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QUESTION:-

4. (SW EX. 12.10) Consider the IV regression model l'} = n + 119ng + ,(32Wi + m where Zi is an instrument. Suppose that data on W} are not available and the model is estimated omitting Wi from the regression. a) Suppose that Zi and W3; are uncorrelated. Is the IV estimator consistent? Hint: recall the 1V estimator is gSLS = 2:: (sample covariance of Y and Z divided by sample covariance of X and Z). b) Suppose that Zg and WE: are correlated. Is the IV estimator consistent? 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 le fertility.Rda. The data are from the 1979 census CE! and contain observations on more than 250,000 married women aged 2135 with two or more children. Last week you estilnated the regression of weeksml on morekids using samesex as an instrtnnent. 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 (Le. X2 with the appropriate degrees of freedom], the pvalue, and ymn' conclusion. a) Do a Hausman test for endogeneity. Is there evidence that morekids is endogenous? b) Do a weak instruments test. Is samesex a weak instrument for morekids? c) Repeat part a) and b) using both samesex and the interaction term samesexxboylst 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