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Prior elicitation in dynamic models

Nick Firoozye writes:

I know that prior elicitation is a tricky area (and my prior is parameters are often hidden because we’re not supposed to have opinions about them). The means of circumventing having to have opinions about actual parameters is to use prior predictive densities. And, as far as I know about that (a second or third-hand knowledge) is that one either has to have loads of information about the prior predictive density, as in percentiles. If not, we can resort to Robust Bayes (I see you’ve written on this topic before. It seems not as successful as I’d hoped).

But, I am interested in VARs or other dynamic models. It’s not difficult to use fitted VAR parameters to get conditional forecasts (see for example Waggoner and Zha or Geweke and Whiteman, which is sort of a Brownian Bridge on a set of (intricately) correlated random walks. They are an exceptionally good way of generating scenarios, testing the reasonableness of dynamic models.

My question is shouldn’t it be enough to get a Prior Conditional Forecast as a means of eliciting priors? For example, I can stick GDP, CPI, Fed Funds, and some yield curve factors in a model. I specify a prior, and condition on a specific scenario, e.g., Fed hikes 2 times over the next year, generating conditional forecasts for the remaining variables. I then adjust my prior in such a way as to make these conditional forecasts seem “reasonable”, a way of eliciting information about the prior, without actually looking at the data. My sense is running the (prior) model through enough scenarios would be equivalent to eliciting all enough relevant information about prior densities. Of course this starts to sound like experimental design.

Asking a trader to come up with a reasonable yield-curve shape given some hypothetical Fed moves or some combination of Fed Funds and Inflation, etc, is not super difficult. In fact, this may just be asking questions that traders and other market participants can answer.

Does anyone do this? If not, does it seem reasonable?

My reply: I don’t have any experience with vector autoregressions. But, yeah, what you’re saying sounds reasonable to me. It’s sort of a reparameterization.

2 Comments

  1. FWIW, a former student and I wrote a paper where the priors for the VAR are derived from priors from te impulse-response functions of the structural VAR.

    link

  2. Nick says:

    Stephen, thanks for the paper. One difference of course between a prior on an impulse response and a prior on conditional forecasts is that conditional forecasts also use the covariance of innovations, so are a bit more dynamic/realistic, while of course impulse response functions are responses to one-time shocks.

    But your paper does make me believe that it is quite reasonable to think that I can use priors on conditional forecasts as a mean of eliciting parameter priors. Thanks.