Objective Bayes Factors for Gaussian Directed Acyclic Graphical Models

Abstract. We propose an objective Bayesian method for the comparison of all Gaussian directed acyclic graphical models defined on a given set of variables. The method, which is based on the notion of fractional Bayes factor (BF), requires a single default (typically improper) prior on the space of unconstrained covariance matrices, together with a prior sample size hyper‐parameter, which can be set to its minimal value. We show that our approach produces genuine BFs. The implied prior on the concentration matrix of any complete graph is a data‐dependent Wishart distribution, and this in turn guarantees that Markov equivalent graphs are scored with the same marginal likelihood. We specialize our results to the smaller class of Gaussian decomposable undirected graphical models and show that in this case they coincide with those recently obtained using limiting versions of hyper‐inverse Wishart distributions as priors on the graph‐constrained covariance matrices.     

CENTRAL BANK REPUTATION AND THE MONETIZATION OF DEFICITS: THE 1981 ITALIAN MONETARY REFORM

In 1981 the Bank of Italy was freed from the obligation to purchase the unsold public debt at the Treasury auctions. Since then, the Bank of Italy has reduced debt monetization. The paper seeks to explain this policy shift by analyzing a game between the monetary and fiscal authorities. The fiscal authority is imperfectly informed about the central bank preferences. An equilibrium exists in which the central bank does not monetize, so as to establish a reputation of being independent. Monetization raises fiscal deficits and may raise public debt relative to a non-accommodative policy.     

A Probabilistic Perspective on Re-Identifiability

A quasi-identifier is a set of attributes that can be used to re-identify entries in anonymized data sets. A group of individuals is considered about whom quasi-identifying numerical information is disclosed such as date of birth, age, weight, and height. The fraction of individuals is determined whose information is unique in that group and hence is identifiable unambiguously. Nonuniformity can be captured well by a single number, the Kullback-Leibler distance. For example sets of real microdata, given approximations based on Kullback-Leibler distances are accurate. Second, the effect of disclosing more specific or less specific information is analyzed experimentally. Third, the effect of correlation between numerical attributes is measured. A formula gives the re-identifiability level. The approximations are validated using publicly available demographic data sets.     

RULES AND DISCRETION WITH NONCOORDINATED MONETARY AND FISCAL POLICIES

The time inconsistency of optimal monetary policy is due to the effects of tax distortions. Thus the issue of how to improve upon the time-consistent suboptimal monetary policy is related to that of the coordination of monetary and fiscal policy. We present a model with three players (the central bark, the fiscal authority, and wage setters) in which distortionary taxes are explicitly modelled. We show that binding commitments to monetary rules are not necessarily welfare improving if monetary and fiscal policy are not coordinated. We also examine the effects of different degrees of independence of the central bank.