Question

Suppose you estimate the following model by OLS: wage = β0 + β1educ + β2exper + u wage : hourly age in dollars educ : years of education exper : years of experience You obtain the following fitted model using STATA, where standard errors are given in parenthesis wage [ = 3.5 + 0.9educ + 1.5exper (2.0) (0.7) (0.5) Number obs. : 523 R 2 = 0.45 For the following questions, make use to the relevant statistical tables. If you find that the degrees of freedom exceed 120, then use the critical values in the ∞ row. (a) At the 1% level, conduct a test of the hypothesis that β2 = 0 against the alternative that β2 > 0. Formally write out the null hypothesis. Show how you calculate the appropriate test statistic, and make careful note of the degrees of freedom, the critical value of your test statistic, and whether or not you reject the null. (b) Now, at the 5% level conduct a test of the null that experience and education jointly have no effect on wage against the alternative that this is not true. Formally state the null and alternative hypotheses. Show how you compute the appropriate test statistic, and make note of degrees of freedom, critical values, and whether or not you reject the null.

Answer 1

Given wage = po + B, edu + Be exp. + u (a to: ß220 20 Since n is large, we'll use the stat Zstat a Hai ß2 15-0 3 in determining Zerut at 17 ( right tail) 2-33 Since 2stat > Zout at ing level significance, therefore, we reject the and conclude that years of experie- mill hypothesis of insu nce and is si significant wages. For Eteit since here joint signifi- joint significance we'll use the cance involves the whole regression R?/(k-1) Clapészyna) cb Estat -

IV 0.45/9 0.55 7520 Ho: B, B2=0 Ha. Bit or Beto = 225 is 3 Fort, therefore ve Fout at St. with (2,520 of freedom is Since Estat ? reject the mall hypothesis of sig. nificance, and conclude that the firem variables are jointly significant. no &