jaromir-benes
commented
5 years ago Hi Michael
Your approach is perfectly alright. The only problem may potentially arise when estimating the parameters of the system. Because r is now an observable, its prediction errors (which will depend on the particular process you assume for r in the transition equations) will enter the likelihood function and may thus affect the estimates. I recommend that you run a few experiments to see how serious the problem is. My hunch is that setting a fixed relatively large(r) std dev for the shock in the r equation may minimize the problem.
If you still need to get around the problem, you may resort to an alternative (yet less elegant) approach. Keep in mind though that this approach only works in backward-looking models. Remove r_ from the measurement variables/equations, and set up the following transition equation for the real rate: r = ss_r + eps_r where eps_r is a shock and ss_r is a constant parameter that is only introduced if you care about the steady state of the model; otherwise it can be zero. Make sure you set the std deviation for eps_r to 0. Then, when running the Kalman filter, supply the path for eps_r (and hence also for r) through the option 'Vary=' (this option can be used to supply time-varying paths for std deviations and/or means of shocks to allow them to temporarily deviate from their default values assigned in the model object).
exog = struct( ); exog.eps_r = some time series defined on the entire filter range
m.std_eps_r = 0;
[ ... ] = filter(m, d, range, 'Vary=', exog);
Setting std_eps_r=0 is important here so that this shocks is not treated stochastically and is not used to explain the variability in the other observables.
Hope this helps. Let me know if you need any clarification...
Best Jaromir
On Wed, Dec 5, 2018 at 9:39 PM Michael Kirker notifications@github.com wrote:
I have a general question (rather than a bug report) on the "best practice" for modelling exogenous variables within and IRIS model file for a (semi-)structural model.
I am look at replicating the model of r-star by Holston, Laubach, and Williams (https://www.frbsf.org/economic-research/files/wp2016-11.pdf). They solve the model by treating the path of (real) interest rates as exogenous in the state space form of the model (there is no policy rule closing the model). In the notation of Hamilton's 1994 textbook ( http://web.pdx.edu/~crkl/readings/Hamilton94.pdf), the state space of the model is y = A'x + H'xi + w (y= measurement variables, x=observed variables that are exogenous or predetermined, xi=states), where x = [r{t-1} r{t-2} y{t-1} y{t-2} pi{t-1} pi{t-2,4}] is the only place in the model that interest rates, r, enter.
What is the best way to include an exogenous series within the IRIS model file? My current approach is to model the series as a random walk inside the transition equations, and then have a simple observable equation like r_=r. But is there a better approach I should be adopting?
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michaelkirker
I have a general question (rather than a bug report) on the "best practice" for modelling exogenous variables within and IRIS model file for a (semi-)structural model.
I am look at replicating the model of r-star by Holston, Laubach, and Williams (https://www.frbsf.org/economic-research/files/wp2016-11.pdf). They solve the model by treating the path of (real) interest rates as exogenous in the state space form of the model (there is no policy rule closing the model). In the notation of Hamilton's 1994 textbook (http://web.pdx.edu/~crkl/readings/Hamilton94.pdf), the state space of the model is y = A'x + H'xi + w (y= measurement variables, x=observed variables that are exogenous or predetermined, xi=states), where x = [r{t-1} r{t-2} y{t-1} y{t-2} pi{t-1} pi{t-2,4}] is the only place in the model that interest rates, r, enter.
What is the best way to include an exogenous series within the IRIS model file? My current approach is to model the series as a random walk inside the transition equations, and then have a simple observable equation like r_=r. But is there a better approach I should be adopting?