c. Test the hypothesis that marital status can be excluded from the system by running a Wald test. First write the null and alternative hypothesis. Then write the Wald statistics, describe each element and describe how would your conclusion be based on the Wald test statistics. (You may use the test that maintains Assumption SGLS.3) 3. Consider the system of equations Hi = Xi_+ 14; (1) where i indexes the cross section observation, y; and u; are vectors of length G, Xi is G x K, Zi is the G X L matrix of instruments, and?_is a vector of length K. Define ? - E(ugu;). Make the following four assumptions: (1) E(Zu;) =0; (2) rankE(ZX.) = K; (3) E(ZZ;) is nonsingular; (4) E(Z'nZ:) is nonsingular; a Define a generalized method of moment method, i.e. what is the quantity we try to mimimize? What is the corresponding?_? b What is the optimal weighting matrix? Explain clearly your notations. What is the corre- sponding?_? 1. Consider the supply and demand model on page 28 of lecture notes for week 5. We have a demand equation and a supply equation: Demand :q = (1 + (2p + caps + aradi + uj Supply :q =$ 1 18 2p 48 apf + 12 a Run an OLS using the demand equation only. Interpret 62. Is the sign as expected? Why or why not? b Run an 2SLS instead by using the following steps. 1) identify the endogenous variable (12) and the instrument variables. 2) Write the reduced eqaution for endogenous variable. Run an OLS and get yz. 3) Replace the endogenous variable by yz in both the demand equation and the supply equation and run OLS to get aand?_