Using simulation methods for bayesian econometric models: inference, development,and communication

Abstract

This paper surveys the fundamental principles of subjective Bayesian inference in econometrics and the implementation of those principles using posterior simulation methods. The emphasis is on the combination of models and the development of predictive distributions. Moving beyond conditioning on a fixed number of completely specified models, the paper introduces subjective Bayesian tools for formal comparison of these models with as yet incompletely specified models. The paper then shows how posterior simulators can facilitate communication between investigators (for example, econometricians) on the one hand and remote clients (for example, decision makers) on the other, enabling clients to vary the prior distributions and functions of interest employed by investigators. A theme of the paper is the practicality of subjective Bayesian methods. To this end, the paper describes publicly available software for Bayesian inference, model development, and communication and provides illustrations using two simple econometric models.

Assessing the distinguishability of models and the informativeness of data

“…A related resampling technique that uses the parametric bootstrap has also been proposed by Wagenmakers, Ratcliff, Gomez and Iverson (in press), though their focus is more on local analyses of model mimicry. Similar procedures are discussed in a more explicitly Bayesian framework by Geweke (1999aGeweke ( , 1999b. Wagenmakers et al provide a nice discussion of the relationship between these techniques.…”

“…The p(x, y | M X , θ) quantity is the probability of generating a data set from model X at some parameters θ that yields the same fits x and y as the original data set D. Note that x and y are statistics of the data set D and the model set (X and Y), and do not carry as much information as the data itself (and is therefore called the "partial information" Bayesian marginal by Geweke 1999aGeweke , 1999b. Indeed the relationship between p(x, y | M) and p(D | M) may be non-trivial.…”

Toward a Taylor rule for fiscal policy

“…We use the Modified Harmonic Mean estimator by Geweke (1999) to calculate the marginal data density ω of each model i . The marginal data density for model i is:…”

Do central banks respond to exchange rate movements? A structural investigation

“…However, there is overwhelming empirical evidence across countries of a far lower degree of pass through. 18 The theoretical model could be modified along the lines in Monacelli (2003), where producers set their prices in terms of consumers' currency. This assumption alters the central bank's policy trade-off and introduces a potentially much larger role for exchange rate stabilization.…”