Starting with the “partial adjustment model” suggested by Lintner [10, 11], this paper examines the dividend policies of individual firms. The Lintner model, in which the change in dividends from year t-1 to year t is regressed on a constant, the level of dividends for t-1, and the level of profits for t, explains dividend changes for individual firms fairly well relative to other models tested. But a model in which the constant term is suppressed and the level of earnings for t-1 is added, provides the best predictions of dividends on a year of data not used in fitting the regressions. Though the dividend policy of individual firms is certainly a subject of economic interest, perhaps much of the novelty of the paper is methodological: specifically, the way in which a validation sample, simulations, and prediction tests are used to investigate results obtained from a pilot sample. To avoid spurious results that could follow from the extensive data-dredging involved in finding “good-fitting” divid...

Dividend Policy: An Empirical Analysis

A new book in the Econometric Exercises series, this volume contains questions and answers to provide students with useful practice, as they attempt to master Bayesian econometrics. In addition to many theoretical exercises, this book contains exercises designed to develop the computational tools used in modern Bayesian econometrics. The latter half of the book contains exercises that show how these theoretical and computational skills are combined in practice, to carry out Bayesian inference in a wide variety of models commonly used by econometricians. Aimed primarily at advanced undergraduate and graduate students studying econometrics, this book may also be useful for students studying finance, marketing, agricultural economics, business economics or, more generally, any field which uses statistics. The book also comes equipped with a supporting website containing all the relevant data sets and MATLAB computer programs for solving the computational exercises.

/pdf/bayesian-econometric-methods-229aundtrj.pdf

Bayesian Econometric Methods

In two recent articles, Sims (1988) and Sims and Uhlig (1988/1991) question the value of much of the ongoing literature on unit roots and stochastic trends. They characterize the seeds of this literature as ‘sterile ideas’, the application of nonstationary limit theory as ‘wrongheaded and unenlightening’, and the use of classical methods of inference as ‘unreasonable’ and ‘logically unsound’. They advocate in place of classical methods an explicit Bayesian approach to inference that utilizes a flat prior on the autoregressive coefficient. DeJong and Whiteman adopt a related Bayesian approach in a group of papers (1989a,b,c) that seek to re-evaluate the empirical evidence from historical economic time series. Their results appear to be conclusive in turning around the earlier, influential conclusions of Nelson and Plosser (1982) that most aggregate economic time series have stochastic trends. So far these criticisms of unit root econometrics have gone unanswered; the assertions about the impropriety of classical methods and the superiority of flat prior Bayesian methods have been unchallenged; and the empirical re-evaluation of evidence in support of stochastic trends has been left without comment.



This paper breaks that silence and offers a new perspective. We challenge the methods, the assertions, and the conclusions of these articles on the Bayesian analysis of unit roots. Our approach is also Bayesian but we employ what are known in the statistical literature as objective ignorance priors in our analysis. These are developed in the paper to accommodate explicitly time series models in which no stationarity assumption is made. Ignorance priors are intended to represent a state of ignorance about the value of a parameter and in many models are very different from flat priors. We demonstrate that in time series models flat priors do not represent ignorance but are actually informative (sic) precisely because they neglect generically available information about how autoregressive coefficients influence observed time series characteristics. Contrary to their apparent intent, flat priors unwittingly bias inferences towards stationary and i.i.d. alternatives where they do represent ignorance, as in the linear regression model. This bias helps to explain the outcome of the simulation experiments in Sims and Uhlig and some of the empirical results of DeJong and Whiteman.



Under both flat priors and ignorance priors this paper derives posterior distributions for the parameters in autoregressive models with a deterministic trend and an arbitrary number of lags. Marginal posterior distributions are obtained by using the Laplace approximation for multivariate integrals along the lines suggested by the author (Phillips, 1983) in some earlier work. The bias towards stationary models that arises from the use of flat priors is shown in our simulations to be substantial; and we conclude that it is unacceptably large in models with a fitted deterministic trend, for which the expected posterior probability of a stochastic trend is found to be negligible even though the true data generating mechanism has a unit root. Under ignorance priors, Bayesian inference is shown to accord more closely with the results of classical methods. An interesting outcome of our simulations and our empirical work is the bimodal Bayesian posterior, which demonstrates that Bayesian confidence sets can be disjoint, just like classical confidence intervals that are based on asymptotic theory. The paper concludes with an empirical application of our Bayesian methodology to the Nelson-Plosser series. Seven of the 14 series show evidence of stochastic trends under ignorance priors, whereas under flat priors on the coefficients all but three of the series appear trend stationary. The latter result corresponds closely with the conclusion reached by DeJong and Whiteman (1989b) (based on truncated flat priors). We argue that the DeJong-Whiteman inferences are biased towards trend stationarity through the use of flat priors on the autoregressive coefficients, and that their inferences for some of the series (especially stock prices) are fragile (i.e. not robust) not only to the prior but also to the lag length chosen in the time series specification.

/pdf/to-criticize-the-critics-an-objective-bayesian-analysis-of-56bweahlgy.pdf

To criticize the critics: An objective bayesian analysis of stochastic trends

In this article, a summary of some research bearing on the statistical analysis of econometric models is reviewed. Many estimation, testing, and prediction techniques used in econometrics have just large-sample justifications. Selected Bayesian inference results relating to econometric models are reviewed. On the problem of constructing econometric models, an approach that is a blend of traditional econometric and modern time series analysis techniques is described. Many statistical problems requiring further analysis are noted. It is concluded that better solutions to these problems, better data, more sophisticated use of economic theory, application of more rigorous diagnostic checks, including forecasting checks and use of well-designed simulation experiments, probably will produce improved macroeconometric models.

Statistical Analysis of Econometric Models

Statistical analysis of econometric models

In this paper the problem of choosing among point estimators on the basis of their small sample properties is discussed from the sampling point of view. The indeterminacy of most Monte Carlo studies is analysed and resolved within the framework of statistical decision theory. A first order autoregressive model is worked through in detail both for its own sake and to illustrate how a complete Monte Carlo study might be done.

Hodson Thornber

Papers

Finite Sample Monte Carlo Studies: An Autoregressive Illustration