Identify VFCI shock in VAR

[matdehaven]

• Heteroskedasticity
• Choleskey, VFCI first
• Choleskey, Interest, then VFCI
• Event identification?
• t-distribution?

[matdehaven]

For Heteroskedastic identification, first simplify VAR down to 4 variables (Inflation, output, interest, vfci), then run heteroskedastic method. Then try with larger VAR.

[matdehaven]

Try the svars package id.cv function for heteroskedasticity, which only allows 2 or 3 regimes (instead of n) first, as it should be easier to implement.

[matdehaven]

• For Choleskey ID, create chart pack with forecast error variance decompositions, historical shocks, etc.

[matdehaven]

For event-based restriction set identification, see Uncertainty and Business Cycles: Exogenous Impulse or Endogenous Response? (Ludvigson, Ma, Ng 2021)

I like this framework, but we need to think about if we can argue for certain dates at a quarterly frequency when there was a VFCI-type shock, and preferably not other confounding shocks.

[matdehaven]

I've tried the example from Chris Sim's VARmodels and I get an output for the SVAR IRFS that does not make sense:

irfsvrpym.pdf

[matdehaven]

@fernando-duarte, I've run VAR identification schemes using two volatility regimes (split at 1990) and with t-distributed errors:

• Heteroskedastic ID
• t-distribution ID

Both are new identification methods using our standard empirical VAR. They both successfully return 11 "identified" shocks, but without any labels. I then pick the shocks that explain a high amount of the FEVD at the business cycle frequency for unemployment / vfci, as this seems like the best measure of being similar to the business cycle shock. I then compare the IRFs, and they look relatively similar (most similar for one of the t-distribution shocks).

But I don't see how this really adds new information to our interpretation of the Business Cycle shock. These new methods don't provide any interpretation, because they are both statistical identification schemes. And while the t-distribution shock does look the most similar to the business cycle shock, I think it actually is best interpreted as a monetary policy shock instead.

[fernando-duarte]

I've tried the example from Chris Sim's VARmodels and I get an output for the SVAR IRFS that does not make sense:

irfsvrpym.pdf

I got the same when I tried. It looks like we need to increase the number of posterior draws, or maybe make the optimizer try more iterations or go for more precision. The reduced-form results did look OK.

[fernando-duarte]

@fernando-duarte, I've run VAR identification schemes using two volatility regimes (split at 1990) and with t-distributed errors:

• Heteroskedastic ID
• t-distribution ID

Both are new identification methods using our standard empirical VAR. They both successfully return 11 "identified" shocks, but without any labels. I then pick the shocks that explain a high amount of the FEVD at the business cycle frequency for unemployment / vfci, as this seems like the best measure of being similar to the business cycle shock. I then compare the IRFs, and they look relatively similar (most similar for one of the t-distribution shocks).

But I don't see how this really adds new information to our interpretation of the Business Cycle shock. These new methods don't provide any interpretation, because they are both statistical identification schemes. And while the t-distribution shock does look the most similar to the business cycle shock, I think it actually is best interpreted as a monetary policy shock instead.

One idea we had was to construct the business cycle shock as a combination of the identified structural shocks. Or at least try to relate the business cycle shocks to the structural shocks we can label.

Maybe step 1 is to see if the structural shocks are very different from the reduced form shocks (in other papers, with monthly data, sometimes they are essentially the same). Then perhaps looking at the IRF of the identified shocks can help us label some of them.