1 Take home exercise Note: When submitting the script used to find the answers, please make sure that each question is clearly commented. Further comments about what you are trying to do at each step are encouraged. Consider the following dgp: It = H2 + P2ªt-1 + Ezt (1) Ut = Hy + Pyt-1 + Ey,t (2) where Ezt ~ N(0, 02), Ey,t ~ N(0, 02), and Cov(Ez,t, Ey,t) = 0 1. Using the parameterisation in Table 1: i. Simulate N samples of x and y for a sample of length T=100, where N=1000. ii. For each i E N: estimate the following model: yt = a + B+ + & iii. Plot the histogram of the estimated ? iv. Find the median ? as well as the 95% confidence interval. Can you reject the null hypothesis that 8 = 0? 2. Repeat [1.]: i. a. setting pz = Py = 0.99 b. setting pz =Py= 1 ii. In each case, can we reject the null hypothesis 8 = 0? Why or why not? iii. Are the estimates of 8 in 2[i.][a.] and 2[i.][b.] significantly different from each other? parameter value 0.05 Pz 0.8 Py 0.8 02 0.02 0.01 0.005 Table 1: Parameter Values (Initial)