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Hi,

I am using the Smets and Wouters 2007 model, including some variables concerning the fiscal sector and one fiscal policy rule. My question is which data to include in order to estimate the fiscal policy?
In the original model, all real variables are in per capita terms (obtained dividing real aggregate variables by the labour force). Inflation rate is the quarter by quarter variation in the GDP deflator. In the end all
variables are demeaned and detrended using a linear trend, with the exception of the nominal interest rate which is detrended with the same trend as inflation and then demeaned. And then the measurement equations have the following form:

dy = y - y(-1) + gamma1;
dc = c - c(-1) + gamma1;
di = i - i(-1) + gamma1;
dw = w - w(-1) + gamma1;
robs = r + constr;
lobs = l + constl;
piobs = pi + constpi;

Although i made the transformation needed I am not sure what kind of measurement equation to use in order for the fiscal policy rule. Shall i take the difference between them, include the observations just like in the inflation, interest and employment or is there any other alternative?

Best Regards,
Angelos Markou

Please read Pfeifer(2013): "A Guide to Specifying Observation Equations for the Estimation of DSGE Models" at https://sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf.
You say your data is demeaned, but the measurement equations seem to contain a constant, which would be wrong. Regarding observation equations for a fiscal sector, you might want to take a look at the web Appendix to Born/Peter/Pfeifer (2013): Fiscal News and Macroeconomic Volatility, Journal of Economic Dynamics and Control, 2013, Vol. 37(12), pp. 2582-2601 at https://sites.google.com/site/bornecon/research/BPP_OnlineAppendix_Corrected.pdf?attredirects=0 and more generally at Leeper/Plante/Traum (2010): Dynamics of fiscal financing in the United States, Journal of Econometrics https://ideas.repec.org/a/eee/econom/v156y2010i2p304-321.html

Thank you very much for your reply. Your suggestions had been very helpful!