Priors about observables in vector autoregressions

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 convergence theorems for the algorithm. As an application, we first show that the results in Christiano et al. (1999) are very sensitive to the introduction of various priors that are widely used. These priors turn out to be associated with undesirable priors on observables. But an empirical prior on observables helps clarify the relevance of these estimates: we find much higher persistence of output responses to monetary policy shocks than the one reported in Christiano et al. (1999) and a significantly larger total effect.

Estimating Bayesian decision problems with heterogeneous priors

In many areas of economics there is a growing interest in how expertise andpreferences drive individual and group decision making under uncertainty. Increasingly, we wish to estimate such models to quantify which of these drive decisionmaking. In this paper we propose a new channel through which we can empirically identify expertise and preference parameters by using variation in decisionsover heterogeneous priors. Relative to existing estimation approaches, our \Prior-Based Identification" extends the possible environments which can be estimated,and also substantially improves the accuracy and precision of estimates in thoseenvironments which can be estimated using existing methods.

Security prices and market transparency: the role of prior information

This paper analyzes the role of traders' priors (proper versus improper) on the implications of market transparency by comparing a pre-trade transparent market with an opaque market in a set-up based on Madhavan (1996). We show that prices may be more informative in the opaque market, regardless of how priors are modelled. In contrast, the comparison of market liquidity and volatility in the two market structures are affected by prior specification. Key words: Market microstructure, Transparency, Prior information

The Role of model uncertainty and learning in the U.S. postwar policy response to oil prices

This paper studies optimal monetary policy in a framework that explicitly accounts for policymakers' uncertainty about the channels of transmission of oil prices into the economy. More specfically, I examine the robust response to the real price of oil that US monetary authorities would have been recommended to implement in the period 1970 2009; had they used the approach proposed by Cogley and Sargent (2005b) to incorporate model uncertainty and learning into policy decisions. In this context, I investigate the extent to which regulator' changing beliefs over different models of the economy play a role in the policy selection process. The main conclusion of this work is that, in the specific environment under analysis, one of the underlying models dominates the optimal interest rate response to oil prices. This result persists even when alternative assumptions on the model's priors change the pattern of the relative posterior probabilities, and can thus be attributed to the presence of model uncertainty itself.

Population genetic structure and demography analysis in palinurus elephas populations from atlantic and mediterranean waters

Report for the scientific sojourn at the University of Reading, United Kingdom, from January until May 2008. The main objectives have been firstly to infer population structure and parameters in demographic models using a total of 13 microsatellite loci for genotyping approximately 30 individuals per population in 10 Palinurus elephas populations both from Mediterranean and Atlantic waters. Secondly, developing statistical methods to identify discrepant loci, possibly under selection and implement those methods using the R software environment. It is important to consider that the calculation of the probability distribution of the demographic and mutational parameters for a full genetic data set is numerically difficult for complex demographic history (Stephens 2003). The Approximate Bayesian Computation (ABC), based on summary statistics to infer posterior distributions of variable parameters without explicit likelihood calculations, can surmount this difficulty. This would allow to gather information on different demographic prior values (i.e. effective population sizes, migration rate, microsatellite mutation rate, mutational processes) and assay the sensitivity of inferences to demographic priors by assuming different priors.

Intrinsic test of independence in contingency tables

A condition needed for testing nested hypotheses from a Bayesianviewpoint is that the prior for the alternative model concentratesmass around the small, or null, model. For testing independencein contingency tables, the intrinsic priors satisfy this requirement.Further, the degree of concentration of the priors is controlled bya discrete parameter m, the training sample size, which plays animportant role in the resulting answer regardless of the samplesize.In this paper we study robustness of the tests of independencein contingency tables with respect to the intrinsic priors withdifferent degree of concentration around the null, and comparewith other “robust” results by Good and Crook. Consistency ofthe intrinsic Bayesian tests is established.We also discuss conditioning issues and sampling schemes,and argue that conditioning should be on either one margin orthe table total, but not on both margins.Examples using real are simulated data are given

Market Transparency, Market Quality and Sunshine Trading

This paper analyzes the implications of pre-trade transpareny on market performance. We find that transparency increases the precision held by agents, however we show that this increase in precision may not be due to prices themselves. In competitive markets, transparency increases market liquidity and reduces price volatility, whereas these results may not hold under imperfect competition. More importantly, market depth and volatility might be positively related with proper priors. Moreover, we study the incentives for liquidity traders to engage in sunshine trading. We obtain that the choice of sunshine/dark trading for a noise trader is independent of his order size, being the traders with higher liquidity needs more interested in sunshine trading, as long as this practice is desirable. Key words: Market Microstructure, Transparency, Prior Information, Market Quality, Sunshine Trading

Approximate knowledge of rationality and correlated equilibria

We extend Aumann's theorem [Aumann 1987], deriving correlated equilibria as a consequence of common priors and common knowledge of rationality, by explicitly allowing for non-rational behavior. Wereplace the assumption of common knowledge of rationality with a substantially weaker one, joint p-belief of rationality, where agents believe the other agents are rational with probability p or more. We show that behavior in this case constitutes a kind of correlated equilibrium satisfying certain p-belief constraints, and that it varies continuously in the parameters p and, for p sufficiently close to one,with high probability is supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend the analysis to characterizing rational expectations of interimtypes, to games of incomplete information, as well as to the case of non-common priors.

Estimating multi-country VAR models

This paper describes a methodology to estimate the coefficients, to test specification hypothesesand to conduct policy exercises in multi-country VAR models with cross unit interdependencies, unit specific dynamics and time variations in the coefficients. The framework of analysis is Bayesian: a prior flexibly reduces the dimensionality of the model and puts structure on the time variations; MCMC methods are used to obtain posterior distributions; and marginal likelihoods to check the fit of various specifications. Impulse responses and conditional forecasts are obtained with the output of MCMC routine. The transmission of certain shocks across countries is analyzed.

Forecasting and turning point predictions in a Bayesian panel VAR model

We provide methods for forecasting variables and predicting turning points in panel Bayesian VARs. We specify a flexible model which accounts for both interdependencies in the cross section and time variations in the parameters. Posterior distributions for the parameters are obtained for a particular type of diffuse, for Minnesota-type and for hierarchical priors. Formulas for multistep, multiunit point and average forecasts are provided. An application to the problem of forecasting the growth rate of output and of predicting turning points in the G-7 illustrates the approach. A comparison with alternative forecasting methods is also provided.

Universality of optimal measurements

We present optimal and minimal measurements on identical copies of an unknown state of a quantum bit when the quality of measuring strategies is quantified with the gain of information (Kullback-or mutual information-of probability distributions). We also show that the maximal gain of information occurs, among isotropic priors, when the state is known to be pure. Universality of optimal measurements follows from our results: using the fidelity or the gain of information, two different figures of merits, leads to exactly the same conclusions for isotropic distributions. We finally investigate the optimal capacity of N copies of an unknown state as a quantum channel of information.

Bayes linear spaces

Linear spaces consisting of σ-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended