Bayesian methods (original) (raw)

Macroeconomic Modelling and Bayesian Methods

Journal of Quantitative Economics, 2017

This paper discusses the evolution of macroeconomic modelling. In particular, it focuses in particular on Bayesian methods and provides some applications of the Bayesian vector autoregression methods to the Indian economy.

On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14

SSRN Electronic Journal, 2000

This paper starts with a brief description of the introduction of the likelihood approach in econometrics as presented in Cowles Foundation Monographs 10 and 14. A sketch is given of the criticisms on this approach mainly from the first group of Bayesian econometricians. Publication and citation patterns of Bayesian econometric papers are analyzed in ten major econometric journals from the late 1970s until the first few months of 2014. Results indicate a cluster of journals with theoretical and applied papers, mainly consisting of Journal of Econometrics, Journal of Business and Economic Statistics and Journal of Applied Econometrics which contains the large majority of high quality Bayesian econometric papers. A second cluster of theoretical journals, mainly consisting of Econometrica and Review of Economic Studies contains few Bayesian econometric papers. The scientific impact, however, of these few papers on Bayesian econometric research is substantial. Special issues from the journals Econometric Reviews, Journal of Econometrics and Econometric Theory received wide attention. Marketing Science shows an ever increasing number of Bayesian papers since the middle nineties. The International Economic Review and the Review of Economics and Statistics show a moderate time varying increase. An upward movement in publication patterns in most journals occurs in the early 1990s due to the effect of the 'Computational Revolution'. The paper continues using a visualization technique to connect papers and authors around important empirical subjects such as forecasting in macro models and finance, choice and and equilibrium in micro models and marketing, and around more methodological subjects as model uncertainty and sampling algorithms. The information distilled from this analysis shows names of authors who contribute substantially to particular subjects. Next, subjects are discussed where Bayesian econometrics has shown substantial advances, namely, implementing stochastic simulation methods due to the computational revolution; flexible and unobserved component model structures in macroeconomic and finance; hierarchical structures and choice models in microeconomics and marketing. Three issues are summarized where Bayesian and frequentist econometricians differ: Identification, the value of prior information and model evaluation; dynamic inference and nonstationarity; vector autoregressive versus structural modeling. A topic of debate amongst Bayesian econometricians is listed as objective versus subjective econometrics. Communication problems and bridges between statistics and econometrics are summarized. A few non-Bayesian econometric papers are listed that have had substantial influence on Bayesian econometrics. Recent advances in applying simulation based Bayesian econometric methods to policy issues using models from macro-and microeconomics, finance and marketing are sketched. The paper ends with a list of subjects that are important challenges for twenty-first century Bayesian econometrics: Sampling methods suitable for use with big data and fast, parallelized and GPU, calculations, complex economic models which account for nonlinearities, analysis of implied model features such as risk and instability, incorporating model

Bayesian applications in econometrics

2010

The thesis considers several related aspects of Bayesian inference in econometrics. Particular attention is given to model-comparisons, distributed lags, and the sampling properties of estimators. In Chapter III the natural-conjugate Bayes (β˜) and Ordinary Least Squares (βˆ) estimators for the linear model are compared, and a condition is derived and investigated under which β˜ is preferred to βˆ in terms of matrix mean squared error. In a limiting case a test statistic is obtained and shown to be related to another well-known test. Two observable substitute statistics are shown to be consistent but upward-biased. The bias is studied in a limited Monte Carlo experiment. Bayesian inferential methods are advocated in Chapter IV for the seasonal adjustment of economic time-series. This is motivated by Chapter III and the application in Chapter VIII. A well-known classical procedure is shown to be a special case of the Bayesian method. Bayesian analyses of distributed lag models are su...

Historical Developments in Bayesian Econometrics after Cowles Foundation Monographs 10, 14

SSRN Electronic Journal, 2000

After a brief description of the first Bayesian steps into econometrics in the 1960s and early 70s, publication and citation patterns are analyzed in ten major econometric journals until 2012. The results indicate that journals which contain both theoretical and applied papers, such as Journal of Econometrics, Journal of Business and Economic Statistics and Journal of Applied Econometrics, publish the large majority of high quality Bayesian econometric papers in contrast to theoretical journals like Econometrica and the Review of Economic Studies. These latter journals published, however, a few papers that had a substantial impact on Bayesian research. The journals Econometric Reviews and Econometric Theory published key invited papers and special issues that received wide attention, while Marketing Science shows an ever increasing number of papers since the middle nineties. The International Economic Review and the Review of Economics and Statistics show a moderate time varying increase. The early nineties indicate an upward movement in publication patterns in most journals probably due to the effect of the 'Computational Revolution'. Next, a visualization technique is used to connect papers and authors around important theoretical and empirical themes such as forecasting, macro models, marketing models, model uncertainty and sampling algorithms. The information distilled from this analysis shows the names of authors who contribute substantially to particular themes. This is followed by a discussion of those topics that pose interesting challenges for discussion amongst Bayesian econometricians, namely the computational revolution, unobserved component and flexible model structures, choice models, IV models, dynamic models and forecasting. Three issues are summarized where Bayesian and frequentist econometricians differ: Identification, the value of prior information and model evaluation; dynamic inference and nonstationarity; and vector autoregressive versus structural modeling. A major topic of debate amongst Bayesian econometricians is listed as objective versus subjective econometrics and communication problems and bridges between statistics and econometrics are summarized. The paper ends with a list of four important themes that will be a challenge for twenty-first century Bayesian econometrics: Sampling methods which are suitable for parallelization and GPU calculations, complex economic models which can account for nonlinearities, analysis of implied model features such as risk and instability and incorporating model incompleteness in econometric analysis.

Introduction to Bayesian Econometrics Introduction to Bayesian Econometrics

This concise textbook is an introduction to econometrics from the Bayesian viewpoint. It begins with an explanation of the basic ideas of subjective probability and shows how subjective probabilities must obey the usual rules of probability to ensure coherency. It then turns to the definitions of the likelihood function, prior distributions, and posterior distributions. It explains how posterior distributions are the basis for inference and explores their basic properties. The Bernoulli distribution is used as a simple example. Various methods of specifying prior distributions are considered, with special emphasis on subject-matter considerations and exchange ability. The regression model is examined to show how analytical methods may fail in the derivation of marginal posterior distributions, which leads to an explanation of classical and Markov chain Monte Carlo (MCMC) methods of simulation. The latter is proceeded by a brief introduction to Markov chains. The remainder of the book is concerned with applications of the theory to important models that are used in economics, political science, biostatistics, and other applied fields. These include the linear regression model and extensions to Tobit, probit, and logit models; time series models; and models involving endogenous variables.

Simulation Based Bayesian Econometric Inference: Principles and Some Recent Computational Advances

SSRN Electronic Journal, 2000

In this paper we discuss several aspects of simulation based Bayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluating integrals by simulation methods is a crucial ingredient in Bayesian inference. Next, the most popular and well-known simulation techniques are discussed, the Metropolis-Hastings algorithm and Gibbs sampling (being the most popular Markov chain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed sampling methods: adaptive radial based direction sampling [ARDS], which makes use of a transformation to radial coordinates, and neural network sampling, which makes use of a neural network approximation to the posterior distribution of interest. Both methods are especially useful in cases where the posterior distribution is not well-behaved, in the sense of having highly non-elliptical shapes. The simulation techniques are illustrated in several example models, such as a model for the real US GNP and models for binary data of a US recession indicator.