Journal of International Development
J. Int. Dev. 15, 709–725 (2003)
Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/jid.1025
MORE ON THE EFFECTIVENESS OF PUBLIC
SPENDING ON HEALTH CARE AND
EDUCATION: A COVARIANCE
STRUCTURE MODEL
EMANUELE BALDACCI,* MARIA TERESA GUIN-SIU* and LUIZ DE MELLO*
International Monetary Fund, Washington, DC, USA
Abstract: Using data for a sample of developing countries and transition economies, this
paper estimates the relationship between government spending on health care and education
and selected social indicators. Unlike previous studies, where social indicators are used as
proxies for the unobservable health and education status of the population, this paper
estimates a latent variable model. The findings suggest that public spending is an important
determinant of social outcomes, particularly in the education sector. Overall, the latent
variable approach yields better estimates of a social production function than the traditional
approach, with higher elasticities of social indicators with respect to income and spending,
therefore providing stronger evidence that increases in public spending do have a positive
impact on social outcomes. Copyright # 2003 John Wiley & Sons, Ltd.
1 INTRODUCTION
Social programmes such as health care and education are generally believed to have a
bearing on human development, and, consequently, increased government spending in
those programmes is expected to result in better social outcomes. However, recent
empirical studies have noted that the impact on outcome indicators of government
spending on social programmes is weak, both in developed and developing countries.
In general, income per capita is a more powerful determinant of school enrollment and
immunization rates, for instance, than the resources spent by the government on programs
aimed at improving social outcomes.
In the case of health care, many studies using data for both developed and developing
countries show that income is the major determinant of the population’s health status,
while the ratio to GDP of public spending on health care, as well as the share of public
outlays in total health care spending, are relatively poor predictors of cross-country
Copyright # 2003 John Wiley & Sons, Ltd.
*Correspondence to: E. Baldacci, M. T. Guin-Siu and L. de Mello, Suite 3-700, Fiscal Affairs Department,
International Monetary Fund, 700 19th Street, Washington, DC, 20431, USA. E-mail: ebaldacci@imf.org
differentials in health indicators (Filmer and Pritchett, 1999; Filmer et al., 2000; Jack,
1999). Recent research on OECD countries suggests, however, that there is a positive,
albeit weak, relationship between public spending on health care and premature mortality
(Or, 2000). In education, a stronger relationship is often reported between public spending
and social indicators when cross-country differences in socio-demographic and economic
indicators are taken into account (Flug et al., 1998). In the same vein, Gupta et al. (2003)
show that both the level and the composition of spending on education, proxying for the
efficiency of government spending, are important determinants of enrolment rates,
persistence rates through grade 4, and primary school dropout rates. However, as in the
case of health care, income tends to dominate the correlation between public spending and
outcomes.
The usual culprits for the generally weak estimated relationship between social
indicators and public spending are data deficiencies (e.g., exclusion of private and sub-
national outlays in total spending data and dearth of disaggregated data on the distribution
of indicators by income class) as well as econometric problems (e.g., ill-specified reduced-
form estimating equations and poorly defined identification tests). This paper focuses on
the latter issue and seeks to address econometric problems by using a latent variable model
(covariance structure model), which, to our knowledge, has not been used in the empirical
literature. The main argument for using a latent variable model is that the health and
education status of the population are unobservable, multi-dimensional concepts and, as
such, cannot be measured by a unique social indicator in a social production function.
Based on the latent variable model, we find strong evidence that public spending affects
school enrolment positively. Moreover, both real income and the intra-sectoral composi-
tion of public spending on education tend to have a higher positive elasticity than in the
traditional approach. Another finding of the paper is that unfavourable initial conditions,
such as high illiteracy rates, reduce the effectiveness of social spending. On health care,
the empirical findings are less clear-cut and, in general, the elasticity of public spending on
health outcomes is lower than in the traditional approach. There is, however, a significant
non-linear negative relationship between public spending and mortality rates, with the
estimated elasticity of spending being higher for a sub-sample of low-income countries.
These results are in line with claims that the poor benefit more from public spending on
health care, and that the relationship between public spending and the health status of the
poor is stronger in low-income countries.
1
In addition, the effect of initial enrolment rates
becomes stronger and income elasticities tend to be lower in poorer countries.
This paper is organized as follows. Section 2 briefly describes the methodology for
estimating the latent variable (or covariance structure) model. Section 3 presents the data
and the estimation results following the traditional approach. Section 4 reports the results
of the latent variable model. Section 5 concludes and presents some policy implications of
the empirical analysis.
2 COVARIANCE STRUCTURE MODELS
The conventional approach to estimating the relationship between health and education
status and government spending is to treat social indicators as outputs and public spending
1
Gupta et al. (2001) and Bidani and Ravallion (1997) find that the poor are affected more favorably by
public spending on health care than the non-poor. The authors use disaggregated data on the distribution
of indicators by income class to analyse the impact of public health spending on the poor.
710 E. Baldacci et al.
Copyright # 2003 John Wiley & Sons, Ltd. J. Int. Dev. 15, 709–725 (2003)
on social programs as an input in a social production function. The problem with this
approach is that the true outputs in this production function are not observable and,
therefore, the use of intermediate health and education indicators as direct proxies for
outcomes biases parameter estimates to the extent that these proxies are poor correlates
with the unobservable output variable (Jack, 1999). The use of nonparametric estimators
in the empirical analysis does not solve this problem, because it does not address the issue
of how to correctly measure the dependent variable.
2
To overcome this problem we argue in this paper that the social production function
should be estimated using a latent variable model.
3
In a nutshell, this methodology differs
from the traditional approach, because instead of regressing observable social indicators
on government spending and control variables, it uses these indicators as determinants of
an unobservable, latent variable. Subsequently, the information available in the covariance
matrix of both the usual explanatory variables and the social indicators is used to estimate
the empirical association between government spending and the unobservable output
variable.
4
Covariance structure models are useful statistical tools in the estimation of
structural relationships involving unobservable variables, such as well-being, trust, and
happiness,
5
and when the relevant variables define multidimensional concepts, such as
poverty or, as in the case at hand, the population’s health and education status.
6
In particular, covariance structure models can be interpreted as a synthesis of two
different models (Long, 1983b): (i) a measurement or confirmatory factor model, which
has been widely used in social sciences; and (ii) a standard structural equation model,
where the relevant variables are not affected by measurement errors, as in the standard
regression analysis. The factor model assumes that a vector of p observed variables x can
be generated by a corresponding vector n of q unobserved variables with an error term d:
x ¼ Kn þ d ð1Þ
where K is a matrix of factor loadings in which each
i; j
measures the correlation between
the latent variable
j
and the observed variable x
i
; i ¼ð1; ...; pÞ and j ¼ð1; ...; qÞ.
For two vectors of observable variables (x and y), equation (1) can be defined as a
system:
x ¼ K
x
n þ d and y ¼ K
y
g þ e ð2Þ
where the observable variables in vectors x and y are defined as deviations from their
means and the unobserved variables in vectors n and g are uncorrelated with the error
2
For empirical studies on nonparametric estimations of social production functions see, for instance, Tulkens and
Van den Eeckaut (1995).
3
See Alesina and La Ferrara (2000), for a recent example of an application of latent variable methodology to
economic problems.
4
If data are available for a set of observable variables that are known to be associated with the latent variable,
covariance structure models allow for estimating the relationship between the unobserved variables and the set of
observable regressors. This can be done by decomposing the covariance matrix of the observable variables (or the
correlation matrix when the observable variables are standardized) according to a model describing the
correlations among the latent factors measured by the observable variables.
5
Covariance structure models are also useful in dealing with variables measured with error, and in statistical
problems involving simultaneity and interdependence among the relevant variables. See Goldenberger and
Duncan (1973), for more information.
6
For a discussion of the multidimensional nature of health status, see for instance Wang et al. (1999).
Public Spending on Health Care and Education 711
Copyright # 2003 John Wiley & Sons, Ltd. J. Int. Dev. 15, 709–725 (2003)
terms. In addition, the error terms are assumed to be uncorrelated across the equations in
the system.
The second part of the covariance structure model (the structural equation model)
consists of defining the causal relationships among the latent variables defined in equation
(2), the description of the causal effects, and the assignment of the explained and
unexplained variances. The structural equation model can be written as:
g ¼ Bg þ Cn þ f ð3Þ
where and are the vectors of, respectively, endogenous and exogenous latent variables,
defined in equation (2); B is a matrix of regression coefficients associated with the
endogenous latent variables, with zero diagonal elements, and let I B be non-singular; C
is a matrix of parameters, capturing the effect of the exogenous latent variables on the
endogenous latent variables; and f is a vector of random disturbances.
All variables are defined in equation (3) as deviations from their means and the vector of
exogenous latent variables is assumed to be uncorrelated with the random error terms. The
variance-covariance matrix of x and y can be expressed in terms of all the parameters of
the system, given some necessary overall identification restriction (Jo
¨
reskog and So
¨
rbom,
1989). The usual identification restrictions for structural equation models apply to
equation (3) in the absence of measurement errors.
The covariance structure model (2)–(3) can be estimated for a covariance matrix R
defined as E [zz
0
], where z is a vector constructed by stacking the variables in y on the top
of those in x. The predicted covariance matrix can be defined as:
R ¼
K
y
A CUC
0
þ W
A
0
K
0
y
þ H
"
K
y
ACUK
0
y
K
x
UC
0
A
0
K
0
x
K
x
UK
0
x
þ H
ð4Þ
where A ¼ I B; U is the covariance matrix of n, W is the covariance matrix of f, and H
and H
"
are the covariance matrices of d and e, respectively.
Assuming that all variables are normally distributed, the parameters in equation (2) can
be estimated by maximum likelihood, by minimizing the following expression:
tr R
1
S
þ logjRjlogjSj½r þ sðÞ; ð5Þ
where r and s denote, respectively, the number of endogenous and exogenous latent
variables, and S is the observed covariance matrix.
Goodness-of-fit measures include (1) an
2
statistic, which can be used to test the
estimated model against the alternative that the covariance matrix is unconstrained;
7
(2) an
adjusted goodness-of-fit statistic, which measures the share of total variance explained by
the model; and (3) the root mean squared error, defined as the average of the fitted
residuals, which can be used when the relevant variables are standardized.
8
7
If the probability of the test exceeds classical significance levels, the null hypothesis is accepted and the model is
a good representation of the real covariance matrix of the population.
8
The significance of each parameter can be also tested using a z-statistic distributed as a t-ratio under
multivariate normality.
712 E. Baldacci et al.
Copyright # 2003 John Wiley & Sons, Ltd. J. Int. Dev. 15, 709–725 (2003)
3 DATA AND PRELIMINARY FINDINGS
3.1 The Data
Data on public spending on health care and education, as well as the relevant social
indicators, are available for a sample of 94 developing countries and transition economies
9
in the period 1996–98.
10
The dataset contains information on three groups of variables:
public social spending, social indicators, and a set of variables that are known to affect
the relationship between social spending and outcomes. Health status indicators in-
clude infant and child mortality rates, as well as DPT immunization rates (children
aged 1 or less).
Education attainment indicators include primary and secondary school enrolment rates,
in addition to persistence through grade 5.
11
The control variables comprise socio-
demographic factors (i.e., fertility rates, secondary enrolment rates for girls, and adult
illiteracy rates), proxies for economic development (urbanization rates and GDP per
capita), and sector-specific indicators (pupil-teacher ratios and the ratio of public spending
on education per pupil in primary and tertiary education).
The descriptive statistics, reported in Table 1, show that the public spending ratios are
on average lower in our sample than those of high-income countries, as expected, but are
in line with the middle-income country average (Chu et al., 1995). The standard deviations
are high, at almost half of the mean for most of the variables. Also, spending per pupil is
much lower for primary than tertiary education, suggesting that the composition of
education spending is a factor that could contribute to the large differences in social
outcomes in the sample. With regard to social indicators and control variables, gross
school enrolment rates are much higher for primary education than for secondary
education. The standard deviation of the ratio of public outlays to GDP, measuring
government size, is high, reflecting the inclusion of transition economies and higher-
income countries in the sample.
Turning to raw correlations, public spending on education is positively correlated with
school enrolment rates but the correlation between public spending and persistence
through grade 5 is not statistically significant. Public outlays on health care correlate
negatively with infant and child mortality, and positively with access to sanitation and
DPT immunization rates.
12
As expected, the ratio of public spending per pupil in tertiary
education to that in primary education, measuring the intrasectoral composition of
9
The original dataset of 111 countries exhibited considerable dispersion in many indicators. Principal component
analysis and cluster analysis (Bouroche and Saporta, 2002; Morrison, 1990) were used to assess the sources of
variance in the data and to identify the potential outliers in the sample. Based on these results, the original sample
was reduced to 94 countries, after eliminating 17 outliers.
10
We used the World Bank’s World Development Indicators data base as a source for social indicators and
national statistical data for central government spending on health and education.
11
The choice of indicators used to measure the efficiency of public spending on health care and education was
guided by their appropriateness as proxies for education and health care performance and the availability of
internationally comparable data for a wide range of countries. See Gupta and others (2000) for more information
on international social development goals and performance indicators.
12
Public outlays on health care are typically positively correlated with life expectancy at birth (Anderson et al.,
2000; Or, 2000), although the correlation between public spending and income is much stronger (Pritchett
and Summers, 1996; Filmer and Pritchett, 1999). Spending on health care is also usually negatively
correlated with malnutrition rates (Peters et al., 1999).
Public Spending on Health Care and Education 713
Copyright # 2003 John Wiley & Sons, Ltd. J. Int. Dev. 15, 709–725 (2003)
