## Potential output, the Clark model and State Space Models

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eca05jpm
Posts: 9
Joined: Wed Apr 16, 2014 2:58 am

### Potential output, the Clark model and State Space Models

Good afternoon,

I've been trying to estimate potential output using the Clark model on UK data and had no success getting plausible estimates.
I'd be very grateful if someone could point out what it is I'm doing wrong.

I have considered two models:

The first is the standard Clark model

@signal gdp = trend + cycle

@state trend = c(1) + trend(-1) + [var = exp(c(2))]
@state cycle = c(3)*cycle(-1) + c(4)*lcycle(-1) + [var = exp(c(5))]
@state lcycle = cycle(-1)

param c(1) 0.006 c(2) 0.2 c(3) 1.6 c(4) -0.7 c(5) 1

GDP is in logs and the cycle follows a AR(2) process.
I've set the initial parameters as above. I believe 0.006 is consistent with the UK economy's long-run average growth rate of 0.6 per cent a quarter.

The autocorrelation of the output gap is 1.6 and -0.7 respectively, so persistent a bit less than a random walk. These were taken based on a reference output gap which I had to hand.

I'm quite unsure as to what variances I should specify and suspect this is the problem - since the cycle component pops out as being roughly half of GDP and is not centred on 0.

The second model allows for a time-varying potential growth rate, which seems for plausible given the UKs recent growth performance.

@signal gdp = trend + gap
@state trend = trend(-1) + dtrend(-1) + [var = exp(c(1)]
@state dtrend = dtrend(-1) + [var = exp(c(2))]
@state gap = c(3)*gap(-1) + c(4)*gap2(-1) + [var = exp(c(5))]
@state lgap = gap(-1)

param c(1) 0.01 c(2) 0.1 c(3) 1.6 c(4) -0.7 c(5) 1

Once again, I cannot get sensible estimates, much to my disappointment.

I've attached the workfile, which contains the data, the reference output gap series and the two models.

I'd be very grateful for any help. I've had a look at other threads on this subject but I can't seem to do any better than this even after taking them on board.

I was able to replicate the HP filter in state space and compare real-time and ex ante estimates of the output gap, with the help of those threads - most helpful.

All the best,

Jamie
Attachments
clark.wf1

NicolasR
Posts: 90
Joined: Mon Nov 04, 2013 6:22 pm
Location: Here

### Re: Potential output, the Clark model and State Space Models

Hi,

I belive you should introduce starting values for the state variables, you can do it like this for the Clark model:

Code: Select all

`@signal gdp = trend + cycle@state trend = c(1) + trend(-1) + [var = exp(c(2))] @state cycle = c(3)*cycle(-1) + c(4)*lcycle(-1) + [var = exp(c(5))] @state lcycle = cycle(-1) param c(1) 0.006 c(2) 0.2 c(3) 1.6 c(4) -0.7 c(5) 1@mprior a0@vprior p0`

Where ao is a vector object (3x1) and its first coordinate is the starting values for the trend variable, the second is for the cycle variable and the third is for the lcycle. And po is a symetric matrix object (3x3), if you set all the matrix equal to "NA" EViews will introduce diffuse prios to the variance of the states variables, you can see EViews User Guide for more details.

Best Regards.

eca05jpm
Posts: 9
Joined: Wed Apr 16, 2014 2:58 am

### Re: Potential output, the Clark model and State Space Models

Hi everyone, thanks very much for the helpful suggestion from Nicholasr.

I now have a model which is the same as the first Clark model I posted above - a time varying drift assumption, I think would be asking too much from one time series so I have held it fixed.

Model is based on 100 * the log of real GDP per capita in the UK - 1965Q1-2013Q4.

The model:

y = ystar + cycle (signal)
ystar = ystar(-1) + drift + e1 (state)
cycle = c(2)*cycle(-1) + e2 (state)

Parameters:
I have pre-filtered the series to provide starting estimates of the parameters.

The drift assumption is set to 0.4, which (since the series is 100*logGDP) is equivalent to 0.4 per cent growth a quarter.
I obtained that by regressing the filtered trend on itself (coefficent unity) and estimating a constant.

I used the residuals from that OLS regression to estimate the variance of the error term, which was 0.1.
Since the variance of the error term is specified in Eviews as var = exp(c1), I specified c1 as -2.3 (this is because ln(0.1)= 2.3).
Good to know if I have entered the variance correctly?

I ran an OLS regression of the filtered gap component and found the AR coefficient to be 0.8.
I used the variance of the OLS residuals to specify the variance of the cyclical shocks (e2).
The variance was 0.6 so I set c(4) to -0.46. i.e. var = exp(c(4)) so -0.46 is ln(0.6).
Again, good to know if I got that right.

Starting values:
I set the starting level of potential to the actual level and cycle to zero in the vector v1.
I also set the starting variances - setting the covariance between trend and the cycle as zero.
The covariance between trend & trend and cycle & cycle at NA (diffuse).

Sadly, despite my best efforts, the results I get from conducting this (what I thought would be relatively simple) exercise are silly.

If anyone has a tiny bit of time to help me understand why it's not working or correct any code errors I have made, I'd be most appreciative.

Workfile attached.

All the best,

Jamie

ps, all this is based on a paper by Morley et al - I have replicated the equations and the parameters aren;t that much different. So I am most puzzled. Link is: https://research.stlouisfed.org/confere ... morley.pdf
Page 17 has the parameters.
Attachments
clark2.wf1

Did you use forum search?
Posts: 1516
Joined: Thu Nov 20, 2008 12:04 pm

### Re: Potential output, the Clark model and State Space Models

I can assure you that you are not the only or the first person who experience this problem. You can find many examples by simply searching the forum. A recent discussion, for instance, can be found here: viewtopic.php?f=4&t=834
Other than that, your model assumes cycle to follow an AR(1) process instead of an AR(2). You also use a different sample period, assuming you have the exact same data.

eca05jpm
Posts: 9
Joined: Wed Apr 16, 2014 2:58 am

### Re: Potential output, the Clark model and State Space Models

Hi guys,

Thanks to Trubador for the suggestions - I still wasn't able to get the Clark model to work properly.
Just in case anyone else is tempted to use it, I would suggest don't bother.
Further reading revealed that the model is not well-identified - you really need to make some other restrictive assumptions in order to get a sensible output gap series.

Happy to be proved wrong and thanks again for taking the time to look at it.

Jamie

Did you use forum search?
Posts: 1516
Joined: Thu Nov 20, 2008 12:04 pm

### Re: Potential output, the Clark model and State Space Models

I totally understand the frustration, but unfortunately economic systems do not behave like phsyical ones. Measurement errors can be very large and the relationships can be quite vague, which often prevents us from making valid and reliable inferences. State space models are extremely powerful tools, but there is a trade-off between flexibility and robustness. A few improvements can be made on EViews' State Space object, but still you'll have to figure out the most appropriate model for the data at hand. And that could require (too many) trial and error attempts...

eallanuy
Posts: 2
Joined: Mon Apr 15, 2013 8:00 pm

### Re: Potential output, the Clark model and State Space Models

good evening! im new to state space, and i would like to ask the implication if we set the Clark model to the following specification:
log_gdp = sv1 + sv2
@state sv1 = sv1(-1) + sv3(-1)+[var=exp(c(1))]
@state sv3=sv3(-1) +[var=exp(c(1))]
@state sv2 = c(1)*sv2(-1)+c(2)*sv4(-1)+[var=exp(c(1))]
@state sv4=sv2(-1)
@mprior vec01
@vprior sym01

lauren29
Posts: 12
Joined: Wed May 21, 2014 1:44 am

### Re: Potential output, the Clark model and State Space Models

Hello
I am currently working on the Clark model as well. I ve been trying different initial conditions, but I still dont know which one to use. I would just like to say that I ve been using a different sample (starting in 1984 to avoid structural breaks and thus focus on the Great moderation period), and my results are not too bad.

The "problem" that I have is that I am not sure which graph corresponds to the estimated output gap. For the past weeks, I v been looking at: Graph state series--->(Smoothed) Dsturbances Estimates--> the second graph, thinking that it corresponds to the output gap. But I have big doubts today... Does anyone know which graph corresponds to the estimated gap ?
Thanks a lot

Did you use forum search?
Posts: 1516
Joined: Thu Nov 20, 2008 12:04 pm

### Re: Potential output, the Clark model and State Space Models

Smoothed State Estimates would be the appropriate choice...

lauren29
Posts: 12
Joined: Wed May 21, 2014 1:44 am

### Re: Potential output, the Clark model and State Space Models

Hello
I am still trying to get sensible results for the Clark model. I feel like I m not too far but I have the following question:
Is it odd that when I estimate my SSPACE model I find :
-that convergence has been achieved after (only!) one iteration
-coefficient estimates are extremely close to my starting values ?

I am aware that Eviews keep the coefficients in the "c" object, (thanks to that post : viewtopic.php?f=4&t=971), so I paid attention to clear it each time I run a new SSPACE model.
I will be grateful if anyone could give a piece of advice. Please find my file attached

Sspace: MODEL_STABLE
Method: Maximum likelihood (Marquardt)
Date: 06/06/14 Time: 18:38
Sample: 1984Q1 2013Q4
Included observations: 120
User prior mean: A0
User prior variance: V0
Convergence achieved after 1 iteration

Coefficient Std. Error z-Statistic Prob.

C(1) 0.660002 1.69E-06 390528.0 0.0000
C(2) -11.99997 1.91E-05 -627788.8 0.0000
C(3) 1.170003 5.71E-06 205078.3 0.0000
C(4) -0.310002 7.40E-06 -41878.36 0.0000
C(5) -12.00001 2.28E-05 -526596.0 0.0000

Final State Root MSE z-Statistic Prob.

TREND 968.9368 0.005483 176701.6 0.0000
CYCLE -0.494761 0.005016 -98.63140 0.0000
LCYCLE -0.603664 0.004891 -123.4181 0.0000

Log likelihood -1664228. Akaike info criterion 27737.22
Parameters 5 Schwarz criterion 27737.33
Diffuse priors 3 Hannan-Quinn criter. 27737.26

where v0 is a(3x3) matrix set to NA (starting values for variance) and a0 is a vector(3x1) as
887
0
0
for the starting values of the state variables
Last edited by lauren29 on Thu Feb 26, 2015 9:04 am, edited 1 time in total.

lauren29
Posts: 12
Joined: Wed May 21, 2014 1:44 am

### Re: Potential output, the Clark model and State Space Models

Hello
After what I would call "manual iteration"with the starting value for the variances,and the following SSPACE object

Code: Select all

`@signal lgdp=trend+cycle@state trend=c(1) + trend(-1) +  [var=exp(c(2))]@state cycle=c(3) * cycle(-1) + c(4) *lcycle(-1)  +  [var=exp(c(5))]@state lcycle=cycle(-1)param  c(1)0.66 c(2) -8.767 c(3) 1.17 c(4) -0.31 c(5) -8.767@mprior a0@vprior v0`

I found the following results :

Sspace: MODEL_STABLE
Method: Maximum likelihood (Marquardt)
Date: 06/24/14 Time: 21:11
Sample: 1984Q1 2013Q4
Included observations: 120
Estimation settings: tol= 0.00010, derivs=accurate numeric
Initial Values: C(1)=0.66000, C(2)=-8.76700, C(3)=1.17000, C(4)=-0.31000,
C(5)=-8.76700
User prior mean: A0
User prior variance: V0
Convergence achieved after 11 iterations

Coefficient Std. Error z-Statistic Prob.

C(1) 0.694013 6.34E-05 10939.36 0.0000
C(2) -8.259447 0.000697 -11849.23 0.0000
C(3) 1.158282 0.000279 4152.163 0.0000
C(4) -0.260656 0.000315 -827.0112 0.0000
C(5) -8.867983 0.001254 -7074.360 0.0000

Final State Root MSE z-Statistic Prob.

TREND 969.0074 0.032489 29825.66 0.0000
CYCLE -0.559521 0.028538 -19.60648 0.0000
LCYCLE -0.640282 0.028227 -22.68369 0.0000

Log likelihood -49878.91 Akaike info criterion 831.3985
Parameters 5 Schwarz criterion 831.5147
Diffuse priors 3 Hannan-Quinn criter. 831.4457

I am not gonna lie, I am quite happy with the results.
However, I wonder, the information criterion are quite high, aren't they? I m used to models where they are close to 2, do you think the "penalty" for estimating 5 coefficients could be held responsible?
Similarly I found the log likelihood rather low..
I aim at comparing this specification to other models, so I would be grateful if anyone could help me to decide what to do with that model. Is it accetable?

Best regards
Attachments
gdp_us6.wf1

houji
Posts: 3
Joined: Mon Mar 20, 2023 3:19 pm

### Re: Potential output, the Clark model and State Space Models

Has anyone tried the bivariate version of the Clark model, where cyclical component of unemployment is related to output?

I was trying to build the model, but Eviews does not allow for transition equations in which the state variable appears contemporaneously in the equation of another state variable. Does anyone know any programs that can do that?