## Kalman filter and NAIRU

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mpetroks
Posts: 6
Joined: Thu Apr 12, 2018 3:23 am

### Kalman filter and NAIRU

Hello!

I am new in using EViews, so I need some help.

I would like to model NAIRU in the European Union countries with unemployment rate. I have quarterly rates from the beginning of 2000 until 2017Q3 for all the 28 EU countries.

I have already modelled NAIRUs with Hodrick-Prescott filter but now I would like to do it with Kalman filter as well.

I have read different posts and EViews user's guide as well but I still think I need some help.

From where should I start and is it enough if I use only unemployment rate? What is the logic behind state and signal equations? How should I write them down in EViews in order to model NAIRU with unemployment rate?

Also, one option for writing signal equation for modelling NAIRU would be that NAIRU is dependent on the previous value. But I have no clue how to make this state-space model with quarterly unemployment rate and if this information is enough for NAIRU.

I hope You can help me at least a little bit

mpetroks
Posts: 6
Joined: Thu Apr 12, 2018 3:23 am

### Re: Kalman filter and NAIRU

Hello!

Now I have tried to estimate something but I am not sure if this is right or not.

For example, I have formed these signal and state equations basically for all the European Union countries (this specific example is for Spain):

@signal hicp_es=c(1)*hicp_lag_es + c(2)*(unemp_es-nairu) + c(3)*hicp_foodenergy_es + [var=exp(c(4))]

@state nairu=nairu(-1)+[var=0.04]

param c(1) .0 c(2) .0 c(3) .0 c(4) .0

HICP is taken from Eurostat and is harmonised index of consumer prices (excluding food and energy prices) and foodenergy states for only for food and energy prices. I have converted monthly data to quarterly data by myself since I have quarterly data for unemployment rate.

HICP lag was calculated in EViews.

Does it seem that there are something missing or extremely wrong?

Because, for example, in this case, I have received final state value 27 something (if I have chosen in the estimation box EViews legacy). If I change it to BFGS, for example, then the value will be -900 something... But the same equations for Germany give me the final state value about 990 (with EViews legacy) which is of course wrong and also, the probabilities of c(2) and c(3) are above 0.05.

These equations were actually taken from one of the examples in this forum.

Please let me know if there is something extremely wrong.

startz
Non-normality and collinearity are NOT problems!
Posts: 3443
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Kalman filter and NAIRU

Why are you fixing the value of the NAIRU variance?

mpetroks
Posts: 6
Joined: Thu Apr 12, 2018 3:23 am

### Re: Kalman filter and NAIRU

I took it from here viewtopic.php?f=4&t=4366.

I now tried to estimate without fixing the value of the NAIRU variance and then for some countries, it works (with my previously defined state and signal equations) but for some countries, it does not work. It gives NA-s.

Also, there is a big difference when I use EViews legacy for estimating or for example, BFGSS.

Using my data, what do You consider to be the most relevant for estimation? As EViews legacy gives the most logical results, it seems that this is the right one but I am not sure.

startz
Non-normality and collinearity are NOT problems!
Posts: 3443
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Kalman filter and NAIRU

This is a nonlinear estimation, different starting values and different algorithms converge to different places or may not converge at all. In general, if different approaches give different values you should choose the one with the highest log-likelihood.

mpetroks
Posts: 6
Joined: Thu Apr 12, 2018 3:23 am

### Re: Kalman filter and NAIRU

Thank You. I have one more question.

I now try to estimate NAIRU with the same equations but I want unemployment gap (unemp_de-nairu) to be AR(2), for example.

How can I do it in the same specification window in the way that all my other equations and names will not change?