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In a state-space representation, the measurement equation is something of this form $O_t=H_t s_t + u_t$, where $O_t$ are the observational data at time $t$, $H_t$ is a possibly time-dependent matrix relating the state $s_t$ and the observational data. We can see $u_t$ as the measurement errors at time $t$.

However, in Herbst and Schorfheide book (Bayesian estimation of DSGE models),

we have $s_t$ dependent on $y_{t}$, but not $y_{t-1}$, while the measurement equations are of the form:

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Is this a typo? Should I add the $y_{t-1}$ term to $s_t$?

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After asking this same question on the dynare forum, I got the answer that it's really a typo, and I should augment the state vector.

The interesting thing is that afterwards, I rerun the Gensys function of Sims(2002), and I got a solution for an indeterminate model, which is a bit strange.

Augmenting the state vector by a lag from a previously already present variable shouldn't change the model, since I just added the equation y_{t-1}=y_{t-1}to the model. However, the gensys function states that it does.

This makes me wonder if there's something wrong with the code in Sims(2002).

If anyone knows more, please feel free to share. Thanks

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