Question

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d) Afler OLS estimation the following results are obtained (estimated standand emors for the estimated coefficients are in parentheses) In(wage)-0.36+0.09EDUC-.1SFEMALE+0O2EXPER o6) CI) O) Col) OIFEMALE EXPER (,003) R-0.37,n-526 Conduct a significance test to see whether years of education have a significant effect on wages 5 marks) ECO107/1005 e) Conduct an ovcrall F-iest to determine whether there is ovcrall regression significance 10 marks] Another OLS regression is conducted that gives the following results (estimated standard errors for the estimated coefficients are in parentheses): In(waga)- 083+0.07EDUC-36FEMALE 09) (o1) (04 R-0.30,-526 Test to see whether EXPER, and FEMALE EXPER, are jointly significant. (10 marks] g) Comparing the resalts from parts d) and ), discuss the issue of omitted variable bias (15 marks d) 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) (01) (11) 01) ,OIFEMALE EXPER 003) R 0.37,n-526. Conduct a significance test to see whether years of education have a significant effect on wages. 5 marks] [ECO1007/1005] 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 g) Comparing the results from parts d) and dicuss the issue of omitted variable bias. [15 marks]

Answer 1

(d) Test statistic = t = 0.09/0.01 = 9 p-value = P(t > 91t ~ t526-4-1) = 0.0000 < 0.05 Hence years of education have a significant ef fect on wages R2 526-41 = 76.4960 (e) Value of F-1-R2 × 4 p-value P(F > 76.4960|F ~ F4.52) = 0.0000 < 0.05 Hence overall regression is significant R? _ 526-4-1 (f) Value of F = = 14.1553 where, Ri- 0.37, R2 0.30 p - value- P(F> 14.1553 FF2,521)0.0000 0.05 Hence EXPER, and FEMALEEXPER, are jointly significant (g) Since omitted-variable bias occurs when a statistical model leaves out one or more relevant variables and EXPER, and FEMALE EXPER, are jointly significant so model in (f) suf fers from omitted variable bias