Variance of endogenous variables in OSR

In OSR computations, the variance-covariance matrix of endogenous variables appears to be different from the one reported by stoch_simul (order=1).

In OSR, the variance-covariance matrix is computed by the following code (last line of get_variance_of_endogenous_variables.m)
vx1(i_stat,i_stat) = ghx(:,i_stat_0)*vx(i_stat_0,i_stat_0)*ghx(:,i_stat_0)'+ghu*Sigma_e*ghu';while in stoch_simul, the matrix is computed as in line 143 of th_autocovariances.m
v(stationary_vars,stationary_vars) = aa*vx*aa'+ bb*M_.Sigma_e*bb';
The difference between the two expressions is in the first term. While in stoch_simul the entire vx matrix is employed, in OSR only a sub matrix of vx identified by i_stat_0 indices is used. Numerically, the difference in terms of the value of the loss function (specified in OSR) is noticeable (20% for my model). Is there really a need for the two computations of the same matrix to be different?

I don’t get the point. In OSR, only the variance for variables in the loss function are selected. But the big covariance matrices from which the entries are selected are identical.

It is true that in OSR (in the line of code cited above) the variance-covariance matrix is computed only for the variables specified in the loss function. For example, if there are 3 variables in the loss function, the matrix is [3x3]. When running stoch_simul, I compute statistics for exactly the same variables. As a shortcut, the statistics can be also obtained by disp_th_moments(oo_.dr,‘x1’;‘x2’;‘x3’]).

The difference between the computations in osr and in stoch_simul lies in the computation of the first term in the two lines of code above. In OSR/get_variance_of_endogenous_variables because of i_stat_0 the dimension of matrices in the expression ghx(:,i_stat_0)**vx(i_stat_0,i_stat_0)ghx(:,i_stat_0)’ could be, for example, [3x50]x50x50]x[50x3]. In stoch_simul/disp_th_moments the dimension of matrices in aa**vxaa’ could be [3x120]x120x120]x[120x3]. In both cases, the resulting variance-covariance matrices are [3x3], but the matrices are not the same.

The issue seems to boil down to imposing abs(Au)<options_.Schur_vec_tol in line 51 of get_variance_of_endogenous_variables.m (in addition to abs(ghxu)<options_.Schur_vec_tol) and not imposing the restriction in th_autocovariances.m.

I see. According to my understanding, this should only matter for unit root variables. Could you provide me with an example mod-file where the problem occurs?