Question

Suppose the following model of wage determination: log(w) 5.40 0.0654edu + 0.0140exp + 0.0117tenu + 0.199marr - 0.188f - 0.091south + 0.184urban (0.0025) (0.0032) (0.039) (0.027) (0.11) (0.0063) (0.038) (0.026) n 935, R2 .253. where w monthly earnings, edu = years of education, exp tenu-years with current employer, marr 1 if married, f 1 if female, south 1 if live in south, years of work experience, urban 1 if live in urban area Interpret the coefficient of the variable f. Is it significant? a. b. Which of two groups, married women and single men, does earn more? How much? c. Which of two groups, urban married women and single not urban men, does earn more? How much? d. The variables exp2 and tenu2 are added in this model, and the F statistic for joint significance of exp and ten2 is about 1.49. What is your educated guess about the magnitude of the p-value? Interpret this outcome.

Answer 1

(a) here we use t-test and statistic t=0.188/0.038=4.95 with n-p=935-8=927 df

the critical t(0.05/2,927)=1.96 is less than calculated t=4.95, so it is significant

(b) for married women the marr=1 and f=1 and its combined coefficient=0.199*1-0.188*1=0.011

for single men the marr=0 and f=0 and its combined coefficient=0.199*0-0.188*0=0

so married women will urn more by 0.011 units

(c) for urban married women the, urban=1, marr=1 and f=1 and its combined coefficient=0.184*1+0.199*1-0.188*1=0.195

for single not urban men the urban=0, marr=0 and f=0 and its combined coefficient=0*0.184+0.199*0-0.188*0=0

urban married women will earn more by 0.195 units

(d) here f=1.49 will follow F(2,927) and corresponding p-value=0.23 and it is not significant at alpha=0.05, so adding these two variables have no impact on the model