1 The following equation was estimated using the data in CEOSALI.RAW: log(salary) 4.322 + .276 log(sales) +.0215 roe (.324) (.033) n 209, R2 .282. (.0129) .00008 roe (.00026) This equation allows roe to have a diminishing effect on log(salary). Is this generality ne essary? Explain why or why not. Co 2 Let B. B......ẞ, be the OLS estimates from the regression of y, on x1,2 For nonzero constants CC, argue that the OLS intercept and slopes from the regression of coy, on ca.... Cai=1, 2, ....., are given by BocoBo B₁ = (cd/c₁)B... B₁ = (code)B (Hint: Use the fact that the B, solve the first order conditions in (3.13), and the B, must solve the first order conditions involving the rescaled dependent and independen variables.] 3 Using the data in RDCHEM RAW, the following equation was obtained by OLS: rdintens 2.613+.00030 sales-.0000000070 sales (.429) (.00014) n 32, R2 .1484. (.0000000037) (i) At what point does the marginal effect of sales on rdintens become negative? (ii) Would you keep the quadratic term in the model? Explain. (iii) Define salesbil as sales measured in billions of dollars: salesbil sales/1.000. Rewrite the estimated equation with salesbil and salesbil as the independent variables. Be sure to report standard errors and the R-squared. [Hint: Note that salesbil sales(1,000)².] (iv) For the purpose of reporting the results, which equation do you prefer? 4 The following model allows the return to education to depend upon the total amount of both parents' education, called pareduc: log(wage) =Bo+ Beduc + Beduc-pareduc + Byexper + Batenure + u. (i) Show that, in decimal form, the return to another year of education in this model is Alog(wage)/Aeduc = B₁+ B-pareduc. What sign do you expect for B₂? Why? (ii) Using the data in WAGE2.RAW, the estimated equation is log(wage) 5.65+.047 educ+.00078 educ-pareduc + (.13) (.010) (.00021) .019 exper+.010 tenure (.004) (.003) n=722, R2.169.