Supplement13-1 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Supplement 13: An example of regression example of regression analysisanalysis

A test of the relation between A test of the relation between fertility rate and mortality rate?fertility rate and mortality rate?

Supplement13-2 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Are mortality and fertility related?

Demographers have pointed out that in many cases mortality decline precedes fertility decline, which suggests a causal link from falling mortality to falling fertility.

The model of Barro and Becker (1989) implies falling mortality rates tend to lower the cost of having a surviving child, hence fertility actually increases, not decreases, as mortality declines. (Instead of emphasizing mortality decline, the Barro-Becker framework points to the quantity-quality tradeoff as an explanation for fertility decline: parents choose to have smaller families in order to invest more in the education of each child.)

Barro, Robert and Gary S. Becker (1989): “Fertility Choice in a Model of Economic Growth,” Econometrica 57(2): 481-501.

Supplement13-3 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Are mortality and fertility related?

Kalemli-Ozcan (2003) argues when mortality is stochastic and parents want to avoid the possibility of ending up with very few (or zero) surviving children, a “precautionary” demand for children arises.

Extending the theoretical model of Barro and Becker (1989), Doepke (2005) predicts a negative relationship between mortality and fertility.

Kalemli-Ozcan, Sebnem (2003) “A Stochastic Model of Mortality, Fertility, and Human Capital Investment.” Journal of Development Economics, 70 (1): 103-118

Doepke, Matthias (2005): “Child Mortality and Fertility Decline: Does the Barro-Becker Model Fit the Facts?” Journal of Population Economics, 18(2): 337-366.

Supplement13-4 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Are income and fertility related?

Burdsall (1988) suggest the so-called Norm curve, which describes fertility as a monotonically declining function of per capita income.

Birdsall, N. (1988): “Economic Approaches to Population Growth”, in Handbook of Development Economics, by H. Chenery and T.N. Srinivasan, Eds, Vol. 1, Elsevier: Amsterdam.

Supplement13-5 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Theme of this project

We use fertility data across countries to estimate the relationship between fertility and mortality and per capita income.

Supplement13-6 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Data sources and description

World Development Indicator (WDI) 2002, available from the HKU main library.

Time: year 2000 only. 172 countries (out of 207) with relevant variables

GDP per capita (in 1995 US$) – a proxy for income per capita.

Infant mortality rate (per 1,000 live births) Fertility rate (births per woman)

Drop 35 countries: 32 countries did not report GDP per capita. Additional 3 countries did not report fertility rate.

Do not consider adult illiteracy rate because substantial number of developed countries (such as UK and US) did not report this variable.

Supplement13-7 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Descriptive statistics: Fertility rate

count 172

mean 3.15

Standard deviation 1.60 1st quartile 1.77

minimum 1.02 median 2.63

maximum 7.22 3rd quaritle 4.42

range 6.20 interquartile range 2.64

0 1 2 3 4 5 6 7 8

Hong Kong

34.3% countries below replacement fertility rate: (=2.1).

Supplement13-8 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Descriptive statistics: Mortality rate

count 172

mean 38.76

Standard deviation 35.99 1st quartile 10.01

minimum 2.90 median 23.60

maximum 153.60 3rd quaritle 60.00

range 150.70 interquartile range 50.00

0 50 100 150 200 250

Hong Kong

Supplement13-9 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Descriptive statistics: GDP per capita

count 172

mean 6,617.45

Standard deviation 10,809.61 1st quartile 528.212

minimum 115.88 median 1,611.19

maximum 56371.99 3rd quaritle 5,372.00

range 56256.12 interquartile range 4,843.79

0 10000 20000 30000 40000 50000 60000

Hong Kong Luxembourg

Supplement13-10 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

y = -7E-05x + 3.6178

R2 = 0.2245

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fert

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y ra

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Scatter plot: fertility vs. GDP per capita

(x)

(y)

Supplement13-11 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Scatter plot: fertility vs. mortality

y = 0.0382x + 1.6748

R2 = 0.739

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mortality rate, infant

fert

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y ra

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(x)

(y)

Supplement13-12 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Regression model I:

Fertility = 3.617 0.07005 GDP

Stderror (0.1263) (0.00998)

P-value [5.71E-67]

[5.18E-11]

Economically, we expect fertility rate to lower by 0.07005 per woman when the per capita income increases by US$1000.

Statistically different from zero at 1% level of significance.

Or: fertility rate to lower by 7 per 100 women

Supplement13-13 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Regression model I:

ANOVA

Source SS df MS F p-value

Regression 98.05 1 98.05 49.22 5.18E-11

Residual 338.63 170 1.99

Total 436.68 171 　 　 　

R-square 0. 225

The explanatory variable (per capita income) explains 22.5% of the variation in fertility rate.

Rejects the hypothesis that all coefficients are jointly zero.

Supplement13-14 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Regression model II:

Fertility = 1.7950 - 0.00973 GDP + 0.0367 mortality

Stderror (0.1230) (0.00664) (0.0020)

P-value [9.44E-32]

[0.1446] [2.83E-42]

Economically, holding mortality rate constant, we expect fertility rate to lower by 0.00973 per woman when the per capita income increases by US$1000.

Economically, holding per capita income constant, we expect the fertility rate to rise by 0.0367 per woman when mortality increases by 1 infant death per thousand births.

Statistically different from zero at 1% level of significance.

Not statistically different from zero even at 10% level of significance.

Supplement13-15 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Regression model II:

ANOVA

Source SS df MS F p-value

Regression 324.125 2 162.0623 243.34 1.76E-50

Residual 112.555 169 0.666

Total 436.677 171 　 　 　

R-square 0.742

The explanatory variables together explain 74.2% of the variation in fertility rate.

Rejects the hypothesis that all coefficients are jointly zero.

Supplement13-16 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Regression model III:

Fertility = 1.6748 + 0.0382 mortality

Stderror (0.0919) (0.0017)

P-value [7.89E-42]

[1.86E-51]

Economically, we expect fertility rate to increase by 0.0382 per woman when mortality increases by 1 infant death 1 per 1000 birth.

Statistically different from zero at 1% level of significance.

Supplement13-17 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Regression model III:

ANOVA

Source SS df MS F p-value

Regression 322.69 1 322.69 481.28 1.86E-51

Residual 113.98 170 0.67

Total 436.68 171 　 　 　

R-square 0. 739

The explanatory variable (per capita income) explains 73.9% of the variation in fertility rate.

Rejects the hypothesis that all coefficients are jointly zero.

Supplement13-18 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

Conclusion

Fertility rate is strongly directly related to mortality rate. When mortality rate is included, the explanatory power of income

per capita on fertility rate seems small.

Cautions: Although the model setup seems to suggest a low mortality

rate will cause a low fertility rate. The reverse could be true. Countries with a low fertility rate may spend more on infant survival and hence a low mortality rate.

The true relationship need not be linear, e.g., Strulik and Sikandar (2002).

Strulik, Holger and Siddiqui Sikandar (2002): “Tracing the income-fertility nexus: Nonparametric Estimates for a Panel of Countries,” Economics Bulletin, 15 (5): 1-9.

Supplement13-19 Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data

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Supplement 13: Supplement 13: An example of regression analysis example of regression analysisA test of the relation between A test of the relation between fertility rate and mortality rate?fertility rate and mortality rate?