BAYESIAN INFERENCE METHODS FOR UNIVARIATE AND MULTIVARIATE GARCH MODELS: A SURVEY

This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non‐parametric approaches for GARCH models that avoid imposing arbitrary parametric distributional assumptions. These novel approaches implicitly assume infinite mixture of Gaussian distributions on the standardized returns which have been shown to be more flexible and describe better the uncertainty about future volatilities. Finally, the survey presents an illustration using real data to show the flexibility and usefulness of the non‐parametric approach.     

BAYESIAN ESTIMATION OF T–G RIDGE MODEL

Ridge type analysis of the Theil–Goldberger mixed model, considered earlier by Saxena and Bhatta–charya (1983) for the non–Bayesian set–up, is discussed from the Bayesian view–point when a has a closed prior and the loss–function being squared error.     

BAYESIAN MODEL SELECTION AND FORECASTING IN NONCAUSAL AUTOREGRESSIVE MODELS

In this paper, we propose a Bayesian estimation and forecasting procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, yielding predictive densities as a by‐product. We show that the posterior model probabilities provide a convenient model selection criterion in discriminating between alternative causal and noncausal specifications. As an empirical application, we consider US inflation. The posterior probability of noncausality is found to be high—over 98%. Furthermore, the purely noncausal specifications yield more accurate inflation forecasts than alternative causal and noncausal AR models. Copyright © 2010 John Wiley & Sons, Ltd.     

NONPARAMETRIC AND SEMIPARAMETRIC METHODS FOR ECONOMIC RESEARCH

Abstract. Developments in the vast and growing literatures on nonparametric and semiparametric statistical estimation are reviewed. The emphasis is on useful methodology rather than statistical properties for their own sake. Some empirical applications to economic data are described. The paper deals separately with nonparametric density estimation, nonparametric regression estimation, and estimation of semiparametric models.     

crs: A PACKAGE FOR NONPARAMETRIC SPLINE ESTIMATION IN R

crs is a library for R written by Jeffrey S. Racine (Maintainer) and Zhenghua Nie. This add‐on package provides a collection of functions for spline‐based nonparametric estimation of regression functions with both continuous and categorical regressors. Currently, the crs package integrates data‐driven methods for selecting the spline degree, the number of knots and the necessary bandwidths for nonparametric conditional mean, IV and quantile regression. A function for multivariate density spline estimation with mixed data is also currently in the works. As a bonus, the authors have also provided the first simple R interface to the NOMAD (‘nonsmooth mesh adaptive direct search’) optimization solver which can be applied to solve other mixed integer optimization problems that future users might find useful in other settings. Although the crs package shares some of the same functionalities as its kernel‐based counterpart—the np package by the same author—it currently lacks some of the features the np package provides, such as hypothesis testing and semiparametric estimation. However, what it lacks in breadth, crs makes up in speed. A Monte Carlo experiment in this review uncovers sizable speed gains compared to its np counterpart, with a marginal loss in terms of goodness of fit. Therefore, the package will be extremely useful for applied econometricians interested in employing nonparametric techniques using large amounts of data with a small number of discrete covariates. Copyright © 2014 John Wiley & Sons, Ltd.     

BAYESIAN STATE SPACE MODELS IN MACROECONOMETRICS

State space models play an important role in macroeconometric analysis and the Bayesian approach has been shown to have many advantages. This paper outlines recent developments in state space modelling applied to macroeconomics using Bayesian methods. We outline the directions of recent research, specifically the problems being addressed and the solutions proposed. After presenting a general form for the linear Gaussian model, we discuss the interpretations and virtues of alternative estimation routines and their outputs. This discussion includes the Kalman filter and smoother, and precision-based algorithms. As the advantages of using large models have become better understood, a focus has developed on dimension reduction and computational advances to cope with high-dimensional parameter spaces. We give an overview of a number of recent advances in these directions. Many models suggested by economic theory are either non-linear or non-Gaussian, or both. We discuss work on the particle filtering approach to such models as well as other techniques that use various approximations – to either the time state and measurement equations or to the full posterior for the states – to obtain draws.     

RECENT PROGRESS IN APPLIED BAYESIAN ECONOMETRICS

Abstract. Bayesian methods are widely used by theoretical econometricians and statisticians but have not won widespread acceptance from applied researchers. After briefly describing the basic of the Bayesian approach, we discuss several issues relating to the empirical application of Bayesian methods. The existing Bayesian empirical literature is also partially summarized. The remainder of the paper offers a non-technical survey of some recent computational advances in Bayesian econometrics. The overall goal is to persuade economists that Bayesian methods are both computationally feasible and easy to implement in empirical research.     

STATISTICAL INFERENCE VIA BOOTSTRAPPING FOR MEASURES OF INEQUALITY

In this paper we consider the use of bootstrap methods to compute interval estimates and perform hypothesis tests for decomposable measures of economic inequality. Two applications of this approach, using the Gini coefficient and Theil's entropy measures of inequality, are provided. Our first application employs pre- and post-tax aggregate state income data, constructed from the Panel Study of Income Dynamics. We find that although casual observation of the inequality measures suggests that the post-tax distribution of income is less equal among states than pre-tax income, none of these observed differences are statistically significant at the 10% level. Our second application uses the National Longitudinal Survey of Youth data to study youth inequality. We find that youth inequality decreases as the cohort ages, but between age-group inequality has increased in the latter half of the 1980s. The results suggest that (1) statistical inference is essential even when large samples are available, and (2) the bootstrap procedure appears to perform well in this setting. © 1997 by John Wiley & Sons, Ltd.     

MULTI-STEP ESTIMATION FOR FORECASTING

We delineate conditions which favour multi-step, or dynamic, estimation for multi-step forecasting. An analytical example shows how dynamic estimation (DE) may accommodate incorrectly-specified models as the forecast lead alters, improving forecast performance for some misspecifications. However, in correctly-specified models, reducing finite-sample biases does not justify DE. In a Monte Carlo forecasting study for integrated processes, estimating a unit root in the presence of a neglected negative moving-average error may favour DE, though other solutions exist to that scenario. A second Monte Carlo study obtains the estimator biases and explains these using asymptotic approximations.     

PRE-TEST ESTIMATION AND TESTING IN ECONOMETRICS: RECENT DEVELOPMENTS

Abstract. This paper surveys a range of important developments in the area of preliminary-test inference in the context of econometric modelling. Both pre-test estimation and pre-test testing are discussed. Special attention is given to recent contributions and results. These include analyses of pre-test strategies under model mis-specification and generalised regression errors; exact sampling distribution results; and pre-testing inequality constraints on the model's parameters. In many cases, practical advice is given to assist applied econometricians in appraising the relative merits of pre-testing. It is shown that there are situations where pre-testing can be advantageous in practice     

EXCHANGE RATE FUNDAMENTALS,FORECASTING, AND SPECULATION: BAYESIAN MODELS IN BLACK MARKETS

Although speculative activity is central to black markets for currency, the out‐of‐sample performance of structural models in those settings is unknown. We substantially update the literature on empirical determinants of black market rates and evaluate the out‐of‐sample performance of linear models and non‐parametric Bayesian treed Gaussian process (BTGP) models against the random walk benchmark. Fundamentals‐based models outperform the benchmark in out‐of‐sample prediction accuracy and trading rule profitability measures given future values of fundamentals. In simulated real‐time trading exercises, however, the BTGP achieves superior realized profitability, accuracy and market timing, while linear models do no better than a random walk. Copyright © 2013 John Wiley & Sons, Ltd.     

METHODS,TRENDS AND CONTROVERSIES IN CONTEMPORARY BENEFIT TRANSFER

Abstract Benefit transfer uses research results from pre‐existing primary research to predict welfare estimates for other sites of policy significance for which primary valuation estimates are unavailable. Despite the sizable literature and the ubiquity of benefit transfer in policy analysis, the method remains subject to controversy. There is also a divergence between transfer practices recommended by the scholarly literature and those commonly applied within policy analysis. The size, complexity and relative disorganization of the literature may represent an obstacle to the use of updated methods by practitioners. Recognizing the importance of benefit transfer for policymaking and the breadth of associated scholarly work, this paper reviews and synthesizes the benefit transfer literature. It highlights methods, trends and controversies in contemporary research, identifies issues and challenges facing benefit transfer practitioners and summarizes research contributions. Several areas of future research on benefit transfers naturally emerge.     

DETAILED ESTIMATION OF WORKLIFE EXPECTANCY FOR THE MEASUREMENT OF HUMAN CAPITAL: ACCOUNTING FOR MARRIAGE AND CHILDREN

Abstract Measuring an individual's human capital at a point in time as the present actuarial value of expected net lifetime earnings has a lengthy history. Calculating such measures requires accurate estimates of worklife expectancy. Here, worklife estimates for men and women in the USA categorized by educational attainment, race, marital status, parental status and current labour force status are presented. Race has a much larger impact on the worklife expectancy of men than women. Education is associated with larger worklife differentials for women. The association between marriage and worklife expectancy is significant, but of opposite sign, for men and women: married women (men) have a lower (higher) worklife expectancy than single women (men). Parenthood is associated with a reduction in the worklife expectancy of women; the association is smaller and varies from positive for some education/marital status groups to negative for others for men.     

DIRECT MULTI-STEP ESTIMATION AND FORECASTING

Abstract.  This paper surveys the literature on multi-step forecasting when the model or the estimation method focuses directly on the link between the forecast origin and the horizon of interest. Among diverse contributions, we show how the current consensual concepts have emerged. We present an exhaustive overview of the existing results, including a conclusive review of the circumstances favourable to direct multi-step forecasting, namely different forms of non-stationarity and appropriate model design. We also provide a unifying framework which allows us to analyse the sources of forecast errors and hence of accuracy improvements from direct over iterated multi-step forecasting.