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

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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 (CI) measured in thousands of dollars Having collected that data on FL, CIi, their age differences (ADi), and the gender of the child (G = 1 if the child is daughter and zero otherwise). The researcher estimates the following regressions assuming homoskedasticity: Cli = 3.67+0.33 Flit 2.1 In(AD); (0.36) (0.71) (0.14) (0.21)(0.014) In(C) 0.23 + 0.0047Flit 0.35 In(AD)-0.56 Gi; (0.19)(0.002) (0.08) Cli = 4.03 + 0.29 Flit 2.3 In(AD)-0.15 Gi-0.11 FI, x G. (0.19)(0.003) (0.34) (0.12) P-values are provided in the parentheses. The dataset contains 520 observations. The R2's of the first, second, and third regressions are 0.253, 0.184, and 0.261, respectively. Answer the following questions: (a) What is the interpretation for the coefficient on FI, in regressions (1) and (2)? (b) What is the interpretation for the coefficient on FIi in regression (3)? (c) What is the interpretation for the coefficient on F× Gi in regression (3)? (d) What is the interpretation for the coefficient on log (ADi) 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)1)->For every one unit increase in FI, CI increases by 0.33

2)->For every one unit increase in FI, lnCI increases by 0.0047, hence CI gets multiplied by exp(0.0047)=1.0047

b)Assuming all other terms are constant, for every one unit increase in FI, CI increases by (0.29-0.11G)

c)FI*G represent they effect the CI at a higher order. Both are interconnected.

d)1)->log(AD) in 1) represents, the increment in CI would be very low with every unit increase in AD. For every one unit increase in AD, CI approximately by 2.1*AD assuming taylors series expansion

2)->For every one unit increment in AD,CI gets multiplied by 0.35AD assuming taylors series expansion

e)At 5% significance level, we fail to reject H0 because 0.08>0.05

f)At 5% significance level, we fail to reject H0

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