Estimation and stochastic singularity

Hi All,

I have a question about the way dynare does the estimation. I am attaching a set of mod files that illustrates my concern. There are 3 observable variables and 3 shocks in the model.

nk_simdata.mod simulates data from a simple New Keynesian model and saves the data on 3 variables, ys, pis, and rs. So, run this file before running the others.

nk_estimate.mod uses the simulated data to estimate the model’s parameters.

nk_estimate_sing.mod is similar to nk_estimate.mod except that it comments out one line in the estimated_params block as shown below

stderr eas,uniform_pdf, , ,0, 0.03;
// stderr exs,uniform_pdf, , ,0, 0.03;
stderr ers,uniform_pdf, , ,0, 0.03;

As a result, nk_estimate_sing.mod does not estimate the standard deviation of exs. In fact, it seems to set it to zero; it shows that the shocks exs are in fact all zero when it displays them in SmoothedShocks figures.

What surprised me is that the estimation did not fall over. Shouldn’t the Kalman filter find the model in nk_estimate_sing.mod to be stochastically singular? And if, not, how should I interpret the estimation results from nk_estimate_sing.mod? What is going on?

Many thanks,
nk_estimate_sing.mod (1.26 KB)
nk_simdata.mod (857 Bytes)
nk_estimate.mod (1.25 KB)

You are correct. There is stochastic singularity in this case. More recent versions of Dynare check for this and provide an error.