- Homework 1: Modeling the World Fertility Transition
The spreadsheet “Total Fertility Rates and Income-S2020.xlxs” on Canvas contains data on total fertility rates (TFR, expected number of children born per woman entering her child-bearing years) and per-capita income (GNP, thousands of US$, adjusted for purchasing power) for a sample of countries for which these data were available both in 1980 and 2009.
Research in the economics of the family hypothesizes that the demand for children decreases with income. As countries become richer, the value of people’s time increases. Children are a very time-intensive “commodity.” Thus, we’d expect total fertility rates to decrease as countries’ per-capita incomes rise. In addition, people in richer countries do not depend on their children for support in old age—pensions and social security reduce the “asset demand for children.”
- Please answer the following questions in the space provided here and submit your assignment (both this Word document and your Excel spreadsheet with data and calculations)
- Derive summary statistics on the TFR and GNP using the “Total Fertility Rates and Income” data.
- What is the mean TFR in 1980?
- What is the mean TFR in 2009?
- Is the mean TFR significantly different between the two years? Use a test of the difference between means at the p=.05 significance level to answer this last question, and state your test statistic.
- Consider the following simple OLS regression model:
- Now estimate the simple OLS regression model in Question 2, USING EXCEL(the excel spreadsheet we used for the API and FLE model would be a good template for doing this), and use it to answer the following questions:
- Over time, other things that affect fertility may change. For example, women become more educated, and this may have an effect on women’s willingness to have children that is independent of income. Does knowing this change the way you feel about the reliability of your OLS estimates? Why or why not?
- How might you use the “year” variable to control for other variables that might be affecting fertility over time? Please write the equation of the model only.
- Using EXCEL, please estimate a multiple regression model that controls for changes in fertility over time, independent of income. (That is, add a year variable to your model.)
- Report the estimated coefficient on your time variable, and explain what it means.
- Is your econometric estimate of the effect of income on fertility unchanged? Why or why not?
- Which does a better job of explaining the variation in total fertility around the world mean, the simple or multiple regression model? Explain.
- Please use your model in Question 5 to predict the TFR for Spain in 2009. Is your model a good predictor of Spain’s TFR in 2009? Why or why not?
- Now use your model in Question 5 to predict the TFR for China in 2009. Is your model a good predictor of China’s TFR in 2009? Why or w not? If not, why do you suppose your model is not a good predictor of TFR in China?
- What might a better model to predict fertility look like, if you could get data on any additional variables at the country level? Be sure to explain the THEORY behind including these new variables in your analysis.
…where the subscript ‘it’ refers to country iat time t. Do not estimate it yet, but tell us YOUR theory about what the sign of b1is likely to be, and why.
- What is your econometric estimate of b1? What does it mean?
- What is the elasticity of TFR with respect to GNP, estimated at the means of the two variables?
- Report the R-squared for this regression and interpret it (explain what it tells us).
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