# Parameter drift with parameters' bounds

Dears,

I’m trying to estimate some parameters drifts but these parameters are bounded. For example, if I assume capital share in CD production function itself follows AR (1) process. Y_t=A_t*K_t^(alpha_t)*L_t^(1-alpha_t), and alpha_t=(1-rho)alpha+rhoalpha_(t-1).
I can put the persistence and standard deviation into estimation and specify the bound for these estimated parameters. Yet how can I guarantee that alpha_t is between 0 and 1 for all the times.
I read related literature and people suggest to use the smoothed Kalman filter. Can any one elaborate more about it? And how to implement this smoother in dynare? Is there any sample code to follow?

Best,
House

Hi, any one could help?

1. What is the reference for what you are trying to do?
2. In general, if you work with a log-linear approximation, there is not way to bound variables (like your capital share) due to linearity. One has to live with this and hope that the data do not assign much probability to it violating the theoretical bounds.

I read the relevant part of Seoane (2016). Unfortunately, the implementation is somewhat involved and only possible in Dynare with modifications to `dsge_likelihood.m`
The idea is the following: for each draw of the MCMC, you run the Kalman smoother on the model. If the smoothed “parameters” (which are actually variables now, because they are time-varying) violate the imposed bounds, you reject this draw.

[quote=“jpfeifer”]I read the relevant part of Seoane (2016). Unfortunately, the implementation is somewhat involved and only possible in Dynare with modifications to `dsge_likelihood.m`
The idea is the following: for each draw of the MCMC, you run the Kalman smoother on the model. If the smoothed “parameters” (which are actually variables now, because they are time-varying) violate the imposed bounds, you reject this draw.[/quote]

Dear Johannes,

You mean that currently it’s impossible to implement the algorithm in Seoane (2016) using dynare? Just want to confirm this issue.

Best,
Sihao

It is not prepackaged, but can be implemented in a few lines of code.