Priors about observables in vector autoregressions

Abstract

Standard practice in Bayesian VARs is to formulate priors on the autoregressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. We show how this kind of prior can be used in a VAR under strict probability theory principles. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical situations with a very large number of parameters. We prove various

Monetary Policy with Judgment

“…Equation ( 18), however, provides a simple way to evaluate the prior, by asking the following question: What interest rate decision is associated with the prior distribution over the DSGE parameters described in Table 1? This exercise is similar in spirit to the prior predictive checks, as discussed in Lancaster (2004), Geweke (2005), Geweke (2010), and Jarociński and Marcet (2019) in time series models, and in Del Negro and Schorfheide ( 2008), Lombardi and Nicoletti (2012), and Faust and Gupta (2012) in DSGE models. The difference is that instead of checking whether the model and the priors are compatible with specific moments of the observables, we compute the optimal interest rate decision that minimizes the central banker's expected loss using the prior distribution.…”

“…This exercise is reminiscent of the prior predictive checks advocated, for instance, by Lancaster (2004), Geweke (2005), Geweke (2010), and Jarociński and Marcet (2019) in time series models, and by Del Negro and Schorfheide ( 2008), Lombardi and Nicoletti (2012), and Faust and Gupta (2012) in DSGE models. 2 It is important to stress that our interpretation is that choosing priors is equivalent to endowing the central banker with specific judgmental decisions.…”

Monetary Policy with Judgment

“…This exercise is reminiscent of the prior predictive checks advocated, for instance, by Lancaster (2004), Geweke (2005), Geweke (2010), and Jarociński and Marcet (2019) in time series models, and by Del Negro and Schorfheide (2008), Lombardi andNicoletti (2012), andFaust andGupta (2012) in DSGE models. 2 It is important to stress that our interpretation is that choosing priors is equivalent to endowing the central banker with specific judgmental decisions.…”

Prior knowledge elicitation: The past, present, and future

“…gives rise to an integral equation when the distributions concerning the observables y are known (Aitchison and Dunsmore, 1975;Winkler, 1980;Wolpert et al, 2003;Gribok et al, 2004;Akbarov, 2009;Jarociński and Marcet, 2019). Suppose that p(y) is elicited from the expert, the likelihood p(y|θ) is specified by the analyst, and the analyst is looking for an unknown prior p(θ).…”