Exercise 8.44 shows the results of separate regressions for foreign-born and California born mother-daughter pairs. Predict the estimated coefficients if this regression is run, using all 10,619 observations:

where D = 0 if the mother is California born and D = 1 if the mother is foreign born. What advantage is there to running a single regression instead of two separate regressions?

Exercise 8.44

Chapter 8 includes a discussion of a study comparing the economic status of 4,121 women who immigrated to California from another county with the economic status of their adult daughters. Economic status was measured by ZIP-code income percentile. For example, if the mother lived in a ZIP code with a 30th-percentile median income and her adult daughter lived in a ZIP code with a 35th-percentile median income, this was characterized as an increase in economic status. The equation Y = α + βX + ε was estimated using the natural logarithms of ZIP-code percentiles for each mother-daughter pair. The coefficient β is the elasticity of Y with respect to X; for example, if β = 0.5, then a 1 percent increase in X is predicted to give an 0.5 percent increase in Y. A similar equation was estimated for 6,498 California-born mothers and their adult daughters. Here are the results (the standard errors are in parentheses):

a. Is the dependent variable the logarithm of the mother’s income percentile or the daughter’s income percentile? Explain your reasoning.

b. Does the sign of the estimated slope make sense to you?

c. Are the estimated slopes statistically significant at the 5 percent level?

d. The estimated elasticity is used to measure intergenerational economic mobility.
Does a larger elasticity indicate more or less mobility? Explain your reasoning.

e. Do these results suggest that there is more economic mobility for the daughters of foreign-born mothers or the daughters of California-born mothers?

Transcribed Image Text:

Ya+BD+BX +3DX +