 0.712 0.780 0.779
HRV 0.813 0.783 0.864 0.864 0.813 0.808 0.912 0.911
HUN 0.798 0.794 0.903 0.903 0.834 0.814 0.930 0.928
IDN 0.679 0.679 0.708 0.708 0.679 0.679 0.744 0.743
ISL 0.512 0.472 0.930 0.930 0.458 0.458 0.894 0.894
ITA 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
KAZ 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
KGZ 0.571 0.571 0.619 0.619 0.571 0.571 0.625 0.618
KOR 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
LBN 0.913 0.913 0.978 0.860 0.913 0.913 0.966 0.844
LTU 0.772 0.762 0.893 0.893 0.772 0.770 0.915 0.914
LVA 0.665 0.661 0.901 0.901 0.696 0.684 0.931 0.923
MDA 0.614 0.552 0.784 0.784 0.614 0.564 0.810 0.799
MEX 0.707 0.629 0.773 0.773 0.707 0.636 0.787 0.783
52
Table A.1 (continued)
PISA Math Score PISA Science Score
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
MKD 0.653 0.653 0.694 0.694 0.653 0.653 0.726 0.724
NLD 0.789 0.772 0.970 0.970 0.851 0.805 0.975 0.970
NOR 0.482 0.448 0.934 0.934 0.482 0.457 0.921 0.921
NZL 0.607 0.575 0.948 0.948 0.655 0.642 0.989 0.968
PAN 0.855 0.855 0.740 0.727 0.855 0.855 0.776 0.765
PER 0.704 0.704 0.702 0.702 0.704 0.704 0.727 0.725
POL 0.855 0.794 0.934 0.934 0.855 0.830 0.955 0.954
ROM 0.955 0.882 0.884 0.866 0.955 0.881 0.869 0.869
RUS 0.915 0.907 0.976 0.927 0.915 0.912 0.972 0.953
SVK 0.946 0.945 0.987 0.960 0.946 0.933 0.958 0.953
SVN 0.764 0.720 0.945 0.945 0.785 0.768 0.970 0.963
SWE 0.524 0.479 0.923 0.923 0.490 0.486 0.911 0.911
THA 0.781 0.700 0.780 0.780 0.781 0.711 0.801 0.801
TTO 0.715 0.639 0.777 0.777 0.715 0.645 0.790 0.786
TUN 0.556 0.556 0.689 0.689 0.556 0.556 0.745 0.737
TUR 0.782 0.719 0.809 0.809 0.782 0.731 0.832 0.832
URY 0.716 0.647 0.790 0.790 0.716 0.660 0.816 0.812
USA 0.805 0.795 0.894 0.894 0.900 0.852 0.947 0.946
VNM 0.756 0.692 0.924 0.924 0.815 0.807 0.993 0.985
53
Table A.2 Efficiency Score for Selected Education Indicators (Single Input - Output)
School enrollment, primary (% gross) Secondary Education Gross
Enrollment Input Efficiency Output Efficiency Input Efficiency Output Efficiency
Country FDH DEA FDH DEA FDH DEA FDH DEA
AGO 0.985 0.715 0.991 0.840 0.613 0.613 0.170 0.170 ALB 0.645 0.645 0.926 0.776 0.651 0.651 0.639 0.588 ARG 0.910 0.617 0.778 0.778 0.571 0.571 0.644 0.644 ARM 0.642 0.642 0.883 0.738 0.647 0.647 0.740 0.677 ATG 0.944 0.944 0.913 0.890 AUS 0.614 0.614 0.887 0.757 1.000 1.000 1.000 1.000 AUT 0.526 0.526 0.690 0.690 0.648 0.549 0.708 0.708 AZE 0.865 0.865 0.909 0.851 0.867 0.867 0.992 0.892 BDI 0.966 0.776 0.886 0.886 0.550 0.550 0.172 0.172 BEN 0.964 0.696 0.831 0.831 0.559 0.559 0.295 0.295 BFA 0.554 0.554 0.566 0.566 0.559 0.559 0.156 0.156 BGD 0.877 0.613 0.920 0.780 0.596 0.596 0.347 0.347 BGR 0.695 0.695 0.920 0.771 0.701 0.701 0.740 0.721 BLR 0.584 0.584 0.836 0.704 BLZ 0.772 0.555 0.768 0.768 0.527 0.527 0.540 0.540 BOL 0.513 0.513 0.690 0.690 0.519 0.519 0.575 0.575 BRA 0.928 0.671 0.831 0.831 0.756 0.571 0.726 0.726 BRB 0.529 0.529 0.670 0.670 0.750 0.577 0.736 0.736 BWA 0.413 0.413 0.737 0.737 0.421 0.421 0.576 0.576 CAF 0.560 0.560 0.626 0.626 CAN 0.614 0.614 0.835 0.712 0.875 0.663 0.728 0.728 CHE 0.687 0.687 0.943 0.786 0.703 0.703 0.764 0.747 CHL 0.655 0.655 0.900 0.760 0.662 0.662 0.718 0.669 CHN 0.666 0.666 0.960 0.819 0.672 0.672 0.654 0.617 CIV 0.557 0.557 0.580 0.580 0.563 0.563 0.199 0.199
CMR 0.856 0.580 0.907 0.758 0.582 0.582 0.304 0.304 COG 0.791 0.564 0.765 0.765 COL 0.994 0.717 0.988 0.839 0.600 0.600 0.663 0.663 COM 0.551 0.551 0.717 0.717 CPV 0.822 0.588 0.767 0.767 0.560 0.560 0.609 0.609 CRI 0.782 0.529 0.777 0.777 0.592 0.493 0.700 0.700 CYP 0.422 0.422 0.689 0.689 0.431 0.431 0.688 0.688 CZE 0.793 0.793 0.926 0.831 0.801 0.801 0.940 0.816 DEU 0.688 0.688 0.948 0.791 0.979 0.740 0.814 0.794 DJI 0.563 0.563 0.449 0.449
DNK 0.278 0.278 0.689 0.689 0.400 0.377 0.859 0.859 DOM 0.720 0.720 0.958 0.818 0.724 0.724 0.759 0.610
54
Table A.2 (continued) School enrollment, primary (% gross) Secondary Education Gross Enrollment
Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA
ECU 0.935 0.644 0.950 0.796 0.585 0.585 0.585 0.585 EGY 0.636 0.636 0.927 0.771 0.641 0.641 0.645 0.586 ESP 0.706 0.706 0.963 0.814 1.000 0.989 1.000 0.991 EST 0.585 0.585 0.837 0.706 0.830 0.640 0.737 0.737 ETH 0.551 0.551 0.657 0.657 0.557 0.557 0.234 0.234 FIN 0.384 0.384 0.685 0.685 0.551 0.456 0.778 0.778 FJI 0.600 0.600 0.885 0.745
FRA 0.536 0.536 0.731 0.731 0.764 0.658 0.801 0.801 GAB 0.805 0.805 0.533 0.465 GBR 0.525 0.525 0.731 0.731 0.646 0.546 0.707 0.707 GEO 1.000 0.736 1.000 0.858 0.678 0.678 0.741 0.704 GHA 0.532 0.532 0.736 0.736 0.538 0.538 0.421 0.421 GIN 0.558 0.558 0.597 0.597 0.564 0.564 0.280 0.280
GMB 0.560 0.560 0.586 0.586 0.565 0.565 0.380 0.380 GNB 0.844 0.620 0.922 0.780 GTM 0.943 0.651 0.971 0.808 0.640 0.640 0.483 0.438 GUY 0.616 0.616 0.721 0.616 0.748 0.639 0.712 0.712 HND 0.791 0.575 0.772 0.772 0.539 0.539 0.494 0.494 HRV 0.670 0.670 0.839 0.718 0.677 0.677 0.764 0.725 HTI 0.576 0.576 0.317 0.317
HUN 0.651 0.651 0.890 0.750 0.794 0.671 0.792 0.736 IDN 0.649 0.649 0.945 0.794 0.654 0.654 0.629 0.581 IND 0.592 0.592 0.904 0.767 0.598 0.598 0.444 0.444 IRN 0.752 0.752 0.993 0.868 0.757 0.757 0.851 0.708 ISL 0.344 0.344 0.675 0.675 0.494 0.412 0.782 0.782 ITA 0.821 0.821 0.930 0.849 1.000 0.860 1.000 0.894 JAM 0.533 0.533 0.636 0.636 KAZ 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 KEN 0.812 0.592 0.773 0.773 0.552 0.552 0.426 0.426 KGZ 0.536 0.536 0.700 0.700 0.542 0.542 0.616 0.616 KHM 1.000 0.740 1.000 0.853 0.602 0.602 0.308 0.308 KNA 0.971 0.971 0.806 0.796 KOR 0.668 0.668 0.884 0.756 0.678 0.678 0.779 0.740 LAO 1.000 0.739 1.000 0.854 0.621 0.621 0.340 0.340 LBN 0.913 0.913 0.909 0.872 0.913 0.913 0.814 0.761 LKA 0.757 0.757 0.913 0.800 0.760 0.760 0.925 0.772 LSO 0.521 0.521 0.744 0.744 0.527 0.527 0.330 0.330 LTU 0.626 0.626 0.886 0.731 0.888 0.662 0.806 0.727 LVA 0.532 0.532 0.704 0.704 0.541 0.541 0.694 0.694
55
Table A.2 (continued) School enrollment, primary (% gross) Secondary Education Gross Enrollment
Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA
MAR 0.914 0.623 0.927 0.781 0.571 0.571 0.440 0.440 MDA 0.500 0.500 0.638 0.638 0.507 0.507 0.628 0.628 MDG 1.000 1.000 1.000 1.000 0.569 0.569 0.231 0.231 MEX 0.576 0.576 0.859 0.718 0.583 0.583 0.631 0.631 MKD 0.616 0.616 0.744 0.635 0.623 0.623 0.596 0.596 MLI 0.562 0.562 0.545 0.545 0.567 0.567 0.278 0.278
MNG 0.916 0.664 0.969 0.812 0.623 0.623 0.669 0.669 MOZ 0.543 0.543 0.723 0.723 0.548 0.548 0.172 0.172 MRT 0.585 0.585 0.803 0.677 0.590 0.590 0.185 0.185 MUS 0.699 0.699 0.941 0.792 0.705 0.705 0.718 0.704 MWI 0.975 0.908 0.960 0.960 0.555 0.555 0.229 0.229 MYS 0.553 0.553 0.693 0.693 0.562 0.562 0.491 0.491 NAM 0.441 0.441 0.746 0.746 0.448 0.448 0.457 0.457 NER 0.549 0.549 0.461 0.461 NGA 0.643 0.643 0.783 0.655 0.647 0.647 0.307 0.281 NIC 1.000 0.742 1.000 0.851 0.580 0.580 0.492 0.492 NLD 0.543 0.543 0.731 0.731 0.776 0.755 0.881 0.881 NOR 0.315 0.315 0.681 0.681 0.454 0.388 0.795 0.795 NPL 0.997 0.916 0.953 0.953 0.567 0.567 0.363 0.363 NZL 0.417 0.417 0.680 0.680 0.596 0.556 0.852 0.852 OMN 0.751 0.751 0.985 0.860 0.764 0.764 0.941 0.788 PAK 0.612 0.612 0.780 0.664 0.617 0.617 0.247 0.247 PAN 0.836 0.836 0.968 0.891 0.839 0.839 0.758 0.665 PER 0.675 0.675 0.963 0.795 0.680 0.680 0.735 0.699 PHL 0.955 0.691 0.992 0.831 0.648 0.648 0.671 0.615 POL 0.620 0.620 0.878 0.720 0.757 0.634 0.787 0.704 PRY 0.586 0.586 0.863 0.728 0.592 0.592 0.482 0.482 ROM 0.813 0.813 0.872 0.793 0.818 0.818 0.933 0.824 RUS 0.762 0.762 0.916 0.806 0.769 0.769 0.885 0.746 RWA 0.979 0.894 0.949 0.949 0.557 0.557 0.220 0.220 SAU 0.458 0.458 0.706 0.706 0.657 0.509 0.740 0.740 SDN 0.613 0.613 0.585 0.498 SEN 0.537 0.537 0.557 0.557 0.543 0.543 0.253 0.253 SLB 0.815 0.559 0.782 0.782 SLE 1.000 0.782 1.000 0.873 0.569 0.569 0.239 0.239 SLV 1.000 0.712 1.000 0.840 0.624 0.624 0.473 0.473 SVK 0.788 0.788 0.930 0.832 0.795 0.795 0.922 0.797 SVN 0.541 0.541 0.674 0.674 0.550 0.550 0.690 0.690 SWE 0.522 0.355 0.750 0.750 0.505 0.376 0.719 0.719
56
Table A.2 (continued) School enrollment, primary (% gross) Secondary Education Gross Enrollment
Input Efficiency Output Efficiency Input Efficiency Output Efficiency Country FDH DEA FDH DEA FDH DEA FDH DEA
SWZ 0.765 0.562 0.776 0.776 0.522 0.522 0.411 0.411 TCD 0.575 0.575 0.745 0.622 0.580 0.580 0.161 0.161 TGO 0.977 0.747 0.863 0.863 THA 0.648 0.648 0.869 0.731 0.655 0.655 0.647 0.598 TJK 0.560 0.560 0.675 0.675 0.565 0.565 0.611 0.611
TKM 0.711 0.711 0.818 0.694 TTO 0.566 0.566 0.863 0.728 0.577 0.577 0.627 0.627 TUN 0.763 0.519 0.750 0.750 0.521 0.521 0.649 0.649 TUR 0.641 0.641 0.900 0.752 0.649 0.649 0.659 0.604 TZA 0.562 0.562 0.622 0.622 0.568 0.568 0.214 0.214 UGA 0.918 0.642 0.937 0.793 0.574 0.574 0.190 0.190 UKR 0.510 0.510 0.715 0.715 0.517 0.517 0.682 0.682 URY 0.863 0.601 0.919 0.771 0.589 0.589 0.646 0.646 USA 0.620 0.620 0.881 0.723 0.634 0.634 0.757 0.681 VCT 0.552 0.552 0.713 0.713 VEN 0.591 0.591 0.840 0.712 0.599 0.599 0.600 0.600 VNM 0.558 0.558 0.728 0.728 0.564 0.564 0.515 0.515 VUT 0.923 0.673 0.819 0.819 ZAF 0.527 0.527 0.666 0.666 0.643 0.536 0.700 0.700 ZAR 0.557 0.557 0.683 0.683 ZWE 0.533 0.533 0.691 0.691 0.539 0.539 0.300 0.300
57
Table A.3 Efficiency Score for Selected Education Indicators (Two Inputs – Single Output)
Input (Public Expenditure‐ Adult Literacy Rate)
Primary Net Enrollment Secondary Net Enrollment
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
AGO 0.962 0.847 0.873 0.824 0.963 0.838 0.545 0.306
ALB 0.869 0.798 0.941 0.937 0.940 0.833 0.933 0.766
AZE 1.000 0.942 1.000 0.970
BDI 0.947 0.820 0.931 0.926 0.904 0.792 0.477 0.346
BEN 0.984 0.964 0.959 0.958 1.000 1.000 1.000 1.000
BFA 0.951 0.910 0.660 0.660 0.973 0.910 0.585 0.478
BGD 1.000 0.948 1.000 0.917 1.000 0.957 1.000 0.839
BGR 0.904 0.845 0.965 0.962 0.927 0.854 0.961 0.794
BLR 0.816 0.679 0.930 0.930 0.983 0.845 0.840 0.840
BOL 0.757 0.656 0.906 0.904 0.911 0.731 0.851 0.692
BRA 0.740 0.654 0.941 0.938 1.000 0.811 1.000 0.822
CAF 0.975 0.921 0.696 0.695 0.974 0.918 0.361 0.284
CHL 0.868 0.750 0.944 0.940 0.938 0.832 0.976 0.767
CHN 1.000 1.000 1.000 1.000 0.928 0.825 0.913 0.753
CIV 0.947 0.875 0.709 0.708 0.969 0.894 0.722 0.655
CMR 0.923 0.815 0.954 0.899 0.964 0.801 0.746 0.533
COG 0.804 0.719 0.917 0.909 0.874 0.710 0.685 0.513
COL 0.877 0.719 0.925 0.922 1.000 0.861 1.000 0.817
COM 0.957 0.861 0.826 0.823 1.000 0.908 1.000 0.833
CPV 0.856 0.766 0.973 0.971 1.000 0.833 1.000 0.790
CRI 0.727 0.623 0.980 0.976 1.000 0.850 1.000 0.868
CYP 0.551 0.504 0.982 0.982 0.923 0.717 0.756 0.756
DOM 1.000 0.848 1.000 0.878 0.999 0.862 0.898 0.731
ECU 0.873 0.742 0.952 0.949 0.995 0.859 1.000 0.820
EGY 1.000 0.904 1.000 0.980 1.000 0.900 1.000 0.848
ESP 1.000 0.867 1.000 0.997 1.000 1.000 1.000 1.000
EST 0.771 0.677 0.963 0.963 0.980 0.828 0.847 0.847
GEO 0.953 0.952 1.000 0.998 0.916 0.873 0.984 0.828
GHA 0.816 0.742 0.858 0.852 0.914 0.750 0.848 0.592
GIN 1.000 0.958 1.000 0.799 1.000 0.992 1.000 0.856
GMB 0.965 0.890 0.704 0.702 1.000 0.963 1.000 0.928
GNB 0.989 0.890 0.965 0.691
GTM 1.000 0.841 1.000 0.920 1.000 0.835 1.000 0.642
GUY 0.961 0.780 0.816 0.814 1.000 0.883 1.000 0.829
HND 0.857 0.732 0.961 0.960 0.857 0.725 0.796 0.626
HRV 0.851 0.728 0.880 0.880 0.997 0.850 0.976 0.799
58
Table A.3 (continued)
Input (Public Expenditure‐ Adult Literacy Rate)
Primary Net Enrollment Secondary Net Enrollment
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
IDN 0.898 0.797 0.924 0.921 0.898 0.803 0.812 0.694
IND 0.939 0.836 0.975 0.919 1.000 0.854 1.000 0.742
IRN 1.000 1.000 1.000 1.000 1.000 0.917 1.000 0.876
ITA 0.891 0.854 0.977 0.977 1.000 0.891 1.000 0.850
KAZ 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
KEN 0.855 0.741 0.851 0.843 0.910 0.746 0.759 0.572
KGZ 0.812 0.673 0.883 0.883 0.860 0.747 0.691 0.691
KHM 0.997 0.871 0.982 0.962
LAO 1.000 0.926 1.000 0.945 1.000 0.903 1.000 0.673
LBN 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.739
LKA 1.000 0.993 1.000 0.995 1.000 0.983 1.000 0.974
LSO 0.798 0.709 0.807 0.801 0.835 0.713 0.647 0.501
LTU 0.845 0.733 0.971 0.971 0.981 0.832 0.811 0.811
LVA 0.737 0.649 0.974 0.974 0.980 0.789 0.827 0.827
MAR 0.951 0.824 0.973 0.967 1.000 0.829 1.000 0.724
MDA 0.742 0.629 0.878 0.878 0.861 0.715 0.688 0.688
MDG 0.905 0.795 0.662 0.385
MEX 0.819 0.709 0.958 0.954 0.898 0.751 0.851 0.694
MLI 0.968 0.933 0.621 0.621 0.995 0.972 0.895 0.768
MNG 0.858 0.796 0.966 0.966 0.928 0.819 0.947 0.749
MOZ 0.931 0.851 0.878 0.875 0.931 0.827 0.461 0.375
MUS 0.921 0.863 0.967 0.964 0.996 0.880 0.937 0.827
MWI 0.966 0.858 0.989 0.984 0.886 0.794 0.581 0.415
MYS 0.802 0.681 0.983 0.980 0.791 0.658 0.713 0.577
NAM 0.632 0.568 0.879 0.877
NER 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.639
NPL 0.987 0.880 0.988 0.982 1.000 0.866 1.000 0.750
PAK 1.000 0.898 1.000 0.734 1.000 0.898 1.000 0.500
PAN 1.000 1.000 1.000 1.000 1.000 0.906 1.000 0.723
PER 0.921 0.848 0.948 0.945 0.971 0.887 0.962 0.838
PHL 0.908 0.824 0.940 0.937 0.946 0.816 0.873 0.736
PRY 0.882 0.723 0.895 0.891 0.894 0.729 0.715 0.572
ROM 0.954 0.854 0.918 0.906 0.982 0.916 0.987 0.879
RUS 0.915 0.852 0.962 0.959 0.915 0.861 0.973 0.812
RWA 0.967 0.835 0.979 0.973 0.876 0.781 0.573 0.388
SAU 0.547 0.488 0.933 0.930 1.000 0.817 1.000 0.840
59
Table A.3 (continued)
Input (Public Expenditure‐ Adult Literacy Rate)
Primary Net Enrollment Secondary Net Enrollment
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
FDH DEA FDH DEA FDH DEA FDH DEA
SEN 0.902 0.820 0.716 0.714 0.924 0.830 0.718 0.591
SLE 1.000 1.000 1.000 1.000 1.000 0.997 1.000 0.863
SLV 0.983 0.816 0.944 0.943 0.983 0.811 0.854 0.703
SWZ 0.752 0.663 0.811 0.803 0.834 0.679 0.759 0.546
TCD 1.000 1.000 1.000 0.854 1.000 0.992 1.000 0.580
TGO 0.965 0.835 0.947 0.942 0.981 0.828 0.875 0.646
THA 0.894 0.782 0.938 0.935 0.967 0.871 0.986 0.818
TUN 1.000 0.721 1.000 0.993 1.000 0.820 1.000 0.843
TUR 0.896 0.754 0.951 0.948 0.969 0.816 0.929 0.745
TZA 0.894 0.777 0.847 0.841 0.895 0.767 0.409 0.322
UGA 0.914 0.814 0.990 0.933 0.914 0.788 0.342 0.239
UKR 0.749 0.660 0.961 0.961 0.912 0.755 0.755 0.755
URY 0.857 0.725 0.983 0.983 0.927 0.785 0.751 0.751
VNM 0.902 0.778 0.989 0.986
ZAF 0.975 0.767 0.935 0.754
ZAR 0.895 0.766 0.516 0.405
ZWE 0.830 0.710 0.879 0.877 0.832 0.697 0.523 0.413
60
Table A.4 Efficiency Score for Selected Health Indicators (Single Inputs – Output)
Disability Adjusted Life Expectancy Immunization, DTP
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
AGO 0.504 0.504 0.76 0.746 0.439 0.439 0.704 0.704
ALB 0.527 0.527 0.954 0.94 0.775 0.638 0.997 0.997
ARG 0.551 0.551 0.951 0.94 0.495 0.495 0.944 0.941
ARM 0.521 0.521 0.927 0.913 0.454 0.454 0.951 0.951
ATG 0.844 0.594 0.96 0.952 0.826 0.68 1 0.997
AUS 1 1 1 1 0.415 0.415 0.929 0.929
AUT 0.768 0.653 0.98 0.98 0.31 0.31 0.918 0.918
AZE 0.619 0.619 0.875 0.874 0.565 0.565 0.899 0.897
BDI 0.472 0.472 0.7 0.7 0.404 0.404 0.962 0.962
BEN 0.481 0.481 0.777 0.759 0.413 0.413 0.789 0.789
BFA 0.476 0.476 0.711 0.711 0.409 0.409 0.915 0.915
BGD 0.491 0.491 0.882 0.863 0.424 0.424 0.968 0.968
BGR 0.529 0.529 0.924 0.911 0.463 0.463 0.941 0.941
BHR 0.897 0.897 0.984 0.975 0.881 0.881 1 0.999
BHS 0.586 0.586 0.921 0.916 0.523 0.523 0.983 0.98
BLR 0.529 0.529 0.893 0.88 0.472 0.472 0.987 0.987
BLZ 0.503 0.503 0.888 0.871 0.433 0.433 0.967 0.967
BOL 0.492 0.492 0.899 0.88 0.423 0.423 0.957 0.957
BRA 0.528 0.528 0.928 0.915 0.465 0.465 0.978 0.978
BRB 0.519 0.519 0.955 0.94 0.448 0.448 0.922 0.922
BWA 0.531 0.531 0.717 0.707 0.467 0.467 0.961 0.961
CAF 0.475 0.475 0.583 0.582 0.407 0.407 0.43 0.43
CAN 0.849 0.771 0.986 0.986 0.343 0.343 0.916 0.916
CHE 1 1 1 1 0.34 0.34 0.968 0.968
CHL 0.86 0.857 0.995 0.988 0.51 0.51 0.944 0.941
CHN 0.534 0.534 0.933 0.921 0.973 0.973 1 1
CIV 0.49 0.49 0.712 0.696 0.421 0.421 0.792 0.792
CMR 0.491 0.491 0.722 0.707 0.423 0.423 0.853 0.853
COG 0.501 0.501 0.752 0.737 0.431 0.431 0.828 0.828
COL 0.732 0.515 0.96 0.94 0.425 0.425 0.906 0.906
COM 0.478 0.478 0.826 0.807 0.411 0.411 0.853 0.853
CPV 0.495 0.495 0.906 0.888 0.429 0.429 0.957 0.957
CRI 0.973 0.777 0.98 0.979 0.394 0.394 0.906 0.906
CYP 1 1 1 1 1 0.823 1 0.999
CZE 0.706 0.578 0.95 0.95 0.42 0.414 0.993 0.993
DEU 0.776 0.612 0.974 0.974 0.311 0.311 0.961 0.961
DJI 0.473 0.473 0.785 0.785 0.406 0.406 0.85 0.85
61
Table A.4 (continued)
Disability Adjusted Life Expectancy Immunization, DTP
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
DMA 0.512 0.512 0.915 0.899 0.442 0.442 0.986 0.986
DNK 0.532 0.496 0.967 0.967 0.278 0.278 0.931 0.931
DOM 0.546 0.546 0.933 0.922 0.477 0.477 0.863 0.863
DZA 0.773 0.527 0.957 0.942 0.444 0.444 0.96 0.96
ECU 0.784 0.558 0.961 0.947 0.454 0.454 0.877 0.877
EGY 0.537 0.537 0.89 0.879 0.472 0.472 0.962 0.962
ERI 0.48 0.48 0.778 0.76 0.412 0.412 0.945 0.945
ESP 1 0.943 1 0.998 0.386 0.386 0.977 0.977
EST 0.536 0.536 0.943 0.93 0.461 0.461 0.947 0.947
ETH 0.476 0.476 0.749 0.749 0.408 0.408 0.691 0.691
FIN 0.917 0.752 0.982 0.98 0.384 0.382 0.994 0.994
FJI 0.512 0.512 0.814 0.8 0.927 0.927 1 1
FRA 0.768 0.73 0.99 0.99 0.318 0.318 0.996 0.996
GAB 0.598 0.598 0.794 0.791 0.521 0.521 0.766 0.764
GBR 0.853 0.665 0.973 0.973 0.344 0.344 0.957 0.957
GEO 0.526 0.526 0.915 0.902 0.46 0.46 0.929 0.929
GHA 0.485 0.485 0.791 0.773 0.419 0.419 0.934 0.934
GIN 0.478 0.478 0.732 0.715 0.409 0.409 0.597 0.597
GMB 0.476 0.476 0.805 0.805 0.408 0.408 0.98 0.98
GNB 0.48 0.48 0.704 0.687 0.412 0.412 0.861 0.861
GRC 0.981 0.798 0.982 0.981 0.85 0.85 1 1
GRD 0.534 0.534 0.892 0.88 0.466 0.466 0.973 0.973
GTM 0.513 0.513 0.894 0.879 0.446 0.446 0.869 0.869
GUY 0.49 0.49 0.83 0.812 0.425 0.425 0.973 0.973
HND 0.483 0.483 0.897 0.877 0.415 0.415 0.98 0.98
HRV 0.46 0.46 0.932 0.931 0.399 0.399 0.967 0.967
HTI 0.481 0.481 0.765 0.747 0.413 0.413 0.638 0.638
HUN 0.515 0.515 0.933 0.917 0.953 0.953 1 1
IDN 0.548 0.548 0.878 0.868 0.484 0.484 0.816 0.814
IND 0.507 0.507 0.832 0.817 0.44 0.44 0.825 0.825
IRN 0.574 0.574 0.931 0.924 0.854 0.703 1 0.998
ISL 0.878 0.869 0.999 0.995 0.37 0.37 0.937 0.937
ITA 0.899 0.879 0.998 0.994 0.373 0.373 0.965 0.965
JAM 0.513 0.513 0.936 0.92 0.444 0.444 0.935 0.935
JOR 0.478 0.478 0.938 0.916 0.422 0.414 0.991 0.991
KAZ 0.632 0.632 0.86 0.856 0.576 0.576 0.993 0.991
KEN 0.485 0.485 0.784 0.766 0.416 0.416 0.918 0.918
KGZ 0.481 0.481 0.861 0.842 0.413 0.413 0.971 0.971
KHM 0.491 0.491 0.829 0.812 0.423 0.423 0.89 0.89
62
Table A.4 (continued)
Disability Adjusted Life Expectancy Immunization, DTP
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
FDH DEA FDH DEA FDH DEA FDH DEA
KNA 0.59 0.59 0.973 0.971
KOR 1 0.99 1 0.999 0.561 0.561 0.987 0.985
LAO 0.505 0.505 0.802 0.787 0.439 0.439 0.811 0.811
LBN 0.803 0.757 0.988 0.976 0.485 0.485 0.821 0.818
LCA 0.514 0.514 0.942 0.926 0.444 0.444 0.99 0.99
LKA 0.541 0.541 0.948 0.937 0.802 0.66 0.997 0.997
LSO 0.467 0.467 0.571 0.571 0.396 0.396 0.944 0.944
LTU 0.536 0.536 0.915 0.902 0.473 0.473 0.948 0.948
LUX 0.962 0.888 0.992 0.991 0.897 0.897 1 1
LVA 0.554 0.554 0.91 0.901 0.498 0.498 0.941 0.938
MAR 0.515 0.515 0.922 0.907 0.933 0.933 1 1
MDA 0.476 0.476 0.862 0.862 0.409 0.409 0.905 0.905
MDG 0.478 0.478 0.77 0.752 0.41 0.41 0.73 0.73
MEX 0.56 0.56 0.95 0.941 0.49 0.49 0.931 0.928
MKD 0.504 0.504 0.925 0.908 0.441 0.441 0.961 0.961
MLI 0.48 0.48 0.744 0.726 0.413 0.413 0.698 0.698
MNG 0.525 0.525 0.828 0.815 0.463 0.463 0.988 0.988
MOZ 0.475 0.475 0.688 0.688 0.407 0.407 0.775 0.775
MRT 0.495 0.495 0.853 0.836 0.427 0.427 0.75 0.75
MUS 0.592 0.592 0.92 0.915 0.528 0.528 0.993 0.991
MWI 0.47 0.47 0.663 0.663 0.402 0.402 0.934 0.934
MYS 0.655 0.655 0.94 0.938 0.596 0.596 0.983 0.981
NAM 0.494 0.494 0.733 0.718 0.423 0.423 0.867 0.867
NER 0.474 0.474 0.72 0.72 0.407 0.407 0.703 0.703
NGA 0.511 0.511 0.766 0.753 0.446 0.446 0.506 0.506
NIC 0.718 0.571 0.971 0.949 0.415 0.415 0.99 0.99
NLD 0.711 0.609 0.981 0.981 0.28 0.28 0.975 0.975
NOR 0.759 0.697 0.987 0.987 0.305 0.305 0.949 0.949
NPL 0.481 0.481 0.859 0.839 0.414 0.414 0.906 0.906
NZL 0.782 0.671 0.981 0.981 0.305 0.305 0.938 0.938
OMN 1 1 1 1 1 1 1 1
PAK 0.507 0.507 0.823 0.808 0.439 0.439 0.743 0.743
PAN 0.746 0.638 0.978 0.959 0.43 0.43 0.843 0.843
PER 0.785 0.709 0.983 0.969 0.462 0.462 0.921 0.921
PHL 0.515 0.515 0.865 0.85 0.448 0.448 0.804 0.804
PNG 0.478 0.478 0.741 0.724 0.411 0.411 0.737 0.737
POL 0.788 0.546 0.958 0.945 0.786 0.647 0.997 0.997
PRY 0.501 0.501 0.929 0.911 0.429 0.429 0.889 0.889
ROM 0.528 0.528 0.926 0.912 0.462 0.462 0.929 0.929
63
Table A.4 (continued)
Disability Adjusted Life Expectancy Immunization, DTP
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
FDH DEA FDH DEA FDH DEA FDH DEA
RUS 0.577 0.577 0.861 0.855 0.515 0.515 0.984 0.982
RWA 0.477 0.477 0.778 0.778 0.41 0.41 0.986 0.986
SAU 0.99 0.99 0.988 0.988 1 1 1 1
SDN 0.494 0.494 0.835 0.818 0.426 0.426 0.918 0.918
SEN 0.482 0.482 0.803 0.785 0.415 0.415 0.906 0.906
SLB 0.472 0.472 0.758 0.757 0.405 0.405 0.952 0.952
SLE 0.478 0.478 0.701 0.684 0.411 0.411 0.882 0.882
SLV 0.493 0.493 0.932 0.912 0.425 0.425 0.921 0.921
SVK 0.497 0.497 0.947 0.928 0.442 0.433 0.991 0.991
SVN 0.678 0.665 0.969 0.968 0.392 0.392 0.965 0.965
SWE 0.742 0.696 0.989 0.989 0.284 0.284 0.99 0.99
SWZ 0.473 0.473 0.613 0.613 0.403 0.403 0.937 0.937
TCD 0.484 0.484 0.712 0.696 0.416 0.416 0.372 0.372
TGO 0.478 0.478 0.748 0.73 0.41 0.41 0.85 0.85
THA 0.546 0.546 0.952 0.941 1 1 1 1
TJK 0.486 0.486 0.874 0.854 0.418 0.418 0.96 0.96
TKM 0.57 0.57 0.851 0.844 0.512 0.512 0.986 0.983
TON 0.486 0.486 0.876 0.856 0.422 0.422 0.815 0.815
TTO 0.697 0.697 0.946 0.912 0.631 0.631 0.93 0.928
TUN 0.759 0.542 0.961 0.944 0.441 0.441 0.99 0.99
TUR 0.799 0.686 0.978 0.966 0.475 0.475 0.978 0.978
TZA 0.482 0.482 0.752 0.735 0.415 0.415 0.929 0.929
UGA 0.479 0.479 0.725 0.708 0.412 0.412 0.798 0.798
UKR 0.496 0.496 0.875 0.857 0.43 0.43 0.535 0.535
URY 0.722 0.498 0.958 0.937 0.422 0.422 0.958 0.958
USA 0.562 0.494 0.952 0.952 0.316 0.316 0.958 0.958
UZB 0.495 0.495 0.859 0.841 0.89 0.74 0.999 0.999
VCT 0.506 0.506 0.893 0.877 0.436 0.436 0.986 0.986
VEN 0.605 0.605 0.94 0.937 0.542 0.542 0.822 0.82
VNM 0.494 0.494 0.917 0.898 0.425 0.425 0.912 0.912
VUT 0.481 0.481 0.789 0.771 0.413 0.413 0.652 0.652
WSM 0.481 0.481 0.895 0.874 0.411 0.411 0.629 0.629
YEM 0.497 0.497 0.827 0.81 0.43 0.43 0.726 0.726
ZAF 0.514 0.514 0.71 0.698 0.445 0.445 0.732 0.732
ZAR 0.475 0.475 0.717 0.717 0.407 0.407 0.745 0.745
ZMB 0.489 0.489 0.659 0.645 0.422 0.422 0.853 0.853
ZWE 0.481 0.481 0.656 0.641 0.412 0.412 0.899 0.899
64
Table A.5 Efficiency Score for Selected Health Indicators (Single Inputs – Output)
Maternal Survival Rate
Infant Survival Rate
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
Country FDH DEA FDH DEA FDH DEA FDH DEA
AGO 0.439 0.439 0.995 0.995 0.439 0.439 0.935 0.935
ALB 0.462 0.462 1.000 1.000 0.462 0.462 0.989 0.988
ARG 0.495 0.495 1.000 1.000 0.509 0.499 0.991 0.990
ARM 0.454 0.454 1.000 1.000 0.454 0.454 0.988 0.988
ATG 0.826 0.602 0.996 0.996
AUS 0.882 0.416 1.000 1.000 0.697 0.646 0.999 0.998
AUT 0.659 0.625 1.000 1.000 0.520 0.495 0.999 0.999
AZE 0.565 0.565 1.000 1.000 0.565 0.565 0.971 0.971
BDI 0.404 0.404 0.993 0.993 0.404 0.404 0.946 0.945
BEN 0.413 0.413 0.996 0.996 0.413 0.413 0.934 0.933
BFA 0.409 0.409 0.996 0.996 0.409 0.409 0.941 0.941
BGD 0.424 0.424 0.998 0.998 0.424 0.424 0.967 0.967
BGR 0.776 0.463 1.000 1.000 0.541 0.512 0.994 0.994
BHR 0.856 0.856 1.000 1.000 1.000 1.000 1.000 1.000
BHS 0.523 0.523 0.999 0.999 0.537 0.534 0.992 0.992
BLR 1.000 0.472 1.000 1.000 0.792 0.733 0.999 0.999
BLZ 0.433 0.433 1.000 1.000 0.433 0.433 0.988 0.987
BOL 0.423 0.423 0.998 0.998 0.423 0.423 0.968 0.968
BRA 0.465 0.465 1.000 1.000 0.465 0.465 0.986 0.986
BRB 0.448 0.448 1.000 1.000 0.461 0.449 0.990 0.990
BWA 0.467 0.467 0.999 0.999 0.467 0.467 0.964 0.964
CAF 0.407 0.407 0.991 0.991 0.407 0.407 0.905 0.904
CAN 0.577 0.344 1.000 1.000 0.576 0.491 0.997 0.997
CHE 0.723 0.341 1.000 1.000 0.571 0.524 0.998 0.998
CHL 0.510 0.510 1.000 1.000 0.595 0.585 0.995 0.995
CHN 0.467 0.467 1.000 1.000 0.480 0.471 0.991 0.991
CIV 0.421 0.421 0.994 0.994 0.421 0.421 0.928 0.928
CMR 0.423 0.423 0.994 0.994 0.423 0.423 0.939 0.939
COG 0.431 0.431 0.996 0.996 0.431 0.431 0.961 0.960
COL 0.425 0.425 0.999 0.999 0.425 0.425 0.987 0.987
COM 0.411 0.411 0.997 0.997 0.411 0.411 0.941 0.941
CPV 0.429 0.429 1.000 1.000 0.429 0.429 0.981 0.981
CRI 0.394 0.394 1.000 1.000 0.460 0.429 0.994 0.993
CYP 1.000 0.596 1.000 1.000 1.000 1.000 1.000 1.000
CZE 0.867 0.409 1.000 1.000 0.949 0.700 1.000 0.999
DEU 0.661 0.547 1.000 1.000 0.522 0.494 0.998 0.998
DJI 0.406 0.406 0.998 0.998 0.406 0.406 0.943 0.942
65
Table A.5 (continued)
Maternal Survival Rate Infant Survival Rate
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
Country FDH DEA FDH DEA FDH DEA FDH DEA
DMA 0.442 0.442 0.978 0.978
DNK 0.590 0.489 1.000 1.000 0.466 0.439 0.998 0.998
DOM 0.477 0.477 0.999 0.999 0.477 0.477 0.975 0.975
DZA 0.444 0.444 0.999 0.999 0.444 0.444 0.980 0.979
ECU 0.454 0.454 0.999 0.999 0.454 0.454 0.983 0.982
EGY 0.472 0.472 1.000 1.000 0.472 0.472 0.980 0.980
ERI 0.412 0.412 0.995 0.995 0.412 0.412 0.965 0.965
ESP 0.819 0.386 1.000 1.000 0.647 0.631 0.999 0.999
EST 0.774 0.462 1.000 1.000 0.774 0.745 0.999 0.999
ETH 0.408 0.408 0.996 0.997 0.408 0.408 0.953 0.953
FIN 0.799 0.375 1.000 1.000 0.869 0.801 1.000 1.000
FJI 0.445 0.445 1.000 1.000 0.445 0.445 0.983 0.982
FRA 0.520 0.466 1.000 1.000 0.519 0.491 0.998 0.998
GAB 0.521 0.521 0.997 0.997 0.521 0.521 0.963 0.963
GBR 0.578 0.345 1.000 1.000 0.577 0.518 0.998 0.998
GEO 0.460 0.460 1.000 1.000 0.460 0.460 0.990 0.989
GHA 0.418 0.418 0.997 0.997 0.419 0.419 0.955 0.955
GIN 0.409 0.409 0.993 0.993 0.409 0.409 0.936 0.936
GMB 0.408 0.408 0.993 0.993 0.408 0.408 0.956 0.956
GNB 0.412 0.412 0.995 0.995 0.412 0.412 0.935 0.935
GRC 0.871 0.408 1.000 1.000 0.684 0.657 0.999 0.999
GRD 0.466 0.466 1.000 1.000 0.466 0.466 0.989 0.989
GTM 0.446 0.446 0.999 0.999 0.446 0.446 0.975 0.975
GUY 0.425 0.425 0.998 0.998 0.425 0.425 0.973 0.973
HND 0.414 0.414 0.999 0.999 0.415 0.415 0.984 0.984
HRV 0.669 0.399 1.000 1.000 0.669 0.585 0.998 0.998
HTI 0.413 0.413 0.996 0.996 0.413 0.413 0.942 0.942
HUN 0.457 0.457 1.000 1.000 0.767 0.646 0.998 0.997
IDN 0.484 0.484 0.999 0.999 0.484 0.484 0.977 0.977
IND 0.440 0.440 0.998 0.998 0.440 0.440 0.961 0.960
IRN 0.509 0.509 1.000 1.000 0.509 0.509 0.987 0.987
ISL 0.791 0.371 1.000 1.000 1.000 1.000 1.000 1.000
ITA 0.791 0.373 1.000 1.000 0.625 0.600 0.999 0.999
JAM 0.444 0.444 0.999 0.999 0.444 0.444 0.988 0.987
JOR 0.411 0.411 0.999 0.999 0.411 0.411 0.985 0.985
KAZ 0.576 0.576 1.000 1.000 0.576 0.576 0.987 0.987
KEN 0.416 0.416 0.995 0.995 0.416 0.416 0.962 0.962
KGZ 0.413 0.413 0.999 0.999 0.413 0.413 0.979 0.979
KHM 0.423 0.423 0.998 0.998 0.423 0.423 0.969 0.969
66
Table A.5 (continued)
Maternal Survival Rate Infant Survival Rate
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
Country FDH DEA FDH DEA FDH DEA FDH DEA
KNA 0.689 0.628 0.994 0.994
KOR 0.941 0.561 1.000 1.000 0.941 0.896 0.999 0.999
LAO 0.439 0.439 0.998 0.998 0.439 0.439 0.947 0.947
LBN 0.485 0.485 1.000 1.000 0.566 0.539 0.994 0.994
LCA 0.444 0.444 1.000 1.000 0.444 0.444 0.990 0.989
LKA 0.478 0.478 1.000 1.000 0.558 0.507 0.993 0.993
LSO 0.396 0.396 0.995 0.995 0.396 0.396 0.927 0.927
LTU 0.794 0.473 1.000 1.000 0.793 0.697 0.998 0.998
LUX 0.725 0.433 1.000 1.000 1.000 0.955 1.000 1.000
LVA 0.498 0.498 1.000 1.000 0.835 0.659 0.997 0.997
MAR 0.448 0.448 0.999 0.999 0.448 0.448 0.976 0.975
MDA 0.408 0.408 1.000 1.000 0.409 0.409 0.988 0.988
MDG 0.410 0.410 0.996 0.997 0.410 0.410 0.962 0.962
MEX 0.490 0.490 1.000 1.000 0.490 0.490 0.989 0.988
MKD 0.740 0.441 1.000 1.000 0.515 0.457 0.993 0.993
MLI 0.413 0.413 0.994 0.994 0.413 0.413 0.927 0.927
MNG 0.463 0.463 1.000 1.000 0.463 0.463 0.983 0.983
MOZ 0.407 0.407 0.995 0.995 0.407 0.407 0.939 0.939
MRT 0.426 0.426 0.994 0.994 0.427 0.427 0.943 0.942
MUS 0.528 0.528 1.000 1.000 0.528 0.528 0.989 0.989
MWI 0.402 0.402 0.994 0.994 0.402 0.402 0.952 0.952
MYS 0.595 0.595 1.000 1.000 0.999 0.708 0.996 0.996
NAM 0.423 0.423 0.997 0.997 0.423 0.423 0.964 0.964
NER 0.407 0.407 0.994 0.995 0.407 0.407 0.944 0.944
NGA 0.446 0.446 0.992 0.992 0.446 0.446 0.926 0.926
NIC 0.415 0.415 0.999 0.999 0.415 0.415 0.983 0.983
NLD 0.470 0.457 1.000 1.000 0.469 0.438 0.998 0.998
NOR 0.648 0.576 1.000 1.000 0.709 0.591 0.999 0.999
NPL 0.413 0.413 0.997 0.997 0.414 0.414 0.968 0.968
NZL 0.513 0.344 1.000 1.000 0.512 0.430 0.997 0.997
OMN 0.972 0.972 1.000 1.000 1.000 1.000 1.000 1.000
PAK 0.438 0.438 0.998 0.998 0.439 0.439 0.932 0.932
PAN 0.430 0.430 0.999 0.999 0.430 0.430 0.986 0.986
PER 0.462 0.462 0.999 0.999 0.462 0.462 0.988 0.988
PHL 0.448 0.448 0.999 0.999 0.448 0.448 0.979 0.978
PNG 0.411 0.411 0.998 0.998 0.411 0.411 0.955 0.955
POL 1.000 0.469 1.000 1.000 0.786 0.671 0.998 0.998
PRY 0.429 0.429 0.999 0.999 0.429 0.429 0.983 0.983
ROM 0.462 0.462 1.000 1.000 0.540 0.494 0.994 0.993
67
Table A.5 (continued)
Maternal Survival Rate Infant Survival Rate
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
Country FDH DEA FDH DEA FDH DEA FDH DEA
RUS 0.515 0.515 1.000 1.000 0.601 0.580 0.995 0.995
RWA 0.410 0.410 0.997 0.997 0.410 0.410 0.964 0.964
SAU 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
SDN 0.426 0.426 0.997 0.997 0.426 0.426 0.953 0.953
SEN 0.415 0.415 0.997 0.997 0.415 0.415 0.963 0.962
SLB 0.404 0.404 0.999 0.999 0.405 0.405 0.979 0.979
SLE 0.410 0.410 0.986 0.986 0.411 0.411 0.904 0.904
SLV 0.425 0.425 0.999 0.999 0.425 0.425 0.987 0.987
SVK 0.911 0.430 1.000 1.000 0.721 0.578 0.997 0.997
SVN 0.658 0.392 1.000 1.000 0.910 0.818 1.000 1.000
SWE 0.604 0.572 1.000 1.000 0.661 0.535 0.999 0.999
SWZ 0.403 0.403 0.996 0.996 0.403 0.403 0.943 0.942
TCD 0.415 0.415 0.991 0.991 0.416 0.416 0.920 0.920
TGO 0.410 0.410 0.996 0.996 0.410 0.410 0.946 0.946
THA 0.480 0.480 1.000 1.000 0.493 0.483 0.991 0.990
TJK 0.417 0.417 1.000 1.000 0.418 0.418 0.960 0.960
TKM 0.512 0.512 1.000 1.000 0.512 0.512 0.954 0.953
TON 0.421 0.421 0.999 0.999 0.422 0.422 0.987 0.987
TTO 0.630 0.630 0.999 0.999 0.631 0.631 0.988 0.985
TUN 0.441 0.441 0.999 0.999 0.441 0.441 0.989 0.988
TUR 0.475 0.475 1.000 1.000 0.475 0.475 0.988 0.988
TZA 0.415 0.415 0.996 0.996 0.415 0.415 0.957 0.957
UGA 0.411 0.411 0.997 0.997 0.412 0.412 0.955 0.955
UKR 0.429 0.429 1.000 1.000 0.501 0.452 0.993 0.993
URY 0.422 0.422 1.000 1.000 0.493 0.458 0.994 0.993
USA 0.317 0.317 1.000 1.000 0.529 0.405 0.996 0.996
UZB 0.427 0.427 1.000 1.000 0.427 0.427 0.974 0.974
VCT 0.436 0.436 1.000 1.000 0.436 0.436 0.985 0.985
VEN 0.542 0.542 0.999 0.999 0.542 0.542 0.988 0.988
VNM 0.425 0.425 0.999 0.999 0.425 0.425 0.984 0.984
VUT 0.413 0.413 0.999 0.999 0.413 0.413 0.978 0.978
WSM 0.411 0.411 1.000 1.000 0.411 0.411 0.986 0.986
YEM 0.430 0.430 0.959 0.958
ZAF 0.445 0.445 0.999 0.999 0.445 0.445 0.965 0.965
ZAR 0.406 0.406 0.993 0.993 0.407 0.407 0.922 0.922
ZMB 0.422 0.422 0.998 0.998 0.422 0.422 0.952 0.951
ZWE 0.412 0.412 0.996 0.996 0.412 0.412 0.951 0.951
68
Table A.6 Efficiency Score for Selected Health Indicators (Two Inputs – Single Output)
Input (Health Expenditure‐ Adult Literacy Rate)
Disability Adjusted Life Expectancy Immunization, DTP
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
AGO 0.924 0.780 0.824 0.814 0.931 0.765 0.704 0.704
ALB 0.927 0.832 0.993 0.963 0.923 0.754 0.997 0.997
ARG 0.914 0.783 0.956 0.953 0.791 0.642 0.941 0.941
ARM 0.899 0.744 0.970 0.938 0.909 0.693 0.954 0.951
AZE 0.899 0.833 0.916 0.905 0.909 0.843 0.900 0.899
BDI 0.922 0.788 0.840 0.802 0.893 0.830 0.982 0.965
BEN 1.000 0.926 1.000 0.974 1.000 0.921 1.000 0.892
BFA 0.991 0.915 0.988 0.922 1.000 1.000 1.000 1.000
BGD 1.000 0.957 1.000 0.983 1.000 1.000 1.000 1.000
BGR 0.851 0.693 0.929 0.926 0.749 0.613 0.941 0.941
BHR 0.948 0.862 0.984 0.969 0.959 0.871 1.000 0.998
BLR 0.798 0.639 0.898 0.894 0.791 0.647 0.987 0.987
BOL 0.873 0.703 0.909 0.907 0.796 0.665 0.957 0.957
BRA 0.922 0.747 0.939 0.938 0.815 0.679 0.978 0.978
CAF 0.970 0.882 0.768 0.726 0.987 0.865 0.488 0.464
CHL 1.000 1.000 1.000 1.000 0.800 0.649 0.941 0.941
CHN 0.915 0.758 0.976 0.943 0.969 0.969 1.000 1.000
CIV 1.000 0.885 1.000 0.842 1.000 0.874 1.000 0.840
CMR 0.936 0.768 0.782 0.765 0.947 0.743 0.853 0.853
COG 0.914 0.732 0.815 0.782 0.918 0.695 0.828 0.828
COL 0.859 0.823 0.971 0.963 0.685 0.574 0.906 0.906
COM 0.947 0.862 0.968 0.948 0.957 0.847 0.881 0.865
CPV 0.893 0.752 0.974 0.925 0.856 0.708 0.957 0.957
CRI 1.000 0.983 1.000 0.998 0.548 0.489 0.906 0.906
CYP 1.000 1.000 1.000 1.000 0.854 0.722 0.997 0.997
DOM 0.992 0.811 0.976 0.951 0.947 0.696 0.865 0.863
DZA 1.000 1.000 1.000 1.000
ECU 1.000 0.898 1.000 0.975 0.841 0.651 0.877 0.877
EGY 1.000 0.862 1.000 0.946 1.000 0.854 1.000 0.963
ERI 0.904 0.771 0.843 0.836
ESP 1.000 1.000 1.000 1.000 0.428 0.425 0.977 0.977
EST 0.768 0.697 0.947 0.938 0.601 0.528 0.947 0.947
ETH 0.987 0.868 0.987 0.923
GAB 1.000 0.829 1.000 0.830 1.000 0.787 1.000 0.764
GEO 0.900 0.732 0.958 0.928 0.910 0.694 0.932 0.930
GHA 0.882 0.733 0.857 0.835 0.898 0.763 0.934 0.934
69
Table A.6 (continued)
Input (Health Expenditure‐ Adult Literacy Rate)
Disability Adjusted Life Expectancy Immunization, DTP
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
GIN 1.000 0.934 1.000 0.927 1.000 0.918 1.000 0.710
GMB 1.000 0.916 1.000 0.978 1.000 1.000 1.000 1.000
GNB 0.973 0.852 0.825 0.821 1.000 0.884 1.000 0.878
GRC 1.000 0.967 1.000 0.993 0.672 0.672 1.000 1.000
GTM 0.976 0.799 0.969 0.931 0.934 0.724 0.869 0.869
GUY 0.838 0.663 0.863 0.847 0.826 0.703 0.973 0.973
HND 0.866 0.730 0.964 0.915 0.824 0.706 0.980 0.980
HRV 0.745 0.739 0.951 0.943 0.483 0.479 0.967 0.967
HTI 0.964 0.840 0.896 0.879
IDN 0.958 0.769 0.919 0.898 0.965 0.755 0.817 0.815
IND 1.000 0.814 1.000 0.895 1.000 0.782 1.000 0.826
IRN 1.000 0.847 1.000 0.962 1.000 0.849 1.000 0.997
ITA 0.991 0.982 0.998 0.998 0.424 0.408 0.965 0.965
JOR 0.839 0.731 0.950 0.940 0.673 0.637 0.991 0.991
KAZ 0.899 0.755 0.895 0.875 0.909 0.784 0.994 0.992
KEN 0.904 0.731 0.850 0.821 0.890 0.722 0.918 0.918
KGZ 0.850 0.642 0.866 0.865 0.850 0.656 0.971 0.971
KHM 0.945 0.747 0.899 0.869 0.942 0.750 0.890 0.890
LAO 0.990 0.848 0.974 0.887 1.000 0.836 1.000 0.819
LBN 1.000 1.000 1.000 1.000 0.878 0.667 0.818 0.818
LKA 0.987 0.872 0.992 0.969 1.000 0.834 1.000 0.998
LSO 0.784 0.667 0.611 0.608 0.777 0.685 0.944 0.944
LTU 0.671 0.629 0.919 0.911 0.643 0.556 0.948 0.948
LVA 0.788 0.660 0.915 0.911 0.751 0.620 0.938 0.938
MAR 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
MDA 0.788 0.632 0.887 0.885 0.743 0.594 0.905 0.905
MDG 0.889 0.750 0.834 0.819 0.863 0.722 0.730 0.730
MEX 0.959 0.832 0.966 0.961 0.864 0.677 0.928 0.928
MLI 0.995 0.915 0.956 0.931 1.000 0.899 1.000 0.794
MNG 0.912 0.684 0.866 0.836 0.923 0.721 0.991 0.988
MOZ 0.933 0.813 0.826 0.803 0.931 0.788 0.800 0.785
MRT 1.000 0.991 1.000 0.996
MUS 0.979 0.804 0.962 0.941 0.990 0.803 0.994 0.991
MWI 0.843 0.745 0.736 0.734 0.867 0.787 0.953 0.935
MYS 0.963 0.849 0.978 0.961 0.974 0.838 0.984 0.982
NAM 0.779 0.647 0.763 0.753 0.736 0.595 0.867 0.867
70
Table A.6 (continued)
Health Expenditure‐ Adult Literacy Rate
Disability Adjusted Life Expectancy Immunization, DTP
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
FDH DEA FDH DEA FDH DEA FDH DEA
NER 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
NGA 1.000 0.893 1.000 0.881
NPL 0.945 0.848 0.974 0.940 0.927 0.815 0.936 0.910
OMN 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
PAK 1.000 0.867 1.000 0.925 1.000 0.852 1.000 0.754
PAN 0.961 0.888 0.990 0.978 0.616 0.503 0.843 0.843
PER 1.000 0.978 1.000 0.997 0.874 0.677 0.921 0.921
PHL 0.935 0.710 0.904 0.877 0.940 0.681 0.806 0.804
PRY 0.888 0.741 0.940 0.936 0.781 0.615 0.889 0.889
ROM 0.848 0.672 0.931 0.925 0.697 0.576 0.929 0.929
RUS 0.777 0.607 0.865 0.863 0.790 0.640 0.981 0.981
RWA 0.881 0.749 0.864 0.850 0.957 0.841 0.986 0.986
SAU 0.949 0.873 0.988 0.974 0.960 0.864 0.994 0.993
SDN 0.985 0.860 0.978 0.939
SEN 0.976 0.842 0.941 0.932 0.977 0.896 0.936 0.920
SLE 0.978 0.910 0.901 0.870 1.000 1.000 1.000 1.000
SLV 0.969 0.794 0.970 0.952 0.794 0.655 0.921 0.921
SWZ 0.707 0.605 0.653 0.642 0.692 0.615 0.937 0.937
TCD 1.000 0.976 1.000 0.927 1.000 0.959 1.000 0.474
TGO 0.885 0.783 0.848 0.819 0.925 0.772 0.878 0.853
THA 0.950 0.837 0.968 0.963 0.940 0.940 1.000 1.000
TON 0.824 0.630 0.880 0.878 0.783 0.602 0.815 0.815
TUN 1.000 0.977 1.000 0.995 0.807 0.759 0.990 0.990
TUR 0.974 0.910 0.990 0.983 0.715 0.628 0.978 0.978
TZA 0.885 0.728 0.816 0.789 0.893 0.750 0.929 0.929
UGA 0.887 0.739 0.786 0.765 0.870 0.709 0.798 0.798
UKR 0.800 0.620 0.879 0.877 0.747 0.585 0.535 0.535
URY 0.802 0.756 0.963 0.952 0.580 0.528 0.958 0.958
UZB 0.889 0.657 0.873 0.864 0.900 0.728 0.999 0.999
VEN 0.935 0.825 0.983 0.962 0.948 0.768 0.823 0.821
VNM 0.901 0.737 0.932 0.926 0.811 0.652 0.912 0.912
WSM 0.815 0.648 0.899 0.897 0.742 0.568 0.629 0.629
ZAF 0.788 0.629 0.718 0.715 0.760 0.589 0.732 0.732
ZAR 0.883 0.739 0.796 0.776 0.861 0.693 0.745 0.745
ZMB 0.902 0.745 0.714 0.695 0.887 0.678 0.853 0.853
ZWE 0.885 0.696 0.705 0.670 0.855 0.678 0.899 0.899
71
Table A.7 Efficiency Score for Selected Infrastructure Indicators (Single Inputs – Output)
Quality of the Overall Infrastructure Quality of Electricity Supply
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
AGO 0.100 0.100 0.321 0.321 0.100 0.100 0.233 0.233
ALB 0.143 0.143 0.522 0.522 0.143 0.143 0.555 0.555
ARE 0.259 0.254 0.936 0.936 0.259 0.243 0.956 0.956
ARG 0.230 0.230 0.507 0.484 0.230 0.230 0.502 0.491
ARM 0.258 0.258 0.614 0.594 0.258 0.258 0.700 0.687
AUS 0.334 0.193 0.772 0.772 0.364 0.216 0.905 0.905
AUT 1.000 0.614 1.000 0.948 1.000 0.835 1.000 0.987
AZE 0.087 0.087 0.662 0.662 0.087 0.087 0.650 0.650
BDI 0.153 0.153 0.369 0.369 0.153 0.153 0.329 0.329
BEL 0.877 0.699 0.922 0.911 0.877 0.870 0.999 0.992
BEN 0.168 0.168 0.427 0.427 0.168 0.168 0.371 0.371
BFA 0.150 0.150 0.392 0.392 0.150 0.150 0.357 0.357
BGD 0.177 0.177 0.398 0.398 0.177 0.177 0.290 0.290
BGR 0.165 0.165 0.471 0.471 0.165 0.165 0.573 0.573
BHR 0.383 0.258 0.824 0.824 0.139 0.139 0.848 0.848
BIH 0.151 0.151 0.361 0.361 0.151 0.151 0.783 0.783
BLZ 0.163 0.163 0.530 0.530 0.163 0.163 0.603 0.603
BOL 0.104 0.104 0.448 0.448 0.104 0.104 0.582 0.582
BRA 0.664 0.679 0.620 0.664 0.804 0.779
BRB 0.499 0.369 0.848 0.848 0.499 0.325 0.913 0.913
BTN 0.098 0.098 0.676 0.676 0.098 0.098 0.863 0.863
BWA 0.102 0.102 0.650 0.650 0.102 0.102 0.546 0.546
CAN 0.439 0.361 0.878 0.878 0.656 0.440 0.965 0.965
CHE 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
CHL 1.000 0.592 1.000 0.851 0.395 0.395 0.939 0.857
CIV 0.228 0.228 0.612 0.584 0.228 0.228 0.600 0.587
CMR 0.210 0.210 0.458 0.432 0.210 0.210 0.413 0.400
COL 0.133 0.133 0.497 0.497 0.133 0.133 0.747 0.747
CPV 0.109 0.109 0.542 0.542 0.109 0.109 0.324 0.324
CRI 0.242 0.242 0.533 0.512 0.242 0.242 0.847 0.831
CZE 0.411 0.195 0.737 0.737 0.448 0.361 0.936 0.936
DEU 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
DOM 0.217 0.217 0.554 0.525 0.217 0.217 0.295 0.287
DZA 0.084 0.084 0.516 0.516 0.084 0.084 0.647 0.647
ECU 0.098 0.098 0.531 0.531 0.098 0.098 0.556 0.556
EGY 0.377 0.377 0.716 0.599 0.377 0.377 0.741 0.672
EST 0.360 0.210 0.773 0.773 0.142 0.142 0.814 0.814
ETH 0.094 0.094 0.481 0.481 0.094 0.094 0.472 0.472
72
Table A.7 (continued)
Quality of the Overall Infrastructure Quality of Electricity Supply
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
FIN 0.802 0.584 0.963 0.963 0.802 0.753 0.995 0.995
FRA 0.795 0.545 0.958 0.958 0.791 0.64 0.984 0.984
GAB 0.121 0.121 0.459 0.459 0.121 0.121 0.354 0.354
GBR 0.669 0.42 0.856 0.823 1 0.742 1 0.982
GEO 0.136 0.136 0.619 0.619 0.136 0.136 0.723 0.723
GHA 0.162 0.162 0.536 0.536 0.162 0.162 0.438 0.438
GIN 0.57 0.442 0.388 0.57 0.228 0.218
GMB 0.156 0.156 0.638 0.638 0.156 0.156 0.59 0.59
GRC 0.41 0.41 0.939 0.741 0.41 0.41 0.858 0.788
GTM 0.602 0.9 0.801 0.602 0.862 0.828
GUY 0.104 0.104 0.527 0.527 0.104 0.104 0.421 0.421
HND 0.291 0.291 0.571 0.559 0.291 0.291 0.592 0.585
HRV 0.452 0.182 0.713 0.713 0.179 0.179 0.81 0.81
HTI 0.109 0.109 0.306 0.306 0.109 0.109 0.252 0.252
IDN 0.332 0.332 0.563 0.559 0.332 0.332 0.6 0.598
IND 0.136 0.136 0.535 0.535 0.136 0.136 0.481 0.481
IRL 0.235 0.235 0.723 0.692 0.648 0.455 0.949 0.929
IRN 0.28 0.28 0.642 0.627 0.28 0.28 0.765 0.754
ISL 0.559 0.545 0.934 0.934 0.973 0.959 0.999 0.999
ISR 1 1 1 1 1 1
ITA 0.26 0.26 0.639 0.619 0.26 0.26 0.861 0.845
JOR 0.434 0.216 0.745 0.745 0.172 0.172 0.836 0.836
JPN 0.367 0.32 0.896 0.896 0.367 0.332 0.951 0.951
KAZ 0.162 0.162 0.596 0.596 0.162 0.162 0.648 0.648
KEN 0.187 0.187 0.556 0.556 0.187 0.187 0.535 0.535
KHM 0.135 0.135 0.536 0.536 0.135 0.135 0.445 0.445
KOR 0.404 0.307 0.855 0.855 0.404 0.199 0.889 0.889
KWT 0.15 0.15 0.687 0.687 0.15 0.15 0.735 0.735
LKA 0.18 0.18 0.669 0.669 0.18 0.18 0.702 0.702
LSO 0.1 0.1 0.466 0.466 0.1 0.1 0.532 0.532
LTU 0.448 0.204 0.731 0.731 0.177 0.177 0.816 0.816
LUX 0.418 0.357 0.889 0.889 0.418 0.361 0.945 0.945
LVA 0.197 0.197 0.676 0.676 0.197 0.197 0.778 0.778
MAR 0.198 0.198 0.629 0.629 0.198 0.198 0.767 0.767
MDA 0.223 0.223 0.541 0.515 0.223 0.223 0.648 0.632
MDG 0.294 0.294 0.461 0.452 0.294 0.294 0.342 0.338
MEX 0.169 0.169 0.596 0.596 0.169 0.169 0.636 0.636
MLI 0.161 0.161 0.493 0.493 0.161 0.161 0.501 0.501
MMR 0.14 0.14 0.342 0.342 0.14 0.14 0.418 0.418
73
Table A.7 (continued)
Quality of the Overall Infrastructure Quality of Electricity Supply
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
FDH DEA FDH DEA FDH DEA FDH DEA
MNE 0.145 0.145 0.489 0.489 0.145 0.145 0.572 0.572
MOZ 0.103 0.103 0.418 0.418 0.103 0.103 0.489 0.489
MUS 0.155 0.155 0.69 0.69 0.155 0.155 0.772 0.772
MWI 0.203 0.203 0.458 0.458 0.203 0.203 0.363 0.363
MYS 0.274 0.192 0.834 0.834 0.099 0.099 0.855 0.855
NAM 0.324 0.189 0.774 0.774 0.128 0.128 0.795 0.795
NGA 0.254 0.254 0.423 0.409 0.254 0.254 0.237 0.232
NIC 0.175 0.175 0.45 0.45 0.175 0.175 0.466 0.466
NLD 0.457 0.407 0.903 0.903 0.794 0.706 0.991 0.991
NPL 0.53 0.527 0.453 0.53 0.271 0.257
NZL 0.317 0.132 0.717 0.717 0.125 0.125 0.834 0.834
OMN 0.213 0.136 0.812 0.812 0.213 0.116 0.898 0.898
PAK 0.344 0.344 0.534 0.531 0.344 0.344 0.348 0.347
PAN 0.137 0.137 0.688 0.688 0.137 0.137 0.764 0.764
PER 0.165 0.165 0.477 0.477 0.165 0.165 0.708 0.708
PHL 0.403 0.403 0.692 0.543 0.403 0.403 0.664 0.608
POL 0.158 0.158 0.518 0.518 0.158 0.158 0.782 0.782
PRT 0.656 0.53 0.926 0.888 0.656 0.424 0.94 0.922
PRY 0.217 0.217 0.373 0.354 0.217 0.217 0.459 0.447
ROM 0.137 0.137 0.424 0.424 0.137 0.137 0.633 0.633
RUS 0.205 0.205 0.539 0.539 0.205 0.205 0.667 0.667
RWA 0.113 0.113 0.676 0.676 0.113 0.113 0.604 0.604
SAU 0.247 0.137 0.78 0.78 0.247 0.131 0.895 0.895
SEN 0.16 0.16 0.524 0.524 0.16 0.16 0.352 0.352
SGP 0.719 0.607 0.979 0.979 0.719 0.619 0.989 0.989
SLE 0.197 0.197 0.425 0.425 0.197 0.197 0.324 0.324
SLV 0.622 0.955 0.858 0.622 0.83 0.8
SRB 0.286 0.286 0.469 0.459 0.286 0.286 0.711 0.701
SUR 0.121 0.121 0.623 0.623 0.121 0.121 0.552 0.552
SVK 0.194 0.194 0.62 0.62 0.536 0.312 0.903 0.903
SWZ 0.163 0.163 0.626 0.626 0.163 0.163 0.58 0.58
SYC 0.14 0.14 0.699 0.699 0.14 0.14 0.73 0.73
TCD 0.127 0.127 0.337 0.337 0.127 0.127 0.22 0.22
THA 0.142 0.142 0.696 0.696 0.142 0.142 0.8 0.8
TJK 0.108 0.108 0.518 0.518 0.108 0.108 0.344 0.344
TTO 0.096 0.096 0.651 0.651 0.096 0.096 0.781 0.781
TUN 0.154 0.154 0.698 0.698 0.154 0.154 0.812 0.812
TUR 0.149 0.149 0.703 0.703 0.149 0.149 0.667 0.667
74
Table A.7 (continued)
Quality of the Overall Infrastructure Quality of Electricity Supply
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
TZA 0.186 0.186 0.441 0.441 0.186 0.186 0.345 0.345
UGA 0.152 0.152 0.482 0.482 0.152 0.152 0.364 0.364
UKR 0.504 0.817 0.69 0.504 0.763 0.718
URY 0.173 0.173 0.597 0.597 0.173 0.173 0.841 0.841
USA 0.449 0.361 0.872 0.872 0.449 0.327 0.925 0.925
VEN 0.093 0.093 0.411 0.411 0.093 0.093 0.364 0.364
VNM 0.12 0.12 0.465 0.465 0.12 0.12 0.53 0.53
YEM 0.398 0.398 0.575 0.449 0.398 0.398 0.248 0.226
ZAF 0.284 0.284 0.718 0.702 0.284 0.284 0.552 0.544
ZMB 0.346 0.346 0.516 0.514 0.346 0.346 0.516 0.515
ZWE 0.751 0.665 0.626 0.751 0.321 0.314
75
Table A.8 Efficiency Score for Selected Infrastructure Indicators (Two Inputs – Single Output)
Input (Public ‐ Private Capital Expenditure)
Quality of overall infrastructure Quality of Electricity Supply
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
AGO 1 1 1 1 1 1 1 1
ALB 0.625 0.385 0.522 0.522 0.625 0.425 0.555 0.555
ARE 1 1 1 1 1 0.954 1 0.978
ARG 0.964 0.519 0.593 0.525 0.964 0.574 0.502 0.496
ARM 0.684 0.494 0.614 0.594 0.684 0.559 0.7 0.687
AUS 0.729 0.601 0.772 0.772 0.729 0.652 0.905 0.905
AUT 1 0.897 1 0.955 1 0.87 1 0.987
AZE 1 0.828 1 0.9 1 0.787 1 0.849
BDI 0.822 0.499 0.904 0.501 1 0.553 1 0.426
BEL 0.925 0.846 0.922 0.911 0.925 0.911 0.999 0.992
BEN 0.714 0.341 0.427 0.427 0.714 0.356 0.371 0.371
BFA 0.543 0.385 0.441 0.419 0.689 0.424 0.367 0.358
BGD 0.446 0.305 0.398 0.398 0.66 0.291 0.29 0.29
BGR 0.723 0.39 0.471 0.471 0.723 0.489 0.573 0.573
BHR 0.766 0.651 0.824 0.824 0.738 0.626 0.848 0.848
BIH 0.513 0.339 0.387 0.379 0.832 0.706 0.784 0.783
BLZ 0.714 0.5 0.568 0.553 0.895 0.58 0.603 0.603
BOL 0.894 0.484 0.715 0.552 0.894 0.643 0.999 0.675
BRA 0.995 0.799 0.679 0.62 0.995 0.808 0.804 0.779
BRB 1 1 1 1 1 1 1 1
BTN 0.528 0.379 0.676 0.676 0.528 0.453 0.863 0.863
BWA 0.608 0.458 0.65 0.65 0.503 0.404 0.546 0.546
CAN 0.833 0.765 0.912 0.884 0.801 0.781 0.967 0.966
CHE 1 1 1 1 1 1 1 1
CHL 1 0.798 1 0.851 0.903 0.776 0.939 0.857
CIV 1 0.829 1 0.831 1 0.864 1 0.822
CMR 0.864 0.417 0.495 0.446 0.864 0.452 0.413 0.401
COL 0.584 0.411 0.516 0.501 0.736 0.601 0.748 0.747
CPV 0.479 0.341 0.542 0.542 0.479 0.255 0.324 0.324
CRI 0.825 0.477 0.533 0.512 0.933 0.736 0.847 0.831
CZE 0.721 0.594 0.737 0.737 0.721 0.69 0.936 0.936
DEU 1 1 1 1 1 1 1 1
DOM 0.753 0.446 0.554 0.525 0.753 0.351 0.295 0.287
DZA 0.542 0.368 0.516 0.516 0.655 0.461 0.647 0.647
ECU 0.627 0.439 0.569 0.549 0.627 0.477 0.556 0.556
EGY 0.864 0.632 0.782 0.599 0.864 0.696 0.741 0.672
76
Table A.8 (continued)
Input (Public ‐ Private Capital Expenditure)
Quality of overall infrastructure Quality of Electricity Supply
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
dmu FDH DEA FDH DEA FDH DEA FDH DEA
EST 0.73 0.609 0.773 0.773 0.73 0.605 0.814 0.814
ETH 0.605 0.382 0.514 0.492 0.605 0.41 0.473 0.472
FIN 1 0.94 1 0.978 0.858 0.851 0.996 0.995
FRA 0.992 0.917 0.994 0.97 0.851 0.826 0.985 0.984
GAB 0.531 0.338 0.459 0.459 0.531 0.317 0.354 0.354
GBR 1 0.92 1 0.92 1 1 1 1
GEO 0.752 0.525 0.657 0.629 0.752 0.599 0.724 0.724
GHA 0.709 0.537 0.632 0.576 0.709 0.495 0.451 0.442
GIN 1 1 1 1 1 1 1 0.59
GMB 0.839 0.569 0.683 0.651 0.839 0.538 0.591 0.59
GRC 1 0.839 1 0.815 1 0.896 1 0.868
GTM 0.968 0.88 0.942 0.86 1 0.916 1 0.892
GUY 0.976 0.603 0.912 0.685 0.976 0.544 0.722 0.521
HND 0.711 0.498 0.571 0.559 0.711 0.523 0.592 0.585
HRV 0.795 0.634 0.753 0.717 0.795 0.677 0.811 0.81
HTI 0.24 0.23 0.306 0.306 0.516 0.258 0.252 0.252
IDN 0.652 0.483 0.563 0.559 0.652 0.5 0.6 0.598
IND 0.598 0.37 0.535 0.535 0.598 0.36 0.481 0.481
IRL 0.969 0.675 0.781 0.707 0.969 0.845 0.949 0.93
IRN 0.747 0.557 0.642 0.627 0.747 0.651 0.765 0.754
ISL 1 1 1 1 1 1 1 1
ISR 1 1 1 1 1 1 1 1
ITA 0.92 0.622 0.887 0.636 1 0.819 1 0.846
JOR 0.749 0.627 0.745 0.745 0.749 0.657 0.836 0.836
JPN 0.861 0.79 0.951 0.911 0.829 0.778 0.952 0.952
KAZ 0.765 0.501 0.596 0.596 0.765 0.542 0.648 0.648
KEN 0.799 0.499 0.589 0.559 0.799 0.505 0.536 0.535
KHM 0.619 0.472 0.574 0.552 0.619 0.439 0.445 0.445
KOR 0.722 0.647 0.855 0.855 0.684 0.621 0.889 0.889
KWT 0.891 0.711 0.81 0.76 0.891 0.739 0.805 0.763
LKA 0.724 0.526 0.669 0.669 0.715 0.542 0.702 0.702
LSO 0.619 0.383 0.499 0.48 0.619 0.462 0.533 0.533
LTU 0.856 0.685 0.783 0.752 0.856 0.72 0.817 0.816
LUX 1 0.914 1 0.951 0.973 0.9 0.974 0.951
LVA 0.781 0.575 0.676 0.676 0.81 0.634 0.778 0.778
77
Table A.8 (continued)
Input (Public ‐ Private Capital Expenditure)
Quality of overall infrastructure Quality of Electricity Supply
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
FDH DEA FDH DEA FDH DEA FDH DEA
MAR 0.651 0.466 0.629 0.629 0.736 0.556 0.767 0.767
MDA 0.714 0.43 0.541 0.515 0.714 0.529 0.648 0.632
MDG 0.749 0.443 0.461 0.452 0.749 0.443 0.342 0.338
MEX 0.819 0.533 0.633 0.604 0.819 0.568 0.637 0.636
MLI 0.705 0.459 0.528 0.512 0.705 0.502 0.502 0.501
MMR 0.55 0.334 0.404 0.367 0.698 0.466 0.431 0.423
MNE 0.634 0.402 0.489 0.489 0.634 0.487 0.572 0.572
MOZ 0.789 0.414 0.493 0.477 0.789 0.521 0.535 0.523
MUS 0.796 0.592 0.716 0.693 0.796 0.632 0.773 0.772
MWI 0.888 0.523 0.794 0.529 0.888 0.497 0.622 0.385
MYS 0.781 0.759 0.893 0.869 0.781 0.715 0.856 0.855
NAM 0.707 0.599 0.774 0.774 0.707 0.586 0.795 0.795
NGA 0.639 0.417 0.423 0.411 0.863 0.409 0.237 0.232
NIC 0.719 0.354 0.45 0.45 0.719 0.408 0.466 0.466
NLD 0.93 0.872 0.967 0.942 0.93 0.915 0.992 0.992
NPL 0.762 0.649 0.527 0.453 0.762 0.649 0.271 0.257
NZL 0.778 0.642 0.768 0.748 0.778 0.705 0.835 0.835
OMN 0.802 0.746 0.868 0.852 0.802 0.784 0.899 0.898
PAK 0.993 0.618 0.754 0.584 0.993 0.535 0.45 0.37
PAN 0.62 0.474 0.688 0.688 0.62 0.502 0.764 0.764
PER 0.722 0.389 0.477 0.477 0.734 0.562 0.708 0.708
PHL 0.797 0.564 0.692 0.543 0.797 0.609 0.664 0.608
POL 0.694 0.471 0.555 0.533 0.861 0.682 0.783 0.782
PRT 1 0.907 1 0.923 0.98 0.874 0.94 0.923
PRY 0.554 0.387 0.436 0.39 0.953 0.541 0.459 0.454
ROM 0.601 0.321 0.424 0.424 0.713 0.485 0.633 0.633
RUS 0.843 0.509 0.571 0.55 0.843 0.625 0.688 0.668
RWA 0.743 0.571 0.724 0.696 0.743 0.519 0.605 0.605
SAU 0.82 0.715 0.834 0.823 0.82 0.799 0.896 0.896
SEN 0.701 0.411 0.524 0.524 0.701 0.336 0.352 0.352
SGP 0.943 0.881 0.979 0.979 0.768 0.752 0.989 0.989
SLE 0.863 0.454 0.527 0.463 0.863 0.433 0.334 0.33
SLV 1 0.966 1 0.96 1 0.93 1 0.91
SRB 0.845 0.47 0.469 0.459 0.845 0.681 0.711 0.701
SUR 0.522 0.365 0.623 0.623 0.522 0.336 0.552 0.552
SVK 0.801 0.554 0.62 0.62 0.801 0.744 0.903 0.903
SWZ 1 0.818 1 0.818 0.975 0.78 0.996 0.72
SYC 0.677 0.518 0.699 0.699 0.677 0.522 0.73 0.73
78
Table A.8 (continued)
Input (Public ‐ Private Capital Expenditure)
Quality of overall infrastructure Quality of Electricity Supply
Input Efficiency Output Efficiency Input Efficiency Output Efficiency
FDH DEA FDH DEA FDH DEA FDH DEA
TCD 0.389 0.245 0.337 0.337 0.558 0.24 0.22 0.22
THA 0.738 0.552 0.696 0.696 0.738 0.602 0.8 0.8
TJK 0.917 0.578 0.828 0.65 0.917 0.467 0.59 0.407
TUN 0.788 0.593 0.724 0.699 0.788 0.651 0.812 0.812
TUR 0.726 0.558 0.703 0.703 0.726 0.522 0.667 0.667
TZA 0.642 0.332 0.441 0.441 0.642 0.313 0.345 0.345
UGA 0.655 0.353 0.482 0.482 0.655 0.321 0.364 0.364
UKR 0.917 0.749 0.855 0.712 0.917 0.786 0.885 0.733
URY 0.85 0.552 0.64 0.613 0.85 0.73 0.842 0.841
USA 0.945 0.838 0.933 0.914 0.909 0.818 0.926 0.925
VEN 1 0.637 1 0.736 1 0.662 1 0.676
VNM 0.524 0.341 0.465 0.465 0.524 0.412 0.53 0.53
YEM 1 0.805 1 0.809 1 0.681 1 0.449
ZAF 0.852 0.661 0.718 0.702 0.843 0.565 0.552 0.544
ZMB 0.681 0.483 0.516 0.514 0.681 0.483 0.516 0.515
ZWE 1 0.891 1 0.674 1 0.891 1 0.342
79
Table A.9. List of Countries
Code Region Country Code Region Country Code Region Country
AGO AFR Angola GRD LAC Grenada PER LAC Peru
ALB ECA Albania GTM LAC Guatemala PHL EAP Philippines
ARE MNA United Arab Emirates GUY LAC Guyana PNG EAP Papua New Guinea
ARG LAC Argentina HND LAC Honduras POL ECA Poland
ARM ECA Armenia HRV ECA Croatia PRI LAC Puerto Rico
ATG LAC Antigua and Barbuda HTI LAC Haiti PRY LAC Paraguay
AZE ECA Azerbaijan HUN ECA Hungary QAT MNA Qatar
BDI AFR Burundi IDN EAP Indonesia ROM ECA Romania
BEN AFR Benin IND SAS India RUS ECA Russian Federation
BFA AFR Burkina Faso IRN MNA Iran, Islamic Rep. RWA AFR Rwanda
BGD SAS Bangladesh JAM LAC Jamaica SAU MNA Saudi Arabia
BGR ECA Bulgaria JOR MNA Jordan SDN AFR Sudan
BHR MNA Bahrain KAZ ECA Kazakhstan SEN AFR Senegal
BHS LAC Bahamas, The KEN AFR Kenya SGP EAP Singapore
BIH ECA Bosnia & Herzegovina
KGZ ECA Kyrgyz Republic SLB EAP Solomon Islands
BLR ECA Belarus KHM EAP Cambodia SLE AFR Sierra Leone
BLZ LAC Belize KNA LAC St. Kitts and Nevis SLV LAC El Salvador
BOL LAC Bolivia KOR EAP Korea, Rep. SRB ECA Serbia
BRA LAC Brazil KWT MNA Kuwait SUR LAC Suriname
BRB LAC Barbados LAO EAP Lao PDR SVK ECA Slovak Republic
BRN EAP Brunei Darussalam LBN MNA Lebanon SVN ECA Slovenia
BTN SAS Bhutan LCA LAC St. Lucia SWZ AFR Eswatini
BWA AFR Botswana LKA SAS Sri Lanka SYC AFR Seychelles
CAF AFR Central African Rep. LSO AFR Lesotho SYR MNA Syrian Arab Republic
CHL LAC Chile LBR AFR Liberia TCD AFR Chad
CHN EAP China LBY MNA Lybia TGO AFR Togo
CIV AFR Côte d'Ivoire LTU ECA Lithuania THA EAP Thailand
CMR AFR Cameroon LVA ECA Latvia TJK ECA Tajikistan
COG AFR Congo, Rep. MAR MNA Morocco TKM ECA Turkmenistan
COL LAC Colombia MDA ECA Moldova TLS EAP Timor‐Leste
COM AFR Comoros MDG AFR Madagascar TON EAP Tonga
CPV AFR Cabo Verde MEX LAC Mexico TTO LAC Trinidad and Tobago
CRI LAC Costa Rica MKD ECA Macedonia, FYR TUN MNA Tunisia
CZE ECA Czech Republic MLI AFR Mali TUR ECA Turkey
80
Table A.9. Continued
Code Region Country Code Region Country Code Region Country
DJI MNA Djibouti MMR EAP Myanmar TZA AFR Tanzania
DMA LAC Dominica MNE EAP Montenegro, Rep. of UGA AFR Uganda
DOM LAC Dominican Republic
MNG EAP Mongolia UKR ECA Ukraine
DZA MNA Algeria MOZ AFR Mozambique URY LAC Uruguay
ECU LAC Ecuador MRT AFR Mauritania UZB ECA Uzbekistan
EGY MNA Egypt, Arab Rep. MUS AFR Mauritius VCT LAC St. Vincent & Grenadines
ERI AFR Eritrea MWI AFR Malawi VEN LAC Venezuela, RB
EST ECA Estonia MYS EAP Malaysia VNM EAP Vietnam
ETH AFR Ethiopia NAM AFR Namibia VUT EAP Vanuatu
FJI EAP Fiji NER AFR Niger WSM EAP Samoa
GAB AFR Gabon NGA AFR Nigeria YEM MNA Yemen, Rep.
GEO ECA Georgia NIC LAC Nicaragua ZAF AFR South Africa
GHA AFR Ghana NPL SAS Nepal ZAR AFR Congo, Dem. Rep.
GIN AFR Guinea OMN MNA Oman ZMB AFR Zambia
GMB AFR Gambia, The PAK SAS Pakistan ZWE AFR Zimbabwe
GNB AFR Guinea‐Bissau PAN LAC Panama
Table A.9. Continued
Developed countries included in the efficiency estimation for learning scores
Code Country Code Country Code Country
AUS Australia FIN Finland LUX Luxembourg
AUT Austria FRA France MLT Malta
BEL Belgium GBR United Kingdom NLD Netherlands
CAN Canada GRC Greece NOR Norway
CHE Switzerland IRL Ireland NZL New Zealand
CYP Cyprus ISL Iceland PRT Portugal
DEU Germany ISR Israel SWE Sweden
DNK Denmark ITA Italy USA United States
ESP Spain JPN Japan
81
Table A.10. Definition and Source of Variables Definition of Variable Source
Output variables for education
School enrollment, primary (% gross) World Bank WDI
School enrollment, primary (% net) World Bank WDI
School enrollment, secondary (% gross) World Bank WDI
School enrollment, secondary (% net) World Bank WDI
Tertiary level complete, ages 15+ Barro‐Lee Database
Literacy rate, youth total (% of people ages 15‐24) World Bank WDI
Average years of school, ages 15+ Barro‐Lee Database
First level complete, ages 15+ Barro‐Lee Database
second level complete, ages 15+ Barro‐Lee Database
PISA Science scores www.oecd.org/pisa/data
PISA Mathematics scores www.oecd.org/pisa/data
PISA Reading scores www.oecd.org/pisa/data
Quality of primary education, 1‐7 (best) World Economic Forum
Primary education Net Enrollment, net % World Economic Forum
Secondary Education Gross Enrollment, gross % World Economic Forum
Tertiary education enrollment, gross % World Economic Forum
Quality of the education system, 1‐7 (best) World Economic Forum
Quality of math and science education, 1‐7 (best) World Economic Forum
Input variables for education
Public education spending per capita in PPP terms, calculated World Bank WDI
Literacy rate, adult total (% of people ages 15 and above) World Bank WDI
Teachers per pupil, equal the reciprocal of pupils per teacher World Bank WDI
Output variables for health
Life expectancy at birth, total (years) World Bank WDI
Immunization, DPT (% of children ages 12‐23 months) World Bank WDI
Immunization, measles (% of children ages 12‐23 months) World Bank WDI
Disability Adjusted Life Expectancy Institute for Health Metrics and
Evaluation (IHME)
Tuberculosis cases/100,000 pop. World Economic Forum
Maternal Mortality Ratio (per 100 000 live births) World Health Organization
Infant mortality rate (probability of dying between birth and age 1 per 1000 live births)
World Health Organization
Input variables for health
Literacy rate, adult total (% of people ages 15 and above) World Bank WDI
public spending on health per capita in PPP terms, calculated World Bank WDI
public spending on health per capita in PPP terms, calculated World Bank WDI
Output variables for Infrastructure
Quality of overall infrastructure, 1‐7 (best) World Economic Forum
Quality of roads, 1‐7 (best) World Economic Forum
Quality of railroad infrastructure, 1‐7 (best) World Economic Forum
82
Table A.10 (Continued)
Definition of Variable Source
Quality of port infrastructure, 1‐7 (best) World Economic Forum
Quality of air transport infrastructure, 1‐7 (best) World Economic Forum
A. Transport infrastructure World Economic Forum
Quality of electricity supply, 1‐7 (best) World Economic Forum
Input variables for Infrastructure
Private investment spending per capita in real terms, calculated World Economic Outlook
Public investment spending per capita in real terms, calculated World Economic Outlook
Variables used in the calculation World Bank WDI
Pupil‐teacher ratio, primary World Bank WDI
Public spending on education, total (% of GDP) World Bank WDI
GDP per capita, PPP (constant 2011 international $) World Bank WDI
Health expenditure, private (% of GDP) World Bank WDI
Health expenditure, public (% of GDP) World Bank WDI
GDP (constant 2010 US$) World Economic Outlook
GDP (current US$) World Economic Outlook
National Currency per PPP dollar (Units National Currency per PPP dollar) World Economic Outlook
Population (Millions of Persons) World Economic Outlook
Variables used in the Panel Tobit regression
Wages and salaries (% of total public expenditure) World Bank WDI
Total government expenditure (% of GDP) World Bank WDI
Share of expenditures publicly financed (public/total) World Bank WDI
GDP per capita in constant 2011 US dollars World Bank WDI
Urban population (% of total) World Bank WDI
Dummy variable for HIV/AIDS WHO mappings of diseases
Gini Coefficient World Bank WDI
Aid (% of fiscal revenue) calculated as Official development assistance World Bank WDI
and official aid (current US$) *official exchange rate * PPP conversion factor
/ Revenue, excluding grants (current LCU)
Institutional Indicators including
a. Worldwide Governance Research Indicators World Bank WDI
Control of Corruption: Estimate World Bank WDI
Government Effectiveness: Estimate World Bank WDI
Political Stability and Absence of Violence/Terrorism: Estimate World Bank WDI
Regulatory Quality: Estimate World Bank WDI
Rule of Law: Estimate World Bank WDI
Voice and Accountability: Estimate World Bank WDI
83
Figure A. 1. Efficiency Frontiers for Education
Free Disposable Hull (FDH) Data Envelopment Analysis (DEA)
AGO
ALB
ARG
ARM
ATG
AUS
AZEBDI
BEN
BFA
BGD
BGR
BLR
BLZ
BOL
BRABRB
BWA
CAF
CAN
CHECHL
CHN
CIV
CMRCOG
COL
COM
CPV CRI CYPDEU
DJI
DNK
DOM
ECU
EGYESP
EST
ETH
FIN
FJIFRA
GBRGEO
GHA
GIN
GMBGNB
GTM
GUY
HND
HRV
HUNIDN IND
IRN ISLITA
KAZ
KEN
KGZ
KHM
KNA
KOR
LAO
LBN
LKA
LSO
LTU LVAMAR
MDA
MEX
MKD
MLI
MNG
MOZ
MRT
MUSMWIMYS
NAM
NER
NGA
NIC
NLD NOR
NPLNZL
OMN
PAK
PANPERPHL
POL
PRYROM
RUSRWA
SAU
SDN
SEN SLB
SLE
SLV
SVNSWE
SWZ
TCD
TGOTHA
TJK
TTO
TUN
TUR
TZA
UGA
UKRURY
USAVCT
VEN
VNM
VUTZWE
5060
7080
9010
0N
et P
rimar
y S
chool
Enr
ollm
ent
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI
Net Primary Enrollment vs Education Expenditure
AGO
ALB
ARG
ARM
ATG
AUS
AZEBDI
BEN
BFA
BGD
BGR
BLR
BLZ
BOL
BRABRB
BWA
CAF
CAN
CHECHL
CHN
CIV
CMRCOG
COL
COM
CPV CRI CYPDEU
DJI
DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FJIFRA
GBRGEO
GHA
GIN
GMBGNB
GTM
GUY
HND
HRV
HUNIDN IND
IRN ISLITA
KAZ
KEN
KGZ
KHM
KNA
KOR
LAO
LBN
LKA
LSO
LTU LVAMAR
MDA
MEX
MKD
MLI
MNG
MOZ
MRT
MUSMWIMYS
NAM
NER
NGA
NIC
NLD NOR
NPLNZL
OMN
PAK
PANPERPHL
POL
PRYROM
RUSRWA
SAU
SDN
SEN SLB
SLE
SLV
SVNSWE
SWZ
TCD
TGOTHA
TJK
TTO
TUN
TUR
TZA
UGA
UKR
URY
USAVCT
VEN
VNM
VUTZWE
5060
7080
90100
Net P
rim
ary
Sch
ool E
nro
llmen
t
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI
Net Primary Enrollment vs Education Expenditure
(a.1) (a.2)
AGO
ALB
ARG
ARM
ATG
AUS
AUT
BDI
BEN
BFA
BGD
BGR
BLR
BLZBOL
BRABRB
CAF
CAN
CHECHLCHN
CIV
CMRCOG
COL
COM
CPV
CRI
CYPCZE
DEU
DJI
DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FJI
FRAGBR
GEO
GHA
GIN
GMBGTM
GUY
HND
HRVHUN
IDN
IND
IRN
ISL
ITA
JAM
KAZ
KEN
KGZKNA
KOR
LAO
LBN
LCA
LKA
LSO
LTU LVA
MAR
MDA
MDG
MEXMKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NER
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRY
ROMRUS
RWA
SAU
SDN SEN
SLBSLE
SLV
SVK
SVN
SWE
SWZ
TCD
TGO
THA
TJKTKMTUNTUR
TZA
UGA
UKRURYUSA
VCT
VEN
VUT
ZAF
ZARZWE
050
100
150
Net S
eco
ndary
Sch
ool E
nro
llment
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI
Net Secondary Enrollment vs Education Expenditure
AGO
ALB
ARG
ARM
ATG
AUS
AUT
BDI
BEN
BFA
BGD
BGR
BLR
BLZBOL
BRABRB
CAF
CAN
CHECHLCHN
CIV
CMRCOG
COL
COM
CPV
CRI
CYPCZE
DEU
DJI
DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FJI
FRAGBR
GEO
GHA
GIN
GMBGTM
GUY
HND
HRVHUN
IDN
IND
IRN
ISL
ITA
JAM
KAZ
KEN
KGZKNA
KOR
LAO
LBN
LCA
LKA
LSO
LTU LVA
MAR
MDA
MDG
MEXMKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NER
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRY
ROMRUS
RWA
SAU
SDN SEN
SLBSLE
SLV
SVK
SVN
SWE
SWZ
TCD
TGO
THA
TJKTKMTUNTUR
TZA
UGA
UKRURYUSA
VCT
VEN
VUT
ZAF
ZARZWE
050
100
150
Net
Sec
ond
ary
Sch
ool
Enr
ollm
ent
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI
Net Secondary Enrollment vs Education Expenditure
(b.1) (b.2)
AGO
ALB
ARG
ARM
AUS
AUT
AZE
BDI
BEN
BFA
BGD
BGR
BLZ
BOL
BRA
BRB
BWA
CAN
CHE
CHL
CHN
CIVCMR
COL
CPV
CRI
CYP
CZE
DEU
DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FRA
GAB
GBR
GEO
GHAGIN
GMB
GTM
GUY
HND
HRV
HUN
IDN
IND
IRN
ISL
ITA
JAM
KAZ
KEN
KGZ
KHM
KOR
LAO
LBN
LKA
LSO
LTU
LVA
MAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NAMNGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRY
ROM
RUS
RWA
SAU
SEN
SLE
SLV
SVK
SVN
SWE
SWZTCD
THA
TJK
TTO
TUN
TUR
TZAUGA
UKR
URY
USA
VEN
VNMZAF
ZWE
020
4060
80100
Tert
iary
Gro
ss E
nro
llment
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/World Economic Forum
Tertiary Gross Enrollment vs Education Expenditure
(c.1)
AGO
ALB
ARG
ARM
AUS
AUT
AZE
BDI
BEN
BFA
BGD
BGR
BLZ
BOL
BRA
BRB
BWA
CAN
CHE
CHL
CHN
CIVCMR
COL
CPV
CRI
CYP
CZE
DEU
DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FRA
GAB
GBR
GEO
GHAGIN
GMB
GTM
GUY
HND
HRV
HUN
IDN
IND
IRN
ISL
ITA
JAM
KAZ
KEN
KGZ
KHM
KOR
LAO
LBN
LKA
LSO
LTU
LVA
MAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NAMNGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRY
ROM
RUS
RWA
SAU
SEN
SLE
SLV
SVK
SVN
SWE
SWZTCD
THA
TJK
TTO
TUN
TUR
TZAUGA
UKR
URY
USA
VEN
VNMZAF
ZWE
020
4060
80100
Tert
iary
Gro
ss E
nro
llment
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/World Economic Forum
Tertiary Gross Enrollment vs Education Expenditure
(c.2)
84
AGO
ALB
ARG
ARM
AUS
AUT
AZE
BDI
BEN
BFABGD
BGRBLZ
BOL
BRA
BRB
BWA
CAN
CHE
CHL
CHN
CIV
CMR
COL
CPV
CRI
CYP
CZE
DEU DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FRA
GAB
GBR
GEO GHA
GIN
GMB
GTM
GUY
HND
HRV
HTI
HUNIDN
IND
IRN
ISL
ITA
JAM
KAZ KEN
KGZKHM
KOR
LAO
LBN
LKA
LSO
LTULVA
MAR
MDA
MDGMEX
MKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAKPAN
PER
PHL
POL
PRY
ROM
RUSRWA
SAU
SEN
SLESLV
SVK
SVN SWE
SWZ
TCD
THA
TJK
TTO
TUN
TUR
TZA
UGA
UKR
URY
USA
VEN
VNM
ZAF
ZWE
23
45
67
Qu
alit
y of
pri
mar
y e
duca
tion
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/World Economic Forum
Quality of primary education vs Education Expenditure
(d.1)
AGO
ALB
ARG
ARM
AUS
AUT
AZE
BDI
BEN
BFABGD
BGRBLZ
BOL
BRA
BRB
BWA
CAN
CHE
CHL
CHN
CIV
CMR
COL
CPV
CRI
CYP
CZE
DEU DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FRA
GAB
GBR
GEO GHA
GIN
GMB
GTM
GUY
HND
HRV
HTI
HUNIDN
IND
IRN
ISL
ITA
JAM
KAZ KEN
KGZKHM
KOR
LAO
LBN
LKA
LSO
LTULVA
MAR
MDA
MDGMEX
MKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAKPAN
PER
PHL
POL
PRY
ROM
RUSRWA
SAU
SEN
SLESLV
SVK
SVN SWE
SWZ
TCD
THA
TJK
TTO
TUN
TUR
TZA
UGA
UKR
URY
USA
VEN
VNM
ZAF
ZWE
23
45
67
Qua
lity
of p
rima
ry e
duc
atio
n
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/World Economic Forum
Quality of primary education vs Education Expenditure
(d.2)
AGO
ALB
ARGARM
AUS
AUT
AZE
BDI
BEN
BFA
BGDBGR
BLZ
BOL
BRA
BRB
BWA
CAN
CHE
CHL
CHN
CIV
CMRCOL
CPV
CRI
CYP
CZE
DEU DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FRA
GAB
GBR
GEO
GHA
GIN
GMB
GTM
GUY
HND
HRV
HTI
HUN
IDN IND
IRN
ISL
ITA JAMKAZ
KEN
KGZ
KHM
KOR LAO
LBN
LKA
LSO
LTULVA
MARMDA
MDGMEX
MKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRY
ROMRUS
RWA
SAU
SEN
SLESLV
SVK
SVN
SWE
SWZ
TCD
THATJK
TTO
TUN
TURTZA
UGA
UKR
URY
USA
VEN
VNM
ZAF
ZWE
23
45
6Q
ual
ity o
f th
e e
duc
atio
n sy
ste
m
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/World Economic Forum
Quality of the education system vs Education Expenditure
(e.1)
AGO
ALB
ARGARM
AUS
AUT
AZE
BDI
BEN
BFA
BGDBGR
BLZ
BOL
BRA
BRB
BWA
CAN
CHE
CHL
CHN
CIV
CMRCOL
CPV
CRI
CYP
CZE
DEU DNK
DOM
ECU
EGY
ESP
EST
ETH
FIN
FRA
GAB
GBR
GEO
GHA
GIN
GMB
GTM
GUY
HND
HRV
HTI
HUN
IDN IND
IRN
ISL
ITA JAMKAZ
KEN
KGZ
KHM
KOR LAO
LBN
LKA
LSO
LTULVA
MARMDA
MDGMEX
MKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
POL
PRY
ROMRUS
RWA
SAU
SEN
SLESLV
SVK
SVN
SWE
SWZ
TCD
THATJK
TTO
TUN
TURTZA
UGA
UKR
URY
USA
VEN
VNM
ZAF
ZWE
23
45
6Q
ual
ity o
f the
edu
catio
n sy
stem
500 1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/World Economic Forum
Quality of the education system vs Education Expenditure
(e.2)
ALB
ARG
AUSAUT
AZE BGR
BRA
CANCHE
CHL
CHN
COL
CRI
CYP
CZE
DEU DNK
DOM
ESP
FIN
FRAGBR
GEO
HRV
HUN
IDN
ISL
ITA
KAZ
KGZ
KOR
LBN
LTULVA
MDAMEX
MKD
NLD
NORNZL
PAN
PER
POL
ROM
RUSSVK
SVN
SWE
THA TTO
TUN
TURURY
USA
VNM
300
350
400
450
500
550
Pis
a M
athem
atic
s Lite
racy
sco
re
1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/NCES
Pisa Mathematics Literacy score vs Education Expenditure
(f.1)
ALB
ARG
AUSAUT
AZE BGR
BRA
CANCHE
CHL
CHN
COL
CRI
CYP
CZE
DEU DNK
DOM
ESP
FIN
FRAGBR
GEO
HRV
HUN
IDN
ISL
ITA
KAZ
KGZ
KOR
LBN
LTULVA
MDAMEX
MKD
NLD
NORNZL
PAN
PER
POL
ROM
RUSSVK
SVN
SWE
THA TTO
TUN
TURURY
USA
VNM
300
350
400
450
500
550
Pis
a M
ath
em
atic
s Lite
racy
sco
re
1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/NCES
Pisa Mathematics Literacy score vs Education Expenditure
(f.1)
85
ALB
ARG
AUS
AUT
AZE
BGR
BRA
CAN
CHE
CHL
CHN
COLCRI
CYP
CZE
DEUDNK
DOM
ESP
FIN
FRAGBR
GEO
HRVHUN
IDN
ISLITA
KAZ
KGZ
KOR
LBN
LTU
LVA
MDAMEX
MKD
NLD NORNZL
PAN
PER
POL
ROM
RUS
SVK
SVNSWE
THATTO
TUN
TUR
URY
USA
VNM
300
350
400
450
500
550
Pis
a R
eadin
g L
itera
cy
1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/NCES
Pisa Reading Literacy vs Education Expenditure
(g.1)
ALB
ARG
AUS
AUT
AZE
BGR
BRA
CAN
CHE
CHL
CHN
COLCRI
CYP
CZE
DEUDNK
DOM
ESP
FIN
FRAGBR
GEO
HRVHUN
IDN
ISLITA
KAZ
KGZ
KOR
LBN
LTU
LVA
MDAMEX
MKD
NLD NORNZL
PAN
PER
POL
ROM
RUS
SVK
SVNSWE
THATTO
TUN
TUR
URY
USA
VNM
300
350
400
450
500
550
Pis
a R
ead
ing L
itera
cy
1000 1500 2000 2500Orthogonalized Public Expditure on Education
Data Source: World Bank WDI/NCES
Pisa Reading Literacy vs Education Expenditure
(g.1)
ALBARG
ARM
AUS
AUT
BDI
BEN
BGD
BGR BLZ
BOL
BRA
BRBBWA
CAF
CANCHE
CHL
CHN
CIV
CMRCOG
COL
CRI
CYP
CZE DEU
DNK
DOM ECU
EGY
ESP
EST
FINFJIFRA
GAB
GBR
GHA
GMB
GTM
GUY
HND
HRV
HTI
HUN
IDN
IND
IRN
ISL
ITAJAM
KAZ
KEN
KGZ
KHM
KOR
LAO
LKA
LSO
LTULVA
MAR
MDA
MEX
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NIC
NLDNOR
NPL
NZL
PAK
PANPER
PHL
POL
PRY
ROM
RUS
RWA
SAU
SDNSEN
SLE
SLV
SVK
SVN SWE
SWZ
TGO
THA
TJKTTO
TUNTUR
TZAUGA
UKR
URY
USA
VEN
VNM
ZAF
ZAR
ZWE
05
1015
Ave
rage
Yea
r of
Sch
ool
500 1000 1500 2000 2500Orthogonalized Public Expenditure on Education
Data Source: World Bank WDI, Barro-Lee database
Average Year of School vs Education Expenditure
ALBARG
ARM
AUS
AUT
BDI
BEN
BGD
BGR BLZ
BOL
BRA
BRBBWA
CAF
CANCHE
CHL
CHN
CIV
CMRCOG
COL
CRI
CYP
CZE DEU
DNK
DOM ECU
EGY
ESP
EST
FINFJIFRA
GAB
GBR
GHA
GMB
GTM
GUY
HND
HRV
HTI
HUN
IDN
IND
IRN
ISL
ITAJAM
KAZ
KEN
KGZ
KHM
KOR
LAO
LKA
LSO
LTULVA
MAR
MDA
MEX
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NIC
NLDNOR
NPL
NZL
PAK
PANPER
PHL
POL
PRY
ROM
RUS
RWA
SAU
SDNSEN
SLE
SLV
SVK
SVN SWE
SWZ
TGO
THA
TJKTTO
TUNTUR
TZAUGA
UKR
URY
USA
VEN
VNM
ZAF
ZAR
ZWE0
510
15A
vera
ge Y
ear of S
chool
500 1000 1500 2000 2500Orthogonalized Public Expenditure on Education
Data Source: World Bank WDI, Barro-Lee database
Average Year of School vs Education Expenditure
(h.1) (h.2)
ALB
ARG
ARM
AUS
AUT
BDI
BEN
BGD
BGR
BLZ
BOL
BRA
BRB
BWA
CAF
CAN
CHE
CHL
CHN
CIV
CMR
COG
COL
CRI
CYP
CZE
DEU
DNK
DOM
ECUEGY
ESP
EST
FIN
FJI FRA
GAB
GBR
GHA
GMB
GTM
GUY
HND
HRV
HTI
HUN
IDNIND
IRN
ISL
ITAJAM
KAZ
KEN
KGZ
KHM
KOR
LAO
LKA
LSO
LTU
LVA
MAR
MDA
MEX
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NIC
NLDNOR
NPL NZL
PAK
PAN
PER
PHL
POL
PRY
ROM
RUS
RWA
SAU
SDN SEN
SLE
SLV
SVK
SVN
SWE
SWZ
TGO
THA
TJK
TTO
TUN
TUR
TZAUGA
UKR
URY
USAVEN
VNM
ZAF
ZAR
ZWE
020
4060
80S
eco
nd
Lev
el C
omp
lete
500 1000 1500 2000 2500Orthogonalized Public Expenditure on Education
Data Source: World Bank WDI, Barro-Lee database
Second Level Complete vs Education Expenditure
ALB
ARG
ARM
AUS
AUT
BDI
BEN
BGD
BGR
BLZ
BOL
BRA
BRB
BWA
CAF
CAN
CHE
CHL
CHN
CIV
CMR
COG
COL
CRI
CYP
CZE
DEU
DNK
DOM
ECUEGY
ESP
EST
FIN
FJI FRA
GAB
GBR
GHA
GMB
GTM
GUY
HND
HRV
HTI
HUN
IDNIND
IRN
ISL
ITAJAM
KAZ
KEN
KGZ
KHM
KOR
LAO
LKA
LSO
LTU
LVA
MAR
MDA
MEX
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NIC
NLDNOR
NPL NZL
PAK
PAN
PER
PHL
POL
PRY
ROM
RUS
RWA
SAU
SDN SEN
SLE
SLV
SVK
SVN
SWE
SWZ
TGO
THA
TJK
TTO
TUN
TUR
TZAUGA
UKR
URY
USAVEN
VNM
ZAF
ZAR
ZWE
020
4060
80S
eco
nd L
eve
l Com
ple
te
500 1000 1500 2000 2500Orthogonalized Public Expenditure on Education
Data Source: World Bank WDI, Barro-Lee database
Second Level Complete vs Education Expenditure
(i.1) (i.2)
86
AGO
ALB ARGARMAZE
BDI
BENBFA
BGD
BGRBLR BOLBRA
CAF
CHLCHN
CIV
CMR COG
COL
COM
CPV CRI CYPDOM ECU
EGY
ESP EST
GAB
GEO
GHA
GIN
GMBGNB
GTMGUY HND
HRVIDN
IND
IRNITA
KEN
KGZ
KHM
LAO
LBN LKA
LSO
LTU LVA
MAR
MDA
MDG
MEX
MLI
MNG
MOZ
MUS
MWI
MYS
NAM
NER
NPL
OMN
PAK
PAN PERPHL PRYROM RUS
RWA
SAU
SEN
SLE
SLVSWZ
TCD
TGO
THA TUNTUR
TZA
UGA
UKRURYVENVNMZAF
ZAR
ZWE
2040
6080
100
You
th L
itera
cy R
ate
0 200 400 600 800 1000Orthogonalized Public Expenditure on Education
Data Source: World Bank WDI
Youth Literacy Rate vs Education Expenditure
AGO
ALB ARGARMAZE
BDI
BENBFA
BGD
BGRBLR BOLBRA
CAF
CHLCHN
CIV
CMR COG
COL
COM
CPV CRI CYPDOM ECU
EGY
ESP EST
GAB
GEO
GHA
GIN
GMBGNB
GTMGUY HND
HRVIDN
IND
IRNITA
KEN
KGZ
KHM
LAO
LBN LKA
LSO
LTU LVA
MAR
MDA
MDG
MEX
MLI
MNG
MOZ
MUS
MWI
MYS
NAM
NER
NPL
OMN
PAK
PAN PERPHL PRYROM RUS
RWA
SAU
SEN
SLE
SLVSWZ
TCD
TGO
THA TUNTUR
TZA
UGA
UKRURYVENVNMZAF
ZAR
ZWE
2040
6080
100
Yout
h L
itera
cy R
ate
0 200 400 600 800 1000Orthogonalized Public Expenditure on Education
Data Source: World Bank WDI
Youth Literacy Rate vs Education Expenditure
(j.1)
(j.2)
87
Figure A.2. Efficiency Frontiers for Health
Free Disposable Hull (FDH) Data Envelopment Analysis (DEA)
AGO
ALBARG
ARM
ATG
AUSAUT
AZE
BDI
BENBFA
BGD
BGR
BHRBHS
BLR
BLZ
BOL
BRABRB
BWA
CAF
CANCHE
CHL
CHN
CIV
CMR
COG
COL
COM
CPV
CRICYPCZE
DEU
DJI
DNK
DOM
DZAECU
EGY
ERI
ESP
EST
ETH
FIN
FJI
FRA
GAB
GBR
GEO
GHA
GIN
GMB
GNB
GRC
GRDGTM
GUY
HND
HRV
HTI
HUN
IDNIND
IRN
ISLITA
JAMJOR
KAZ
KEN
KGZ
KHM
KOR
LAO
LBN
LCALKA
LSO
LTU
LUX
LVAMAR
MDA
MDG
MEXMKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLDNOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
PNG
POL
PRY
ROM
RUS
RWA
SAU
SDN
SEN
SLB
SLE
SLV
SVK
SVN
SWE
SWZ
TCD
TGO
THA
TJK
TKM
TON
TTO
TUNTUR
TZA
UGA
UKR
URY
USA
UZB
VCTVEN
VNM
VUT
WSM
YEM
ZAF ZARZMB
ZWE
5060
7080
90Li
fe E
xpe
cta
ncy
1000 2000 3000 4000 5000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI
Life Expectancy vs Health Expenditure
AGO
ALBARG
ARM
ATG
AUSAUT
AZE
BDI
BENBFA
BGD
BGR
BHRBHS
BLR
BLZ
BOL
BRABRB
BWA
CAF
CANCHE
CHL
CHN
CIV
CMR
COG
COL
COM
CPV
CRICYPCZE
DEU
DJI
DNK
DOM
DZAECU
EGY
ERI
ESP
EST
ETH
FIN
FJI
FRA
GAB
GBR
GEO
GHA
GIN
GMB
GNB
GRC
GRDGTM
GUY
HND
HRV
HTI
HUN
IDNIND
IRN
ISLITA
JAMJOR
KAZ
KEN
KGZ
KHM
KOR
LAO
LBN
LCALKA
LSO
LTU
LUX
LVAMAR
MDA
MDG
MEXMKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLDNOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
PNG
POL
PRY
ROM
RUS
RWA
SAU
SDN
SEN
SLB
SLE
SLV
SVK
SVN
SWE
SWZ
TCD
TGO
THA
TJK
TKM
TON
TTO
TUNTUR
TZA
UGA
UKR
URY
USA
UZB
VCTVEN
VNM
VUT
WSM
YEM
ZAF ZARZMB
ZWE
5060
7080
90Life
Exp
ecta
ncy
1000 2000 3000 4000 5000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI
Life Expectancy vs Health Expenditure
(a.1) (a.2)
AGO
ALB
ARG ARM
ATG
AUSAUT
AZE
BDI
BEN
BFA
BGD
BGR
BHRBHS BLR
BLZBOLBRA
BRB
BWA
CAF
CAN
CHE
CHL
CHN
CIV
CMRCOG
COL
COM
CPV
CRI
CYP CZE
DEU
DJI
DMA
DNK
DOM
DZA
ECU
EGYERI
ESP
EST
ETH
FINFJI FRA
GAB
GBR
GEO GHA
GIN
GMB
GNB
GRC
GRD
GTM
GUYHNDHRV
HTI
HUN
IDNIND
IRN
ISL
ITA
JAM
JORKAZ
KEN
KGZ
KHM
KNAKOR
LAOLBN
LCALKA
LSOLTU
LUX
LVA
MAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NAM
NER
NGA
NICNLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
PNG
POL
PRY
ROM
RUS RWASAU
SDNSEN
SLB
SLE
SLV
SVKSVN
SWE
SWZ
TCD
TGO
THA
TJKTKM
TON
TTO
TUNTUR
TZA
UGA
UKR
URY USA
UZBVCT
VEN
VNM
VUTWSM
YEMZAFZAR
ZMB
ZWE
4060
8010
0Im
mun
izat
ion D
PT
1000 2000 3000 4000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI
Immunization DPT vs Health Expenditure
AGO
ALB
ARG ARM
ATG
AUSAUT
AZE
BDI
BEN
BFA
BGD
BGR
BHRBHS BLR
BLZBOLBRA
BRB
BWA
CAF
CAN
CHE
CHL
CHN
CIV
CMRCOG
COL
COM
CPV
CRI
CYP CZE
DEU
DJI
DMA
DNK
DOM
DZA
ECU
EGYERI
ESP
EST
ETH
FINFJI FRA
GAB
GBR
GEO GHA
GIN
GMB
GNB
GRC
GRD
GTM
GUYHNDHRV
HTI
HUN
IDNIND
IRN
ISL
ITA
JAM
JORKAZ
KEN
KGZ
KHM
KNAKOR
LAOLBN
LCALKA
LSOLTU
LUX
LVA
MAR
MDA
MDG
MEX
MKD
MLI
MNG
MOZMRT
MUS
MWI
MYS
NAM
NER
NGA
NICNLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
PNG
POL
PRY
ROM
RUS RWASAU
SDNSEN
SLB
SLE
SLV
SVKSVN
SWE
SWZ
TCD
TGO
THA
TJKTKM
TON
TTO
TUNTUR
TZA
UGA
UKR
URY USA
UZBVCT
VEN
VNM
VUTWSM
YEMZAFZAR
ZMB
ZWE
4060
80100
Imm
uniz
atio
n D
PT
1000 2000 3000 4000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI
Immunization DPT vs Health Expenditure
(b.1) (b.2)
AGO
ALB
ARG
ARMATG
AUS
AUT
AZE BDI
BEN
BFA
BGD
BGR
BHR
BHS
BLRBLZ
BOL
BRA
BRB
BWA
CAF
CANCHECHL
CHN
CIV
CMRCOG
COL
COM
CPV
CRICYP
CZEDEU
DJI
DMA
DNKDOM
DZAECU
EGY ERIESP
EST
ETH
FIN
FJI
FRA
GAB
GBRGEO
GHA
GIN
GMB
GNB
GRC
GRD
GTM
GUY
HND
HRV
HTI
HUN
IDN
IND
IRN
ISL
ITAJAM
JORKAZ
KEN
KGZ
KHM
KNAKOR
LAO
LBN
LCALKA
LSO
LTU
LUX
LVA
MAR
MDA
MDG
MEX MKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
PNG
POL
PRYROM
RUS
RWA
SAU
SDN
SEN
SLB
SLE
SLV
SVK
SVN
SWE
SWZ
TCD
TGO
THA
TJK
TKM
TON
TTO
TUNTURTZA
UGA
UKR
URY
USA
UZBVCT
VEN
VNM
VUT
WSMYEM
ZAF
ZAR
ZMB
ZWE
5060
7080
9010
0Im
mun
izatio
n M
easl
es
1000 2000 3000 4000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI
Immunization Measles vs Health Expenditure
AGO
ALB
ARG
ARMATG
AUS
AUT
AZE BDI
BEN
BFA
BGD
BGR
BHR
BHS
BLRBLZ
BOL
BRA
BRB
BWA
CAF
CANCHECHL
CHN
CIV
CMRCOG
COL
COM
CPV
CRICYP
CZEDEU
DJI
DMA
DNKDOM
DZAECU
EGY ERIESP
EST
ETH
FIN
FJI
FRA
GAB
GBRGEO
GHA
GIN
GMB
GNB
GRC
GRD
GTM
GUY
HND
HRV
HTI
HUN
IDN
IND
IRN
ISL
ITAJAM
JORKAZ
KEN
KGZ
KHM
KNAKOR
LAO
LBN
LCALKA
LSO
LTU
LUX
LVA
MAR
MDA
MDG
MEX MKD
MLI
MNG
MOZ
MRT
MUS
MWI
MYS
NAM
NER
NGA
NIC
NLD
NOR
NPL
NZL
OMN
PAK
PAN
PER
PHL
PNG
POL
PRYROM
RUS
RWA
SAU
SDN
SEN
SLB
SLE
SLV
SVK
SVN
SWE
SWZ
TCD
TGO
THA
TJK
TKM
TON
TTO
TUNTURTZA
UGA
UKR
URY
USA
UZBVCT
VEN
VNM
VUT
WSMYEM
ZAF
ZAR
ZMB
ZWE
5060
7080
9010
0Im
muni
zatio
n M
easl
es
1000 2000 3000 4000Orthogonalized Public Expditure on Health
Data Source: World Bank WDI
Immunization Measles vs Health Expenditure
(c.1) (c.2)
88
Table B.1. Spearman rank-correlation on input efficiency rankings (DEA)
Note 1. Figures are correlation coefficients from Spearman test, number of observations are in parentheses. 2. ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
PISA
Science
Second Level
Complete
Average year of School
Gross Secondary Enrollment
Net Secondary Enrollment
Gross Primary
Enrollment
Net Primary
Enrollment
DALE
Free Tuberculosis
Infant Survival Rate
Maternal Survival Rate
PISA Science
1.000 (55)
0.72*** (51)
0.80*** (51)
0.74*** (44)
0.76*** (52)
0.63*** (55)
0.78*** (52)
0.19 (55)
0.37*** (55)
0.34** (55)
‐0.18 (55)
Second Level Complete
1.000 (113)
0.97*** (113)
0.96*** (87)
0.95*** (106)
0.80*** (110)
0.85*** (105)
0.23** (113)
0.28*** (106)
0.32*** (113)
0.23**
Average year of School
1.000 (113)
0.95*** (87)
0.95*** (106)
0.75*** (110)
0.87*** (105)
0.28*** (113)
0.30*** (106)
0.36*** (113)
0.17* (113)
Gross Secondary Enrollment
1.000 (103)
0.96*** (103)
0.75*** (101)
0.88*** (100)
0.33*** (102)
0.27*** (93)
0.39*** (103)
0.35*** (101)
Net Secondary Enrollment
1.000 (128)
0.73*** (126)
0.87*** (119)
0.40*** (127)
0.34*** (111)
0.45*** (128)
0.32*** (126)
Gross Primary Enrollment
1.000 (133)
0.74*** (126)
0.08 (132)
0.09 (116)
0.14 (133)
0.13 (131)
Net Primary Enrollment
1.000 (126)
0.50*** (125)
0.41*** (111)
0.50*** (133)
037*** 124)
DALE
1.000 (151)
0.78*** (126)
0.88*** (151)
0.56*** (148)
Free Tuberculosis
1.000 (126)
0.79*** (126)
0.55*** (148)
Infant Survival Rate
1.000 (152)
0.62*** (148)
Maternal Survival Rate
1.000 (148)
89
Table B.2. Spearman rank-correlation on output efficiency rankings (DEA)
Note
3. Figures are correlation coefficients from Spearman test, number of observations are in parentheses. 4. ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
PISA
Science
Second Level
Complete
Average year of School
Gross Secondary Enrollment
Net Secondary Enrollment
Gross Primary
Enrollment
Net Primary
Enrollment
DALE
Free Tuberculosi
s
Infant Survival Rate
Maternal Survival Rate
PISA Science
1.000 (55)
0.21 (51)
0.61*** (51)
0.76*** (44)
0.68*** (52)
‐0.08 (55)
0.53*** (52)
0.39*** (55)
0.43*** (55)
0.64** (55)
0.66*** (55)
Second Level Complete
1.000 (113)
0.84*** (113)
0.71*** (87)
0.69*** (106)
‐0.008 (110)
0.41*** (105)
0.53*** (113)
0.50*** (106)
0.66*** (113)
0.72***
Average year of School
1.000 (113)
0.86*** (87)
0.86*** (106)
‐0.04 (110)
0.55*** (105)
0.69*** (113)
0.66*** (106)
0.85*** (113)
0.86*** (113)
Gross Secondary Enrollment
1.000 (103)
0.91*** (103)
‐0.06 (101)
0.65*** (100)
0.73*** (102)
0.70*** (93)
0.87*** (103)
0.89*** (101)
Net Secondary Enrollment
1.000 (128)
0.0.16* (126)
0.66*** (119)
0.81*** (127)
0.75*** (111)
0.88*** (128)
0.88*** (126)
Gross Primary Enrollment
1.000 (133)
0.38*** (126)
0.10 (132)
‐0.007 (116)
0.08 (133)
0.05 (131)
Net Primary Enrollment
1.000 (126)
0.65*** (125)
0.56*** (111)
0.67*** (126)
0.66*** 124)
DALE
1.000 (151)
0.88*** (126)
0.90*** (151)
0.84*** (148)
Free Tuberculosis
1.000 (126)
0.84*** (126)
0.82*** (148)
Infant Survival Rate
1.000 (152)
0.93*** (148)
Maternal Survival Rate
1.000 (148)
90
Table B.3. Spearman rank-correlation on input efficiency rankings (FDH)
Note 5. Figures are correlation coefficients from Spearman test, number of observations are in parentheses. 6. ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
PISA Science
Second Level
Complete
Average year of School
Gross Secondary Enrollment
Net Secondary Enrollment
Gross Primary
Enrollment
Net Primary
Enrollment
DALE Free Tuberculosis
Infant Survival Rate
Maternal Survival Rate
PISA Science
1.000 (55)
0.69*** (51)
0.80*** (51)
0.69*** (44)
0.71*** (52)
0.41*** (55)
0.76*** (52)
0.18 (55)
0.24* (55)
0.30** (55)
0.26* (55)
Second Level Complete
1.000 (113)
0.91*** (113)
0.87*** (87)
0.80*** (106)
0.50*** (110)
0.83*** (105)
0.19** (113)
0.16* (106)
0.26*** (113)
0.28*** (113)
Average year of School
1.000 (113)
0.88*** (87)
0.86*** (106)
0.44*** (110)
0.85*** (105)
0.30*** (113)
0.24** (106)
0.40*** (113)
0.39*** (113)
Gross Secondary Enrollment
1.000 (103)
0.89*** (103)
0.43*** (101)
0.87*** (100)
0.37*** (102)
0.19* (93)
0.40*** (103)
0.41*** (101)
Net Secondary Enrollment
1.000 (128)
0.35*** (126)
0.82*** (119)
0.47*** (127)
0.34*** (111)
0.51*** (128)
0.47*** (126)
Gross Primary Enrollment
1.000 (133)
0.50*** (126)
‐0.05 (132)
‐0.13 (116)
‐0.11 (133)
‐0.13 (131)
Net Primary Enrollment
1.000 (126)
0.49*** (125)
0.32*** (111)
0.49*** (133)
0.46*** 124)
DALE
1.000 (151)
0.75*** (126)
0.86*** (151)
0.81*** (148)
Free Tuberculosis
1.000 (126)
0.80*** (126)
0.73*** (148)
Infant Survival Rate
1.000 (152)
0.93*** (148)
Maternal Survival Rate
1.000 (148)
91
Table B.4. Spearman rank-correlation on output efficiency rankings (FDH)
Note
Figures are correlation coefficients from Spearman test, number of observations are in parentheses. ***0.01 significance level, ** 0.05 significance level, *0.10 significance level, and insignificant otherwise
PISA Science
Second Level
Complete
Average year of School
Gross Secondary Enrollment
Net Secondary Enrollment
Gross Primary
Enrollment
Net Primary
Enrollment
DALE
Free Tuberculos
is
Infant Survival Rate
Maternal Survival Rate
PISA Science
1.000 (55)
0.20 (51)
0.63*** (51)
0.70*** (44)
0.64*** (52)
‐0.04 (55)
0.47*** (52)
0.34** (55)
0.43*** (55)
0.63** (55)
0.64*** (55)
Second Level Complete
1.000 (113)
0.84*** (113)
0.72*** (87)
0.70*** (106)
0.10 (110)
0.41*** (105)
0.52*** (113)
0.50*** (106)
0.67*** (113)
0.72*** (113)
Average year of School
1.000 (113)
0.87*** (87)
0.86*** (106)
0.06 (110)
0.57*** (105)
0.68*** (113)
0.65*** (106)
0.85*** (113)
0.86*** (113)
Gross Secondary Enrollment
1.000 (103)
0.90*** (103)
0.03 (101)
0.66*** (100)
0.72*** (102)
0.70*** (93)
0.87*** (103)
0.89*** (101)
Net Secondary Enrollment
1.000 (128)
0.20*** (126)
0.68*** (119)
0.79*** (127)
0.74*** (111)
0.86*** (128)
0.88*** (126)
Gross Primary Enrollment
1.000 (133)
0.37*** (126)
0.19** (132)
0.00 (116)
0.11 (133)
0.11 (131)
Net Primary Enrollment
1.000 (126)
0.65*** (125)
0.56*** (111)
0.67*** (133)
0.67*** 124)
DALE 1.000 (151)
0.87*** (126)
0.88*** (151)
0.83*** (148)
Free Tuberculosis
1.000 (126)
0.84*** (126)
0.82*** (148)
Infant Survival Rate
1.000 (152)
0.93*** (148)
Maternal Survival Rate
1.000 (148)
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