Herman K. van Dijk

This essay is about Bayesian econometrics with a purpose . Specifically, six societal challenges and research opportunities that confront twenty first century Bayesian econometricians are discussed using an important feature of modern Bayesian econometrics: conditional probabilities of a wide range of economic events of interest can be evaluated by using simulation-based Bayesian inference. The enormous advances in hardware and software have made this Bayesian computational approach a very attractive vehicle of research in many subfields in economics where novel data patterns and substantial model complexity are predominant. In this essay the following challenges and opportunities are briefly discussed, including the scientific results obtained in the twentieth century leading up to these challenges: Posterior and predictive analysis of everything: connecting micro-economic causality with macro-economic issues; the need for speed: model complexity and the golden age of algorithms; learning about models, forecasts and policies including their uncertainty; temporal distributional change due to polarisation, imbalances and shocks; climate change and the macroeconomy; finally and most importantly, widespread, accessible, advanced high-level training.

We propose a novel and numerically efficient quantification approach to forecast uncertainty of the real price of oil using a combination of probabilistic individual model forecasts. Our combination method extends earlier approaches that have been applied to oil price forecasting, by allowing for sequentially updating of time-varying combination weights, estimation of time-varying forecast biases and facets of miscalibration of individual forecast densities and time-varying inter-dependencies among models. To illustrate the usefulness of the method, we present an extensive set of empirical results about time-varying forecast uncertainty and risk for the real price of oil over the period 1974-2018. We show that the combination approach systematically outperforms commonly used benchmark models and combination approaches, both in terms of point and density forecasts. The dynamic patterns of the estimated individual model weights are highly time-varying, reflecting a large time variation in the relative performance of the various individual models. The combination approach has built-in diagnostic information measures about forecast inaccuracy and/or model set incompleteness, which provide clear signals of model incompleteness during three crisis periods. To highlight that our approach also can be useful for policy analysis, we present a basic analysis of profit-loss and hedging against price risk.

The authors wish to make the following corrections to this paper (Ardia et al

We introduce a combined density nowcasting (CDN) approach to dynamic factor models (DFM) that in a coherent way accounts for time-varying uncertainty of several model and data features to provide more accurate and complete density nowcasts. The combination weights are latent random variables that depend on past nowcasting performance and other learning mechanisms. The combined density scheme is incorporated in a Bayesian sequential Monte Carlo method which rebalances the set of nowcasted densities in each period using updated information on the time-varying weights. Experiments with simulated data show that CDN works particularly well in a situation of early data releases with relatively large data uncertainty and model incompleteness. Empirical results, based on U.S. real-time data of 120 monthly variables, indicate that CDN gives more accurate density nowcasts of U.S. GDP growth than a model selection strategy and other combination strategies throughout the quarter with relatively large gains for the two first months of the quarter. CDN also provides informative signals on model incompleteness during recent recessions. Focusing on the tails, CDN delivers probabilities of negative growth, that provide good signals for calling recessions and ending economic slumps in real time.

We investigate the direct connection between the uncertainty related to estimated stable ratios of stock prices and risk and return of two pairs trading strategies: a conditional statistical arbitrage method and an implicit arbitrage one. A simulation-based Bayesian procedure is introduced for predicting stable stock price ratios, defined in a cointegration model. Using this class of models and the proposed inferential technique, we are able to connect estimation and model uncertainty with risk and return of stock trading. In terms of methodology, we show the effect that using an encompassing prior, which is shown to be equivalent to a Jeffreys’ prior, has under an orthogonal normalization for the selection of pairs of cointegrated stock prices and further, its effect for the estimation and prediction of the spread between cointegrated stock prices. We distinguish between models with a normal and Student t distribution since the latter typically provides a better description of daily changes of prices on financial markets. As an empirical application, stocks are used that are ingredients of the Dow Jones Composite Average index. The results show that normalization has little effect on the selection of pairs of cointegrated stocks on the basis of Bayes factors. However, the results stress the importance of the orthogonal normalization for the estimation and prediction of the spread—the deviation from the equilibrium relationship—which leads to better results in terms of profit per capital engagement and risk than using a standard linear normalization.

This paper presents the parallel computing implementation of the MitISEM algorithm, labeled Parallel MitISEM. The basic MitISEM algorithm provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. We present and discuss four canonical econometric models using a Graphics Processing Unit and a multi-core Central Processing Unit version of the MitISEM algorithm. The results show that the parallelization of the MitISEM algorithm on Graphics Processing Units and multi-core Central Processing Units is straightforward and fast to program using MATLAB. Moreover the speed performance of the Graphics Processing Unit version is much higher than the Central Processing Unit one.

Challenging statements have appeared in recent years in the literature on advances in computational procedures.

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 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 macroeconomics 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 incompleteness, and a natural combination of economic modeling, forecasting and policy interventions.