Hi all,

This is somehow related to an older post of mine. I have a two-sector, two-country model that is calibrated. The exogenous process is the TFP in each sector and each country, hence I have four shocks and four exogenous variables.

```
zT1 = A1T_11*zT1(-1) + A1T_12*zT2(-1) + A1T_13*zN1(-1) + A1T_14*zN2(-1) + eT1 ;
zT2 = A2T_11*zT1(-1) + A2T_12*zT2(-1) + A2T_13*zN1(-1) + A2T_14*zN2(-1) + eT2 ;
zN1 = A1N_11*zT1(-1) + A1N_12*zT2(-1) + A1N_13*zN1(-1) + A1N_14*zN2(-1) + eN1 ;
zN2 = A2N_11*zT1(-1) + A2N_12*zT2(-1) + A2N_13*zN1(-1) + A2N_14*zN2(-1) + eN2 ;
```

where 1 and 2 are countries and T and N are sectors. I estimate the persistence parameters and the variance-covariance matrix outside the model and then I calibrate the values when running the model in Dynare (stoch_simul). To do the estimations, I extract Solow residuals as: ln(Z_ij) = ln(Y_ij) - (1-alpha)*ln(N_ij) for each country i = {1,2} ans sector j = {T, N}, where Y is output and N is hours. Here I emphasise that I perform the estimations in logs!

I want to have a log-linearised model, and I let Dynare do it. Thus, I insert the equations into my model as follows:

```
model;
zT1 = A1T_11*zT1(-1) + A1T_12*zT2(-1) + A1T_13*zN1(-1) + A1T_14*zN2(-1) + eT1 ;
zT2 = A2T_11*zT1(-1) + A2T_12*zT2(-1) + A2T_13*zN1(-1) + A2T_14*zN2(-1) + eT2 ;
zN1 = A1N_11*zT1(-1) + A1N_12*zT2(-1) + A1N_13*zN1(-1) + A1N_14*zN2(-1) + eN1 ;
zN2 = A2N_11*zT1(-1) + A2N_12*zT2(-1) + A2N_13*zN1(-1) + A2N_14*zN2(-1) + eN2 ;
.....
% Output
exp(yT_I1) = exp(zT1)*exp(ST1)^alphaT_1*exp(nT1)^(1-alphaT_1) ;
exp(yT_I2) = exp(zT2)*exp(ST2)^alphaT_2*exp(nT2)^(1-alphaT_2) ;
exp(yN1) = exp(zN1)*exp(SN1)^alphaN_1*exp(nN1)^(1-alphaN_1) ;
exp(yN2) = exp(zN2)*exp(SN2)^alphaN_2*exp(nN2)^(1-alphaN_2) ;
....
end;
```

Is that the correct way?? From reading J. Pfeiffer’s guide on observation equations it seems to be ok. But is it also ok that the Solow residuals were defined/estimated in logs? Again here I want to emphasise that I do not have exp(Z.,.) but " just" Z.,. in levels in defining the exogenous process in the Dynare code. And what does that mean on how my equations appear “on paper”, i.e. output is [ul]Y = exp(Z)*K^alpha * N^(1-alpha) [/ul] or [ul]Y = Z*K^alpha * N^(1-alpha) [/ul] (and what’s the difference…?)

Thanks in advance and sorry if some questions seem primitive.

Best,

Kyriacos