Dear Christian,

It is not totally clear to me which variables in your model you can

observe and which are unobservable, so I will assume that g_t is

observable and u_t, un_t and r_t are not.

You can take the state vector b_t = (one_t, u_t, r_t, un_t)', where

one_t = 1 (more on that below). Then you need

F = (x[1], x[2], x[3], x[2])

and

G = diag(1, 1, 1, x[4])

Since you did not specify the dynamics of u_t and r_t, I am assuming

they follow a random walk. If they are observable, then you can just add

one row to the F matrix for each one of them.

Since you want one_t to be 1 at any time, you should specify in the

prior mean m0[1] = 1 and C0[1,1] = epsilon (in theory this should be

zero, but in order for dlm to work you need a nonsingular C0: taking a

tiny epsilon, 1e-7 say, usually does the job). Similarly, you don't want

one_t to change from one time to the next, so you need to specify W[1,1]

= 0. Other entries in W can be estimated by maximum likelihood.

If you take any of u_t and r_t to be observable, you will also need to

set the corresponding value in the V matrix to a tiny epsilon, for the

same reason that V must be nonsingular. Or, even better, you can take

the observation variance for u_t and/or r_t to be a parameter and you

will end up with a random walk plus noise model (local level model) for

u_t (and/or r_t).

HTH,

Giovanni Petris

On Tue, 2010-10-05 at 22:30 -0400, Christian Schoder wrote:

> Dear r-users!

>

> I have another question regarding the dlm package and I would be very

> happy if someone could give me a hint!

>

> I am using the dlm package to get estimates for an endogenous rate of

> capacity utilization over time. The general form of a state space model

> is

>

> (1) b_t = G * b_t-1 + w_t w_t ~ N(0,W)

>

> (2) y_t= A' * x_t + H' * b_t + v_t v_t ~ N(0,V)

>

> (Hamilton 1984: 372)

>

> The investment function I would like to use for estimating my endogenous

> capacity utilization rate looks like

>

> (3) g_t = x[1] + x[2]*(u_t-un_t) + x[3]*r + v_t

>

> where g_t is the investment rate, r_t is the profit rate, u_t is the

> actual utilization rate and un_t is the 'normal' utilization rate which

> I take as endogenous (=time varying). x[i] are parameters. I'm

> particularly interested in this endogenous normal utilization rate. How

> can I specify a state space model which allows me to estimate it and is

> consistent with the structure of the state space models in the dlm

> package?

>

> In the form found in Hamilton my system would look like

>

> (4) un_t = x[4] * un_t-1 + w_t w_t ~ N(0,W)

>

> (5) g_t = (x[1],x[2],x[3]) * (1,u_t,r_t)' + x[2] * un_t + v_t v_t ~

> N(0,V)

>

> which theoretically can be estimated even with the restriction that the

> parameters of u_t and un_t have opposite signs, but are otherwise equal.

> But how can I do this with the plm package which requires a model of the

> following form:

>

> (6) b_t = G * b_t-1 + w_t w_t ~ N(0,W)

>

> (7) y_t = F * b_t + v_t v_t ~ N(0,V)

>

> How can I write my model in the form of (6) and (7) such that my state

> vector includes un_t and I can get estimates for the normal rate of

> capacity utilization??

>

> I would be very grateful for any help, cause I've been sitting on this

> issue for a while!

>

> Christian

>

> ______________________________________________

>

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https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.