# [R] Restricted VAR parameter estimation

Pfaff, Bernhard Dr. Bernhard_Pfaff at fra.invesco.com
Mon Aug 20 10:00:36 CEST 2007

```Hello Megh,

in principle you can do OLS on an equation-per-equation basis. However,
in this case the estimator might be asymptotically inefficient. One can
use FGLS instead. This is outlined for instance in:

Helmut Luetkepohl, 2007. "Econometric Analysis with Vector
Autoregressive Models," Economics Working Papers ECO2007/11, European
University Institute.

Incidentally, you can also use restrict() [OLS-based] in package vars;
version 1.3-1 has been uploaded to /incoming on CRAN and it should
appear on the mirrors soon.

Best,
Bernhard

>
>I have a VAR model with five macro-economic variables, y[1],
>y[2], y[3], y[4], y[5]. They are related to each other in
>following manner.
>
>y[1,t] = alpha[1,0] + beta[1,1,
>1]*y[1,t-1]+............+beta[1,1, 12]*y[1,t-12] + beta[1,2,
>1]*y[2,t-1]+............+beta[1,2, 12]*y[2,t-12] + e[1,t]
>
>y[2,t] = alpha[2,0] + beta[2,2,
>1]*y[2,t-1]+............+beta[2,2, 12]*y[2,t-12] + e[2,t]
>
>y[3,t] = alpha[3,0] + beta[3,1,
>1]*y[1,t-1]+............+beta[3,1, 12]*y[1,t-12]
>+ beta[3,2, 1]*y[2,t-1]+............+beta[3,2, 12]*y[2,t-12]
>+ beta[3,3, 1]*y[3,t-1]+............+beta[3,3, 12]*y[3,t-12]
>+ beta[3,4, 1]*y[4,t-1]+............+beta[3,4, 12]*y[4,t-12] + e[3,t]
>
>y[4,t] = alpha[4,0] + beta[4,3,
>1]*y[3,t-1]+............+beta[4,3, 12]*y[3,t-12]
>+ beta[4,4, 1]*y[4,t-1]+............+beta[4,4, 12]*y[4,t-12] + e[4,t]
>
>y[5,t] = alpha[5,0] + beta[5,3,
>1]*y[3,t-1]+............+beta[5,3, 12]*y[3,t-12]
>+ beta[5,5, 1]*y[5,t-1]+............+beta[5,5, 12]*y[4,t-12] + e[5,t]
>
>All variables are stationary
>
>Now I want to estimate the coefficients under a VAR[12]
>framework. Is it mathematically correct to estimate
>coefficients of each equaltion with simple OLS separately? Or
>how I can use R [mAr.est() function) to estimate them?
>
>  Regards,
>
>
>
>---------------------------------
>
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>
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