Scenario analysis a la Antolin-Diaz, Petrella and Rubio-Ramirez JME 2021

[giannilmbd]

Antolin-Diaz, Petrella and Rubio-Ramirez JME 2021 (APR) develop algorithm to construct more careful scenario analyses than those typically generated in (B)VAR studies. The focus is on the plausibility of the scenario.

These scenarios are a combination of conditional-on-observations forecasts and conditional-on-shocks forecasts.

An element that sets apart their contribution is to offer a resolution of the multiplicity of conditional-on-observations forecasts by suggesting to pick the one that is the least distant from the unconditional forecast (in terms of Frobenius norm). This is achieved by using the Moore-Penrose inverse in finding the shocks that bring about the conditional forecast. (Note for example the gap between the conditional-forecast produced by BVARSign and that based on APR: both valid but, as I understand, based on a different criterion... or a mistake in my codes ;-) )

Relatedly, they suggest to use the Kullback-Leibler measure of distance between the conditional and unconditional distribution of shocks. (Btw: this criterion would fully reject reality in my example! I wonder whether the criterion is a measure of mis-specification of the model too)

I think this is a verly important development in the assessment of the "balance of risks" especially in policy analyses (as they point out).

Implementing their algorithms starting from the output of BVARSign is quite straightforward (see quick implementation in the attached file).
scenarios.zip

(Please take the file as a proof of concept. I've used the notation of APR.)