Using a life-cycle model with public and private spending in schooling, we find that differences in mortality rates are at least as important as TFP differences in accounting for the variance of log incomes. In particular, elimination of TFP differences would reduce the variance of log income in 48%, while elimination of mortality differences would do so by 51%. In addition, the equilibrium of our model implies a set of human capital estimates for all countries in the sample. We find that these estimates suggest a larger dispersion than standard Mincer-equation estimates. In particular, human capital in poorer countries is substantially lower.
In an apparent contradiction to our results, Acemoglu and Johnson (2006)find that increases in life-expectancy since 1950 did not have much effect on output growth. However, we view our paper and theirs as complementary. First, the reduction in mortality that they refer to is mostly children mortality. In our model, this would be the same as an increase in fertility rates and therefore should actually decrease output. The reason is that having more children around dilutes public expenditures in education and can actually reduce human capital per worker rather than increase it, depending on the response of years of schooling. Second, since different from Acemoglu and Johnson we mostly consider adult mortality, our model is suitable for analyzing events such as the HIV/AIDS pandemic, while theirs is not. Our results mainly suggest that understanding the origin of differences in mortality rates is an important item in the research agenda in cross-country income inequality.
Appendix These two equation can be written as in (2).
Solution to the Individual Problem Note that the set of budget constraints (5) can be written as:
(1+r)i−2 >1. The individual problem can thus be written as:
whereμ andλare Lagrange multipliers. An optimal solution must satisfy:
s:wh1/T =ρπ2c1
The last equation produces:
ci= πi
π2 [ρ(1 +r)]i−2c2 fori= 3, .., I (24) Using this result and (20) one obtains:
c2 = Θwh2−
Then, one can use (24) and (25) to writecj more generally as:
cj =Θj(r)wh2 forj= 2, .., I. Furthermore, one can obtainai as:
ai =whi+ (1 +r)ai−1−ci
Define Φ(r)≡PI
i=2niPi
j=2(1 +r)i−j(θj −Θj(r)). Then
qK =wh2Φ(r) (27)
Furthermore, using (9) and (11):
qK
From (21) and (22) one obtains:
e= γ2 γ1
wh1
T (χ+s)−p. (29)
Moreover, from (22), (25) and (4) it follows that:
p+e = ρπ2γ2c1
i=2ρi−1πi. Equating this expression to (29) and solving for s produces the optimal level of schooling in an interior solution:
s∗= eργ1ψT
The last condition guarantees thats∗ ≥0. In addition, substituting this result into (29) produces the optimal level of private expenditures for an interior solution:
e∗ = 1 +eρψγ1
The last condition guarantees thate∗ ≥0.Furthermore, from (7) and (29):
Corner Solution: e= 0 and s≥0 Next, consider corner solutions of the form e= 0 and s≥0. From equations (21), (25) and (4) one obtains:
χ+s and solving forsgives:
s∗= eργ1T −χ e≥ 0. In this case, equation (30) is still valid because it does not use (21). Imposing s = 0into this equation and solving for eproduces:
e∗ = eργ2wh1−p
This inequality can be rewritten as m ≥ whp . Thus, this case requires m ≥ whp and ργ2ψ ≥ whp . However, one can check that thefirst inequality implies the second under Assumption 1.
Solution to the general equilibrium problem >From (9), (11) and (6) one has that:
wh1 = (1−τw) (1−α)y Mixed Education Equation (13) states that whp
1 = ω³
1−s∗/T +P
2 θini
θ1n1
´. For the case of mixed education we then have that:
p
Solving for whp produces:
p
Alternatively, one can use the definitions of mand m to rewrite this expression as:
p
Substituting the first expression into (31) and the second expression into (32), using (34) and simplifying produces:
or defining sH≡ N1(p+e)Y =ετ+ 13Ye,which uses (10), one obtains
Other General Equilibrium Results Per-capita output can be written as:
y = Akα(h)1−α =A
Moreover, notice that in a stationary equilibriumh satisfies, using (11) and (12):
h =
so that
h yγ2 =
Ã
(1−s∗/T)n1θ1+X
2
θini
!
z(χ+s∗)γ1(s∗H/n1)γ2.
References
[1] Arndt, C. and Lewis, J.D. (2000), “The Macro implications of HIV/AIDS in South Africa: a preliminary assessment.”South African Journal of Economics 68, 856-887.
[2] Barro, R. and Jong-Wha Lee (2000), “International Data on Educational Attainment. Updates and Implications.” NBER Working Paper # 7911.
[3] Bils, M. and Klenow, P. “Does Schooling Cause Growth?” American Economic Review, De-cember 2000, 90(5), pp. 1160-83.
[4] Bloom, D. E. and Mahal, A. S “Does AIDS Pendemic Threaten Economic Growth,” Journal of Econometrics 77: 105-24.
[5] Chiquiar, D. and Hanson, G. H. “International Migration, Self-Selection, and the Distribution of Wages: Evidence from Mexico and the United States”Journal of Political Economy, 2005, Vol 113, No. 3, pp. 239-281.
[6] Córdoba, J. C. and Ripoll, M. “Agriculture, Aggregation, Wage-Gaps, and Cross-Country Income Differences,” Mimeo, 2004.
[7] Corrigan, P., Glomm, G. and Mendez, F. “AIDS crisis and Growth,”Journal of Development Economics 77 (2005) 107-124.
[8] Erosa, A.; Korseshkove, T. and Restuccia D. “On the Aggregate and Distributional Implica-tions of Productivity Differences across Countries.” Mimeo, University of Toronto, February 2006.
[9] Ferreirra, P.C and Pessoa, S.A. “The Costs of Education, Longevity and the Poverty of Na-tions,” Mimeo 2003.
[10] Ferreirra, P.C and Pessoa, S.A. “The Long-Run Economic Impact of AIDS,” Mimeo 2003.
[11] Hall, Robert E. and Jones, Charles I. “Why Do Some Countries Produce So Much More Output Per Worker Than Others?”Quarterly Journal of Economics, February 1999, 114(1), pp. 83-116.
[12] Hendricks, L. “How Important Is Human Capital for Development? Evidence from Immigrant Earnings?”American Economic Review, March 2002, 92(1), pp. 198-219.
[13] Huggett, M., Ventura, G., and Yaron, A. “Human capital and earnings distribution dynamics,”
Journal of Monetary Economics, 2006, Elsevier, vol. 53(2), pages 265-290, March
[14] Klenow, Peter J. and Rodríguez-Clare, Andrés. “The Neoclassical Revival in Growth Eco-nomics: Has It Gone Too Far?” in Ben S. Bernanke and Julio J. Rotemberg, eds., NBER Macroeconomics annual 1997. Cambridge, MA: MIT Press, 1997a, pp. 73-103.
[15] Mankiw, N. Gregory; Romer, David and Weil, David N. “A Contribution to the Empirics of Economic Growth.”Quarterly Journal of Economics, May 1992,107(2), pp. 407-37.
[16] Manuelli, R. E. and Seshadri A. “Human Capital and the Wealth of Nations.” Mimeo, Uni-versity of Wisconsin-Madison, June 2005.
[17] Psacharopoulos, G. and Patrinos H A. “Returns to Investment in Education: A Further Up-date.”Policy Research Working Paper 2881,The World Bank, September 2002.
[18] Ukpolo, V. “AIDS Epidemic and Economic Growth: Testing for Causality,” Journal of Asian and African Studies 39(3), 2004.
[19] Young, Alwyn. “In Sorrow to Bring Forth Children: Fertility amidst the Plague of HIV.”
Mimeo 2005.
[20] Young, Alwyn. “The Gift of the Dying: The Tragedy of AIDS and the Welfare of Future African Generations.”Quarterly Journal of Economics, May 2005,120(2), pp. 420-66.
Figure 1
% Enrollment in Public Schools
0 10 20 30 40 50 60 70 80 90 100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Per capita GDP relative to US
Primary Secondary
Source: UNESCO
Figure 2. Public Education Expenditures per Pupil as a Percentage of GDP per capita
0%
5%
10%
15%
20%
25%
30%
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Per capita GDP relative to US
Figure 3. Optimal Educational Choices ) /(wh p
m m
) /(wh e
)
*/(wh e s
) /(wh p
m m
s*
Figure 4 Demographics
Life Expectancy at Birth
30
Per capita GDP relative to US 1995
Years
Per capita GDP relative to US 1995
Survival Probabilities
Per capita GDP relative to US 1995
Years
Per capita GDP relative to US 1995
Years
Figure 5
Capital Taxes and Labor Taxes (τ)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Per capita GDP relative to US
τ
Figure 6
Educational Variables: Model Vs Data
Panel C Average Years of Schooling
0
Returns to School by Income Levels
0.00
Per capita GDP relative to US
r
Data Model
0.02 0.03 0.04 0.06 0.08 0.11 0.14 0.17 0.20 0.25 0.36 0.51 0.64 0.76 0.82 1.00
0.00
Share of Education Expenditures in GDP
Private Share Public Share
Figure 7
Human Capital Stocks Estimates
Panel A
Human Capital Estimates with Total and Only Public Expenditures (Relative to US)
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Per capita GDP relative to US
human capital relative to US
(CR) - Model with Total Education Expenditures
Human Capital Stocks Compared to Other Estimations (Relative to the US)
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Per capita GDP relative to US
human capital relative to US
Cordoba & Ripoll (2006) Bils & Klenow (2001) Hendricks (2002) 45º
Panel D
Human Capital Stocks Compared to Own Previous Estimates (Relative to US)
human capital relative to US
Cordoba & Ripoll (2006) Cordoba & Ripoll (2004) Panel C
Human Capital Stocks Compared to Other Estimations (Relative to the US)
human capital relative to US
Mankiw, Romer & Weil
Figure 8
Self-Selection of Immigrants
(A)
Implied Self-Selection of Immigrants (Human Capital Immigrant relative to non-immigrant)
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Per capita GDP relative to US
τ CR (2004)
CR
(B)
Predicted Position of Immigrants in Source Country Earnings Distribution
35%
45%
55%
65%
75%
85%
95%
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Per capita GDP relative to US
human capital relative to US
CR 2004 CR Hendricks
Figure 9
Predicted Long Run Effects of the HIV/AIDS Pandemic
Life Expectancy at Birth
30
Per capita GDP relative to US 1995
Ratio
Long Run Human Capital/1995 Human Capital
0.0
Per capita GDP relative to US 1995
Ratio
Long Run Physical Capital/1995 Physical Capital
0.0
Per capita GDP relative to US 1995
Ratio