3. (16 points) A common measure of intergenerational persistence of economic status is the inter- generational earnings elasticity, the slope coefficient from a regression of child's log earnings on a parent's log earnings. The regression results below are from a sample of 3,537 children in the Panel Study of Income Dynamics (PSID). The variable earn is child's earnings, dadearn is father's earnings, and both earnings variables were measured when the person was around age 40. I use father's log earnings as the explanatory variable because, at the time parents' earnings were observed, the gender gap in employment rates was larger than it is now, so earnings are not observed for many mothers. Both sons and daughters are included in the regression sample. Below are the estimates from a regression of child's log earnings on father's log earnings, a nonwhite indicator variable, and an interaction between the nonwhite indicator and father's log earnings. In(earn) = 0.159 + 0.423 In(dadearn) + 0.119 nonwhite - 0.058 nonwhite x In(dadearn) (0.015) (0 026) (0.071) (0.097) 3.1. Among white individuals, if father's earnings increase by 10 percent, by how much are the child's earnings predicted to change? (a) 0.423 percent (b) 4.23 percent (c) 0.0423 percentage points (d) 0.423 percentage points 3.2. Which of the following is a valid interpretation of the estimated coefficient on the interaction term? (a) Father's log earnings are lower, on average, for nonwhite individuals compared to white individuals. (b) For a given percentage increase in father's earnings, the predicted percentage increase in child's earnings is slightly negative. (c) For a given percentage increase in father's earnings, the predicted percentage increase in child's earnings is smaller for nonwhite individuals than for white individuals. (d) As father's log earnings increase, the average value of the nonwhite variable is decreasing. 3.3. Which of the following is a valid interpretation of the estimated coefficient on the nonwhite indicator? (a) Among children in this sample, predicted earnings are 11.9 percent higher for nonwhite individuals than for white individuals. (b) When considering the relationship between child's log earnings and father's log earnings, the intercept is higher for nonwhite individuals than for white individuals. (c) The slope on father's log earnings is higher for nonwhite individuals than for white individuals. (d) To find the slope on father's log earnings for nonwhite individuals, you must add the coefficients on the nonwhite indicator and the interaction term. 3.4. What might be the reason that both child's earnings and father's earnings are in log form in this regression? (a) We want to think in terms of percentage changes in earnings instead of dollar changes in earnings. (b) We want to allow for the possibility that the relationship between child's earnings and father's earnings is non-monotonic (that is, the sign changes). (c) We should log any variable, such as earnings, that only takes on positive values. (d) We want to allow for the possibility that average earnings are different for white and nonwhite individuals