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Problem 2 (Nonlinear least squares using GMM.) (26 points.) Consider the following cross-sectional regression model (notice the index, it is not t, it is 2'): 593' = 91 + 92593.3 + 55; (2) with i = 1, ..., N. The model is nonlinear in the parameters. Assumptions: We have area] = 0 {3) and the errors are cross-sectionally uncorrelated and homoskedastic. (1) (4 points.) Using Matlab, simulate a and a rst and then y so that the relation in Eq. (2) is satised. Set N = 1000. You can chose all of the parameters. (Notice that if you are drawing iid errors with mean zero that are independent of the a: observations, the assumptions are satised.) In choosing the parameters, keep in mind that I am expecting something that is realistic. For example, something similar to the scatterplot below. (2) (5 points) Use the Assumption in Eq. (3) to come up with a set of moment condi- tions. (Recall1 you want to have more moment conditions than parameters or the same number. In this case, you have 3 parameters. You need at least 3 moment conditions. Hint: ls E[ f (121:)5i] = 0, for any f , given Eq. (3)? If so1 you can choose three, or more, different fs. Two are natural (see Problem 1), the others you need to come up with but you have exibility). (3) (4 points.) Estimate your model by GMM on your simulated data. (4) (5 points.) Compute the GMM variance and the corresponding standard errors for all parameter estimates