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Supplement 13: An example of regression analysis

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

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Supplement 13: An example of regression analysis

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

  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. 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. 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. Theme of this project • We use fertility data across countries to estimate the relationship between fertility and mortality and per capita income.

  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. Descriptive statistics: Fertility rate 34.3% countries below replacement fertility rate: (=2.1). Hong Kong

  8. Descriptive statistics: Mortality rate Hong Kong

  9. Descriptive statistics: GDP per capita Hong Kong Luxembourg

  10. Scatter plot: fertility vs. GDP per capita (y) (x)

  11. Scatter plot: fertility vs. mortality (y) (x)

  12. Regression model I: Statistically different from zero at 1% level of significance. Economically, we expect fertility rate to lower by 0.07005 per woman when the per capita income increases by US$1000. Or: fertility rate to lower by 7 per 100 women

  13. Regression model I: Rejects the hypothesis that all coefficients are jointly zero. The explanatory variable (per capita income) explains 22.5% of the variation in fertility rate.

  14. Regression model II: Statistically different from zero at 1% level of significance. Not statistically different from zero even at 10% level of significance. 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. 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.

  15. Regression model II: Rejects the hypothesis that all coefficients are jointly zero. The explanatory variables together explain 74.2% of the variation in fertility rate.

  16. Regression model III: Statistically different from zero at 1% level of significance. Economically, we expect fertility rate to increase by 0.0382 per womanwhen mortality increases by 1 infant death 1 per 1000 birth.

  17. Regression model III: Rejects the hypothesis that all coefficients are jointly zero. The explanatory variable (per capita income) explains 73.9% of the variation in fertility rate.

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

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