Consider a wage equation for U.S. working married women, log(wagei)=0+1educi+2experi+3experi2+ui where exper and exper 2 denotes years (and years squared) of work experience, while educ stands for years of education. We have good reasons to believe that exper and exper 2 are exogenous variables. On the other hand, the error term u is thought to be correlated with educ because of omitted ability, as well as other factors, such as quality of education and family background. (a) Suppose that we can collect data on husband, mother, and father education - huseduc motheduc and fatheduc - and that we want to use these three variables as instruments for the endogenous variable educ. Write down the first stage equation that you should run in this case. (b) Using data on 428 working married women in the US, you want to test whether the 3 instruments you have been considering are relevant. For that, you have just obtained the output of the following two regressions. Perform an F test (it's ok to assume errors are homoscedastic!) to look into this question. Based on the results of you test, would you conclude that the instruments are relevant or not? Regression 1 educi=12.36936+0.564919experi0.0019043experi2R2=0.0049 Regression 2 educ i=5.538311+0.374977 exper i0.0006002 exper i2+0.1141532 motheduc i +0.1060801 fatheduc i+0.3752548 huseduciR2=0.4286 Consider a wage equation for U.S. working married women, log(wagei)=0+1educi+2experi+3experi2+ui where exper and exper 2 denotes years (and years squared) of work experience, while educ stands for years of education. We have good reasons to believe that exper and exper 2 are exogenous variables. On the other hand, the error term u is thought to be correlated with educ because of omitted ability, as well as other factors, such as quality of education and family background. (a) Suppose that we can collect data on husband, mother, and father education - huseduc motheduc and fatheduc - and that we want to use these three variables as instruments for the endogenous variable educ. Write down the first stage equation that you should run in this case. (b) Using data on 428 working married women in the US, you want to test whether the 3 instruments you have been considering are relevant. For that, you have just obtained the output of the following two regressions. Perform an F test (it's ok to assume errors are homoscedastic!) to look into this question. Based on the results of you test, would you conclude that the instruments are relevant or not? Regression 1 educi=12.36936+0.564919experi0.0019043experi2R2=0.0049 Regression 2 educ i=5.538311+0.374977 exper i0.0006002 exper i2+0.1141532 motheduc i +0.1060801 fatheduc i+0.3752548 huseduciR2=0.4286