Kalman filter and NAIRU, declaring space/state

[jfca283]

Hi
I'm replicating a paper, which modelled the NAIRU like this:

equation 1 says output is equal to a tendency, h, and a cycle, x. Eq 2 says the tendency is explained by a tendency also, g, and a random error.
Eq 3 explains that tendency g. Eq4 says the cyclical component of output is defined by an AR(2). Eq 5,6,7 have similar explanations. Forget equation 8, i made a mistake repeating that one.
So, i'm a bit lost declaring the model under Kalman filter
The first matrix is the state, the second one the transition or signal

So how i do declare the state and space under Eviews? I've read example but nothing useful. Multiplying the matrix that generates the states i get

@state y=h+x
@state u=c(1)*x+ c(2)*x(-1)+ c(3)*x(-2)+ s+[var = exp(c(4))]

@signal h=h(-1)+g(-1)+[var = exp(c(5))]
@signal x=c(6) x(-1)+c(7) x(-2)+[var = exp(c(4))]
@signal x(1)=x(-1) //@signal sv2=sv1(-1)? i don't know how to express this correctly.
@signal s=s(-1)+[var = exp(c(8))]
@signal g=g(-1)+[var = exp(c(9))]

Please, give some help. I'm not used to work with Kalman filter. Thanks in advance for your time and interest.

[trubador]

There are plenty of examples in the forum. Besides, you should read "Specifying a State Space Model in EViews" section in the manual, before going forward.

Higher order lag specifications can be handled through state augmentation. In your case, AR(2) process can be implemented as follows:

Code: Select all

@state x = c(6)*x(-1) + c(7)*x1(-1) + [var = exp(c(8))] @state x1 = x(-1)

[jfca283]

Thanks, i'll give a try to what you wrote.

[jfca283]

When i run this state/space specification

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@state y=h+x @state u=c(1)*x+ c(2)*x(-1)+ c(3)*x(-2)+ s+[var = exp(c(4))] @state x=c(5)*x(-1)+c(6)*x1(-1)+[var = exp(c(7))] @state x1=x(-1) @signal h=h(-1)+g(-1)+[var = exp(c(8))] @signal s=s(-1)+[var = exp(c(9))] @signal g=g(-1)+[var = exp(c(10))]

i get the following error
"H is not defined"
I uploaded the wfl where i'm working on. Help me please.

[startz]

You need data for the signal variables. You don't have any for h.

[jfca283]

But in the paper, the author says h and x are unknown. He clearly says those equations represent states. But under eviews, they should represent @signal? I want to declare i really don't know Kalman implementation. The only data i have is Y and U, which are gdp and unemployment. The paper illustrates the other values, like tendency and cycle. The fist equation shows gdp=h(tendency)+x(cycle). The rest of the equations are similar. That's why i don't have more data. I'm not sure if i express myself in the right way.

[trubador]

Your specification does not correctly match that of authors. You should have only two signal equations (i.e. y and u), the rest will be state equations.

[jfca283]

Code: Select all

@signal pib=h+x @signal u=c(1)*x+ c(2)*x(-1)+ c(3)*x1(-1)+ s+[var = exp(c(4))] @state h=h(-1)+g(-1)+[var = exp(c(5))] @state x=c(6)*x(-1)+c(7)*x1(-1)+[var = exp(c(8))] @state x1=x(-1) @state s=s(-1)+[var = exp(c(9))] @state g=g(-1)+[var = exp(c(10))]

It didn't work:
Invalid lags or leads for state variables in signal equation
"@signal u=c(1)*x+ c(2)*x(-1)+ c(3)*x1(-1)+ s+[var = exp(c(4))]"

From the theory, i recall that an estimation like the one i'm trying, i'd should give starting values for the h,x,s,g,and so and also for variances. That's what i remember, am i right?

[trubador]

The following specification should work:

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@signal pib=h+x @signal u=c(1)*x+ c(2)*x1+ c(3)*x2+ s+[var = exp(c(4))] @state h=h(-1)+g(-1)+[var = exp(c(5))] @state x=c(6)*x(-1)+c(7)*x1(-1)+[var = exp(c(8))] @state x1=x(-1) @state x2 = x1(-1) @state s=s(-1)+[var = exp(c(9))] @state g=g(-1)+[var = exp(c(10))]

EViews handles the inital conditions by default. However, when it is not possible to solve for the initial conditions, state levels are initialized to zero and state variances are initialized to a very large number to represent the great uncertainty surrounding the initial values (i.e. diffuse priors). If you want to use your own values, you should create appropriate vectors/matrices and supply them via @mprior and/or @vprior. Initialization of coefficients (e.g. c(1), c(2), ...), on the other hand, can be handled by param command.

Given the complexity of your model, I am pretty sure that you will experience other estimation problems. So, I suggest you to go through the examples in the forum and the manual, before going forward...

[jfca283]

Ok, it runs flawless. I haven't check the accuracy of the estimation. But, if i want to declare initial states for the variables, how do i make it? can you give me a link? By the way, thanks for your help. Not even in weeks i'd would have made it. Thanks again.

[trubador]

EViews' help files, users guide and Startz's "EViews Illustrated" would be good places to begin with. Other than that, you can search this forum for discussions and solutions on similar issues...

[jfca283]

i've been searching and i found a code @mprior or @vprior, but neither the manual nor on the forum detail how to use those functions.

[EViews Glenn]

EViews 7 User's Guide II
Chapter 33. State Space Models and the Kalman Filter
Specifying Initial Conditions, p. 497-498.