1. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-1 example of regression analysis Supplement 13: An example of regression analysis A test of the relation between fertility rate and mortality rate?

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

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

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

5. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-5 Theme of this project We use fertility data across countries to estimate the relationship between fertility and mortality and per capita income.

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

7. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-7 Descriptive statistics: Fertility rate count172 mean3.15 Standard deviation1.601st quartile1.77 minimum1.02median2.63 maximum7.223rd quaritle4.42 range6.20interquartile range2.64 Hong Kong 34.3% countries below replacement fertility rate: (=2.1).

8. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-8 Descriptive statistics: Mortality rate count172 mean38.76 Standard deviation35.991st quartile10.01 minimum2.90median23.60 maximum153.603rd quaritle60.00 range150.70interquartile range50.00 Hong Kong

9. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-9 Descriptive statistics: GDP per capita count172 mean6,617.45 Standard deviation10,809.611st quartile528.212 minimum115.88median1,611.19 maximum56371.993rd quaritle5,372.00 range56256.12interquartile range4,843.79 Hong Kong Luxembourg

10. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-10 Scatter plot: fertility vs. GDP per capita (x) (y)

11. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-11 Scatter plot: fertility vs. mortality (x) (y)

12. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-12 Regression model I: Fertility=3.617  0.07005GDP 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

13. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-13 Regression model I: ANOVA SourceSSdfMSFp-value Regression 98.051 49.225.18E-11 Residual 338.631701.99 Total 436.68171 R-square0. 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.

14. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-14 Regression model II: Fertility=1.7950-0.00973GDP+0.0367mortality 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.

15. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-15 Regression model II: ANOVA SourceSSdfMSFp-value Regression 324.1252162.0623243.341.76E-50 Residual 112.5551690.666 Total 436.677171 R-square0.742 The explanatory variables together explain 74.2% of the variation in fertility rate. Rejects the hypothesis that all coefficients are jointly zero.

16. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-16 Regression model III: Fertility=1.6748+0.0382mortality 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.

17. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-17 Regression model III: ANOVA SourceSSdfMSFp-value Regression322.691 481.281.86E-51 Residual 113.981700.67 Total 436.68171 R-square0. 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.

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

19. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Supplement13-19 - END - Supplement 13: example of regression analysis An example of regression analysis A test of the relation between fertility rate and mortality rate?