Estimation with the diffuse_filter option


From the Dynare manual, “When diffuse_filter is used the lik_init option of estimation has no effect. When there are nonstationary exogenous variables in a model, there is no unique deterministic steady state.”

I am not able to estimate my model without this option when using US gdp data that has been transform using the ideas in , “A Guide to Specifying Observation Equations for the Estimation of DSGE Models.”

The gdp_obs (transformed data) is stationary, but when I try to estimate the model issues arise with the likelyhood function.

When I add the diffuse_filter option to the estimation command there is no problem with the estimation.

My question,

1 What is gained or lost by using this option?

2 What is the best practice to test that I have a unique deterministic steady state in the model.

Thank you,

  1. Nothing is lost. The Kalman filter is just initialized with a bigger covariance matrix. It might take more observations for it to converge to the steady state
    Kalman filter, but this is usually not a problem.
  2. Use the check; command to see whether your model has a unit root. Note that the non-stationarity ameliorated by the diffuse_filter option relates to the model not to the data. Even after using a correct observation equation, it might be needed. The reason is that the standard Kalman filter initializes the recursion by the unconditional variance of the states. But for non-stationary model variables, this object does not exists. This necessitates to use the diffuse Kalman filter.