Income with Long Lags
4.2 The Evolution of the Preston Curve Elasticity Over Time
While the foregoing Section focuses on properly accounting for short-run transi- tional dynamics between life expectancy and per capita income, in this Section we look more closely at the corresponding long-run equilibrium relationship. To this end, we set up a truly annual ECM analogous to that in Equation (6), and allow the parameters in the level relationship between life expectancy and per capita income to vary over time. In particular, we specify
lli f eit= τt+ p X j=1 κjt· lli f ei,t− j+ q X j=0 γjt· lgd pi,t− j+ uit, (7)
with t = t0,t1, ...,2010, t0= 1970 + max(p, q), or, written as an ECM,
∆lli f eit = τt+ ϕt· lli f ei,t−1+
q X j=1 γjt ·lgdpi,t−1 + p−1 X j=1 ψjt· ∆lli f ei,t− j+ q−1 X j=1 πjt· ∆lgd pi,t− j+ uit (8)
= ϕt· lli f ei,t−1− at− bt· lgd pi,t−1
+ p−1 X j=1 ψjt· ∆lli f ei,t− j+ q−1 X j=1 πjt· ∆lgd pi,t− j+ uit, (9) where ϕt=Ppj=1κjt− 1, at= −τt/ϕt, bt= −Pqj=1γjt /ϕt, ψjt= −Ps= j+1p κst, and
πjt= −Pqs= j+1γjt. The time-varying coefficients could be estimated in a state- space model framework, in which Equation (9) represents the measurement equa-
tion. For each drifting coefficient one would specify a state equation, in which the coefficient would typically evolve according to a unit root process. A computa- tionally less burdensome approach is to approximate the evolution of the drifting coefficients by polynomials in time, that is, for example, to specify
bt=
τ(b)
X
j=0
ωj· cj(t). (10)
We let cj(t) be Chebyshev polynomials, choose p = q = 10, approximate the long-
run Preston curve parameters at and bt by second-order polynomials in time, and
the remaining short-run dynamics by first-order polynomials in time.13 The es-
timation results for the long-run Preston curve parameters are reported in Figure 17.14 The first row displays results for the full sample, and the second as well as the last for the high- and the low-HDI countries only.
13In fact, we estimate Equation (8) instead of (9), and we approximate ϕ
tas well as Pqj=1δjt
by first- and third-order polynomials. We then divide the polynomial forPqj=1δjtby that for ϕtto
obtain the coefficients of interest atand btfrom Equation (9). As a result, the resulting polynomial
for btdoes not necessarily look like a quadratic polynomial when plotting it. The results are robust
to alternative choices of the lag and polynomial orders.
14We only plot the estimated functionals from 1980, as with a lag order of ten there do not
Figure 17: The Evolution of the Error-Correction Preston Curve with Time- Varying Coefficients 19800 1990 2000 1 2 3 4 5 6 Year Full Sample: Intercept
1980 1990 2000 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 Year Full Sample: Log GDP
19800 1990 2000 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Year High−HDI Countries: Intercept
1980 1990 2000 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 Year High−HDI Countries: Log GDP
1980 1990 2000 −4 −2 0 2 4 6 8 Year Low−HDI Countries: Intercept
1980 1990 2000 −0.5 0 0.5 1 Year Low−HDI Countries: Log GDP
In the full sample, the Preston curve elasticity estimates decrease over time, are not statistically significant at the beginning of the sample period and turn statistically insignificant again from the mid 1990s. When splitting the sample, the long-run Preston curve elasticity estimates remain statistically significant for the high-HDI
countries only, but even for the high-HDI countries decrease over time and turn statistically insignificant from the end of the 1990s. For the low-HDI countries, the Preston curve income elasticity is not statistically significantly different from zero over the entire sample period. As in Section 4.1, the point estimates of the slope of the long-run Preston curve are slightly larger for the high-HDI coun- tries than for the full sample; notice, however, the non-trivial extent of estimation uncertainty in Figure 17. At the minimum, the time-varying coefficients ECM suggests a substantial decline in the long-run income elasticity of life expectancy both in the full and the high-HDI country sample. Beyond that, there appears to be a high probability for the income elasticity in the Preston curve having turned statistically insignificant more recently even for the countries close to the health technology frontier.15
Conclusion
In this paper, we investigate the relationship between life expectancy and per capita income. We claim that the income elasticity in the standard Preston curve is likely to be overestimated due to the failure of controlling for countries’ distance to the health technology frontier, and that the income elasticity of life expectancy has substantially declined even in countries close to the health technology frontier. Our results are based on simple sample splits and basic econometric techniques
15Similar findings are obtained when looking at the static Preston curve estimates from Equation
on the one hand, and a slightly more elaborate simulation exercise in which we assess the ability of different DGPs, each representing a competing theory about the importance of per capita income for the determination of life expectancy, to produce the patterns found in the actual data on the other hand.
We find that for countries far away from the health technology frontier, even though we cannot conclude with certainty, the effects of income growth on life expectancy are, relative to those of health technology adoption, close to zero. Our results thus suggest that, whether or not income can be ruled out as a determi- nant of life expectancy in countries far away from the health technology frontier, policymakers in developing countries should be concerned about the factors un- derlying their countries’ delayed convergence to the health technology frontier rather than about how to most effectively spur income growth. A casual look at Figure 1 suggests that for a country far away from the health technology fron- tier, adopting the health technologies already in place in the countries closer to the frontier would result in an improvement of life expectancy of at least 14%. In order to achieve the same improvement in life expectancy via growth in per capita income (assuming for the moment the income elasticity estimate was sta- tistically significantly different from zero), per capita income would have to grow
by about 3200%!16 Considering that technology adoption to a large extent con-
sists of introducing relatively inexpensive vector control measures, disseminating
16For large g
xthe approximation gx= (x1− x0)/x0≈ log(x1) − log(x0) is misleading. With an
estimated income elasticity of 0.04 the log difference in per capita income a country far away from the technological frontier has to trace out in order to achieve an increase in life expectancy of 14% is 3.5. Thus, the growth in per capita income associated with an improvement in life expectancy by 14% is explog( ˜x) − log(x)− 1 = exp(3.5) − 1 ≈ 32.
basic information on healthy behavior (avoiding indoor burning of solid fuels, hand washing, promoting safer sex, breastfeeding, etc.), providing sugar-salt re- hydrating therapies, antibiotics, vaccinations and so on, puts into stark contrast what policymakers in developing countries can expect from policies focusing on health technology adoption vis-à-vis income-growth centered policies. For exam- ple, a package of six vaccines assembled by the World Health Organization costs less than $1, and deworming costs just 50 cents a year.17 Enhanced accountability of local governments, a free press, empowerment and education of their people are certainly key to creating an environment conducive to the adoption of health technologies. Globalization, by facilitating the spread of technologies, ideas and behaviors, may significantly speed up this process. By supporting the flow of health technologies from developed to developing countries, international orga- nizations such as the World Health Organization or the United Nations may also play a crucial role.
Finally, we provide evidence suggesting that even for the countries close to the health technology frontier the role of income for the determination of life ex- pectancy has substantially weakened during the last two to three decades. Health conditions are thus becoming increasingly disconnected to per capita income in developed countries. Living a healthier life requires new insights about healthy behavior (smoking, obesity, stress, diet), their spread and adoption on a large scale. The individual’s behavior thus appears to gain importance for the prolon- gation of life in developed countries, too.
A
Appendix
A.1
Countries Included and Subsamples
The countries included in our baseline specification with HDRO data are:
Afghanistan, Albania, Algeria, Angola, Argentina, Armenia, Australia, Austria, Azerbaijan, Bangladesh, Barbados, Belarus, Belgium, Belize, Benin, Bolivia, Brazil, Bulgaria, Burkina Faso, Burundi, Cambodia, Canada, Cape Verde, Chad, Chile, China, Colombia, Comoros, Congo, Congo (Democratic Republic of the), Costa Rica, Croatia, Cyprus, Czech Republic, Côte d’Ivoire, Denmark, Djibouti, Dominican Republic, Ecuador, Egypt, El Salvador, Estonia, Ethiopia, Fiji, Fin- land, France, Gambia, Georgia, Germany, Ghana, Greece, Guatemala, Guinea, Guinea-Bissau, Guyana, Haiti, Honduras, Hong Kong, China (SAR), Hungary, Iceland, India, Indonesia, Ireland, Italy, Jamaica, Japan, Jordan, Kazakhstan, Kenya, Korea (Republic of), Kyrgyzstan, Lao People’s Democratic Republic, Latvia, Liberia, Lithuania, Luxembourg, Madagascar, Malaysia, Maldives, Mali, Malta, Mauritania, Mauritius, Mexico, Micronesia (Federated States of), Moldova (Re- public of), Mongolia, Morocco, Nepal, Netherlands, New Zealand, Nicaragua, Niger, Nigeria, Norway, Pakistan, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Poland, Portugal, Romania, Russian Federation, Rwanda, Sao Tome and Principe, Senegal, Sierra Leone, Singapore, Slovakia, Slovenia, Solomon Is- lands, Spain, Sri Lanka, Sudan, Suriname, Sweden, Switzerland, Syrian Arab Re- public, Tajikistan, Thailand, The former Yugoslav Republic of Macedonia, Togo,
Tonga, Trinidad and Tobago, Tunisia, Turkey, Turkmenistan, Ukraine, United Kingdom, United States, Uruguay, Uzbekistan, Venezuela (Bolivarian Republic of), Viet Nam .
The high-HDI countries are:
Albania, Algeria, Argentina, Armenia, Australia, Austria, Azerbaijan, Barbados, Belarus, Belgium, Belize, Bolivia, Brazil, Bulgaria, Canada, Cape Verde, Chile, China, Colombia, Costa Rica, Croatia, Cyprus, Czech Republic, Denmark, Do- minican Republic, Ecuador, Egypt, El Salvador, Estonia, Fiji, Finland, France, Georgia, Germany, Greece, Guatemala, Guyana, Honduras, Hong Kong, China (SAR), Hungary, Iceland, India, Indonesia, Ireland, Italy, Jamaica, Japan, Jordan, Kazakhstan, Korea (Republic of), Kyrgyzstan, Latvia, Lithuania, Luxembourg, Malaysia, Maldives, Malta, Mauritius, Mexico, Micronesia (Federated States of), Moldova (Republic of), Mongolia, Morocco, Netherlands, New Zealand, Nicaragua, Norway, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Romania, Rus- sian Federation, Singapore, Slovakia, Slovenia, Spain, Sri Lanka, Suriname, Swe- den, Switzerland, Syrian Arab Republic, Tajikistan, Thailand, The former Yu- goslav Republic of Macedonia, Tonga, Trinidad and Tobago, Tunisia, Turkey, Turkmenistan, Ukraine, United Kingdom, United States, Uruguay, Uzbekistan, Venezuela (Bolivarian Republic of), Viet Nam .
The low-HDI countries are:
Afghanistan, Angola, Bangladesh, Benin, Burkina Faso, Burundi, Cambodia, Chad, Comoros, Congo, Congo (Democratic Republic of the), Côte d’Ivoire, Djibouti,
Ethiopia, Gambia, Ghana, Guinea, Guinea-Bissau, Haiti, Kenya, Lao People’s Democratic Republic, Liberia, Madagascar, Mali, Mauritania, Nepal, Niger, Nige- ria, Pakistan, Papua New Guinea, Rwanda, Sao Tome and Principe, Senegal, Sierra Leone, Solomon Islands, Sudan, Togo .
A.2
Figures
Figure 18: The Cross-Sectional Distribution of Life Expectancy When Control- ling for the Sub-Saharan African Average Level of Life Expectancy
10 20 30 40 50 60 70 80 90 100 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 2010 1970
A.3
Tables
Table 4: Death and Poverty Around the World in 2002
Millions of Deaths per Year Treatments, Prevention World Low-Income High-Income
Respiratory Infections Antibiotics 3.96 2.90 0.34
HIV/AIDS HAART 2.78 2.14 0.02
Perinatal Deaths Pre- and post-natal care 2.46 1.83 0.03 Diarrheal Diseases Oral rehydration therapy 1.80 1.50 0.00
Tuberculosis Public health: DOTS 1.57 1.09 0.01
Malaria Partially treatable 1.27 1.24 0.00
DPT/Measles/Polio Vaccinations 1.12 1.07 0.00
Percent of Deaths
Ages 0 to 4 18.4 30.2 0.9
Ages 60 and Above 50.8 34.2 75.9
Note: HAART stands for Highly-active anti-retroviral therapy, perinatal deaths are deaths in the first seven days of life, and are typically associated with low birthweight, DOTS stands for directly-observed treatment short course, and is treatment combined with community monitoring to ensure full compliance, and DPT stands for diphtheria, pertussis (whooping cough) and tetanus. Low income and high income are World Bank designations and correspond (approximately) to below $5,000 and above $10,000 PPP in Figure 1. Note that the middle-income countries are not shown, so that the world figures are not the sum of the low-income and high-income figures. Figures are for 2002, are based on WHO data, and are subject to substantial margins of error. Table and note reproduced from Deaton (2007).
Table 5: p-Values
Correlation t-Value Preston Curve Elas-
ticity R2 Kolmogorov- Smirnov Test (p- Value) Pbγ ∈ [bγ( j,r)± 2 · stdbγ( j,r)] Data -0.022 -1.45 0.095 0.68 Preston Curve DGP 0.007 [−0.014;0.04] [−0.78;2.51]0.004 [0.093;0.113]0.064 [0.659;0.785]0.104 0.003 0.46 Independent Shocks DGP 0.799 [−0.054;−0.01] [−3.52;−0.57]0.755 [0.074;0.096]0.977 [0.469;0.618]1 0.645 0.97 Preston/Independent Shocks Mixing DGP 0.333 [−0.042;0.007] [−2.5;0.42]0.251 [0.083;0.104]0.705 [0.585;0.725]0.77 0.645 0.99 4 9
Table 6: p-Values for the Double Preston Curve and the Error-Correction Model
Correlation t-Value Preston Curve Elas-
ticity R2 Kolmogorov- Smirnov Test (p- Value) Pbγ ∈ [bγ( j,r)± 2 · stdbγ( j,r)] Data -0.022 -1.45 0.095 0.68 Double Preston DGP 0.123 [−0.031;0.015] [−1.91;0.93]0.091 [0.085;0.105]0.574 [0.619;0.75]0.449 0.36 0.94 ECR DGP 0.268 [−0.039;0.01] [−2.54;0.61]0.244 [0.084;0.104]0.701 [0.603;0.739]0.612 0.008 0.97
Double ECR Preston DGP 0.208
[−0.034;0.011] [−2.11;0.7]0.17 [0.083;0.103]0.673 [0.595;0.735]0.717 0.369 0.97 ECR/Independent Shocks DGP 0.441 [−0.045;0.003] [−2.74;0.19]0.362 [0.083;0.104]0.722 [0.585;0.721]0.792 0.645 0.99 5 0
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