Time‐varying intercepts and equilibrium analysis: an extension of the dynamic almost ideal demand model

Demographic effects and user costs in demand systems have usually been modelled explicitly. A more robust approach is a state space formulation of the demand system, where time‐varying intercepts account for the effects of unobservable variables. The author embeds such a system in a vector autoregressive distributed lag model, with a Bayesian hierarchical prior. The model is estimated by a Markov chain Monte Carlo method on samples involving quarterly US and UK data. In the US case, the results are compared with a previously published cointegration analysis of the same data. Copyright © 2002 John Wiley & Sons, Ltd.     

A Bayesian mixed logit–probit model for multinomial choice

In this paper, we introduce a new flexible mixed model for multinomial discrete choice where the key individual- and alternative-specific parameters of interest are allowed to follow an assumption-free nonparametric density specification, while other alternative-specific coefficients are assumed to be drawn from a multivariate Normal distribution, which eliminates the independence of irrelevant alternatives assumption at the individual level. A hierarchical specification of our model allows us to break down a complex data structure into a set of submodels with the desired features that are naturally assembled in the original system. We estimate the model, using a Bayesian Markov Chain Monte Carlo technique with a multivariate Dirichlet Process (DP) prior on the coefficients with nonparametrically estimated density. We employ a “latent class” sampling algorithm, which is applicable to a general class of models, including non-conjugate DP base priors. The model is applied to supermarket choices of a panel of Houston households whose shopping behavior was observed over a 24-month period in years 2004–2005. We estimate the nonparametric density of two key variables of interest: the price of a basket of goods based on scanner data, and driving distance to the supermarket based on their respective locations. Our semi-parametric approach allows us to identify a complex multi-modal preference distribution, which distinguishes between inframarginal consumers and consumers who strongly value either lower prices or shopping convenience.     

Bayesian and Frequentist Inference for Ecological Inference: The R×C Case

In this paper we propose Bayesian and frequentist approaches to ecological inference, based on R × C contingency tables, including a covariate. The proposed Bayesian model extends the binomial-beta hierarchical model developed by K ing , R osen and T anner (1999) from the 2×2 case to the R × C case. As in the 2×2 case, the inferential procedure employs Markov chain Monte Carlo (MCMC) methods. As such, the resulting MCMC analysis is rich but computationally intensive. The frequentist approach, based on first moments rather than on the entire likelihood, provides quick inference via nonlinear least-squares, while retaining good frequentist properties. The two approaches are illustrated with simulated data, as well as with real data on voting patterns in Weimar Germany. In the final section of the paper we provide an overview of a range of alternative inferential approaches which trade-off computational intensity for statistical efficiency.     

A Geo-Additive Bayesian Discrete-Time Survival Model and its Application to Spatial Analysis of Childhood Mortality in Malawi

We describe a flexible geo-additive Bayesian survival model that controls, simultaneously, for spatial dependence and possible nonlinear or time-varying effects of other variables. Inference is fully Bayesian and is based on recently developed Markov Chain Monte Carlo techniques. In illustrating the model we introduce a spatial dimension in modelling under-five mortality among Malawian children using data from Malawi Demographic and Health Survey of 2000. The results show that district-level socioeconomic characteristics are important determinants of childhood mortality. More importantly, a separate spatial process produces district clustering of childhood mortality indicating the importance of spatial effects. The visual nature of the maps presented in this paper highlights relationships that would, otherwise, be overlooked in standard methods.     

Modeling and calculating the effect of treatment at baseline from panel outcomes

We propose and examine a panel data model for isolating the effect of a treatment, taken once at baseline, from outcomes observed over subsequent time periods. In the model, the treatment intake and outcomes are assumed to be correlated, due to unobserved or unmeasured confounders. Intake is partly determined by a set of instrumental variables and the confounding on unobservables is modeled in a flexible way, varying both by time and treatment state. Covariate effects are assumed to be subject-specific and potentially correlated with other covariates. Estimation and inference is by Bayesian methods that are implemented by tuned Markov chain Monte Carlo methods. Because our analysis is based on the framework developed by Chib [2004. Analysis of treatment response data without the joint distribution of counterfactuals. Journal of Econometrics, in press], the modeling and estimation does not involve either the unknowable joint distribution of the potential outcomes or the missing counterfactuals. The problem of model choice through marginal likelihoods and Bayes factors is also considered. The methods are illustrated in simulation experiments and in an application dealing with the effect of participation in high school athletics on future labor market earnings.     

Estimating Long-term Trends in Tropospheric Ozone Levels

This paper develops Bayesian methodology for estimating long-term trends in the daily maxima of tropospheric ozone. The methods are then applied to study long-term trends in ozone at six monitoring sites in the state of Texas. The methodology controls for the effects of meteorological variables because it is known that variables such as temperature, wind speed and humidity substantially affect the formation of tropospheric ozone. A semiparametric regression model is estimated in which a nonparametric trivariate surface is used to model the relationship between ozone and these meteorological variables because, while it is known that the relatinship is a complex nonlinear one, its functional form is unknown. The model also allows for the effects of wind direction and seasonality. The errors are modeled as an autoregression, which is methodologically challenging because the observations are unequally spaced over time. Each function in the model is represented as a linear combination of basis functions located at all of the design points. We also estimate an appropriate data transformation simulataneously with the functions. The functions are estimated nonparametrically by a Bayesian hierarchical model that uses indicator variables to allow a non-zero probability that the coefficient of each basis term is zero. The entire model, including the nonparametric surfaces, data transformation and autoregression for the unequally spaced errors, is estimated using a Markov chain Monte Carlo sampling scheme with a computationally efficient transition kernel for generating the indicator variables. The empirical results indicate that key meteorological variables explain most of the variation in daily ozone maxima through a nonlinear interaction and that their effects are consistent across the six sites. However, the estimated trends vary considerably from site to site, even within the same city.     

Nonlinear Time Series Modelling: An Introduction

Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear model are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of model. Finally forecasting and impulse response analysis is developed.     

A Study of Vertical Integration and Vertical Divestiture: The Case of Store Brand Milk Sourcing in Boston

This article investigates whether a retailer’s store brand supply source impacts vertical pricing and supply channel profitability. Using chain‐level retail scanner data, a random coefficients logit demand model is estimated employing a Bayesian estimation approach. Supply models are specified conditional on demand parameter estimates. Bayesian decision theory is applied to select the best fitting pricing model. Results indicate that a vertically integrated retailer engages in linear pricing for brand manufacturers’ products while competing retailers make nonlinear pricing contracts with brand manufacturers for branded products and store brands. A simulated vertical divestiture based on real world events provides evidence for improved channel efficiency.     

A Bayesian analysis of the multinomial probit model using marginal data augmentation

We introduce a set of new Markov chain Monte Carlo algorithms for Bayesian analysis of the multinomial probit model. Our Bayesian representation of the model places a new, and possibly improper, prior distribution directly on the identifiable parameters and thus is relatively easy to interpret and use. Our algorithms, which are based on the method of marginal data augmentation, involve only draws from standard distributions and dominate other available Bayesian methods in that they are as quick to converge as the fastest methods but with a more attractive prior specification. C-code along with an R interface for our algorithms is publicly available.¹     

Bayesian analysis of a Tobit quantile regression model

This paper develops a Bayesian framework for Tobit quantile regression. Our approach is organized around a likelihood function that is based on the asymmetric Laplace distribution, a choice that turns out to be natural in this context. We discuss families of prior distributions on the quantile regression vector that lead to proper posterior distributions with finite moments. We show how the posterior distribution can be sampled and summarized by Markov chain Monte Carlo methods. A method for comparing alternative quantile regression models is also developed and illustrated. The techniques are illustrated with both simulated and real data. In particular, in an empirical comparison, our approach out-performed two other common classical estimators.     

Beta-product dependent Pitman–Yor processes for Bayesian inference

Multiple time series data may exhibit clustering over time and the clustering effect may change across different series. This paper is motivated by the Bayesian non-parametric modelling of the dependence between clustering effects in multiple time series analysis. We follow a Dirichlet process mixture approach and define a new class of multivariate dependent Pitman–Yor processes (DPY). The proposed DPY are represented in terms of vectors of stick-breaking processes which determine dependent clustering structures in the time series. We follow a hierarchical specification of the DPY base measure to account for various degrees of information pooling across the series. We discuss some theoretical properties of the DPY and use them to define Bayesian non-parametric repeated measurement and vector autoregressive models. We provide efficient Monte Carlo Markov Chain algorithms for posterior computation of the proposed models and illustrate the effectiveness of the method with a simulation study and an application to the United States and the European Union business cycle.     

Bayesian inference for periodic regime-switching models

We present a general class of nonlinear time-series Markov regime-switching models for seasonal data which may exhibit periodic features in the hidden Markov process as well as in the laws of motion in each of the regimes. This class of models allows for non-trivial dependencies between seasonal, cyclical and long-term patterns in the data. To overcome the computational burden we adopt a Bayesian approach to estimation and inference. This paper contains two empirical examples as illustration, one uses housing starts data while the other employs US post-Second World War industrial production. © 1998 John Wiley & Sons, Ltd.     

Bayesian stochastic search for VAR model restrictions

We propose a Bayesian stochastic search approach to selecting restrictions for vector autoregressive (VAR) models. For this purpose, we develop a Markov chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modeling of inflation transmission from producer price index (PPI) components to the consumer price index (CPI).     

A Cost System Approach to the Stochastic Directional Technology Distance Function with Undesirable Outputs: The Case of us Banks in 2001–2010

This paper offers a methodology to address the endogeneity of inputs in the directional technology distance function (DTDF)‐based formulation of banking technology which explicitly accommodates the presence of undesirable nonperforming loans—an inherent characteristic of the bank's production due to its exposure to credit risk. Specifically, we model nonperforming loans as an undesirable output in the bank's production process. Since the stochastic DTDF describing banking technology is likely to suffer from the endogeneity of inputs, we propose addressing this problem by considering a system consisting of the DTDF and the first‐order conditions from the bank's cost minimization problem. The first‐order conditions also allow us to identify the ‘cost‐optimal’ directional vector for the banking DTDF, thus eliminating the uncertainty associated with an ad hoc choice of the direction. We apply our cost system approach to the data on large US commercial banks for the 2001–2010 period, which we estimate via Bayesian Markov chain Monte Carlo methods subject to theoretical regularity conditions. We document dramatic distortions in banks' efficiency, productivity growth and scale elasticity estimates when the endogeneity of inputs is assumed away and/or the DTDF is fitted in an arbitrary direction. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian Graphical Models for STructural Vector Autoregressive Processes

This paper proposes a Bayesian, graph‐based approach to identification in vector autoregressive (VAR) models. In our Bayesian graphical VAR (BGVAR) model, the contemporaneous and temporal causal structures of the structural VAR model are represented by two different graphs. We also provide an efficient Markov chain Monte Carlo algorithm to estimate jointly the two causal structures and the parameters of the reduced‐form VAR model. The BGVAR approach is shown to be quite effective in dealing with model identification and selection in multivariate time series of moderate dimension, as those considered in the economic literature. In the macroeconomic application the BGVAR identifies the relevant structural relationships among 20 US economic variables, thus providing a useful tool for policy analysis. The financial application contributes to the recent econometric literature on financial interconnectedness. The BGVAR approach provides evidence of a strong unidirectional linkage from financial to non‐financial super‐sectors during the 2007–2009 financial crisis and a strong bidirectional linkage between the two sectors during the 2010–2013 European sovereign debt crisis. Copyright © 2015 John Wiley & Sons, Ltd.     

Professional forecasters and real-time forecasting with a DSGE model

This paper analyses the real-time forecasting performance of the New Keynesian DSGE model of Galí, Smets and Wouters (2012), estimated on euro area data. It investigates the extent to which the inclusion of forecasts of inflation, GDP growth and unemployment by professional forecasters improve the forecasting performance. We consider two approaches for conditioning on such information. Under the “noise” approach, the mean professional forecasts are assumed to be noisy indicators of the rational expectations forecasts implied by the DSGE model. Under the “news” approach, it is assumed that the forecasts reveal the presence of expected future structural shocks in line with those estimated in the past. The forecasts of the DSGE model are compared with those from a Bayesian VAR model, an AR(1) model, a sample mean and a random walk.     

Modelling dependence using skew t copulas: Bayesian inference and applications

We construct a copula from the skew t distribution of Sahu et al. ( 2003 ). This copula can capture asymmetric and extreme dependence between variables, and is one of the few copulas that can do so and still be used in high dimensions effectively. However, it is difficult to estimate the copula model by maximum likelihood when the multivariate dimension is high, or when some or all of the marginal distributions are discrete‐valued, or when the parameters in the marginal distributions and copula are estimated jointly. We therefore propose a Bayesian approach that overcomes all these problems. The computations are undertaken using a Markov chain Monte Carlo simulation method which exploits the conditionally Gaussian representation of the skew t distribution. We employ the approach in two contemporary econometric studies. The first is the modelling of regional spot prices in the Australian electricity market. Here, we observe complex non‐Gaussian margins and nonlinear inter‐regional dependence. Accurate characterization of this dependence is important for the study of market integration and risk management purposes. The second is the modelling of ordinal exposure measures for 15 major websites. Dependence between websites is important when measuring the impact of multi‐site advertising campaigns. In both cases the skew t copula substantially outperforms symmetric elliptical copula alternatives, demonstrating that the skew t copula is a powerful modelling tool when coupled with Bayesian inference. Copyright © 2010 John Wiley & Sons, Ltd.     

On leverage in a stochastic volatility model

This paper is concerned with the specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications co-exist in the literature. One is the Euler approximation to the well-known continuous time SV model with leverage effect and the other is the discrete time SV model of Jacquier et al. (J. Econometrics 122 (2004) 185). Using a Gaussian nonlinear state space form with uncorrelated measurement and transition errors, I show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain and interpret the leverage effect in the model of Jacquier et al. Empirical comparisons of these two models via Bayesian Markov chain Monte Carlo (MCMC) methods further reveal that the specification of Jacquier et al. is inferior. Simulation experiments are conducted to study the sampling properties of Bayes MCMC for the conventional model.     

VAR FORECASTING USING BAYESIAN VARIABLE SELECTION

This paper develops methods for automatic selection of variables in Bayesian vector autoregressions (VARs) using the Gibbs sampler. In particular, I provide computationally efficient algorithms for stochastic variable selection in generic linear and nonlinear models, as well as models of large dimensions. The performance of the proposed variable selection method is assessed in forecasting three major macroeconomic time series of the UK economy. Data‐based restrictions of VAR coefficients can help improve upon their unrestricted counterparts in forecasting, and in many cases they compare favorably to shrinkage estimators. Copyright © 2011 John Wiley & Sons, Ltd.