The likelihood of the parameters in structural macroeconomic models typically has non-identification regions over which it is constant. When sufficiently diffuse priors are used, the posterior piles up in such non-identification regions. Use of informative priors can lead to the opposite, so both can generate spurious inference. We propose priors/posteriors on the structural parameters that are implied by priors/posteriors on the parameters of an embedding reduced-form model. An example of such a prior is the Jeffreys prior. We use it to conduct Bayesian limited-information inference on the new Keynesian Phillips curve with a VAR reduced form for US data.
