Forecast error variance in multivariate Kalman Filter became singular

[timxwatson]

Hi there,

I am getting the following error when I try and estimate the attached model:

initial_estimation_checks:: The forecast error variance in the multivariate Kalman filter became
singular.

wsnff.mod (6.3 KB)
dsge_est1.xlsx (39.5 KB)
wagesub_stst1.mod (942 Bytes)

This seems strange because stochastic simulation runs fine on the calibrated model, and I can estimate the model if I drop one of the GDP related variables (i.e. Government investment or consumption for example). Also, estimation still doesn’t work when I initialize the Kalman Filter with the calibrated parameters. I don’t think there is a problem with the model- the model diagnostics all suggest the model is fine.

Just wondering if anyone had any tips on solving this problem? It would be nice to estimate the model with all of the components of closed economy GDP included if possible.

[timxwatson]

Apologies, with correct files this time!
wsnff.mod (6.2 KB)
wagesub_stst1.mod (942 Bytes)
dsge_est1.xlsx (20.9 KB)

[jpfeifer]

That is not feasible. See

Cannot have more observed variables than shocks?

Yes, that is true. The problem is known as “stochastic singularity”. The problem is that in a linear model if you have fewer shocks than observables, there will be an exact linear combination implied between observables. That in turn means that the density of observing that variables is either 1 (the exact linear combination in the model holds in the data; rarely the case) or 0 (the exact linear combination does not hold; the typical case). As you can imagine with a log density of minus infinity…

[timxwatson]

Hi Professor- thanks for your response- There are an equal number of shocks and observable series in the model. That is not the problem. Adding more shocks does not solve the problem.

[jpfeifer]

Don’t focus on the number of shocks. The problem also arises when there is an exact linear combination of observables implied by the model. You wanted

@timxwatson

all of the components of closed economy GDP included

That is an exact linear combination due to
Y=C+I+G
and explains why it works when you drop one of those.