Solved – Why is there a need to do OLS regression of VECM

cointegrationleast squaresrvector-error-correction-model

I am trying to use the R package "urca". It has functions cajorls and cajools, which do ordinary least squares (OLS) regression of restricted and unrestricted vector error correction model (VECM) respectively. Both functions take in the VECM estimated using Johansen procedure and return the regression parameters and cointegrating vectors.

I do not understand, why is there a need to do OLS regression of VECM? Using Johansen test on the data (by calling ca.jo) will give me the cointegrating vectors. What is the difference between cointegrating vectors of VECM and OLS regression of VECM?

Best Answer

Well ca.jo will give you the parameters for the long-run cointegrating relationship(s), but not the error correction/lags parameters, which are obtained by the cajools. Note that for alternative, slightly more direct way, you can also use the function VECM from package "tsDyn".

The reason for calling these function "OLS" is that, once your ECT(s) have been obtained by maximum-likelihood, the ML estimator for the other parameters is equivalent to a OLS regression, conditional on the ML parameters for the cointegrating relationship.

Related Solutions

Solved – Why does ca.jo has a minimum lag order of 2

I updated the package tsDyn (version 0.9-40 submitted to CRAN), so that its VECM() function can handle your case of lag=1. Note that:

With function VECM(), use lag=0 for the case you described as lag=1
A warning will be printed, as fevd(), irf(), predict() et al are not guaranteed to work
If you want no intercept, use: include="none"

Example:

library(tsDyn)
data(barry)
summary(VECM(barry, lag=0, estim="ML"))

#############
###Model VECM 
#############
Full sample size: 324   End sample size: 323
Number of variables: 3  Number of estimated slope parameters 6
AIC -4871.5     BIC -4848.83    SSR 29.3275
Cointegrating vector (estimated by ML):
   dolcan    cpiUSA    cpiCAN
r1      1 -0.021234 0.0402079


            ECT                 Intercept         
Equation dolcan -0.0004(0.0011)     0.0024(0.0030)    
Equation cpiUSA -0.0436(0.0155)**   0.3685(0.0413)*** 
Equation cpiCAN -0.0824(0.0214)***  0.4649(0.0572)***

Time Series – OLS vs ML Estimation of VECM

You are asking a complicated questions, to which there are no clear answers.

Is (1) more efficient than (2)? Note actually that the Johansen ML estimator has a strange finite-sample distribution with no finite moments, and hence has a large variance. So it is most likely not more efficient than the "Granger 2-SLS". On the other side, "Granger 2-SLS" has a large bias in the first stage, which contaminates the second stage. A simple correction for that involves adding leads and lags in the first stage, as done by Saikonnen's estimator.
Will (2) and (3) give exactly the same estimates? Mmh... I do not think you can use this procedure, as the restrictions due to B obviously have to be imposed with knowledge of B. So these will be the same only if you know in advance B, but then the restricted OLS procedure is of little interest...
Should any of the alternatives, or maybe yet another approach, be generally preferred? There is no final answer to that, as in every case in statistics, it depends... There have been quite a lot of theoretical and Monte-Carlo comparisons, of these estimators, check Maddala and Kim (1998) for a discussion, or, one among others, or Gonzalo (1994).
and 5. as you asked these questions in a separate post: Estimation of VECM via ML and OLS maybe you could remove from this one?

Refs:

G. S. Maddala and I-M. Kim (1998) Unit roots, Cointegration and Structural Change, Cambridge University Press
Gonzalo, Jesus, (1994) "Five alternative methods of estimating long-run equilibrium relationships," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 203-233. http://www.eco.uc3m.es/~jgonzalo/teaching/PhDTimeSeries/gonzalojec94.pdf

Best Answer

Related Solutions

Solved – Why does ca.jo has a minimum lag order of 2

Time Series – OLS vs ML Estimation of VECM

Related Question