Abstract: We demonstrate improvements in predictive power when introducing spline functions to take account of highly non-linear relationships between firm failure and earnings, leverage, and liquidity in a logistic bankruptcy model. Our... more
Abstract: We demonstrate improvements in predictive power when introducing spline functions to take account of highly non-linear relationships between firm failure and earnings, leverage, and liquidity in a logistic bankruptcy model. Our results show that modeling excessive non-linearities yields substantially improved bankruptcy predictions, on the order of 70 to 90 percent, compared with a standard logistic model.
Abstract: We model a regression density nonparametrically so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the components changing smoothly as a function of... more
Abstract: We model a regression density nonparametrically so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the components changing smoothly as a function of the covariates. The model extends existing models in two important ways.
Sungbae An and Frank Schorfheide have provided an excellent review of the main elements of Bayesian inference in Dynamic Stochastic General Equilibrium (DSGE) models. Bayesian methods have, for reasons clearly outlined in the paper, a... more
Sungbae An and Frank Schorfheide have provided an excellent review of the main elements of Bayesian inference in Dynamic Stochastic General Equilibrium (DSGE) models. Bayesian methods have, for reasons clearly outlined in the paper, a very natural role to play in DSGE analysis, and the appeal of the Bayesian paradigm is indeed strongly evidenced by the flood of empirical applications in the area over the last couple of years.
Abstract: Vector autoregressions have steadily gained in popularity since their introduction in econometrics 25 years ago. A drawback of the otherwise fairly well developed methodology is the inability to incorporate prior beliefs... more
Abstract: Vector autoregressions have steadily gained in popularity since their introduction in econometrics 25 years ago. A drawback of the otherwise fairly well developed methodology is the inability to incorporate prior beliefs regarding the system's steady state in a satisfactory way. Such prior information are typically readily available and may be crucial for forecasts at long horizons.
Abstract: The degree of empirical support of a priori plausible structures on the cointegration vectors has a central role in the analysis of cointegration. Villani (2000) and Strachan and van Dijk (2003) have recently proposed finite... more
Abstract: The degree of empirical support of a priori plausible structures on the cointegration vectors has a central role in the analysis of cointegration. Villani (2000) and Strachan and van Dijk (2003) have recently proposed finite sample Bayesian procedures to calculate the posterior probability of restrictions on the cointegration space, using the existence of a uniform prior distribution on the cointegration space as the key ingredient.
The multivariate split normal distribution extends the usual multivariate normal distribution by a set of parameters which allows for skewness in the form of contraction/dilation along a subset of the principal axes. This article derives... more
The multivariate split normal distribution extends the usual multivariate normal distribution by a set of parameters which allows for skewness in the form of contraction/dilation along a subset of the principal axes. This article derives some properties for this distribution, including its moment generating function, multivariate skewness, and kurtosis, and discusses its role as a population model for asymmetric principal components analysis.
Abstract. We introduce a Bayesian approach to model assessment in the class of graphical vector autoregressive processes. As a result of the very large number of model structures that may be considered, simulation-based inference, such as... more
Abstract. We introduce a Bayesian approach to model assessment in the class of graphical vector autoregressive processes. As a result of the very large number of model structures that may be considered, simulation-based inference, such as Markov chain Monte Carlo, is not feasible. Therefore, we derive an approximate joint posterior distribution of the number of lags in the autoregression and the causality structure represented by graphs using a fractional Bayes approach.
Abstract. Smooth mixtures, ie mixture models with covariate-dependent mixing weights, are very useful flexible models for conditional densities. Previous work shows that using too simple mixture components for modeling heteroscedastic... more
Abstract. Smooth mixtures, ie mixture models with covariate-dependent mixing weights, are very useful flexible models for conditional densities. Previous work shows that using too simple mixture components for modeling heteroscedastic and/or heavy tailed data can give a poor fit, even with a large number of components. This paper explores how well a smooth mixture of symmetric components can capture skewed data.
Abstract In this paper, we compare the empirical properties of closed-and open-economy DSGE models estimated on Euro area data. The comparison is made along several dimensions; we examine the models in terms of their marginal likelihoods,... more
Abstract In this paper, we compare the empirical properties of closed-and open-economy DSGE models estimated on Euro area data. The comparison is made along several dimensions; we examine the models in terms of their marginal likelihoods, forecasting performance, variance decompositions, and their transmission mechanisms of monetary policy.
We consider Bayesian inference about the dimensionality in the multivariate reduced rank regression framework, which encompasses several models such as MANOVA, factor analysis and cointegration models for multiple time series. The... more
We consider Bayesian inference about the dimensionality in the multivariate reduced rank regression framework, which encompasses several models such as MANOVA, factor analysis and cointegration models for multiple time series. The fractional Bayes approach is used to derive a closed form approximation to the posterior distribution of the dimensionality and some asymptotic properties of the approximation are proved.
Abstract We propose a general class of models and a unified Bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high-dimensional set of covariates. Our model is a finite... more
Abstract We propose a general class of models and a unified Bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high-dimensional set of covariates. Our model is a finite mixture of component models with covariate-dependent mixing weights. The component densities can belong to any parametric family, with each model parameter being a deterministic function of covariates through a link function.
Abstract This paper uses an estimated open-economy dynamic stochastic general equilibrium model for the euro area to examine if during 1993Q4–2002Q4 constant interest rate forecasts (CIRFs), commonly used by inflation-targeting central... more
Abstract This paper uses an estimated open-economy dynamic stochastic general equilibrium model for the euro area to examine if during 1993Q4–2002Q4 constant interest rate forecasts (CIRFs), commonly used by inflation-targeting central banks, are viewed as being in line with the central bank's historical policy behaviour. In the sense of Leeper and Zha (2003), a CIRF is defined as a modest intervention of the policy rule if it does not trigger the agents to revise their expectations about the inflation-targeting policy.
Abstract: Structural VARs have been extensively used in empirical macroeconomics during the last two decades, particularly in analyses of monetary policy. Existing Bayesian procedures for structural VARs are at best confined to a severly... more
Abstract: Structural VARs have been extensively used in empirical macroeconomics during the last two decades, particularly in analyses of monetary policy. Existing Bayesian procedures for structural VARs are at best confined to a severly limited handling of cointegration restrictions. This paper extends the Bayesian analysis of structural VARs to cover cointegrated processes with an arbitrary number of cointegrating relations and general linear restrictions on the cointegration space.
The Riksbank has had an inflation target of 2 per cent since 1995. To achieve this target the Executive Board of the Riksbank regularly decides on the repo rate level. Research has shown that monetary policy works with a time lag of 1–2... more
The Riksbank has had an inflation target of 2 per cent since 1995. To achieve this target the Executive Board of the Riksbank regularly decides on the repo rate level. Research has shown that monetary policy works with a time lag of 1–2 years before achieving its maximum effect (Christiano, et al., 2005). Consequently, effective monetary policy must be forward-looking and a central part of the Riksbank's work consists of forecasting future economic developments.
Abstract: Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface... more
Abstract: Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface models, they are likely to be less successful in that setting because of the curse of dimensionality, especially when there are more than a couple of covariates.
A distinguishing feature of cointegration models, and many other multivariate models, is that only spaces spanned by parameter vectors are identified. We point out that traditional distance measures, such as the Euclidean measure, are not... more
A distinguishing feature of cointegration models, and many other multivariate models, is that only spaces spanned by parameter vectors are identified. We point out that traditional distance measures, such as the Euclidean measure, are not reasonable to use when measuring distances between spaces. This point has been either missed or ignored in many simulation studies where inappropriate distance measures have been used.
We introduce a non-Gaussian dynamic mixture model for macroeconomic forecasting. The locally adaptive signal extraction and regression (LASER) model is designed to capture relatively persistent AR processes (signal) which are contaminated... more
We introduce a non-Gaussian dynamic mixture model for macroeconomic forecasting. The locally adaptive signal extraction and regression (LASER) model is designed to capture relatively persistent AR processes (signal) which are contaminated by high frequency noise. The distributions of the innovations in both noise and signal are modeled robustly using mixtures of normals. The mean of the process and the variances of the signal and noise are allowed to shift either suddenly or gradually at unknown locations and unknown numbers of times. The model is then capable of capturing movements in the mean and conditional variance of a series, as well as in the signal-to-noise ratio. Four versions of the model are estimated by Bayesian methods and used to forecast a total of nine quarterly macroeconomic series from the US, Sweden and Australia. We observe that allowing for infrequent and large parameter shifts while imposing normal and homoskedastic errors often leads to erratic forecasts, but that the model typically forecasts well if it is made more robust by allowing for non-normal errors and time varying variances. Our main finding is that, for the nine series we analyze, specifications with infrequent and large shifts in error variances outperform both fixed parameter specifications and smooth, continuous shifts when it comes to interval coverage.
Keywords: Bayesian inference; Forecast evaluation; Regime switching; State space modeling; Dynamic mixture models
Keywords: Bayesian inference; Forecast evaluation; Regime switching; State space modeling; Dynamic mixture models
Research Interests:
A general model is proposed for flexibly estimating the density of a continuous response variable conditional on a possibly high-dimensional set of covariates. The model is a finite mixture of asymmetric student t densities with... more
A general model is proposed for flexibly estimating the density of a continuous response variable conditional on a possibly high-dimensional set of covariates. The model is a finite mixture of asymmetric student t densities with covariate-dependent mixture weights. The four parameters of the components, the mean, degrees of freedom, scale and skewness, are all modeled as functions of the covariates. Inference is Bayesian and the computation is carried out using Markov chain Monte Carlo simulation. To enable model parsimony, a variable selection prior is used in each set of covariates and among the covariates in the mixing weights. The model is used to analyze the distribution of daily stock market returns, and shown to more accurately forecast the distribution of returns than other widely used models for financial data.
Keywords: Bayesian inference; Markov chain Monte Carlo; Mixture of experts; Variable selection; Volatility modeling
Keywords: Bayesian inference; Markov chain Monte Carlo; Mixture of experts; Variable selection; Volatility modeling
Structural econometric auction models with explicit game-theoretic modeling of bidding strategies have been quite a challenge from a methodological perspective, especially within the common value framework. We develop a Bayesian analysis... more
Structural econometric auction models with explicit game-theoretic modeling of bidding strategies have been quite a challenge from a methodological perspective, especially within the common value framework. We develop a Bayesian analysis of the hierarchical Gaussian common value model with stochastic entry introduced by Bajari and Hortaçsu. A key component of our approach is an accurate and easily interpretable analytical approximation of the equilibrium bid function, resulting in a fast and numerically stable evaluation of the likelihood function. We extend the analysis to situations with positive valuations using a hierarchical gamma model. We use a Bayesian variable selection algorithm that simultaneously samples the posterior distribution of the model parameters and does inference on the choice of covariates. The methodology is applied to simulated data and to a newly collected dataset from eBay with bids and covariates from 1000 coin auctions. We demonstrate that the Bayesian algorithm is very efficient and that the approximation error in the bid function has virtually no effect on the model inference. Both models fit the data well, but the Gaussian model outperforms the gamma model in an out-of-sample forecasting evaluation of auction prices. This article has supplementary material online.
Research Interests:
Regression density estimation is the problem of exibly estimating a response distribution as a function of covariates. An important approach to regression density estimation uses mixtures of experts models and our article considers... more
Regression density estimation is the problem of
exibly estimating a response distribution as a function of covariates. An important approach to regression density estimation uses mixtures of experts models and our article considers flexible mixtures of heteroscedastic experts (MHE) regression models where the response distribution
is a normal mixture, with the component means, variances and mixture weights all varying as a function of covariates. Our article develops fast variational approximation methods for inference. Our motivation is that alternative computationally intensive MCMC methods for tting mixture models are difficult to apply when it is desired to fit models repeatedly in exploratory analysis and model choice. Our article makes three
contributions. First, a variational approximation for MHE models is described where the variational lower bound is in closed form. Second, the basic approximation can be improved by using stochastic approximation methods to perturb the initial solution to
attain higher accuracy. Third, the advantages of our approach for model choice and evaluation compared to MCMC based approaches are illustrated. These advantages are particularly compelling for time series data where repeated re tting for one step ahead prediction in model choice and diagnostics and in rolling window computations is very common.
exibly estimating a response distribution as a function of covariates. An important approach to regression density estimation uses mixtures of experts models and our article considers flexible mixtures of heteroscedastic experts (MHE) regression models where the response distribution
is a normal mixture, with the component means, variances and mixture weights all varying as a function of covariates. Our article develops fast variational approximation methods for inference. Our motivation is that alternative computationally intensive MCMC methods for tting mixture models are difficult to apply when it is desired to fit models repeatedly in exploratory analysis and model choice. Our article makes three
contributions. First, a variational approximation for MHE models is described where the variational lower bound is in closed form. Second, the basic approximation can be improved by using stochastic approximation methods to perturb the initial solution to
attain higher accuracy. Third, the advantages of our approach for model choice and evaluation compared to MCMC based approaches are illustrated. These advantages are particularly compelling for time series data where repeated re tting for one step ahead prediction in model choice and diagnostics and in rolling window computations is very common.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Bayesian priors are often used to restrain the otherwise highly over-parametrized vector autoregressive (VAR) models. The currently available Bayesian VAR methodology does not allow the user to specify prior beliefs about the... more
Bayesian priors are often used to restrain the otherwise highly over-parametrized vector autoregressive (VAR) models. The currently available Bayesian VAR methodology does not allow the user to specify prior beliefs about the unconditional mean, or steady state, of the system. This is unfortunate as the steady state is something that economists usually claim to know relatively well. This paper develops easily implemented methods for analyzing both stationary and cointegrated VARs, in reduced or structural form, with an informative prior on the steady state. We document that prior information on the steady state leads to substantial gains in forecasting accuracy on Swedish macro data. A second example illustrates the use of informative steady-state priors in a cointegration model of the consumption-wealth relationship in the USA.
A neglected aspect of the otherwise fairly well developed Bayesian analysis of cointegration is point estimation of the cointegration space. It is pointed out here that, due to the well known non-identification of the cointegration... more
A neglected aspect of the otherwise fairly well developed Bayesian analysis of cointegration is point estimation of the cointegration space. It is pointed out here that, due to the well known non-identification of the cointegration vectors, the parameter space is not Euclidean and the loss functions underlying the conventional Bayes estimators are therefore questionable. We present a Bayes estimator of the cointegration space which takes the curved geometry of the parameter space into account. This estimate has the interpretation of being the posterior mean cointegration space and is invariant to the order of the time series, a property not shared with many of the Bayes estimators in the cointegration literature. An overall measure of cointegration space uncertainty is also proposed. Australian interest rate data are used for illustration. A small simulation study shows that the new Bayes estimator compares favorably to the maximum likelihood estimator.
Keywords: Bayesian inference; Cointegration analysis; Estimation; Grassman manifold; Subspaces
Keywords: Bayesian inference; Cointegration analysis; Estimation; Grassman manifold; Subspaces