Question

5) Simulate data according to the following. Please provide a log ile and any supporting exhibits x = 12 ,50 e N(0,1) a) Provide an estimate of the coefficients in y + + є b) Are Bi,B2 "near" the true values? c) Store the coefficients in a matrix B d) Repeat the simulation 100 times, estimating the equation and storing the coefficients each iirte e) What is the distribution of simulated coefficients A, B2? a. b. c. Mean Standard Deviation Relate these to the true values of the coefficients and the first two moments of the OLS estimator

Please complete the above question using STATA software.

I am not sure what you mean when you said you cannot complete it in the space provided- only a log file is needed.

Answer 1

> #Q. a) > X = 1: 50 > e = rnorm (50, 0, 1) > Y = 1 + 2*X + e > Beta2hat = (sum(X*Y) - 50*mean(X) *mean(Y))/sum((X-mean (X))^2) > Betalhat = mean (Y)-Beta2hat*mean (X) > #The values of coefficients are > Betalhat [1] 1.260601 > Beta2hat [1] 1.99297 > #Q.b) yes, beta 1hat and beta2hat are near to their true values but slightly differ. > #Q.c) > B = matrix (c(Betalhat, Beta2hat), byrow = TRUE, nrow = 2) > B#coeffient Matrix [,1] [1,] 1.260601 [2,] 1.992970 > #Q.d) > BetaMatrix = matrix (nrow = 2, ncol = 100) > for(i in 1: 100) + { + e = rnorm (50, 0, 1) + Y = 1 + 2*X + e + BetaMatrix [2, i] = (sum(X*Y) -50*mean (X) *mean (Y))/sum((X-mean(X))^2) + BetaMatrix [i, i] = mean (Y) -Beta2hat*mean (X) + } > # First and second row of BetaMatrix represent the estimate of beta1 and beta 2 respectively. > #Q. e) .a) > meanbeta 1 = mean (BetaMatrix [1,]) > meanbeta 2 = mean (BetaMatrix [2,]) > meanbeta 1 [1] 1.178654 > meanbeta 2 [1] 1.99916 > #Q.e)b) > SDbeta 1 = (var (BetaMatrix [1]))^0.5 > SDbeta 2 = (var (BetaMatrix [2,]))^0.5 \r\n > e = rnorm (50, 0, 1) > Y = 1 + 2*X + e > Beta2hat = (sum (X*Y) - 50* mean (X) *mean (Y))/sum ((X -mean (X))^2)