Atlantic Economic Journal

, Volume 41, Issue 2, pp 115–122

The Wealth-Health Nexus: New Global Evidence

Authors

    • Centre for Energy Policy and EconomicsETH Zurich
Article

DOI: 10.1007/s11293-012-9347-x

Cite this article as:
Jaunky, V.C. Atl Econ J (2013) 41: 115. doi:10.1007/s11293-012-9347-x
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Abstract

Using a world sample of countries, this paper re-examines the U-shaped relationship between per capita GDP (wealth) and life expectancy at birth (health). Since cross-sectional dependence across countries is detected, second-generation panel unit root and cointegration tests are employed. All the variables are found to be integrated in one order as well as cointegrated. Various quadratic specifications are also employed and the hypothesis is confirmed.

Keywords

Per capita GDPLife expectancyCross-sectional dependencePanel FMOLS

JEL

I15C33O11

Introduction

Healthcare improvements constitute a major moral prerogative to any nation. Healthy citizens, whether unskilled or skilled, enhance an economy’s productive capacity by being both physically and mentally apt. As such, the question of whether better health care can stimulate economic growth intrinsically arises. There is an on-going debate in literature on the impact of increased life expectancy on the wealth of nations and diverse results have been obtained.

Cervellati and Sunde (2011) theorized a non-monotonic connection between life expectancy and economic growth, “… in which the demographic transition represents an important turning point for population dynamics and hence plays a central role for the transition from stagnation to growth” (page 103). For instance, this concept is seen graphically illustrated in Fig. 1.
https://static-content.springer.com/image/art%3A10.1007%2Fs11293-012-9347-x/MediaObjects/11293_2012_9347_Fig1_HTML.gif
Fig. 1

The U-shaped hypothesis. Source: Computed

During infant stages of development, any improvements on the level of health lead to a fall in wealth because of the occurrence of the Malthusian population effect. The latter postulates an exponential expansion in population growth. Yet, this effect is only temporary as fertility is apt to drop. As further health improvements occur beyond the turning point α, human capital accumulations and economic development are stimulated. This eventually causes population growth rate to fall (Hansen 2012).

Various studies have investigated the impact of life expectancy on economic growth. Acemoglu and Johnson (2007) find a negative but statistically insignificant impact whereas Zhang and Zhang (2005), Bloom et al. (2009), Turan (2009) and Aghion et al. (2010) uncover a significantly positive one. Hansen (2012) is among the first to provide evidence of a U-shaped relationship using a world panel of 119 countries throughout the period of 1940–1980. Yet, while the models used in literature rely heavily on cross-sectional studies which may not adequately capture the effects of health, some have employed panel data of little importance given to non-stationary series, which can lead to spurious inferences.

This paper revisits the implications of health on wealth by employing state-of-the-art panel data techniques. Using the 2011 World Development Indicators data from The World Bank Group, 107 countries for the 1970–2009 period are selected. Table 1 shows the descriptive statistics for real gross domestic product (GDP) per capita (at constant 2000) and life expectancy at birth. Referring to Fig. 2, the scatter plot for the year 2009 does reflect a slight U-shaped relationship between the two variables.
Table 1

Descriptive statistics for the period 1970–2009

Data

Mean

Standard deviation

Minimum

Maximum

Real GDP per Capita ($)

6105.71

8738.81

57.78

56388.99

Life Expectancy (years)

63.68

11.46

26.82

82.93

Computed

https://static-content.springer.com/image/art%3A10.1007%2Fs11293-012-9347-x/MediaObjects/11293_2012_9347_Fig2_HTML.gif
Fig. 2

Scatter diagram for the year 2009. Source: Computed

Results

To investigate whether a U-shaped relationship exists, the following quadratic regression is run:
$$ LGD{P_{it }}={\beta_0}+{\beta_1}LE{X_{it }}+{\beta_2}LEX_{it}^2+{\varepsilon_{it }}, $$
(1)
where LGDPit denotes the natural logarithm of real GDP per capita for country i and year t and measures the level of wealth of in an economy. LEXit denotes the natural logarithm of life expectancy at birth for country i and year t. Also, it is used as a proxy for the general health conditions of a population (Acemoglu and Johnson 2007). β1 and β2 estimate the impacts of life expectancy on real GDP per capita. If a U-shaped relationship prevails between wealth and health levels, the expected outcomes will be β1 < 0 and β2 > 0. β0 is the constant term while εit is the error term.

Prior to estimating the above equation, some preliminary tests are conducted. According to the Hausman’s (1978) specification test, the null hypothesis (H0) of no systematic difference in coefficients between the fixed-effects (FE) and random-effects (RE) panel data models is rejected with the test statistics equal to χ2(2) = 245.68 [0.000]*. The FE panel data model best fits the data. The Greene (1993) groupwise heteroskedasticity test statistics are χ2(106) = 15955.74 [0.000]* and χ2(106) = 15998.47 [0.000]* for the FE and RE panel data models respectively. Thus, the H0 of homoskedasticity is rejected. Next, the Wooldridge (2002) no first-order autocorrelation (AR(1)) test statistic is F(1,106) = 289.25 [0.000]*. The H0 is rejected. The Pesaran (2004) test of H0 no cross-sectional dependence (CSD) is equal to 38.02 [0.000]* for the FE panel data model. The p-value is in square brackets. The presence of CSD is found. In addition to the FE and RE panel data models, the Prais and Winsten (1954) heteroskedastic panel corrected standard error model which can control for AR(1) specific to each panel is applied (StataCorp 2007).

As exposed in Table 4, the U-shaped hypothesis is supported. Since β1 and β2 are statistically significant at the 1 % level, a precise and meaningful value of α can be obtained from the models. For instance, a 99 % confidence interval for α is reported for the FE, RE, and PW panel data models. All α’s are found to lie within this estimated interval. Their p-values are also computed to be 0.000, implying they are statistically significant from zero. Nevertheless, these three models are based on the stationarity assumption and ignore any non-stationary process of the series which can result in spurious inferences. Efficient models such as the fully modified ordinary least squares (FMOLS) model need be considered. Preliminary tests such as panel unit root and cointegration tests are accordingly required. When performing panel unit root tests, two distinct specifications are utilized. One test includes a constant term only while the other contains both a constant term and a time trend. Macroeconomic data tends to display a trend over time. It is more fitting to consider a regression with a constant and a trend at level form. Since first-differencing tends to extract any deterministic trends, inferences will be carried out by considering a constant term only.

Pesaran (2007) recommends a test of the H0 of a unit root which allows for the presence of CSD patterns. To control for these patterns, the standard augmented Dickey-Fuller (ADF) regression models are augmented with the cross-sectional averages of the lagged levels and the first-differences of the individual series. The test is based on the cross-sectionally ADF (CADF) statistics. As revealed in Table 2(a), the results from the Pesaran test corroborate with the earlier tests. All variables are once more found to follow an I(1) process. Kwiatkowski et al. (1992) recommend a test of the H0 of the stationarity hypothesis to complement the H0 of a unit root. Such joint testing is known as confirmatory analysis (Romero-Ávila 2008). The test of the H0 of stationarity as suggested by Hadri and Kurozumi (2012) is applied. This test allows the Lagrange multiplier (LM) test to control for CSD. Although it is similar to the KPSS test, the regression is augmented by the cross-sectional average of the observations à la Pesaran (2007). As illustrated in Table 2(b), both ZAspc and ZAla test statistics confirm an I(1) process for all three series.
Table 2

(a): Pesaran panel unit root test statistics (b): Hadri and Kurozumi panel unit root test statistics

Variables

Deterministics

Level form

First-difference

t-bar

Z

t-bar

Z

LGDPit

Constant

−1.399

4.192 [1.000]

−2.161

−4.191 [0.000]*

Constant + Trend

−2.001

3.987 [1.000]

−2.487

−1.729 [0.042]+

LEXit

Constant

−1.779

0.011 [0.504]

−2.346

−6.233 [0.000]*

Constant + Trend

−2.317

0.271 [0.607]

−2.462

−1.432 [0.076]

\( LEX_{it}^2 \)

Constant

−1.798

−0.198 [0.422]

−2.342

−6.186 [0.000]*

Constant + Trend

−2.308

0.372 [0.645]

−2.468

−1.507 [0.066]

Variables

Deterministics

Level form

First-difference

ZAspc

ZAla

ZAspc

ZAla

LGDPit

Constant

−0.098

−0.063

0.092

0.208

Constant + Trend

3.935*

3.730*

1.820+

2.144*

LEXit

Constant

−1.995

−1.982

−1.119

−1.212

Constant + Trend

4.264*

4.334*

3.906*

3.772*

\( LEX_{it}^2 \)

Constant

−1.980

−1.969

−1.120

−1.197

Constant + Trend

4.585*

4.644*

4.159*

4.066*

Computed. Note: The Bartlett kernel which is equal to 4(T/100)2/9 ≈ 4 is used for the lag order. Critical values for the t-bar statistics without and with trend at 1 %, 5 % and 10 % significance levels are −2.140, −2.060 and −2.010; and −2.620, −2.540 and −2.500 respectively. The normalized Z test statistic is compared to the 1 %, 5 % and 10 % significance levels with the one-sided critical values of −2.326, −1.645 and −1.282 correspondingly. *, + and denotes 1 %, 5 % and 10 % significance level correspondingly. P-value is given in square brackets. The H0 of stationarity is tested. The ZAspc and ZAla test statistics are compared to the 1 %, 5 % and 10 % significance levels with the one-sided critical values of 2.326, 1.645 and 1.282 respectively. Following Kwiatkowski et al. (1992), the number of lags is set on the order of T1/2 ≈ 7

Karlsson and Löthgren (2000) issue a caveat where the rejection of the panel unit root can be driven by a few stationary series and consequently the whole panel may erroneously be modelled as stationary. The Narayan and Popp (2010) time-series unit root tests1 of two breaks in the level and slope for LGDPit, LEXit and \( LEX_{it}^2 \) are performed where 12, 17, and 13 countries are found to be I(0) respectively. Per se, the Pesaran (2007) test is redone by excluding those countries and no major difference to the results is found. The Westerlund (2007) cointegration tests are next performed. Ga and Gt test statistics test the H0 of no co-integration for at least one of the cross-sectional units. Pa and Pt test statistics use the pooled information over all of the cross-sectional units to test the H0 of no co-integration for the whole panel. To control for CSD, robust critical values are obtained through 5,000 bootstrap replications. As shown in Table 3, H0 is rejected when referring to the Gt and Pt test statistics. These panel unit roots and cointegration tests form part of the second-generation tests as they can effectively control for CSD. The first-generation tests rely mainly on the assumption of cross-sectional independence.
Table 3

Westerlund panel cointegration test statistics

Statistics

Without trend

With trend

Value

Z

P-value

Robust P-value

Value

Z

P-value

Robust P-value

Gt

−2.737

−13.378

0.000*

0.000*

−3.729

−14.769

0.000*

0.000*

Ga

−4.076

3.306

1.000

0.037+

−4.489

12.901

1.000

1.000

Pt

−16.084

−4.810

0.000*

0.000*

−25.647

−2.199

0.014+

0.027+

Pa

−2.988

−1.033

0.151

0.001*

−5.428

7.743

1.000

0.970

Computed. Note: All these statistics are distributed standard normally. Critical values of one-sided tests for 1 %, 5 % and 10 % significance levels are −2.326, −1.645 and −1.282 respectively. The lag and lead lengths are set to one

The panel FMOLS estimates are presented in Table 4. The latter can effectively deal with both serial correlation and heteroskedasticity of residuals while controlling for any potential endogeneity of regressors. For instance, while health improvements can be positively related to income, the reverse is also true. Higher incomes make healthy goods and services such as good nutritious diet, proper sanitation, high-tech medical care, etc., more accessible and generate greater longevity. Healthcare may potentially be considered as endogenous and this may produce biased estimates. Moreover, to control for CSD, common time dummies are included (Pedroni 2001). A negative impact of health on wealth is first encountered. On the other hand, when considering the possibility of a non-linear relationship, wealth is found to be on a U-shaped path in the country level of health. Additionally, the panel FMOLS model reveals a turning point at around 54 years of life expectancy as compared to only 35 or 47 years as per the conventional models.
Table 4

Regressions

Statistics

FE

RE

PW

FMOLS

β0

1.19

72.98

0.71

74.33

−6.13

63.57

(0.29)*

(16.40)*

(0.31) +

(16.33)*

(0.53)*

(5.62)*

β1

1.55

−34.26

1.66

−35.06

3.32

−32.27

−0.57

−39.88

(0.07)*

(8.09)*

(0.07)*

(8.05)*

(0.13)*

(2.80)*

(−1.41)

(1.75)*

β2

4.45

4.56

4.53

4.99

(1.00)*

(0.99)*

(0.35)*

(0.22)*

R2

0.15

0.31

0.68

0.74

0.95

0.96

Greene (1993)

14333.29*

5955.74*

14321.66*

15998.47*

Pesaran (2004)

63.36*

38.02*

58.51*

31.928*

Observations

4280

4280

4280

4280

4280

4280

4280

4280

Countries

107

107

107

107

107

107

107

107

α

46.91

46.53

35.15

54.38

C.I.

[40.09,53.73]

[39.89,53.18]

[31.77,38.52]

Computed. R2 is the within-R2 for FE and overall-R2 for RE models. Standard errors are in parentheses. C.I. denotes a 99 % confidence interval

Conclusions

The paper investigates the relationship between wealth and health status using a world panel data for the period 1970–2009. A U-shaped relationship is uncovered. However, conventional estimators reveal a turning point of about 35 and 47 years, while a much greater value of 54 years is obtained when applying an efficient estimator such as the panel FMOLS. In sum, health effects on wealth are inclined to vary over different stages of economic development. Policymakers should therefore take for this non-monotonic relationship into account when designing healthcare schemes.

Footnotes
1

Detailed results are available upon request.

 

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© International Atlantic Economic Society 2012