Hi Professor,

I want to estimate the standard deviations of two shock and also the correlation between them. Suppose I have two exogenous process:

a_t = rho_a*a_{t-1}+e_a,
b_t = rho_b*b_{t-1}+e_b.

And the variance-covariance matrix of e_a and e_b is:

sigma_a^2, phi*sigma_a*sigmab;

phi*sigma_a*sigmab, sigma_b^2 ].

How should I estimate phi, sigma_a, and sigma_b simutanously? Is the following lines right?

[code]var a b;

varexo sigma_a sigma_b;

parameters phi rho_a rho_b;

rho_a=0.9;rho_b=0.9;phi=0.5;

model;

a = rho_a*a(-1)+e_a;
b = rho_b*b(-1)+e_b;

end;

shocks;

var sigma_a; stderr 0.1;

var sigma_b; stderr 0.1;

var sigma_a, sigmab=phi*sigma_a*sigma_b;

end;

estimated_params;

stderr sigma_a, , 0.000000000001,100,INV_GAMMA2_PDF,0.1,2;

stderr sigma_b, , 0.000000000001,100,INV_GAMMA2_PDF,0.1,2;

phi, ,.00000001,.99999999999,BETA_PDF,0.33,0.23;

end;

estimated_params_init;

stderr sigma_a, 0.1;

stderr sigma_b, 0.1;

phi, 0.5;

end;

estimation(…);[/code]

Dynare can run the above code. But it seems that the value of phi doesn’t effect the result.

Can you help me? Thanks!