# Restricted VAR model

I'm trying to estimate macroeconomic VAR model in R using package vars. Since I need to omit simultaneously all coefficients with t-ratio in absolute value less than 1.65, I used package function restrict with adequate restriction matrix.

After that, $R^2$ for unemployment equation jumped from 29,2% (in the unrestricted model) to more than 61% (in the restricted model). That surprises me.

Why does this happen? If I estimate same equation individualy with OLS, $R^2$ stays approximately same (around 29%).

I read somewhere that restriction should be made with FGLS instead of OLS because OLS estimation could give inefficient coefficients. In R restrict is done using OLS.

Can I use impulse response function and variance decomposition for analyzing relationships between variables and get valid results even if coefficients are inefficient?

• Can you show your estimations in more detail? Oct 14, 2016 at 7:57

Why does this happen?

In method = ser case, it estimates the equations repeatedly until all t-values are absolutely less than thresh. In this case:

If I estimate same equation individually

You are (probably) estimating the equation just once. It is equal to choosing method = "manual" and setting resmat, based on insignificant parameters.

Can I use impulse response function and variance decomposition for analyzing relationships between variables and get valid results even if coefficients are inefficient?

The answer depends on the type of application. In this case, the results are inefficient, but how much inefficiency matters in your application?! However, I think the refvar function of MTS package generates the FGLS estimation of a restricted VAR.

(Please note that I couldn't find any documentation for refvar, but by studying the source, it seems that it is a somehow a strange FGLS, because is uses identity matrix as the covariance matrix, although it estimates an unrestricted VAR first.)

• thank you for your answer. R^2 mentioned above is the result of method="manual", and it's quite different from R^2 coming from 4 OLS equations with same variables. My application is not to forecast central values, but to estimate correlated distributions of the macroeconomic variables on a relatively short time horizon. Is my model adequate enough to do so?
– Mare
Mar 8, 2017 at 12:22