Problem 2 A researcher wants to investigate the relationship between the annual

Question

Problem 2 A researcher wants to investigate the relationship between the annual income of a father (FI) and the annual income of his oldest child (CI4) measured in thousands of dollars. Having collected that data on Fl, CI, their age differences (AD,), and the gender of the child (G 1 if the child is a daughter and zero otherwise). The researcher estimates the following regressions assuming homoskedasticity: Cli (0.2) + (0325F1, + (236) In (AD) 0.23 + 0.0047Flit (031)In (AD)-0 = (0.2) (0.014) (0.19) (0.002) 40 (0.36) In (C1.) = (0.06) CI- +0.25Fli + 2.3In (AD)-0.14G,-0.10F4xGi ) )() (0.19) (0.003) (0.34) (0.12) P-values are provided in the parentheses. The dataset contains 500 observations. The R2's of the first, second, and third regressions are 0.25, 0.18, and 0.26, respectively. Answer the following questions: (a) What is the interpretation for the coefficient on Fl, in regressions (1) and (2)? (b) What is the interpretation for the coefficient on FI in regression (3)? (c) What is the interpretation for the coefficient on Fli × Gi in regression (3)? (d) What is the interpretation for the coefficient on In(AD) in regressions (1) and (2)? (e) Test at the 5% significance level the null hypothesis that gender has no effect on the child's income in regression specification (2). (f) Test at the 5% significance level the null hypothesis that gender has no effect on the child's income in regression specification (3).

Explanation / Answer

a) The equation (1), is a linear equation where a unit change in FIi keeping all the other variables 0 will increase the child's income by 0.325

In equation (2), a unit change in FIi  keeping all the other variables 0 will increase the child's income exponentially, i.e. exp(0.0047) = 1.000471

b) In equation (3), a unit change in FIi  keeping all the other variables 0 will increase the childs income by 0.25

c) In equation (3), a combined effect of two variable FIi and Gi  has a negative impact on the log of child's income

d) In equation (1), a unit change in the ln(ADi) keeping all the other variables  0, will increase the child's income by 2.1

In equation (2), a unit change in the ln(ADi) keeping all the other variables  0, will increase the log of child's income by 0.35

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