Simulating a Simultaneous System Parameter estimates of the Klein macroeconomic model for the U.S., 1921 to 1941. Parameter OLS IV FIML 0 16.237 16.555 16.461

Simulating a Simultaneous System Parameter estimates of the Klein macroeconomic model for the U.S., 1921 to 1941. Parameter OLS IV FIML α0 16.237 16.555 16.461 α1 0.193 0.017 0.177 α2 0.090 0.216 0.210 α3 0.796 0.810 0.728 β0 10.126 20.278 24.130 β1 0.480 0.150 0.007 β2 0.333 0.616 0.670 β3 -0.112 -0.158 -0.172 γ0 1.497 1.500 1.028 γ1 0.439 0.439 0.317 γ2 0.146 0.147 0.253 γ3 0.130 0.130 0.096 Gauss file(s) linear_simulation.g Matlab file(s) linear_simulation.m Consider the bivariate model y1,t = β1y2,t + α1x1,t + u1,t y2,t = β2y1,t + α2x2,t + u2,t, where y1,t and y2,t are the dependent variables, x1,t ∼ N(0, 100) and x1,t ∼ N(0, 9) are the independent variables, u1,t and u2,t are normally distributed disturbance terms with zero means and covariance matrix V =  σ11 σ12 σ12 σ22  =  1 0.5 0.5 1  , and β1 = 0.6, α1 = 0.4, β2 = 0.2 and α2 = −0.5.

(a) Construct A, B and hence compute Π = −AB−1 .

(b) Simulate the model for T = 500 observations and plot the simulated series of y1,t and y2,t.