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2sls is 2 staged least squares

You are using variable 4- to instrument for c,- in the equation y1- = a + BC,- + X157 | uni. X2- is the vector of controls. Assume that z:- is exogenous; that is, 2?; satises the conditional independence assumption given the controls. (a) Write down the rst stage equation for ZSLS. (b) Let 7T be the rst-stage coeicient on 2%. What can you say about the hypothesis H0 : ,3 = 0 if the tstatistic for 1r equals 1.2 (with the pvalue of 0.23) and the t statistic for ,3 from the second stage (properly corrected for multiple stages) equals 3.6 (pvalue=0.0003)? Would you reject, fail to reject, or unable to test the hypothesis? Explain. (c) How would your answer to (b) change if the tstatistic for 7r is 5.12 (pvalue=0.00001) and the second stage tstatistic for ,8 is 0.8 (pvalue=0.42)? Explain. ((1) Write down the reduced form equation for y,-. Is it okay to estimate this equation using OLS? Why or why not? (e) How would you test H0 : 6 = 0 using the reduced form estimates? Which tstatistic would you use and how would you interpret the results