Recursive Structural Models Gauss file(s) linear_recursive.g Matlab file(s) linear_recursive.m Simulate the trivariate structural model for T = 200 observations y1,t = 1x1,t + u1,t y2,t

Recursive Structural Models Gauss file(s) linear_recursive.g Matlab file(s) linear_recursive.m Simulate the trivariate structural model for T = 200 observations y1,t = α1x1,t + u1,t y2,t = β1y1,t + α2x1,t + u2,t y3,t = β2y1,t + β3y2,t + α3x1,t + u3,t, where {x1,t, x2,t, x3,t} are normal random variables with zero means and respective standard deviations of {1, 2, 3}. The parameters are β1 = 0.6, β2 = 0.2, β3 = 1.0, α1 = 0.4, α2 = −0.5 and α3 = 0.2. The disturbance vector ut = (u1,t, u2,t, u3,t) is normally distributed with zero means and covariance matrix V =   2 0 0 0 1 0 0 0 5   .

(a) Estimate the model by maximum likelihood and compare the parameter estimates with the population parameter values.

(b) Estimate each equation by ordinary least squares and compare the parameter estimates to the maximum likelihood estimates. Briefly discuss why the two sets of estimates are the same.