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When a VAR is estimated and tested on the test data the RMSE of the model was around 25. However when I estimated a restricted VAR by setting coefficients of the lagged terms of the dependent variable to 0, the RMSE reduced to 10.

I also estimated the same equation by imposing restrictions as above using OLS. But the coefficients obtained were different from what I obtained through the restricted VAR model and the RMSE was higher than what I obtained through the restricted VAR.

Why forecast accuracy is very high in Restricted VAR but not in individual OLS estimate?

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  • $\begingroup$ setting coefficients of the lagged terms of the dependent variable: in a VAR, every variable is a dependent variable, and every regressor is a lag of one of the dependent variables. What variables were left on the right hand side after your restrictions? $\endgroup$ Nov 6, 2021 at 13:59
  • $\begingroup$ I have 5 variables in my VAR. Though I fit a VAR my main focus is on predicting and interpreting one variable (suppose gdp). I set the effect of gdp(-1), gdp(-2) and gdp(-3) on gdp to 0. $\endgroup$
    – Geek_Tech
    Nov 6, 2021 at 14:03

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If you have the same model but different estimates, then obviously the estimation method must be different. I presume your restricted VAR model was estimated using generalized least squares (GLS) which under some assumptions is known to be the efficient estimator. Equation-by-equation ordinary least squares (EbE OLS) is efficient for an unrestricted VAR but not for a restricted one.

The difference in forecast accuracy must also be a result of the different estimators. Whether GLS beat OLS by chance or it is a genuinely better estimator in your case is an open question. A Diebold-Mariano test could offer some insight into that.

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  • $\begingroup$ Yes, the restricted VAR was estimated using GLS. Thank you very much for pointing that out. $\endgroup$
    – Geek_Tech
    Nov 6, 2021 at 17:14
  • $\begingroup$ @RichardHardly I didn't know about that option. The answer was very clear and precise! Really appreciate it. $\endgroup$
    – Geek_Tech
    Nov 10, 2021 at 16:34

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