1 | P a g e

Impact of Maternal and Child Health on Economic Growth:

New Evidence Based Granger Causality and DEA Analysis

Final version: March 2013

Arshia Amiria, Ulf-G Gerdtham

b,c,d

a Research assistant, Shiraz, Iran

b Department of Economics, Lund University, Lund, Sweden

c Health Economics & Management, Institute of Economic Research, Lund University, Lund,

Sweden d Centre for Primary Health Care Research, Lund University, Lund, Sweden

Study commissioned by

the Partnership for Maternal, Newborn & Child Health (PMNCH)

2 | P a g e

Table of contests

Executive Summary Page 3

1. Introduction Page 7

1.1. Background Page 7

1.2. Rationale Page 7

1.3. Objectives of the study Page 8

2. Methodology Page 9

2.1. Data Page 9

2.2. Empirical strategy Page 9

3. Result Page 11

3.1. Granger Causality of health outcomes and GDP per capita Page 11

3.2. The result of a Barro inspired growth model using DEA method Page 16

4. Conclusions and discussion Page 21

5. Apendix Page 23

5.1. Fixed effect panel data analysis Page 23

5.2. Data Envelopment Analysis (DEA) Page 25

References Page 29

3 | P a g e

Executive Summary Background

The health of women, mothers and children is fundamental to development, as reflected in

Millennium Development Goals (MDGs) 4 (reducing child mortality) and 5 (improving maternal

health and achieving universal access to reproductive health). Significant additional investments

are needed to achieve MDGs 4 and 5 and to improve women’s and children’s health beyond the

MDG target date of 2015. Demonstrating the broader societal returns of investment in women’s

and children’s health can be a critical tool in mobilizing additional resources. Economic

arguments may resonate particularly well with certain stakeholders who influence investment

decisions, such as Ministries of Finance, parliamentarians, bilateral and multilateral donors, and

global and regional development banks.

To support global, regional and national advocacy for increasing resources, demand has been

expressed by members of the Partnership of Maternal, Newborn & Child Health (PMNCH) and

the broader reproductive, maternal, newborn and child health (RMNCH) community for the

synthesis, and if necessary, the generation of evidence on the economic benefits of investing in

RMNCH. To achieve this, a work program has been established under the auspices of PMNCH.

The work program includes a systematic literature review, an econometric study of the

relationship between RMNCH outcomes and economic growth, the development of a

framework/model for estimating the national economic returns of investment in RMNCH, and

technical consultations.

Objectives

The objectives of this study are: (i) to examine whether there are relationships between maternal

and child health outcomes and economic growth in different countries at different income levels,

and, given such relationships, (ii) to estimate the direction and magnitude of these relationships.

Methods

As measures of maternal and child health, we use the under-five mortality rate (the number of

deaths of children under five per 1,000 live births) and the maternal mortality ratio (the number

of deaths per 100,000 live births). Data on mortality in 1990-2010 is taken from the WHO global

data repository (http://apps.who.int/ghodata/) including 180 countries for under-five mortality

and 170 countries for maternal mortality. As a measure of economic growth we use per capita

Gross Domestic Product (GDP) in 1990-2010in 2000 US$ from the World Bank’s World

Development Indicators 2012: http://devdata.worldbank.org/wdi2011.htm.

To examine whether there are relationships between maternal and child mortality and economic

growth we use international country-level panel data and Granger causality analysis to identify

the direction of the relationships between GDP and maternal and child mortality and to estimate

4 | P a g e

the rough magnitude of the effects involved.1

However, because of restrictions in data

availability we are not able to include other related factors in the Granger causality analysis. To

improve the estimate of the effect of reductions in child mortality on GDP, by taking into

account other growth related factors, we follow one of the most influential growth models in

economics proposed by Barro (1990)2 in combination with Data Envelopment Analysis (DEA).

3

Using DEA and the Barro model, we estimate how much a decrease in child mortality may

increase GDP for each country.

Results

Below we report the result of the Granger analysis of the direction of the relationships between

GDP and maternal and child mortality and the results of the DEA analysis of the impact of

reductions in child mortality4 on GDP growth.

A. The Granger analysis of direction of association

i. The under-five mortality and economic growth:

In 105 of 180 (58%) countries, we find bi-directional relationships.5 This indicates that in the

majority of countries, changes in under-five mortality have an impact on GDP and vice versa.

In 49 countries (27%) we find one-way relationships from under-five mortality to GDP. In 14

countries (8%) we find one-way relationships from GDP to under-five mortality. For the

remaining 12 countries (7%), no relationships are found.

ii. Maternal mortality and economic growth:

In 68 of 170 (40%) countries we find bi-directional relationships. One-way relationships from

maternal mortality to GDP are found in 50 countries (29%) and one-way relationships from GDP

to maternal mortality are found in 19 countries (11%). No relationships are found in 33 countries

(19%).

We also find that the magnitude of the effect of reductions in child mortality on GDP in high-

income countries (HICs) and upper middle-income countries (UMICs) is larger than lower-

1 Granger, C.W.J. (1969) Investigating causal relations by econometric models and cross-spectral methods.

Econometrica 37, 424–38. 2Barro, R.J. (1990) Government spending in a simple model of endogenous growth. Journal of Political Economy

98, 103–125. 3We use an explicit endogenous growth model (Barro, 1990), in which public expenditure is considered as an input

of the production function. For y the GDP per unit of labor, we have: y = f(k, d) with k, the private capital by unit of

labor, and d, a “productive public expenditure”, see Ventelou, B. & Bry, X. (2006) The role of public spending on

economic growth: Envelopment methods. Journal of Policy Modeling 28, 403–413. 4In calculating DEA, we made child mortality as the index of child health because of having higher significant

causal relationship with GDP instead of maternal mortality. 5A bi-directional relationship (H↔Y) implies that variation of H (Y) causes variation of Y (H). A unidirectional

relationship from, for example, H to Y (H→Y) means that variation of H has a significant effect on Y, but the

variation of Y has no effect on H.

5 | P a g e

middle-income countries (LMICs) and low-income countries (LICs). However, in contrast, the

magnitude of the effect of GDP on maternal and child health outcomes in LMICs and LICs are

larger relative to HICs and UMICs.

B. Barro growth model / DEA analysis of magnitude

To explore the effects of other growth-related factors in the model, we used DEA analysis in a

Barro framework where in addition to child health we included government spending, population

and (fixed) capital in the model, in order to determine the efficiency rate. The efficiency rate for

each country demonstrates the magnitude of the impact of child health outcomes on GDP. In

Cote d'Ivoire the efficiency rate is 91.5% in 2001 to 2010. This may be interpreted as follows: if

child health increases by one percentage (one percentage point reduction in the under-five

mortality rate), increases GDP by 5% (as an example) in a country with a 100% efficiency rate,

then GDP in Cote d'Ivoire will increase by 4.6% (0.915*5%).

The results of the DEA analysis indicate that reductions in mortality will generally have a large

effect on GDP growth, since the average overall efficiency rates for all countries in the data are

more than 90% (91.1% in 1990-2000 and 92.2% in 2000-2010). As noted above, the results

indicate that a decrease in child mortality would lead to a larger effect on GDP in richer

countries compared with poorer countries, although the difference in the average efficiency rate

between different groups of countries are not statistically significant.

Countries with the highest efficiency rates overall are Bahamas, Canada and Germany. The

lowest efficiency rates overall were found for Madagascar, Paraguay and Singapore. Armenia,

China and the Ukraine have the highest efficiency rates among LMICs, whereas Liberia,

Mozambique and Tanzania have the highest efficiency rates among LICs. Algeria, Guatemala

and Honduras have the lowest efficiency rates among LMIC, whereas Benin, Kenya and

Madagascar have the lowest efficiency rates among LICs.

Discussion

Analysis of the causal direction of the relationships between GDP and maternal and child health

outcomes and the magnitude of the effects is important since the results can provide powerful

arguments for investment in maternal and child health.

We find in general that the relationships between maternal and child health outcomes and GDP

run in both directions, with the majority running from maternal and child health to GDP. We find

evidence that the causal effects of GDP on maternal and child health outcomes are stronger in

LICs and LMICs relative to HICs and UMICs. This may reflect that the effect of marginal health

investments on health outcomes is higher at low levels of GDP, i.e. in countries where the level

of health investments is generally lower.

6 | P a g e

In contrast, the causal effect of maternal and child mortality on GDP is generally stronger in

HICs and UMICs. This may be due to the differences between poor and rich countries with

respect to the human capital level or infrastructure. Human capital is the stock of competencies,

knowledge, social and personality attributes, including creativity, embodied in the ability to

perform labor so as to produce economic value.6 The higher human capital level of richer

countries compared to poorer countries implies that an equal reduction in maternal and child

mortality will cause GDP to increase more in richer countries than in poorer countries.

6Simkovic, M. (2012) Risk-based student leons. Whasington and lee law review 70, 1.

7 | P a g e

1. Introduction

1.1. Background

Reproductive, maternal, newborn & child health (RMNCH) is fundamental to development,

which is reflected in Millennium Development Goals (MDGs) 4 (reducing child mortality) and 5

(improving maternal health and achieving universal access to reproductive health). It has been

demonstrated that significant additional investments are needed to achieve MDGs 4 and 5 and

improve women’s and children’s health beyond the MDG target date of 2015

(http://www.who.int/pmnch/activities/jointactionplan/en/). Developing and presenting economic

arguments that resonate with stakeholders influence investment decisions, such as Ministries of

Finance and Planning, which are critical to mobilize additional resources. These stakeholders

need to be convinced that spending on RMNCH should be seen as an investment, and not simply

a cost.

For a long time the prevailing view among economists was that the link between health and

economic development ran in one direction only, from economic development to investment in

health. This view was articulated in an influential background paper to the World Development

Report 1993 entitled Wealthier is Healthier. It recognized that economic development leads to

improved health outcomes through its impact on indirect pathways to health – such as better

nutrition, water and sanitation, living environment and education – but the reverse direction of

health’s impact on economic development was not fully acknowledged. This paradigm began to

shift about 10 years ago, particularly through the work of the Commission on Macroeconomics

and Health (CMH; http://www.who.int/macrohealth/en/). The CMH demonstrated that the

causality runs in both directions and that "healthier is wealthier".7 Nevertheless, most of the

evidence presented by the CMH was related to the effects of investments in HIV/AIDS and

malaria.

1.2. Rationale

Two of the major objectives of the Partnership for Maternal, Newborn & Child Health

(PMNCH) are (a) to address evidence gaps and (b) to contribute to raise additional funds to

address MDGs 4 and 5.

In 2009, PMNCH developed an investment case for RMNCH in Asia and the Pacific in

collaboration with an informal network of institutions and analysts concerned with the lack of

progress on MDGs 4 and 5 in the region.8 An investment case for Africa was developed in 2010

in collaboration with Harmonization for Health in Africa

(http://www.who.int/pmnch/topics/economics/20110414_investinginhealth_africa/en/).

7For example, a Commission background study by Bloom and Williamson entitled “Demographic transitions and

economic miracles in East Asia” attributed 30-50% of East Asia’s impressive growth in 1965-1990 to reduced infant

and child mortality, lower fertility rates, and improved reproductive health (see Bloom and Williamson, 1997). 8MNCH network for Asia and the Pacific (2009) Investing in maternal, newborn and child health – The case for

Asia and the Pacific. Geneva: WHO and PMNCH.

8 | P a g e

Literature reviews were conducted to inform the investment cases and it became clear that there

is limited evidence on the economic benefits of investing in RMNCH.

To support global, regional and national advocacy for increasing resources, demand has been

expressed by members of PMNCH and the broader RMNCH community for the synthesis, and if

necessary, the generation of evidence on the economic benefits of investing in RMNCH. To

achieve this, a work program has been established under the auspices of PMNCH. The work

program includes a systematic literature review, an econometric study of the relationship

between RMNCH outcomes and economic growth, the development of a framework/model for

estimating the national economic returns of investment in RMNCH, and technical consultations.

1.3. Objectives of the study

The objectives of this study are: (i) to examine whether there are relationships between maternal

and child health outcomes and economic growth in different countries at different income levels,

and, given such relationships, (ii) to estimate the direction and magnitude of these relationships.

In an econometrics analysis between two variables, two main aims are, firstly, finding the

existence and direction of causal relationships between variables and, secondly, measuring the

magnitude of the effects between variables. To reach the first aim, we analyze the causal

relationships between health outcomes (maternal and child mortality) and income, or rather per

capita gross domestic product (GDP). To define the dimension of effect of the relationships in

the first aim, we calculate the efficiency of the health outcomes on increasing GDP in growth

amounts of variables in a Barro framework. Thus in the analysis we use country-level panel data

(180 countries) and Granger causality analysis to identify the direction of relationships between

the health outcomes and GDP and also to perform an approximate estimate of the magnitude of

the effects involved by employing advanced econometric techniques. We describe this in detail

in the next section. A limitation of our Granger analysis is that we are not able to include any

control variables due to limitations in the available data9. We therefore complement the analysis

by a Data Envelopment Analysis (DEA)10

which is applied on a Barro (1990) inspired growth

model. By use of the DEA method, we estimate how much an improvement in the health

outcomes will impact on GDP for each country relative to others, which in turn indicates the

economic return in terms of GDP of potential investments in health in various countries.

Efficiency is a key concept in economic analysis. Since the seminal work of Charnes et al.

(1978), some of the major research has focused on DEA over the last three decades (Cook and

Seiford, 2009). In an economic analysis of variables like economic growth, GDP and

productivity, which can be defined as outputs of a production function, it is important to know

9Since the number of observations in the time dimension is limited in the WHO data set, we are not able to include

control variables in the Granger analysis. 10We use an explicit endogenous growth model (Barro, 1990), in which the public expenditure is considered as an

input of the production function. For y the GDP per unit of labor, we have: y = f(k, d) with k, the private capital by

unit of labor, and d, a “productive public expenditure” (Ventelou and Bry, 2006).

9 | P a g e

that how much these variables can be expected to increase as a result of changes in different

input factor (see Farrell, 1957). In other words, it would be important to find out that what would

be the maximum effect of input variables (like child health) on output (like GDP)? The answer

may be found in DEA. The investigation of efficiency on the relationship between different

health outcomes and GDP would be important to economists in informing policies to improve

the effects of the health outcomes on economic growth.

2. Methodology

2.1. Data

Five variables11

are available on the WHO data website (http://apps.who.int/ghodata/) as

indicators of child health. In the current study, we use the under-five mortality rate (probability

of dying by age 5 per 1,000 live births), which is a commonly used indicator to measure progress

on child health (and is the indicator of MDG4). In addition, to measure maternal health (MDG5),

we use the maternal mortality ratio (number of deaths per 100,000 live births). As a measure of

economic growth we use GDP in 2000 US prices (World Bank’s World Development Indicators

2012; http://devdata.worldbank.org/wdi2011.htm). Data for 1990-2010 was selected to the

analysis.

We include 42 high-income countries (HIC), 38 upper-middle-income countries (UMIC), 50

lower-middle-income countries (LMIC), and 50 low-income countries (LIC), i.e. 180 countries

in total. We use 5-year pooled data from 1990 to 2010 (1990-2010). For the list of countries

included in our data, see Table 4 below.

For the purpose of testing the efficiency of the health outcomes on GDP growth in a Barro model

framework, the data of GDP growth (annual %), population growth (annual %), and general

government final consumption expenditure (annual % growth) are derived from the World

Bank’s World Development Indicators, 2012, in weighted means of the first and last years of two

periods of 1990 to 2000 and 2000 to 201012

, in growth amounts. For the list of available data

during each period see Tables 4 and 5.

2.2. Empirical strategy

In panel data analysis it is possible to classify three main types of approaches. The first one was

pioneered by Holtz-Eakin et al. (1985), which estimates and tests vector autoregression (VAR)

coefficients using panel data by taking the autoregressive coefficients and regression coefficients

slopes as variables. A similar procedure was applied by Hsiao (1986), Holtz-Eakin et al. (1988),

Hsiao (1989), Weinhold (1996), Weinhold (1999), Nair-Reichart and Weinhold (2001) and Choe

11Infant mortality rate (probability of dying between birth and age 1 per 1000 live births), under-five mortality rate

(probability of dying by age 5 per 1000 live births), the number of infant deaths (thousands), the number of under-

five deaths (thousands), and measles immunization coverage among 1-year-olds (%). 12In many growth models, economists commonly calculate their variables in the period of 10 years.

10 | P a g e

(2003). The second approach proposed by Hurlin and Venet (2001), Hurlin (2004a, b), Hansen

and Rand (2004), Judson and Owen (1999) treats the autoregressive coefficients and regression

coefficient slopes as constants using a panel data Fixed Effects (FE) estimator. Adams et al.

(2003) can be treated as the third approach dealing with causality in panel data models. The main

contribution of this approach is proposing a refinement for small data sets (see Adams et al.,

2003, p. 8). However, as stressed by Hoover (2003), the approach by Adams et al. (2003) lacks

rigorous test of invariance that causal inference needs (Erdil and Yetkiner, 2010).

Our study employs the second approach because of its suitability to our data sets, in which we

have relatively a short time dimension but large number of countries. In panel data analysis the

error term uit may be decomposed into country effects μi, time effects £t, and a random term vit.

The country effects represent all country-specific omitted variables and the time effects represent

all omitted variables that have equal effects on all countries. Different ways of modeling these

countries and time-specific terms provide different panel data models. An OLS regression

assumes that μi=0 and £t=0. An FE model assumes that μi and/or £t are fixed constants for each

country and time period respectively, in which an appropriate panel model is OLS with country-

specific and/or time-specific dummy variables. If the FE is the correct specification, but an OLS

is estimated, the estimated effects will be biased if μi is correlated with other explanatory

variables.

To reach the objectives in the study, we use the Granger causality analysis to explore the

direction of the effect of variation between the variables (health outcomes and GDP) using panel

data for individual countries. In testing causality with panel data, it is vital to test heterogeneity

between cross-section units. The first source of heterogeneity is caused by permanent cross

sectional disparities. A pooled estimation without the heterogeneous intercepts may lead to a bias

of the slope estimates and could result in a fallacious inference in causality tests (Hurlin, 2004a;

see Erdil and Yetkiner, 2010). Another basis of heterogeneity caused by heterogeneous

regression coefficients θk is more problematic than the first one, i.e. one should consider the

different sources of heterogeneity of the data generating process. Thus a series of different

causality hypothesis will be tested: two types of homogenous causality hypotheses: 1)

homogenous and instantaneous non-causality hypothesis (HINC) and 2) the homogenous

causality hypothesis (HC) and an overall (homogenous) causality within country income group.

If 1) and 2) are rejected then we test the heterogeneous non-causality hypothesis (HENC). For

more details about panel data analysis and Granger causality tests, see appendix (section 5.1).

If we find causal relationships between health outcomes and economic growth for most

countries, then we assume that that decreases in health outcomes in average increases GDP. For

countries where we cannot identify casual relationships we assume that other factors blurred the

health outcomes-growth relationship. Given that there is in general a significant causal

relationship from health outcomes to GDP, we extend the analysis and calculate the efficiency

rates of health outcomes on GDP using DEA analysis which aims to measure how much GDP

can be increased in different countries at present health outcomes if the efficiency rate of health

11 | P a g e

outcomes on GDP increases. This measure is based on the assumption that there is no room for

further increases in the efficiency rate for those countries at the measured 100% efficiency rate.

DEA analysis is the non-parametric mathematical programming approach to frontier estimation.

The piecewise-linear convex hull approach to frontier estimation, proposed by Farrell (1957),

was considered by only a handful of authors in the two decades following Farrell paper. Authors

such as Afriat (1972) suggested mathematical programming which could achieve the task, but

the method did not receive wide attention until a paper by Charnes et al. (1978) coined the term

DEA. There have since been a large number of papers which have extended and applied the

DEA methodology (Coelli, 1996). For more discussion of DEA see appendix (section 5.2).

3. Results

3.1. Granger Causality of health outcomes and GDP per capita

To reach the objectives in the study, we use the Granger causality analysis to explore the

direction of the effect of variation between the variables (health outcomes and GDP) using panel

data for individual countries. Below we present the results of the Granger causality analysis.

Table 3 shows the values of Wald statistics for testing the two types of homogenous causality

hypotheses: HINC and HC. The results allow us to reject both of the null hypotheses at 1% level

of significance indicating no homogenous causality between GDP and health outcomes (child

mortality and maternal mortality), i.e. the existence of causal relationships appears to differ

across countries. We further test whether the causality is an overall (homogenous) causality for

each country income group or sourced from causality relations for individual countries

(heterogeneous). The test also rejects the existence of a homogeneous causality. The final step is

discovering the existence of causality in the individual countries.

In sum: our results confirm that in the majority of countries there is a feedback (bi-directional)

causal relationship of health outcomes on GDP which indicates that investments in health may

provide returns in terms of higher GDP. We also find that the relationship between under-five

mortality (MDG4) and GDP is often more significant than maternal mortality (MDG5) and GDP.

In the Granger analysis, we find a stronger relationship between health outcomes and GDP in

LIC and LMIC compared to HIC and UMIC which may be due to the level of human capital

dependency and higher marginal effect of health spending on LIC and LMIC. We also find that

the stronger relationships are because the effects of GDP on health are stronger in LIC and LMIC

compared to HIC and UMIC while in contrast it is found that the effects of health on GDP are

stronger in HIC and UMIC compared to LIC and LMIC.

i. Under-five mortality and economic growth:

12 | P a g e

In 105 (58%) of 180 countries we find bi-directional13

relationships (see Tables 1 and 3). This

implies that in the majority of countries, changes in GDP have an impact on under-five mortality

and vice versa. In the context of country groups, the shares of bidirectional causality are

observed at 55%, 29%, 66% and 76% for HIC, UMIC, LMIC and LIC, respectively.

In 49 countries (27% from total) we find a one-way relationship from under-five mortality to per

capita GDP. In 14 countries (8%) we find a one-way relationship from per capita GDP to under-

five mortality. For the remainder 12 countries, we find no significant relationships (7%). The

shares of under-five mortality to GDP causal relation are 19%, 53%, 24% and 18%, and also

from GDP to under-five mortality are 17%, 3%, 8% and 4% for HIC, UMIC, LMIC and LIC,

respectively.

ii. Maternal mortality and economic growth:

In 68 (40%) of 17014

countries we find bi-directional relationships (see Tables 1 and 4). In the

context of country groups, the shares of bidirectional causality are observed at 31%, 9%, 53%

and 55% for HIC, UMIC, LMIC and LIC, respectively.

A one-way relationship from maternal mortality to GDP and the inverse one (GDP_maternal

mortality) are obtained in 50 (29%) and 19 (11%) countries, respectively. The shares of maternal

mortality to GDP causal relation are 29%, 59%, 26% and 12%, and also from GDP to maternal

mortality are 16%, 0%, 10% and 9% for HIC, UMIC, LMIC and LIC, respectively. No

relationships are found in 33 (19%) countries.

Table 1. The percentage of significant relationships and the average size of effect between

MDG4/MDG5 & GDP

Percentage of significant relationships between MDG5 & GDP Average of size of effect

Country group Bilateral MDG4 to GDP GDP to MDG4 MDG4 to GDP GDP to MDG4

HIC 55% 19% 17% -598.87 -0.0041

UMIC 29% 53% 3% -283.99 -0.078

LMIC 66% 24% 8% -174.63 -0.039

LIC 76% 18% 4% -96.21 -0.21

Totality 58% 27% 8% -288.42 -0.083

Percentage of significant relationships between MDG5 & GDP Average of size of effect

Country group Bilateral MDG5 to GDP GDP to MDG5 MDG5 to GDP GDP to MDG5

HIC 31% 29% 16% -397.17 -0.014

13Suppose that we have two variables (H: child health & Y: GDP). If we find a bilateral relationship (H↔Y), it

means that the variation of H causes the variation of Y and our variables have a high effect on each other. If we find

a unidirectional relationship from H to Y (H→Y), it means that the variation of H has a significant effect on Y, but the variation of Y has no effect on H, and similar for Y→H. 14In the analysis of maternal mortality (MDG5) and under-five mortality, we exclude 12 countries due to lack of data

availability in WHO data set (Andorra, Antigua and Barbuda, Argentina, Dominica, Kiribati, Marshall Islands,

Monaco, Palau, San Marino, St. Kitts and Nevis, Seychelles, and Tuvalu are excluded). However, we include 2

countries (West Bank and Gaza and Puerto Rico) in analyzing MDG5 whose MDG4 observations are not available.

13 | P a g e

UMIC 9% 59% 0% -151.38 -0.10

LMIC 53% 26% 10% -117.52 -0.32

LIC 55% 12% 9% -13.02 -1.09

Totality 40% 29% 11% -169.77 -0.38

Notes: In order to compare the size of effect of statistically significant relationships, the average of the coefficients

of first lag of exogenous variable is reported. This amount is a good index for size of effect which is just useful for

comparison, econometrically.

In the statistically significant relationships, interestingly, we also find that the magnitude of the

effect of health on GDP in HICs and UMICs is bigger compared to LMICs and LICs while the

size of the effect of GDP on health in LMICs and LICs are generally bigger compared to HICs

and UMICs. The latter may reflect that the marginal effect of health investments on health

outcomes is more effective in poorer countries. However, at the same time, as indicated by the

former effect, investments in health on GDP may not go in the same direction, for example, since

the quality-improving effect of labor, through better health, on GDP, is higher in richer countries

Over 90% of valid coefficients in the countries are negative, which means that our empirical

results are similar to economic theories that suggest a negative relationship between child

mortality and GDP.

Table 2. Test results for homogenous causality hypotheses

County group Test MDG4→ GDP GDP→ MDG4 MDG5→ GDP GDP→ MDG5

High-income HINC 5.89E+29** 7.17E+27** 5.01E+28** 6.35E+28**

HC 5.91E+29** 1.12E+33** 5.42E+28** 2.66E+32**

Upper-Middle-income HINC 966.69** 3.48** 34.47** 2.83**

HC 980.20** 282240.5** 50.13** 1850.04**

Lower-Middle-income HINC 5.92E+27** 2.41E+29** 9.92E+26** 9.02E+29**

HC 5.96E+27** 4.55E+32** 9.98E+26** 1.30E+33**

Low-income HINC 32.07** 313.85** 1.32E+27** 174.18**

HC 31.64** 1198923.00** 1.35E+27** 1185282.00**

Notes: ** p<0.01%. Most series of GDP and under-five mortality rate contain unit root.

Table 3. Test results for heterogeneous causality hypotheses between under-five mortality

(MDG4) and GDP

HICs Direction UMICs Direction LMICs Direction LICs Direction

Andorra No Argentina Dead-y Albania Bilateral Bangladesh Bilateral

Antigua and

Barbuda Bilateral Belize Bilateral Algeria Bilateral Benin Dead-y

Australia Bilateral Botswana y-Dead Angola Bilateral Burkina Faso Bilateral

Austria Bilateral Brazil Bilateral Armenia Dead-y Burundi Bilateral

Bahamas, The y-Dead Bulgaria No Azerbaijan Dead-y Cambodia Bilateral

Bahrain Bilateral Chile Dead-y Belarus Bilateral Central African

Republic Bilateral

Barbados y-Dead Costa Rica Dead-y Bhutan Dead-y Chad Bilateral

14 | P a g e

Belgium Dead-y Croatia Dead-y Bolivia Bilateral Comoros y-Dead

Brunei Darussalam Bilateral Dominica Dead-y Bosnia and

Herzegovina Bilateral Congo, Rep. Bilateral

Canada Dead-y Equatorial Guinea Bilateral Cameroon y-Dead Cote d'Ivoire Bilateral

Cyprus y-Dead Gabon Dead-y China Dead-y Eritrea Bilateral

Czech Republic Bilateral Grenada Dead-y Colombia Bilateral Ethiopia Bilateral

Denmark Bilateral Hungary Dead-y Congo, Dem.

Rep. Bilateral Gambia, The Bilateral

Estonia Bilateral Kazakhstan Dead-y Cuba Bilateral Ghana Bilateral

Finland y-Dead Latvia No Djibouti Bilateral Guinea Bilateral

France Bilateral Lebanon Bilateral Dominican

Republic Bilateral Guinea-Bissau Bilateral

Germany No Libya Bilateral Ecuador Bilateral Haiti Dead-y

Greece Bilateral Lithuania Dead-y Egypt, Arab Rep. Dead-y India y-Dead

Iceland Bilateral Malaysia Dead-y El Salvador Bilateral Kenya Bilateral

Ireland Bilateral Mauritius No Georgia Dead-y Korea, Rep. Bilateral

Italy Bilateral Mexico Bilateral Guatemala Bilateral Kyrgyz Republic Dead-y

Japan Dead-y Montenegro Dead-y Guyana Bilateral Lao PDR Bilateral

Kuwait Bilateral Oman Bilateral Honduras Dead-y Liberia Bilateral

Luxembourg Dead-y Palau Dead-y Indonesia Bilateral Madagascar Bilateral

Malta Bilateral Panama Dead-y Iran, Islamic Rep. y-Dead Malawi Bilateral

Monaco Bilateral Poland No Iraq Bilateral Mali Bilateral

Netherlands Bilateral Romania Bilateral Jamaica Bilateral Mauritania Bilateral

New Zealand y-Dead Russian Federation No Jordan Dead-y Mongolia Bilateral

Norway Bilateral St. Kitts and Nevis Dead-y Kiribati y-Dead Mozambique Bilateral

Portugal No St. Lucia No Lesotho Dead-y Nepal Bilateral

Qatar Bilateral St. Vincent and the

Grenadines Dead-y Maldives Bilateral Niger Bilateral

San Marino Dead-y Serbia Bilateral Marshall Islands Bilateral Nigeria Bilateral

Saudi Arabia Dead-y Seychelles Dead-y Micronesia, Fed.

Sts. Dead-y Pakistan Bilateral

Singapore Bilateral Slovak Republic Dead-y Moldova Bilateral Papua New

Guinea Bilateral

Slovenia y-Dead South Africa Dead-y Morocco Bilateral Rwanda No

Spain Dead-y Turkey Bilateral Namibia Bilateral Senegal Bilateral

Sweden y-Dead Uruguay Dead-y Nicaragua Bilateral Sierra Leone Bilateral

Switzerland Dead-y Venezuela, RB Bilateral Paraguay Bilateral Solomon Islands Dead-y

Trinidad and Tobago Bilateral Peru Bilateral Sudan Bilateral

United Arab

Emirates Bilateral

Philippines Bilateral Tajikistan Dead-y

United Kingdom No Sri Lanka Dead-y Tanzania Dead-y

United States Bilateral Suriname Bilateral Timor-Leste Bilateral

Swaziland Dead-y Togo Bilateral

Syrian Arab

Republic Bilateral Tuvalu Dead-y

Thailand y-Dead Uganda Bilateral

15 | P a g e

Tonga Bilateral Uzbekistan Dead-y

Tunisia Bilateral Vietnam Bilateral

Turkmenistan Bilateral Yemen, Rep. Bilateral

Ukraine Bilateral Zambia Dead-y

Vanuatu No Zimbabwe Bilateral

Notes: Hurlin (2004a) critical values for Wald statistics for testing causality in micro panels is used to find the valid

coefficients. Cross-section weight is used for having a better determination of our unbalanced observation. Because

of our short available time period we only use one lag of endogenous variables in our Granger analysis.

Table 4. Test results for heterogeneous causality hypotheses between maternal mortality (MDG5)

and GDP

HICs Direction UMICs Direction LMICs Direction LICs Direction

Australia y-Dead Argentina No Albania Bilateral Bangladesh Bilateral

Austria Bilateral Belize No Algeria Dead-y Benin No

Bahamas, The y-Dead Botswana Dead-y Angola Bilateral Burkina Faso Bilateral

Bahrain Dead-y Brazil Dead-y Armenia Dead-y Burundi Bilateral

Barbados Dead-y Bulgaria No Azerbaijan No Cambodia Bilateral

Belgium Dead-y Chile Dead-y Belarus Bilateral Central African

Republic Bilateral

Brunei

Darussalam Dead-y Costa Rica Dead-y Bhutan Dead-y Chad Dead-y

Canada Bilateral Croatia No Bolivia Bilateral Comoros Bilateral

Cyprus y-Dead Equatorial Guinea Bilateral Bosnia and

Herzegovina Bilateral Congo, Dem. Rep. Bilateral

Czech Republic Bilateral Gabon No Cameroon Bilateral Cote d'Ivoire Bilateral

Denmark No Grenada Dead-y China Dead-y Eritrea Bilateral

Estonia Bilateral Hungary Dead-y Colombia Dead-y Ethiopia Bilateral

Finland No Kazakhstan Dead-y Congo, Rep. Bilateral Gambia, The Bilateral

France y-Dead Latvia No Cuba y-Dead Ghana y-Dead

Germany Dead-y Lebanon Dead-y Djibouti Bilateral Guinea Bilateral

Greece No Libya Dead-y Dominican

Republic Dead-y Guinea-Bissau Bilateral

Iceland Bilateral Lithuania Dead-y Ecuador Bilateral Haiti Bilateral

Ireland Dead-y Malaysia Dead-y Egypt, Arab Rep. Dead-y India Bilateral

Italy No Mauritius No El Salvador Bilateral Kenya y-Dead

Japan Dead-y Mexico Dead-y Georgia No Korea, Rep. Dead-y

Kuwait Bilateral Montenegro Dead-y Guatemala No Kyrgyz Republic No

Luxembourg Dead-y Oman Bilateral Guyana y-Dead Lao PDR Bilateral

Malta Bilateral Panama Dead-y Honduras Bilateral Liberia y-Dead

Netherlands No Poland No Indonesia Bilateral Madagascar Bilateral

New Zealand y-Dead Romania No Iran, Islamic Rep. Bilateral Malawi Bilateral

Norway Bilateral Russian Federation Bilateral Iraq Bilateral Mali y-Dead

Portugal No St. Lucia No Jamaica Bilateral Mauritania Bilateral

Puerto Rico Bilateral St. Vincent and the Dead-y Jordan y-Dead Mongolia y-Dead

16 | P a g e

Grenadines

Qatar Bilateral Serbia Dead-y Lesotho Dead-y Mozambique No

Saudi Arabia Dead-y Slovak Republic Dead-y Maldives y-Dead Nepal y-Dead

Singapore y-Dead South Africa Dead-y Micronesia, Fed.

Sts. Dead-y Niger Bilateral

Slovenia Dead-y Turkey Dead-y Moldova Bilateral Nigeria No

Spain No Uruguay Dead-y Morocco Bilateral Pakistan y-Dead

Sweden No Venezuela, RB No Namibia Bilateral Papua New Guinea Bilateral

Switzerland No Nicaragua Bilateral Rwanda Dead-y

United Arab

Emirates Bilateral

Paraguay Bilateral Senegal Dead-y

United

Kingdom Dead-y Peru Bilateral Sierra Leone Bilateral

United States Bilateral Philippines Dead-y Solomon Islands No

Sri Lanka Dead-y Sudan Bilateral

Suriname No Tajikistan No

Swaziland Dead-y Tanzania Dead-y

Syrian Arab

Republic Bilateral Timor-Leste Bilateral

Thailand Bilateral Togo Bilateral

Tonga Bilateral Uganda Bilateral

Tunisia Bilateral Uzbekistan No

Turkmenistan y-Dead Vietnam Bilateral

Ukraine Bilateral Yemen, Rep. y-Dead

Vanuatu No Zambia No

West Bank and

Gaza Dead-y Zimbabwe Dead-y

Note: see table 3.

We conclude from the analysis above that there is evidence that the causal effects in general run

both from GDP to health and from health to GDP, for most countries and for both health

outcomes under study (child mortality and maternal mortality). Below we focus on the causal

relationship running from health to GDP and extend the analysis to a Barro growth model

approach and we also restrict measurement of health to under-five mortality of children which

appeared stronger in the Granger analysis.

3.2. The result of a Barro inspired growth model using DEA method

Numerous factors impact on GDP and there is not any empirical literature in economics which

estimated the exact magnitude of health on GDP. But there are some indexes such as the size of

effect and efficiency rate which are used to compare the magnitudes among countries. This

section presents the results of DEA analysis to measure how far from the frontier different

countries are located, i.e. indicating how much GDP may be increased at the current level of

child mortality. In other words, static efficiency exists at a point in time and focuses on the

maximum potential of GDP which can be increased with the current economic and health

structure of each country in comparison with other countries in the Barro framework. In the first

17 | P a g e

step of our estimation (see above, section 3.1) we tested for causality between under-five

mortality and GDP. Because we find evidence for co-linearity between the lags of our variables,

and because our time period is short (only five times because of availability of data) we are not

allowed to investigate Granger causality between under five mortality and GDP in the Barro

framework or include other variables as control in our causality analysis. However, the aim of

this section is to investigate the efficiency rates of under-five mortality on economic growth in

the Barro model. With respect to the inclusion of other productivity-related factors, we follow

Ventelou and Bry (2006) and apply a DEA analysis in a Barro framework, i.e. we also include

government spending, population and (fixed) capital.

We use an explicit endogenous growth model developed by Barro (1990), in which public

expenditure is considered as an input of the production function. For y the GDP per unit of labor,

we have: y = f(k, d) with k, the private capital by unit of labor, and d, a “productive public

expenditure”. As demonstrated by Barro (1990), this extension of the Solow model allows

generating positive and permanent growth rate for the economy: the law of decreasing returns

(valid for the private capital) could be offset by a continuous flow of public expenditure,

counterbalancing period after period the “falling tendency of the rate of profit” (Ventelou and

Bry, 2006).

To follow Barro, we multiply and include population growth in the Barro function. According to

the result of Granger causality between child mortality and GDP we find a high relationship

between these two, therefore we also include child health data in the Barro model to find

efficiency rate of under-five mortality on increasing economic growth. Then, for y, GDP growth,

we have: y = f(k, l, d, h) with k, the private capital growth, d, government expenditure growth, l,

population growth, and, h, newborn mortality growth15

.

Most economists have tested the Barro model in 10-year periods. Therefore we calculate the

Barro model with DEA in 1990-2000, and 2000-2010. Because of fixed growth of private capital

during short periods we do not include capital growth in our model.

In the study, the efficiency rate for each country shows how much increase in child health may

impact on (positive) GDP growth compared to other countries. In Cote d'Ivoire the efficiency

rate is 91.5% in 2001 to 2010. This may be interpreted as follows: if child health increases by

one percentage (one percentage point reduction in the under-five mortality rate), increases GDP

by 5% (as an example) in a country with a 100% efficiency rate, then GDP in Cote d'Ivoire will

increase by 4.6% (0.915*5%).

The results of efficiency rates are available in tables 6 and 7 during the periods of 1990-2000 and

2000-2010, respectively. For the reason of data availability in the World Development

Indicators, we lose some countries in each period. The result of both CRS and VRS models is

15In linear programming we are not allowed to include negative amounts of variables. Therefore, we multiply

newborn mortality growth to (-1) in the Barro framework.

18 | P a g e

reported. To allow for the possibility of a non-linear path GDP, we mainly rely on the VRS

results. Based on the growth model theories, economists use nonlinear functional forms in order

to describe the path of economic growth, such as, Cobb-Douglas function.

Our result of the DEA analysis indicates that the higher the efficiency rate, the larger effect a

reduction in mortality will have on GDP. The average overall efficiency rates for all countries in

the data are 91.1% in 1990-2000 and 92.2% in 2000-2010. For the period of 1990-2000, the

mean efficiency rates are 91.14%, 94.50%, 89.26% and 90.35% in HIC, UMIC, LMIC and LIC,

respectively. The figures for the later period 2000-2010, are 92.44%, 93.68%, 90.82% and

92.00% in HIC, UMIC, LMIC and LIC, respectively.

In our empirical analysis we find that countries with exceptionally high efficiency are Bahamas,

Canada, Germany, and Trinidad and Tobago in HIC, Bulgaria, Chile, Kazakhstan, Kosovo,

Latvia, and South Africa in UMIC, Armenia, Azerbaijan, Belarus, China, Lesotho, Nicaragua,

and Ukraine in LMIC, Liberia, Mozambique, Tajikistan, Tanzania, and Zambia in LIC. The

lowest efficiency was gained in Brunei Darussalam, Cyprus, Ireland, and Turkey in HIC,

Botswana, Gabon, and Malaysia in LMIC, Algeria, Bangladesh, Bolivia, Colombia, Egypt,

Guatemala, Honduras, Morocco, Namibia, Peru, Philippine, and Syrian in LMIC, Benin,

Gambia, Kenya, and Madagascar in LIC.

Table 5. Summary of DEA result

Mean of efficiency rates

HIC UMIC LMIC LIC Totality

1990-2000 0.91 0.95 0.89 0.9 0.91

2000-2010 0.92 0.94 0.91 0.92 0.92

Highest efficiency rates

The Bahamas Bulgaria Armenia Liberia

Canada Chile Azerbaijan Mozambique

Germany Kazakhstan Belarus Tajikistan

Trinidad and Tobago Kosovo China Tanzania

Latvia Lesotho Zambia

South Africa Nicaragua

Ukraine

lowest efficiency rates

Brunei Darussalam Botswana Algeria Benin

Cyprus Gabon Bangladesh Gambia

Ireland Malaysia Bolivia Kenya

Turkey

Colombia Madagascar

Egypt

Guatemala

Honduras

Morocco

Namibia

Peru

Philippine

Syrian

Table 6. Results of efficiency rates during the period of 1990-2000 using DEA method

Countries CRS VRS Countries CRS VRS Countries CRS VRS

Albania 0.572 0.997 Gabon 0.724 0.828 Papua New Guinea 0.842 0.89

19 | P a g e

Algeria 0.628 0.814 Gambia, The 0.878 0.913 Paraguay 0.642 0.787

Armenia 0.532 1 Germany 0.746 0.921 Peru 0.752 0.832

Australia 0.791 0.878 Greece 0.751 0.895 Philippines 0.766 0.831

Austria 0.776 0.925 Guatemala 0.726 0.802 Poland 0.844 0.972

Bahamas, The 0.659 0.852 Guinea 0.913 0.913 Portugal 0.78 0.942

Bangladesh 0.806 0.848 Honduras 0.757 0.816 Romania 0.544 0.935

Belarus 0.69 0.943 Hungary 0.694 0.941 Russian Federation 0.536 0.939

Belgium 0.781 0.934 Iceland 0.747 0.877 Senegal 0.834 0.888

Belize 0.822 0.847 India 0.832 0.889 Seychelles 0.938 0.975

Benin 0.813 0.846 Indonesia 0.939 0.966 Singapore 0.762 0.795

Bolivia 0.775 0.837 Iran, Islamic Rep. 0.82 0.872 Slovenia 0.737 0.949

Brunei Darussalam 0.694 0.802 Italy 0.808 0.954 South Africa 0.996 1

Bulgaria 0.847 1 Japan 0.665 0.933 Spain 0.771 0.93

Burkina Faso 0.998 0.999 Jordan 0.883 0.883 Sri Lanka 0.754 0.903

Cameroon 0.801 0.888 Kazakhstan 0.625 1 Sudan 0.808 0.853

Canada 0.848 0.919 Kenya 0.692 0.844 Swaziland 0.733 0.944

Cape Verde 0.859 0.889 Latvia 0.521 1 Sweden 0.806 0.932

Chad 0.951 0.988 Lesotho 1 1 Switzerland 0.721 0.89

Chile 1 1 Luxembourg 0.866 0.915 Syrian Arab Republic 0.85 0.87

China 1 1 Madagascar 0.712 0.787 Tanzania 1 1

Colombia 0.533 0.831 Malaysia 0.956 0.973 Thailand 0.805 0.899

Costa Rica 0.949 0.96 Mali 0.868 0.907 Togo 0.795 0.873

Cote d'Ivoire 0.855 0.902 Malta 0.744 0.936 Trinidad and Tobago 0.949 1

Cuba 0.602 0.874 Mauritius 0.918 0.958 Tunisia 0.806 0.866

Cyprus 0.848 0.881 Mexico 0.804 0.866 Turkey 0.73 0.835

Czech Republic 0.789 0.951 Morocco 0.665 0.833 Uganda 0.965 0.966

Denmark 0.787 0.93 Mozambique 0.904 0.912 Ukraine 0.354 0.97

Dominica 0.739 0.979 Namibia 0.904 0.913 United Kingdom 0.833 0.948

Dominican Republic 0.824 0.869 Netherlands 0.833 0.923 United States 0.89 0.946

Ecuador 0.801 0.866 New Zealand 0.796 0.881 Uruguay 0.857 0.939

Egypt, Arab Rep. 0.792 0.854 Nicaragua 1 1 Venezuela, RB 0.789 0.866

El Salvador 0.914 0.959 Norway 0.839 0.933 Yemen, Rep. 0.908 0.908

Ethiopia 0.621 0.765 Oman 0.852 0.89 Zambia 1 1

Finland 0.809 0.931 Pakistan 0.893 0.931

France 0.764 0.917 Panama 0.963 0.978 Note: The unity figure in the table indicates a 100% efficiency rate.

Table 7. Results of efficiency rates during the period of 2000-2010 using DEA method

Countries CRS VRS Countries CRS VRS Countries CRS VRS

Albania 0.705 0.916 Gambia, The 0.587 0.841 Pakistan 0.68 0.933

Argentina 0.664 0.915 Germany 0.546 1 Panama 0.764 0.929

Armenia 0.869 0.975 Greece 0.567 0.91 Paraguay 0.632 0.883

20 | P a g e

Australia 0.624 0.936 Guatemala 0.562 0.828 Peru 0.684 0.847

Austria 0.551 0.945 Guinea 0.793 0.947 Philippines 0.69 0.904

Azerbaijan 1 1 Honduras 0.589 0.844 Poland 0.655 0.936

Bahamas, The 0.556 1 Hungary 0.585 0.953 Portugal 0.492 0.92

Bangladesh 0.635 0.858 Iceland 0.533 0.857 Romania 0.713 0.967

Belarus 1 1 India 0.826 0.939 Russian Federation 0.759 0.956

Belgium 0.536 0.935 Indonesia 0.623 0.89 Senegal 0.671 0.897

Bolivia 0.618 0.873 Ireland 0.528 0.845 Serbia 0.595 0.951

Botswana 0.624 0.846 Italy 0.485 0.934 Singapore 0.721 0.899

Brazil 0.606 0.857 Japan 0.511 0.945 Slovak Republic 0.722 0.945

Brunei Darussalam 0.492 0.874 Jordan 0.783 0.925 Slovenia 0.588 0.909

Bulgaria 0.751 1 Kazakhstan 0.896 0.984 South Africa 0.599 0.9

Cambodia 0.742 0.863 Kenya 0.655 0.884 Spain 0.521 0.89

Canada 0.62 1 Kosovo 0.823 1 Sri Lanka 0.699 0.938

Cape Verde 0.758 0.937 Lao PDR 0.666 0.875 Swaziland 0.553 0.928

Chile 0.645 0.944 Latvia 0.73 1 Sweden 0.593 0.97

China 0.982 0.984 Lebanon 0.762 0.964 Switzerland 0.572 0.97

Colombia 0.64 0.893 Lesotho 0.656 0.926 Syrian Arab Republic 0.569 0.84

Costa Rica 0.688 0.928 Liberia 1 1 Tajikistan 1 1

Cote d'Ivoire 0.515 0.915 Lithuania 0.726 0.984 Tanzania 0.452 0.81

Croatia 0.632 0.981 Luxembourg 0.546 0.853 Thailand 0.645 0.921

Cuba 0.701 0.945 Malaysia 0.569 0.822 Togo 0.599 0.935

Cyprus 0.542 0.84 Malta 0.54 0.935 Tunisia 0.635 0.87

Czech Republic 0.644 0.922 Mauritania 0.727 1 Turkey 0.59 0.808

Denmark 0.498 0.94 Mauritius 0.659 0.948 Uganda 0.836 0.906

Dominican Republic 0.696 0.89 Mexico 0.54 0.904 Ukraine 0.754 1

Ecuador 0.649 0.867 Moldova 0.681 0.985 United Kingdom 0.548 0.936

Egypt, Arab Rep. 0.656 0.837 Morocco 0.694 0.905 United States 0.571 0.978

El Salvador 0.547 0.9 Mozambique 1 1 Uruguay 0.657 0.976

Estonia 0.639 0.942 Namibia 0.633 0.838 Venezuela, RB 0.538 0.874

Ethiopia 1 1 Netherlands 0.516 0.923 Vietnam 0.758 0.909

Finland 0.574 0.97 New Zealand 0.578 0.939 Yemen, Rep. 0.676 0.889

France 0.537 0.964 Nicaragua 0.527 0.867

Gabon 0.556 0.893 Norway 0.517 0.892 Note: see table 6.

21 | P a g e

4. Conclusions and discussion

The analysis of the causal relationship between maternal and child health and GDP and the

magnitude of effect is vital since this indicates potential economic and social returns on

investments. The objectives of this study were to examine if there is a relationship between

maternal and child health on GDP and to estimate the direction and the magnitude of any such

relationships. In the analysis we use panel data Granger analysis based on a simple bivariate

model to provide some initial evidence. After this, the analysis focuses on the causal relationship

on the effect of health (children) on GDP based on a multivariate model in a Barro framework,

using DEA analysis.

We find in general that the relationships between maternal and child health outcomes and GDP

run in both directions, with the majority running from maternal and child health to GDP. We find

evidence that the causal effects of GDP on maternal and child health outcomes are stronger in

LICs and LMICs relative to HICs and UMICs. This may reflect that the effect of marginal health

investments on health outcomes is stronger at low GDP levels, i.e. in countries where generally

the level of health is lower.

However, in contrast, the causal effect of maternal and child mortality on GDP is generally

stronger in HICs and UMICs. This indicates that the improvement of human capital through

health on GDP is more effective in richer countries, i.e. productivity of labor is relatively higher

in a rich country than in a poor country. Human capital is the stock of competencies, knowledge,

social and personality attributes, including creativity, embodied in the ability to perform labor so

as to produce economic value (Simkovic, 2012). The higher human capital level of richer

countries compared to poorer countries implies that an equal reduction in maternal and child

mortality will cause GDP to increase more in richer countries than in poorer countries.

The DEA analysis shows that the efficiency rates of child health (in terms of mortality) on GDP

has increased somewhat over time and also that the efficiency rates tend to be higher in richer

countries, though the differences are small and insignificant over time as well as between

countries at different degrees of development. Thus our results indicate that health investments in

poorer countries may increase GDP and reduce the gap in health between rich and poor

countries. The analysis also indicates that other important factors in driving GDP growth are

investments in human capital and structural factors such as infrastructure.

In sum, this study shows that the efficiency of health investment works through two different

mechanisms which are important to consider in particular in lower income countries. First ly,

health investments will improve the health level and will reduce the gap in health inequality

among countries and different income levels. Secondly, investments in health in lower income

countries which increase the efficiency of health on GDP will in addition lead to higher GDP

levels even at the existing level of health in lower income countries which will increase growth

in GDP and reduce income inequality in the world. One important limitation of this study,

22 | P a g e

however, is that we are not able to identify the most important factors which reduce the

efficiency of health in GDP and this is therefore an important task for future research.

An important direction of future researches to investigate what factors drive the efficiency rate

(impact) of maternal and child health on GDP and also whether the trend continues in efficiency

rates and across countries. One important limitation of this study is that we had to restrict the

analysis to only two variables in the econometric Granger analysis, i.e. one variable of health and

GDP, without control of other potentially confounding variables, such as education, and without

consideration of other aspects of health. Another limitation is the short nature of the time

dimension. Thus we suggest that, following the recommendations of the Commission on

Information and Accountability for Women’s and Children’s Health, WHO and other relevant

organizations, in collaboration with researchers, should continue to support countries in

collecting and analyzing macro and micro-level data that can be used to further study the

interaction between health and economic development.

23 | P a g e

5. Appendix

5.1. Fixed effect panel data analysis

Following Hurlin and Venet (2001)16

, we consider two covariance stationary variables, denoted

by x and y, observed on T periods and on N cross-section units. In the context of Granger (1969)

causality procedure, for each country i from [1, N], the variable x is causing y if we are able to

predict y using all available information on y and x, than if only the historical information on y

had been used. Thus, we use a time-stationary VAR representation, used for a panel data set. For

each country i and time period t, we estimate the following model (Erdil and Yetkiner, 2010):

ti

p

k

p

k

ktikktikti uxyy ,

1 0

,,,

17

As Erdil and Yetkiner (2010) stated, it is assumed that the parameters β are identical for all

individual countries, while the coefficients θ may have country-specific dimensions. Also, the

residuals are assumed to satisfy the standard properties, i.e. they are independently, identically

and normally distributed and free from heteroscedasticity and autocorrelation. The use of panel

data, that is, pooling cross section and time series data in a panel data framework, has a number

of advantages. First, it provides a large number of observations. Second, it increases the degrees

of freedom. Finally, it reduces the co-linearity among explanatory variables. In sum, it improves

the efficiency of Granger-causality tests (Hurlin and Venet, 2001; see Erdil and Yetkiner, 2010).

In testing causality with panel data, it may be important to pay attention to the question of

heterogeneity between cross-section units. The first source of heterogeneity is caused by

permanent cross sectional disparities. A pooled estimation without the heterogeneous intercepts

may lead to a bias of the slope estimates and could result in a fallacious inference in causality

tests (Hurlin, 2004a; see Erdil and Yetkiner, 2010). Another basis of heterogeneity caused by

heterogeneous regression coefficients θk is more problematic than the first one, i.e. one should

consider the different sources of heterogeneity of the data generating process. Thus a series of

different causality hypothesis will be tested. Our strategy for investigating Granger no-causality

test is presented in Table 8.

Table 8. Strategy of FE Granger non-causality test

Steps Tests Direction of null

hypothesis Results and consequences

1. HINC Rejected Go to the 2th step

Accepted We face to invalid coefficients and panel set

2. HC (for all countries) Rejected Go to the 4th step

Accepted Go to the 3th step

16In order to explain and review the background of FE method we reference some parts of the paper of Erdil and

Yetkiner (2010) as a good empirical work can be found in the special issue of Applied Economics on page 3 to 5. 17u is normally distributed with ui,t=αi+εi,t, p is the number of lags, and εi,t are i.i.d. (0, σ2); see also Erdil and

Yetkiner (2010).

24 | P a g e

3. HC (for subgroups) Rejected Go to the 4th step

Accepted We face to homogenous data

4. HENC Rejected A casual relationship exists

Accepted A casual relationship does not exist

Notes: if any of the tests are accepted, the estimations of variables of interest will be biased.

According to Table 8, if we can finish all steps successfully, then we can analyze Granger non-

causality test completely, though if there is homogeneity then our estimation would be biased. If

the coefficients are not different from each other across countries, then this complicates the

analysis since the model must be enlarged with more equations or variables to take into account

the effects of the differences across countries (see Arellano, 2003). Therefore, finding non-

homogenous coefficients in a model is a key standard qualification in the econometrics analysis

(Arellano, 2003). According to Table 8, the first test procedure, labeled as homogenous and

instantaneous non-causality hypothesis (HINC), is directed towards testing to see whether or not

the θk’s of xi,t-k are simultaneously null for all countries i and for all lag k (for more details see

Erdil and Yetkiner, 2010):

H0: all coefficients are equal to zero

jipNH kik ],0[],,1[,0:0

H1: there is at least one statistically significant coefficient

),(,0:1 kiH k

If the HINC null hypothesis is not rejected then we may face invalid coefficients θk in the above

Granger model, though if HINC is rejected, we turn to the second step in which we test the

homogenous causality hypothesis (HC), i.e. we test whether all of the coefficients θ are identical

for all lag k and are statistically different from zero:

H0: all coefficients are identical

],0[],,1[,: ,0 pNH kji

j

k

i

k

H1: there are at least two coefficient which are not identical

),,(,:1 kjiH j

k

i

k

If the HC hypothesis is also rejected, this indicates that the process is non-homogenous and no

homogenous causality relationships may be obtained (Hurlin, 2004a), i.e. if both HINC and HC

tests are rejected then it may be possible to find meaningful causal relationships in the Granger

causality test. If the HC hypothesis is rejected, we turn to the third step and test whether the HC

hypothesis is also rejected within subgroups of countries to see whether the rejection is an

overall characteristic or whether it is due to composition of subgroups, i.e. perhaps θ coefficients

25 | P a g e

are not equal in the total sample of countries but turn out equal within subgroups and then we

would have to face homogeneity anyway. In order to divide our data set in subgroups there is no

obvious unique definition, but it may be natural to divide our country data set in income

subgroups (HICs, UMICs, LMICs and LICs). According to Table 1, if the null hypothesis of the

overall and subgroup HC tests are rejected in the second and third step we finally turn to the

fourth step in which we test the heterogeneous non-causality hypothesis (HENC):

H0: exogenous coefficient and its lags of each country are equal to zero means that there is not a

causal relationship between exogenous and endogenous variables

],0[],,1[,0:0 pNH ki

k

i

H1: exogenous coefficient and its lags of each country are not equal to zero means that there is a

causal relationship between exogenous and endogenous variables

0:1 k

iH

In this step we test the nullity of all the coefficients of the lagged explanatory variable x for each

country. These N individual country tests identify countries for which there are no causal

relationships. If the HENC hypothesis is not rejected, this means that for some countries x does

not cause the variable y. The causal relationship is relevant only for a subgroup of countries for

which the HENC hypothesis is rejected.

As using micro-panels, where there are a large number of cross-section units and a small number

of time series observations, the FE estimator of the coefficients of lagged endogenous variables

are biased and inconsistent (Nickell, 1981; see Erdil and Yetkiner, 2010). However, Nickell

(1981) demonstrates a fall in the size of bias on the coefficients of lagged endogenous variables

with the presence of exogenous regressors. Furthermore, Judson and Owen (1999) provide

Monte Carlo evidence and show that the FE estimator’s bias decreases with T. Finally, there is

one more point to note; Wald test statistics do not have a standard distribution under H0 when T

is small (Hurlin and Venet, 2001). Hurlin (2004a) provides exact critical values for Wald

statistics to test causality in micro panels, which we use to carry out the statistics (Erdil and

Yetkiner, 2010).

5.2. Data Envelopment Analysis (DEA)

Charnes et al. (1978) proposed a model which had an input orientation and assumed constant

returns to scale (CRS). The CRS model which follows (Wu et al., 2006)

s

j

rjj

t

k

rkk

c

xv

yu

E

1

1max

26 | P a g e

Subject to ,10

1

1

s

j

rjj

t

k

rkk

xu

yu

i= 1,…,n

ku ; jv >0, all k, i.

As Wu et al. stated to get a geometric appreciation for the CRS model, one example from Cook

and Seiford (2009) can represent the above modeling, a form such as pictured in Figure 1. This

figure provides an illustration of a single output single input case. The x variable is an input and

also y is the output of our DEA model. An empirical problem related to economic theories is to

identify which variable is input and which one is output. To make our example simpler we probe

a single input single output case. Here, each decision maker unit (DMU) is like a country in our

study. Imagine that x is government expenditure growth and y is economic growth in our Barro

framework. If we solve the model above for each of the DMUs, this amounts to projecting those

DMUs to the left, to a point on the frontier. In the case of country or DMU #3, for example, its

projection to the frontier is represented by the point 3*.Intuitively, one would reasonably

measure the efficiency of DMU #3 as the ratio A/B = 4.2/6 = .70 or 70%.

Figure 1: Constant returns to scale projection in the single input single output case.

27 | P a g e

Source: Cook and Seiford (2009).

Subsequent papers have considered alternative set of assumptions, such as Banker et al. (1984)

who proposed a variable returns to scale (VRS) model. One form of their VRS model is (Wu et

al., 2006)

s

j

rjj

t

k

rkk

c

xvv

yu

E

1

0

1max

Subject to ,10

1

0

1

s

j

rjj

t

k

rkk

xvv

yu

i= 1,…,n

ku ; jv >0; 0v unconstrained in sign.

Where ijX and ikY represent input and output data for the ith country with j ranging from 1 to s

and k from 1 to t, and is a small non-Archimedean quantity (Charnes and Cooper, 1984;

Charnes et al. 1979). Index r indicates the country to be rated, and there are n countries. When

0v is set to 0, the assumption of constant returns to scale is imposed, and the model becomes that

of Charnes et al. (1979). Note that Model (2) is a linear fractional program which can be

transformed to a linear program (Wu et al., 2006)

t

k

rkkr yuE1

max

s.t. 11

0

s

j

rjj xvv

,01

0

1

s

j

ijj

t

k

ikk xvvyu i= 1,…,n

ku ; jv >0; 0v unconstrained in sign,

Therefore, conventional linear programming (LP) methods can be applied to solve a DEA model

in which one seeks to determine which of the n countries defines an envelopment surface that

represents the best practice, referred to as the empirical production function or the efficient

frontier. Efficient in DEA while those countries that do not, are termed in efficient. As Wu et al.

stated, DEA provides a comprehensive analysis of relative efficiencies for multiple input-

multiple output situations by evaluating each country and measuring its performance rather than

an envelopment surface composed of other countries. Those countries are the peer groups for the

28 | P a g e

inefficient units known as the efficient reference set. As the inefficient units are projected onto

the envelopment surface, the efficient units closest to the projection and whose linear

combination comprises this virtual unit form the peer group for that particular country. The

targets defined by the efficient projections give an indication of how this country can improve to

be efficient (source of the DEA methodology is Wu, Yang & Liang, 2006).

In reference to Figure 2, that portion of the frontier from point 1 up to (but not including) point 2,

constitutes the increasing returns to scale portion of the frontier; point 2 is experiencing constant

returns to scale; all points on the frontier to the right of 2 (i.e., the segments from 2 to 3 and from

3 to 4) make up the decreasing returns to the scale portion of the frontier (Cook and Seiford,

2009).In this study, the efficiency rates are calculated with DEAP software (version 2.1), which

calculates the same efficiency rate for all the inputs of each DMU.

Figure 2. The variable returns to scale Frontier.

Source: Cook and Seiford (2009).

29 | P a g e

References

1. Adams, P., Hurd, M.D., McFadden, D., Merrill, A. & Ribiero, T. (2003) Healthy, wealthy and wise? Tests

for direct causal paths between health and socio economic status. Journal of Econometrics 112, 3–56.

2. Afriat, S.N. (1972) Efficiency estimation of production function. International Economic Review 13: 568–

598.

3. Arellano, M., (2003) Panel Data Econometrics, Chapter 2, 'Unobserved heterogeneity', pp. 7-31. Oxford

University Press.

4. Banker, R.D., Charnes, A. & Cooper, W. (1984) Some model for estimating technical and scale

inefficiencies in data envelopment analysis. Management Science 30: 1078–1092.

5. Barro, R.J. (1990) Government spending in a simple model of endogenous growth. Journal of Political

Economy 98: 103–125.

6. Bloom, D.E. & Williamson, J.G. (1997) Demographic transitions and economic miracles in emerging

ASIA, NBER working paper 6268.

7. Chamberlain, G. (1982) Multivariate regression models for panel data. Journal of Econometrics 18, 5–45.

8. Charnes, A. & Cooper, W. (1984) The non-Archimedean CCR ratio for efficiency analysis: a rejoinder to

Boyd and Fare. European Journal of operational Research 15: 333–334.

9. Charnes, A., Cooper, W. & Rhodes, S.E. (1978) Measuring efficiency of decision-making units. European

Journal of operational Research 2(6).

10. Charnes, A., Cooper, W. & Rhodes, S.E. (1979) Measuring efficiency of decision-making units. European

Journal of operational Research 3: 339.

11. Choe, J.I. (2003) Do foreign direct investment and gross domestic investment promote economic growth?

Review of Development Economics 7, 44–57.

12. Coelli, T. (1996) DEAP user guide version 2.1, CEPA working paper 96/08.

13. Cook, W.D. & Seiford L.M. (2009) Data Envelopment Analysis (DEA) - Thirty Years on. European

Journal of Operational Research 192(1), 1–17.

14. Erdil, E. & Yetkiner, H. (2010) The Granger-causality between health care expenditure and output: a panel

data approach.Applied Economics 41: 4, 511–18.

15. Farrell, M.J. (1957) The measurement of productive efficiency. Journal of Royal Statistical Society, Series

A, General 120(3): 253–81.

16. Florens, J.P. & Mouchart, M. (1982) Note on noncausality. Econometrica 50, 583–91.

17. Hansen, H. & Rand, J. (2004) On the causal links between FDI and growth in developing countries, mimeo,

Development Economics Research Group (DERG), Institute of Economics, University of Copenhagen.

18. Holtz-Eakin, D., Newey, W. & Rosen, H. (1985) Implementing causality tests with Panel data, with an

example from local public finance, NBER Technical Paper Series No. 48.

19. Holtz-Eakin, D., Newey, W. & Rosen, H. (1988) Estimating vector autoregressions with panel data.

Econometrica 56, 1371–95.

20. Hoover, K.D. (2003) Some causal lessons from macroeconomics. Journal of Econometrics 112, 121–5.

21. Hsiao, C. (1986) Analysis of Panel Data, Cambridge University Press, Cambridge.

22. Hsiao, C. (1989) Modeling Ontario regional electricity system demand using a mixed fixed and random

coefficients approach. Regional Science and Urban Economics 19(4), 565–87.

23. Hurlin, C. (2004a) Testing Granger causality in heterogeneous panel data models with fixed coefficients,

mimeo, University of Orleans.

24. Hurlin, C. (2004b) A note on causality tests in panel data models with random coefficients, mimeo,

University of Orleans.

25. Hurlin, C. & Venet, B. (2001) Granger causality tests in panel data models with fixed coefficients, mimeo,

University Paris IX.

26. Judson, R.A. & Owen, A.L. (1999) Estimating dynamic panel data models: a guide for macroeconomists.

Economic Letters 65, 9–15.

30 | P a g e

27. Kiviet, J.F. (1995) On bias, inconsistency and efficiency of various estimators in dynamic panel data

models. Journal of Econometrics68, 53–78.

28. Nair-Reichert, U. & Weinhold, D. (2001) Causality tests for cross-country panels: a new look at FDI and

economic growth in developing countries. Oxford Bulletin of Economics and Statistics 63, 153–71.

29. Nickell, S. (1981) Biases in dynamic models with fixed effects. Econometrica 49, 1399–416.

30. Simkovic, M. (2012) Risk-based student leons. Whasington and lee law review 70, 1.

31. Ventelou, B. & Bry, X. (2006). The role of public spending in economic growth: Envelopment methods.

Journal of Policy Modeling, 28, 403–413.

32. Weinhold, D. (1996) Investment, growth and causality testing in panels. Economieet Prevision 126, 163–

75.

33. Weinhold, D. (1999) A dynamic ‘fixed effects’ model for heterogeneous panel data, Unpublished

Manuscript, London School of Economics.

34. Wu, D., Yang, Z. & Liang, L. (2006) Using DEA-neural network approach to evaluate branch efficiency of

a large Canadian bank. Expert Systems with Applications 31, 108–115.