R2 How much does a woman's labor supply fall when she has an additional child? For this exercise you will need to download the data file fertility.Rda. The data are

from the 1979 census and contain observations on more than 250,000 married women aged 21-35 with two or more children. Last week you estimated the regression of weeks ml on more kids using same sex asan instrument. You are going to investigate the validity of that estimation strategy. In each of the following questions please: be sure to state the null and alternative hypotheses you are testing, the asymptotic distribution of the test statistic (i.e. x² with the appropriate degrees of freedom), the p-value, and your conclusion. a) Do a Hausman test for endogeneity. Is there evidence that more kids is endogenous? b) Do a weak instruments test. Is samesex a weak instrument for more kids? c) Repeat part a) and b) using both samesex and the interaction term samesex boylst as instruments. Do your estimates change? d) Do a Sargan test for the model you estimated in part c). Is there evidence that the instruments are endogenous?