question 2

Question II (a) Consider the causal model y - x + u. Given some iid draws (Xi, ui) where Xi and ui are independent standard normals, we obtain Yi = Xi + ui Compute E (YilXi = x) . (b) Based on observations (Xi, Yi), from the above model, we run the following regression Yi = a+ XiB+ errori to obtain the OLS estimator QOLS and BOLS. What would you expect the value of aOLS to be when n - co? What would you expect the value of BOLs to be when n - co? (hint: EX = EX3 = 0, EX2 = 1, and EX4 = 3) (c) Graph the functions y = x and y = a* + x3* in the same graph where a* and * are the limit values of QOLS and BOLS that you find in (b). Do you expect the two functions to be close to each other? Explain