# Measurement Equation/ Observed Variables

Hi All,

I am trying to estimate a Smets and Wouters 2003 model using dynare’s bayesian estimation.

The model is specified in loglinear form in deviation from steady state.

For example if the observed variables are real_GDP_level and Price_level,
and the corresponding variables in the model are Yhat=log(Yt)-log(Y*)
and PIEhat= log(P_t/P_t-1)

How should I transform these observed variables before using them to do bayesian estimation in this model.

Any help would be greatly appreciated.

Thanks,

Abhishek.

Dear Abhishek

if your model is expressed in terms of log deviation for the steady state, your data should reflect that fact. The empirical counter part of the output gap is the difference between the observed data and some smooth function of time (or in other words a time trend). You can use the HP filter to obtain that trend. This is because it is common to consider the mean of a series the steady state level of the series itself. If the series has a trend (like the gdp), the mean is increasing over time, so the steady state as well. If you want the log deviation, simply apply the filter to the log of the series and than subtract it from the log of the series.
As for the inflation rate, if you have the price level, just take the logarithm of it, make the first differences and you will have the inflation rate (if you have quarterly data and you want the annual inflation rate, take ln(P[t])-ln([Pt-4]), while if you want the annualized inflation rate take {ln(P[t])-ln([Pt-1])}*4). For series that have not a trend (and inflation should not have a trend, although Smets and Wuoter remove a linear trend from their series of inflation), their steady state is simply the mean. Hence, again you should demean the series of inflation before estimate the model.

Cheers

Paolo Gelain

Dear Paolo,

Thanks for the reply. It was very helpful.

So for inflation, the steady state in the model is zero since log(1)=0. But in the data we should subtract the mean inflation from inflation to get deviation form.

Also for interest rate, since that is supposed to be stationary we should subtract mean interest rate from levels.

Should it make a difference if we multiply all the series by 100?

Thanks again,
Abhishek