Large Bayesian Vector Autoregressions

© 2020, Springer Nature Switzerland AG. Bayesian vector autoregressions are widely used for macroeconomic forecasting and structural analysis. Until recently, however, most empirical work had considered only small systems with a few variables due to parameter proliferation concern and computational limitations. We first review a variety of shrinkage priors that are useful for tackling the parameter proliferation problem in large Bayesian VARs. This is followed by a detailed discussion of efficient sampling methods for overcoming the computational problem. We then give an overview of some recent models that incorporate various important model features into conventional large Bayesian VARs, including stochastic volatility, non-Gaussian, and serially correlated errors. Efficient estimation methods for fitting these more flexible models are then discussed. These models and methods are illustrated using a forecasting exercise that involves a real-time macroeconomic dataset. The corresponding Matlab code is also provided [Matlab code is available at http://joshuachan.org/]

Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure

© 2020, © 2020 American Statistical Association. We introduce a class of large Bayesian vector autoregressions (BVARs) that allows for non-Gaussian, heteroscedastic, and serially dependent innovations. To make estimation computationally tractable, we exploit a certain Kronecker structure of the likelihood implied by this class of models. We propose a unified approach for estimating these models using Markov chain Monte Carlo (MCMC) methods. In an application that involves 20 macroeconomic variables, we find that these BVARs with more flexible covariance structures outperform the standard variant with independent, homoscedastic Gaussian innovations in both in-sample model-fit and out-of-sample forecast performance

Fast computation of the deviance information criterion for latent variable models

© 2014 Elsevier B.V. The deviance information criterion (DIC) has been widely used for Bayesian model comparison. However, recent studies have cautioned against the use of certain variants of the DIC for comparing latent variable models. For example, it has been argued that the conditional DIC–based on the conditional likelihood obtained by conditioning on the latent variables–is sensitive to transformations of latent variables and distributions. Further, in a Monte Carlo study that compares various Poisson models, the conditional DIC almost always prefers an incorrect model. In contrast, the observed-data DIC–calculated using the observed-data likelihood obtained by integrating out the latent variables–seems to perform well. It is also the case that the conditional DIC based on the maximum a posteriori (MAP) estimate might not even exist, whereas the observed-data DIC does not suffer from this problem. In view of these considerations, fast algorithms for computing the observed-data DIC for a variety of high-dimensional latent variable models are developed. Through three empirical applications it is demonstrated that the observed-data DICs have much smaller numerical standard errors compared to the conditional DICs. The corresponding MATLAB code is available upon request

Comparing hybrid time-varying parameter VARs

© 2018 Elsevier B.V. Empirical questions such as whether the Phillips curve or the Okun's law is stable can often be framed as a model comparison—e.g., comparing a vector autoregression (VAR) in which the coefficients in one equation are constant versus one that has time-varying parameters. We develop Bayesian model comparison methods to compare a class of time-varying parameter VARs we call hybrid TVP-VARs—VARs with time-varying parameters in some equations but constant coefficients in others. Using US data, we find evidence that the VAR coefficients in some, but not all, equations are time varying. Our finding highlights the empirical relevance of these hybrid TVP-VARs

A Bayesian Model Comparison for Trend-Cycle Decompositions of Output

© 2017 The Ohio State University We compare a number of widely used trend-cycle decompositions of output in a formal Bayesian model comparison exercise. This is motivated by the often markedly different results from these decompositions—different decompositions have broad implications for the relative importance of real versus nominal shocks in explaining variations in output. Using U.S. quarterly real GDP, we find that the overall best model is an unobserved components model with two features: (i) a nonzero correlation between trend and cycle innovations and (ii) a break in trend output growth in 2007. The annualized trend output growth decreases from about 3.4% to 1.2%–1.5% after the break. The results also indicate that real shocks are more important than nominal shocks. The slowdown in trend output growth is robust when we expand the set of models to include bivariate unobserved components models

Comparison of haemoglobin H inclusion bodies with embryonic ζ globin in screening for α thalassaemia

Aims - To compare the haemoglobin (Hb) H inclusion test with immunocytochemical detection of embryonic ζ chains in screening for a thalassaemia. Methods - Blood samples from 115 patients with relevant clinical history and hypochromic microcytic indexes were screened using the HbH inclusion test and the Variant Hemoglobin Testing System (BioRad, Hercules, CA, USA). Results - The HbH inclusion test was positive in 61 of 115 cases, three of whom had HbH disease confirmed by electrophoresis. The remaining 58 had α thalassaemia 1. All three HbH cases and 56 of 58 cases of a thalassaemia 1 expressed embryonic ζ chains, giving a specificity of 96.7%. Fifty four of 115 cases had a negative HbH inclusion test, of whom 50 had β thalassaemia trait and three had iron deficiency. No diagnosis was reached for the remaining patient. Conclusion - The immunocytochemical test is as sensitive as the HbH inclusion test in screening for a thalassaemia. The presence of ζ chains is highly specific for a thalassaemia I incorporating the (--/SEA) deletion. The specificity and simplicity of the immunocytochemical test make it the test of choice in screening for α thalassaemia.published_or_final_versio

A regime switching skew-normal model of contagion

© 2019 Walter de Gruyter GmbH, Berlin/Boston. A flexible multivariate model of a time-varying joint distribution of asset returns is developed which allows for regime switching and a joint skew-normal distribution. A suite of tests for linear and nonlinear financial market contagion is developed within the framework. The model is illustrated through an application to contagion between US and European equity markets during the Global Financial Crisis. The results show that correlation contagion dominates coskewness contagion, but that coskewness contagion is significant for Greece. A flight to safety to the US is also evident in the significance of breaks in the skewness parameter in the crisis regime. Comparison to the Asian crisis shows that similar patterns emerge, with a flight to safety to Japan, and Malaysia affected by coskewnes contagion with Hong Kong

Nonparametric estimation in economics: Bayesian and frequentist approaches

© 2017 Wiley Periodicals, Inc. We review Bayesian and classical approaches to nonparametric density and regression estimation and illustrate how these techniques can be used in economic applications. On the Bayesian side, density estimation is illustrated via finite Gaussian mixtures and a Dirichlet Process Mixture Model, while nonparametric regression is handled using priors that impose smoothness. From the frequentist perspective, kernel-based nonparametric regression techniques are presented for both density and regression problems. Both approaches are illustrated using a wage dataset from the Current Population Survey. WIREs Comput Stat 2017, 9:e1406. doi: 10.1002/wics.1406. For further resources related to this article, please visit the WIREs website

Reconciling output gaps: Unobserved components model and Hodrick–Prescott filter

© 2017 Elsevier B.V. This paper reconciles two widely used trend–cycle decompositions of GDP that give markedly different estimates: the correlated unobserved components model yields output gaps that are small in amplitude, whereas the Hodrick–Prescott (HP) filter generates large and persistent cycles. By embedding the HP filter in an unobserved components model, we show that this difference arises due to differences in the way the stochastic trend is modeled. Moreover, the HP filter implies that the cyclical components are serially independent—an assumption that is decidedly rejected by the data. By relaxing this restrictive assumption, the augmented HP filter provides comparable model fit relative to the standard correlated unobserved components model

Stochastic volatility models with ARMA innovations: An application to G7 inflation forecasts

© 2020 International Institute of Forecasters We introduce a new class of stochastic volatility models with autoregressive moving average (ARMA) innovations. The conditional mean process has a flexible form that can accommodate both a state space representation and a conventional dynamic regression. The ARMA component introduces serial dependence, which results in standard Kalman filter techniques not being directly applicable. To overcome this hurdle, we develop an efficient posterior simulator that builds on recently developed precision-based algorithms. We assess the usefulness of these new models in an inflation forecasting exercise across all G7 economies. We find that the new models generally provide competitive point and density forecasts compared to standard benchmarks, and are especially useful for Canada, France, Italy, and the U.S