# Specifying observation equation for interest rate

Dear all,

I want to specify observation equation for interest rate when estimating DSGE model. In my model interest rate is defined in gross terms i.e. R_t =(1+r_t). In the data the interest rate is quoted in annualized terms (net interest rate) while in the model it is defined as quarterly gross interest rate. I divided original data by 100 and subtract the mean. I specified the following observation equation:

R_t_obs = 4*(R-1) + 4RR_hat.

Is my specification correct? Adolfson et al. for example report the following specification:

R_t_obs = 4*(R-1)R + 4R*R_hat.

where R is steady state gross interest rate.

Which specification is correct?

Best

Denote with R_t_obs the quarterly gross interest rate. Then, if

and no logging has taken place to derive a loglinearization, you should have

R_t=1+R_t_obs/400

See also section 4.5.3 of Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”

Dear jpfeifer

thank you for your answer. To clarify my question, please see attached file. I use the model developed by Adolfson et al. (2007) which is log-linearized (variables with hat - % deviations from SS).

Given my data (see attached file), I specified the following observation equation.
R_t_obs = 4*(R-1) + 4RR_hat.

where R is the seady state gross interest rate.

But on the other hand, Adolfson et al. (2007) in their technical appendix report the following specification:
R_t_obs = 4*(R-1)R + 4R*R_hat.

So, the difference is the term: 4*(R-1) vs. 4*(R-1)*R. Could you explain me the intuition behind this specification?

Best,J
Data.xls (32 KB)

Please provide a link to the document you refer to and elaborate on the derivation of your observation equation.