# Using particle filter for linear DSGE models

Hi Johannes,

I was wondering whether using a particle filter for first-order estimation is possible in Dynare? Just want to test that as an alternative comparing to Kalman filter. Thanks!

Why would you want to do that? The Kalman filter is optimal at first order.

Because it’s difficult to find a good example that people actually use particle filter for non-linear DSGE. I think Schofheide also used the particle filter just to estimate Smets-Wouters in one of his papers.

Particle filters are useful when you solve a model with a higher-order approximation. If you use first-order, then policy functions are linear, meaning that the transition functions of the state variables of the filter are linear, therefore you can use linear state space techniques, like the Kalman filter.

However, when policy functions are not linear (like higher order perturbation solutions or projection techniques), you have to use non linear filters as well, like particle filters.

If I am not mistaken, the name “particle” comes from the fact that these filters relies on Monte Carlo simulation (random draws as the “particles”) to obtain the distribution of the variables, differently from the Kalman filter, where such distributions has a closed-form solution.

However, when policy functions are not linear (like higher order perturbation solutions or projection techniques), you have to use non linear filters as well, like particle filters.

I don’t think this is correct. With a linear state-space model your policy functions would be just linear in the end, because your state transitions are linear.

Is the model solution that generates the type of state-space representation, not otherwise. Linear solutions generates a linear state-space, while non linear solutions generates a non linear state-space representation.

If you want a linear state space representation, you have no choice but to rely on first-order solution. However, you still can use a non linear filter while using first-order solution, although this is not recommended.

However, you still can use a non linear filter while using first-order solution, although this is not recommended.

This was exactly what I was asking because I just want to find a working example that people actually use the particle filter to estimate some non-trivial DSGE model.

For an example of particle filters implementation see: “The term structure of interest rates in a DSGE model with recursive preferences”, Jules H. van Binsbergen et al. (2012).

In this paper they use Particle Filter to estimate a model that is solved up to the third order. They employ Maximum Likelihood estimation rather than Bayesian. Theoretically, you could use Dynare to replicate their paper.

I am not aware of any example that estimates with Particle Filter a model that is solved with first-order solution. I would not search too much either since this procedure is heavily inneficient.

Schorfheide did that by estimating Smets-Wouters 07.

Thanks for that reference, I’ll have a look at it.