Question

hi can someone answer part e) f) g) h) with workings olease thanks

2) A cross-sectional study suggests the following wage equation: In(wage,)-α + βι EDUC' + β:FEMALE + β3EXPER, + β4FEMALE EXPERi + ei Where: In(wage): Natural logarithm of f hourly wage; EDUC: Years of education; EXPER: Years of work experience; FEMALE: Dummy which equals 1 if the respondent is female and 0 otherwise; FEMALE EXPER:Interaction between FEMALE, and EXPER a) What is meant by the population level regression equation? [5 marks] b) Differentiate In(wage) with respect to EDUC, and interpret your result. [10 marks] c) Differentiate In(wage) with respect to EXPER, and interpret your result. [15 marks] After OLS estimation the following results are obtained (estimated standard errors for the estimated coefficients are in parentheses): In(wage.)-0.36 + 0.09EDUC-.18FEMALE, + 0.02EXPER, (.06) C01) .01FEMALE EXPER (003) R2 -0.37, n-526. Conduct a significance test to see whether years of education have a significant effect on wages. [5 marks] 2 [ECO1 e) Conduct an overall F-test to determine whether there is overall regression significance. [10 marks] f) Another OLS regression is conducted that gives the following results (estimated standard errors for the estimated coefficients are in parentheses): In(wage.)-0.83+0.07EDUC-36FEMALE (.09) (01) (.04) R2-0.30, n-526 Test to see whether EXPER, and FEMALE EXPER, are jointly significant [10 marks] Compiigthe rsuits from parts d) and s the u f mited variable bias. [15 marks)

Answer 1

MSR e, F-statistic = MSE SSR where, MSR = mean sum of square due to regression _ _ _ SSR sum of square due to regression SSE = sum of square due to error SSE MSEmean sum of square due to error n-4-1 SST = sum of square due to total = SSE+ SSR or, SSE = SST-SSR R2 SSR/4 Hence F = SST- SSR)/(n- 5)41-R2 ((526-5)/4) (0.37/(1 - 0.37)) 76.4960 p-value P(F > 76.4960|F ~ F4.52) = 0.00000 < 0.05 Hence overall regression equation is significant (f) SSRnew-sum of square due to new regression equation = (0.30)SST Sum of square due to EXPER, and FEMALEEXPER SSR - SSRne(0.37) (0.30)) SST 0.07SST. F-statistic SSE(n (0.07)SST/2 n 5 0.07SST n-5 0.07 5 = (52 1/2) * (0.07/(1-0.37)) = 28.9444 p - value- P(F> 28.9444| FF2,521)0.00000.05 Hence EXPER, and FEMALEEXPERi are jointly significant

g. Omitted - variable bias occurs when a regression equation leaves out one or more relevant variables. ALE EXPER are jointly significant, Since EX PERi and FEM so if we omit EXPERi and FEMALE EX PERi then Omitted-variable bias occurs.