# Observation equation of tax income

Hello, Dynare.
In my DSGE model government Tax Labor Revenue is T=W * L * tau_l;
I collected the data on labor income (demeaned, detrended) and wanted to match with the model equation.
So, I put it as:

2. But since my model is log-linearized model with exp(x), I reconsidered it to be:

I estimated the model with both observation equations, first one gives adequate response for positive productivity shock e (it increases output). The second one does not (it decreases output to positive productivity shock e).

Could you please give some suggestions on observation equation for labor tax revenue Without more information on the model specification and the data treatment, it is impossible to tell.

Dear @jpfeifer ,

Sorry for the late response, I could not get into Dynare forum for sometime, it was showing some error.
As for the labor tax income I found in data “labor tax revenue per capita”, I took a log and detrended and also demeaned (my model is stationary, I ignore pop. growth).
I did similar for consumption tax revenue .
My mod file is attached (observation equations #50-51)
DSGE_dynare.mod (8.1 KB)

You should have
\begin{align} TA{X_t} &= {e^{{W_t}}}{e^{{L_t}}}{e^{{\tau _t}}} \hfill \\ \ln \left( {TA{X_t}} \right) &= \ln \left( {{e^{{W_t}}}{e^{{L_t}}}{e^{{\tau _t}}}} \right) = {W_t} + {L_t} + {\tau _t} \hfill \\ \ln \left( {TA{X_t}} \right) - \ln \left( {TAX} \right) &= {W_t} + {L_t} + {\tau _t} - \left( {\bar W + \bar L + \bar \tau } \right) \end{align}

Thank you very much for the confirmation, I was not sure before.