estimation of Engle-Granger 2 step procedure

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happylady
Posts: 5
Joined: Thu Jul 23, 2009 2:10 pm

estimation of Engle-Granger 2 step procedure

Postby happylady » Thu Jul 23, 2009 2:36 pm

Hi;

I have to estimate the engle-granger 2 step procedure of the money demand function.
The model is ln(m2/cpi)=f(ln(ipi), ln(cpi), ln(reer), ln(MLR)) where MLR is minimum lending rate, reer is real effective exchange rate, ipi is industrial production index.

After I estimate the step 1 and the ADF test of the residual of step 1 , I found that my residual is stationary (have cointegration). Thus, I would like to ask that
1. How can I estimate my model above in the step 2 of engle-granger in Eviews?
2. what is function of my model after I have estimate the step 2 procedure?
3. How to interpret the result that I got in the step 2 procedure?


Thank you very very much in advance!

theologos
Posts: 25
Joined: Wed Mar 11, 2009 6:09 am

Re: estimation of Engle-Granger 2 step procedure

Postby theologos » Fri Jul 24, 2009 2:10 am

Hi,

Firstly, you need to clarify the two steps in the Engle-Granger (1987) approach.
1st Step
After ensuring that all the variables are I(1), estimate the static model by OLS

ln(m2/cpi)=c+b1*ln(ipi)+b2* ln(cpi)+b3 ln(reer)+e (1)


2nd Step
Test the null hypothesis that there is no cointegration via testing the recovered residuals from (1). The null is e~I(1) and the alternative is e~I(0). This can be tested by several tests. You may use the ADF test, but the critical values for cointegration are not those provided by e-views. The critical values depend on the number of the variables, the sample size etc. For correct critical values see Mackinnon (1991) where exact critical values can be estimated.

-Regarding question 1
By simply running equation (1) (step 1)

-Regarding question 2
You have established an equilibrium relationship among the variables involved

-Regarding question 3
As usual. Simply given your specification, the estimated coefficients are now long-run elasticities.

Regards

happylady
Posts: 5
Joined: Thu Jul 23, 2009 2:10 pm

Re: estimation of Engle-Granger 2 step procedure

Postby happylady » Fri Jul 24, 2009 3:09 am

hi;

Thank you for your reply. Also, I have another question that

when I found that I have the cointegration in the series as my residual is stationary,
1. what is my Error correction model look like and
2. how can I estimate by using Eviews? and
3. how can i know about how many lag length in my ECM model?

Also, could you please kindly tell me the name of the journal of Mackinnon that you mention to me and also the suggestion about the method
to test for the residual of step1 ( I have 4 exogenous variables and 120 observations)?

Thank you very much!

theologos
Posts: 25
Joined: Wed Mar 11, 2009 6:09 am

Re: estimation of Engle-Granger 2 step procedure

Postby theologos » Fri Jul 24, 2009 3:53 am

The MacKinnon reference is the following:
MacKinnon, j. (1991) critical values for co-integration tests in R.F. Engle and C.W.J. G Cranger (eds.) Long-run relationships, Oxford University Press, pp. 267-276.

The error-correction representation is actually part of the second step. Suppose you have the following static model:
y_(t)=βx_(t)+e_(t) (1)
The error-correction model looks like as follows:
Δy_(t)=γΔx_(t)-(1-α)e_(t-1) (2)

Where:e_(t-1)= y_(t-1)-βx_(t-1), the residuals from the static model
and (1-α) the speed of adjustment term.

To estimate the error correction term in e-views simply recover the residuals from your static model, then calculate the differences for all your variables and run a regression similar to (2). (The recovered residuals enter as a separate variable lagged one period and (1-α) is simply the associated coefficient). The lag length is actually depend on the frequency of your data for example for annual observations, one or two lags are considered satisfactory, alternatively you may use different information criteria like the Akaike information criterion.

regards

farrel
Posts: 85
Joined: Thu Sep 18, 2008 11:13 pm

Re: estimation of Engle-Granger 2 step procedure

Postby farrel » Fri Jan 18, 2019 2:31 am

Whether anyone knows, is it THEORETICALLY correct to estimate the 1st step of Engle/Grenger 2-step procedure, i.e. estimating the long-run relationship with lag of explanatory variable?
For example, relationship between prices and wages:

PRICE = c(1) + c(2) * WAGE_{t-1} + u_{t}

Is it correct to estimate Wage with one lag?

Andrei

dakila
Posts: 393
Joined: Tue Nov 24, 2015 4:57 pm

Re: estimation of Engle-Granger 2 step procedure

Postby dakila » Wed Jan 23, 2019 1:41 am

No

startz
Non-normality and collinearity are NOT problems!
Posts: 3606
Joined: Wed Sep 17, 2008 2:25 pm

Re: estimation of Engle-Granger 2 step procedure

Postby startz » Wed Jan 23, 2019 12:47 pm

dakila wrote:No

Out of curiosity, why not? Assuming that for some reason you are interested in whether price and lagged wage are cointegrated.

farrel
Posts: 85
Joined: Thu Sep 18, 2008 11:13 pm

Re: estimation of Engle-Granger 2 step procedure

Postby farrel » Sun Jan 27, 2019 12:37 pm

I just imagine that usually wages do not pass to prices immediately (due to any reason - price rigidity or nature of wage shock, or how markets are (im)perfect etc.). Then it's would be natural to assume that long-run relationship holds exactly entering wages with lag...
But then, I'm curious whether it breaks any cointegration foundations??!!

Any thoughts??
Andrei


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