Question

5. Fertility, Female Literacy, and more

Think of an economic model that tries to explain the differences across countries in fertility rates with the data on those same countries on female literacy rate. We are fortunate enough to have data for a number of countries both on fertility rates (TFR) and female literacy (FL) rates. And we propose to estimate the following econometric model: TFR= β_0 + FL β_1 + u_i After estimating the parameters of the model the Sum of Squares of the Regression is 56.208, and the Total Sum of Squares is 143.45. Also the estimated value for β_0 is 7.4.

a) Given the information above compute the R-squared of the regression.

b) Explain the meaning of the number calculated in a) as clearly as possible.

c) Explain the meaning of the estimated β_0.

d) What do you think will be the sign of the estimated β_1? Explain the meaning of this parameter.

e) Can you think of other variables that could affect the Total Fertility Rate on top of female literacy, and how? Explain.

Extra Credit: Given your answer in e), what do you think would be the consequence if we tried to explain in the regression framework the TFR both with the FL variable and the one(s) you suggested? What do you think would happen to β_1? (Note: I will ask this same question in the exam, so think hard about it. See if you can come up with a coherent answer.)

Answer 1

a) R^2 is the ratio of ESS or explained sum of squares divided by TSS or total sum of squares.

b) R^2 gives the proportion of the variation in the model explained by the regressors and it is 39% of the variation in total fertility rate explained by variation in female literacy.

c) βo is the intercept coefficient which usually lacks economic interpretation and in this regression it implies the total fertility rate which is independent of the given factors is 7.4. It gives the average fertility rate when all regressors are zero.

d) The expected sign of β1 should be negative as there should be inverse relationship between female literacy and its fertility rate. As women are more literate, their fertility rate declines over the years.

e) factors other than female literacy which affects total fertility rate are years of education, laborforce participation, awareness about population control and various other parameters.