Consider the following utility maximization problem: 5 EoB μ (In ct +y Inkt+1) Inkies) t=0 s.t. kt+1+C₂ = A-k where a € (0,1), ß € (0, 1), y > 0, c, denotes consumption in period t, kt+1 is the amount of capital stock held at the end of period t (and thus at the beginning of period t+1), and A, is the productivity of capital stock in period t. Assume that max {ce, kt+120) 0 In At+1 = p In At + €t+1 for all t, where p € (0, 1) and €t+1 is an independent white noise.
You can guess and verify that the value function in the Bellman equation for this problem takes the following form: V(At, kt) = F + G In At + H Inkt where F, G, and H are constants. Suppose that α = 0.6, p=0.9, y = 0.2, and p = 0.5. Given these parameter values, derive the values of F, G, and H with 2 decimal places (i.e., if the value of F is 1.6875, only answer 1.68). (Note: you do not need to de-trend the model, because there is no trend in A₂.)
Consider y~ N(XB, 0² In). An unbiased estimator for o² is ² = ||y - XB||². n-plly (a) Find the asymptotic distribution of √n-p(ô2-02). You have done this two weeks ago. (b) With the above asymptotic distribution, construct a (1-a)-confidence interval of o2 using Wilson's method.
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