Stochastic singularity even though # shocks = # observables

I am estimating a small open economy version of the Gali, Smets and Wouters (NBER macro annual 2012) unemployment model.
The model is fairly big and has 21 series and 21 shocks. However, I get an error

initial_estimation_checks:: The forecast error variance in the multivariate Kalman filter became singular.
initial_estimation_checks:: This is often a sign of stochastic singularity, but can also sometimes happen by chance
initial_estimation_checks:: for a particular combination of parameters and data realizations.
initial_estimation_checks:: If you think the latter is the case, you should try with different initial values for the estimated parameters.

This is quite surprising because I have as many shocks as observables.

Can the stochastic singularity happen because 2 observables are highly correlated, like detrended employment and detrended output? In the production function, I do not use a technology shock or physical capital, so the model predicts that the employment gap and output gap are perfectly collinear.

This I think is the problem…when I use an additional measurement error for the employment gap…so with 22 shocks and 21 observables…I do not get the stochastic singularity error.

It would be interesting to hear your thoughts.


For that to happen, the variables in the model must be extremely highly correlated. It is usually not about the data. The usual source of the problem is that the model implies at least one observable to be an exact linear combination of the other ones.

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