Tut4sol.pdf - MODELLING WITH ECONOMETRICS ECM2MEC Tutorial...

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MODELLING WITH ECONOMETRICS ECM2MEC Tutorial Week 5 - Solutions Question 1 (i) The estimated equation, with standard errors in parentheses below coefficient estimates, is: ???? ̂ = 8.24 + .190 ?𝑜?ℎ???? + .109 ???ℎ???? + .401??𝑖? + .0506??𝑖? 2 (0.29) (.028) (.020) (.030) (.0083) n = 1230, R 2 = .444 The null hypothesis of a linear relationship between educ and abil is 𝐻 0 : 𝛽 4 = 0 and the alternative is that 𝐻 0 does not hold. The t statistic is about .0506/.0083 6.1, which is a very large value for a t statistic. The p-value against the two-sided alternative is zero to more than four decimal places. (ii) We could rewrite the model by defining, say, 𝜃 1 = 𝛽 1 − 𝛽 2 and then substituting in 𝛽 1 = 𝜃 1 + 𝛽 2 , just as we did with the tutorial last week. The original model becomes: ???? ̂ = 𝛽 0 + 𝜃 1 ?𝑜?ℎ???? + 𝛽 2 (?𝑜?ℎ???? + ???ℎ????) + 𝛽 3 ??𝑖? + 𝛽 4 ??𝑖? 2
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