Discarding impossible draws during forecasting with BVAR?

[jonasdovern]

Dear all,

I produce a distributrion of forecasts based on a B-VAR by means of Gibbs sampling (using the simulate function at each iteration step). Can I simply discard those draws that imply impossible realisations for a particular variable? Or do I make a huge mistake by doing this? (I have a model including the FFR and I would like to neglect all forecasts that include a negative path for this series.)

Thanks a lot for any help!

[TomDoan]

That would probably depend upon how often it happens and why. It's common practice to discard VAR draws which are considered to be unrealistically explosive, which is equivalent to saying that the VAR has the standard distribution but truncated to a region with certain size roots. Discarding non-conforming draws is simply an application of the "rejection method" to that. If the impossible draws are a result of the behavior of the VAR coefficients, then that would be the most straightforward way to handle it.

It's a different matter if you get the bad draws because of the simulated shocks. If your "model" is that the VAR will generate Normally distributed paths subject to the constraint that one component is always non-negative, then discarding an entire path because it fails to stay above zero will bias the simulations away from zero for that variable. On the other hand, the assumption that the errors in the VAR are still Normally distributed when you've already run your interest rate down to .1 is probably unrealistic itself so discarding the entire path might give a reasonable approximation to a more realistic assumption.

[tclark]

Jonas,

You may have found this out already, but in the example you mentioned, discarding forecast draws in which the interest rate turns negative will (at least in U.S. data) tend to push up the forecast distribution for output. That doesn't mean you shouldn't necessarily take the discard approach, but it will have an effect. Because output and interest rates are positively correlated, very low interest rates tend to be associated with low output growth. Accordingly, by tossing out draws with negative interest rates, you will also toss draws with low output. The retained distribution of output forecasts will be higher than it would be if no draws were discarded.

[jonasdovern]

Todd,

thanks for the hint. I haven't implemented this approach yet ... but good to have a prior on what to expect. I'll see what I get.

But actually (from a theoretical point of view) one would like to obtain the opposit effect on output, isnt' it?