## From Cointegration to estimation

Questions and discussions on Time Series Analysis

### Re: From Cointegration to estimation

Hello,

So I stand at this place:

My CATs result is as follows:

I(1)-ANALYSIS
p-r r Eig.Value Trace Trace* Frac95 P-Value P-Value*
6 0 0.743 189.788 179.725 95.514 0.000 0.000
5 1 0.593 105.431 100.924 69.611 0.000 0.000
4 2 0.375 49.753 48.122 47.707 0.031 0.046
3 3 0.182 20.577 20.102 29.804 0.395 0.427
2 4 0.118 8.155 8.043 15.408 0.456 0.468
1 5 0.006 0.355 0.354 3.841 0.551 0.552

I have 2 stationary variables and 4 non-stationary variables! I know 2 cointegrating vectors are added due to stationary variables. 1 cointegrating vector is showing that the model is cointegrated of order 1. Now what is my next step?
ateeb

Posts: 66
Joined: Sat Mar 16, 2019 11:15 am
Location: Kalamazoo, MI, USA

### Re: From Cointegration to estimation

You have three and 1/2 unit roots---that one that you're counting as showing cointegration is rather borderline. Do you have any theoretical reason to believe there actually IS cointegration? If not, the simplest thing to do is to run VAR's on the levels which work with or without cointegration.
TomDoan

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Joined: Wed Nov 01, 2006 5:36 pm

### Re: From Cointegration to estimation

The variables are govt debt, govt expenditure (fiscal policy measure), interest rate (monetary policy measure), stock market index (measure of wealth), output and inflation. and sorry only inflation is stationary ...

so I believe that these variables would be co integrated because they are policies and fiscal and monetary policy does have implications as well as respond to rising debt of government in the long-run ...

However, I see if 1 variable is stationary then it means there are 2 co integrating vectors in my data right? how to proceed?

Furthermore, running VAR in levels ignore the I(1) variables or unit-roots in 5 variables which will make the VAR estimates less precise and worsen their small sample bias as stated by Kilian & Lukhtpul in their book. so ...
ateeb

Posts: 66
Joined: Sat Mar 16, 2019 11:15 am
Location: Kalamazoo, MI, USA

### Re: From Cointegration to estimation

ateeb wrote:The variables are govt debt, govt expenditure (fiscal policy measure), interest rate (monetary policy measure), stock market index (measure of wealth), output and inflation. and sorry only inflation is stationary ...

so I believe that these variables would be co integrated because they are policies and fiscal and monetary policy does have implications as well as respond to rising debt of government in the long-run ...

Sorry, but why does that mean they're cointegrated. Dynamically related (which is what you're describing) is way, way short of cointegrated.

ateeb wrote:However, I see if 1 variable is stationary then it means there are 2 co integrating vectors in my data right? how to proceed?

Furthermore, running VAR in levels ignore the I(1) variables or unit-roots in 5 variables which will make the VAR estimates less precise and worsen their small sample bias as stated by Kilian & Lukhtpul in their book. so ...

And forcing cointegration into a model despite both theory and evidence that it doesn't really exist biases the results.
TomDoan

Posts: 7236
Joined: Wed Nov 01, 2006 5:36 pm

### Re: From Cointegration to estimation

Dear all,
I want to know how I can incorporate a structural break within a cointegrating vector once I detect cointegration with a structural break. For instance, I applied the Johansen cointegration test with a structural break (Johansen, S., R. Mosconi and B. Nielsen (2000). Cointegration analysis in the presence of structural breaks in the deterministic trend. Econometrics Journal, 3, 216-249.) and now I want to estimate the new VECM but incorporating the structural break I found.

Best
PedroClavijo

Posts: 9
Joined: Tue Aug 27, 2019 11:51 pm

### Re: From Cointegration to estimation

Dear Colleagues

For several years, I have been thinking about cointegration regression involving stationary variables as explanatory variables.
I am looking for comments on whether the following procedure is appropriate. I would be very grateful if you could advise me.

Setting:
- y(t)=a + b1*x1(t) + b2*x2(t) + b3*x3(t) +u(t).
- x1(t) and x2(t) are non-stationary, and x3(t) is stationary.
- Assume the cointegration relation y(t) = a + b1*x1(t) + b2*x2(t).
- x1(t) and x2(t) are not cointegrated.

I intend to perform the estimation and test using the following two-step procedure.

Step 1: Estimate y(t)=a + b1*x1(t) + b2*x2(t) + z(t) by FMOLS.

b3*x3(t) will be included in z(t). The endogeneity problem may happen by this inclusion, but, FMOLS should control this problem.

Step 2: We follow Park-Phillips (1989).
Separately estimate y(t) = a + b1*x1(t) + b2*x2(t) + e(t) by OLS and get the (super)consistent estimator of a, b1 and b2 (a', b1' and b2'). Next, using these estimates, compute
y'(t) = y(t) - a' + b1'*x1(t) + b2'*x2(t)
Finally, we perform by IV,
y'(t) = c + b3*x3(t) + error
Note that a few minor assumptions are needed, See Park-Phillips (1989).

A possible problem is that x3(t) may not have zero-mean, because x3(t) is included in z(t). For now, I have no idea on it.

I would be happy if anybody gives me comments.
T_FIELD

Posts: 44
Joined: Sat May 15, 2010 8:03 pm

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