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Problem 1 (Estimating the linear regression model using GMM.) (44 points.) Consider the following regression model: yt = 0121,t + 02 x2, t + ... + 0kick,+ + Et, (1) with t = 1, ..., T. Notice that, more compactly, we can also write yt = x1 0+ Et, where X1,t X 2 , t X. = . . . Ck.t and d = . . . OK Notice, also, that the first regressor can be a column of ones. In this case, Of would correspond to the intercept. Assumptions: 1. Efetxt] = 0. NO E(Et ( Xt, Xt-1 , .. . Et - 1, Et-2, ...) = 0. 3. E( e? ( xt , X t - 1 , . . . Et - 1 , Et -2, ...) = 0. On the assumptions: (1) (3 points.) Explain why Assumption 1. is an assumption of correct specification of the model. (2) (3 points.) Explain why Assumption 2. implies that the errors are uncorrelated. (Hint: the law of iterated expectations may help.) (3) (3 points.) Explain why Assumption 3. implies that the errors are homoskedastic. (Hint: the law of iterated expectations may, again, help. )