In this paper we develop methods for estimation and forecasting in large time-varying parameter v... more In this paper we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computa-tional constraints with likelihood-based estimation of large systems, we rely on Kalman filter estimation with forgetting factors. We also draw on ideas from the dynamic model averaging literature and extend the TVP-VAR so that its dimension can change over time. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting fac-tor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output, and interest rates demonstrates the feasibility and usefulness of our approach.
This paper proposes a mean field variational Bayes algorithm for efficient posterior and predicti... more This paper proposes a mean field variational Bayes algorithm for efficient posterior and predictive inference in time-varying parameter models. Our approach involves: i) computationally trivial Kalman filter updates of regression coefficients, ii) a dynamic variable selection prior that removes irrelevant variables in each time period, and iii) a fast approximate state-space estimator of the regression volatility parameter. In an exercise involving simulated data we evaluate the new algorithm numerically and establish its computational advantages. Using macroeconomic data for the US we find that regression models that combine time-varying parameters with the information in many predictors have the potential to improve forecasts over a number of alternatives.
In this paper we develop methods for estimation and forecasting in large time-varying parameter v... more In this paper we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computa-tional constraints with likelihood-based estimation of large systems, we rely on Kalman filter estimation with forgetting factors. We also draw on ideas from the dynamic model averaging literature and extend the TVP-VAR so that its dimension can change over time. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting fac-tor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output, and interest rates demonstrates the feasibility and usefulness of our approach.
We forecast quarterly US ination based on the generalized Phillips curve using econometric method... more We forecast quarterly US ination based on the generalized Phillips curve using econometric methods which incorporate dynamic model averaging. These methods not only allow for coe ¢ cients to change over time, but also allow for the entire forecasting model to change over time. We nd that dynamic model averaging leads to substantial forecasting improvements over simple benchmark regressions and more sophisticated approaches such as those using time varying coe ¢ cient models. We also provide evidence on which sets of predictors are relevant for forecasting in each period.
The evolution of monetary policy in the U.S. is examined based on structural dynamic factor model... more The evolution of monetary policy in the U.S. is examined based on structural dynamic factor models. I extend the current literature which questions the stability of the monetary transmission mechanism, by proposing and studying time-varying parameters factor-augmented vector autoregressions (TVP-FAVAR), which allow for fast and efficient inference based on hundreds of explanatory variables. Different specifications are compared where the factor loadings, VAR coefficients and error covariances, or combinations of those, may change gradually in every period or be subject to small breaks. The model is applied to 157 post-World War II U.S. quarterly macroeconomic variables. The results clearly suggest that the propagation of the monetary and non-monetary (exogenous) shocks has altered its behavior, and specifically in a fashion which supports smooth evolution rather than abrupt change. The most notable changes were in the responses of real activity measures, prices and monetary aggregat...
We develop efficient Bayesian estimation algorithms for dynamic factor models with time-varying c... more We develop efficient Bayesian estimation algorithms for dynamic factor models with time-varying coefficients and stochastic volatilities for the purpose of monitoring and forecasting with possibly large macroeconomic datasets in the presence of structual breaks. One algorithm can approximate the posterior mean, and the second algorithm samples from the full joint parameter posteriors. We show that our proposed algorithms are fast, numerically stable, and easy to program, which makes them ideal for real time monitoring and forecasting using flexible factor model structures. We implement two forecasting exercises in order to evaluate the performance of our algorithms, and compare them with traditional estimation methods such as principal components and Markov-Chain Monte Carlo.
This paper should not be reported as representing the views of the European Central Bank (ECB). T... more This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB.
This paper proposes a new Bayesian sampling scheme for VAR inference using sign restrictions. We ... more This paper proposes a new Bayesian sampling scheme for VAR inference using sign restrictions. We build on a factor model decomposition of the reduced-form VAR disturbances, which are assumed to be driven by a few fundamental factors/shocks. The outcome is a computationally efficient algorithm that allows to jointly sample VAR parameters as well as decompositions of the covariance matrix satisfying desired sign restrictions. Using artificial and real data we show that the new algorithm works well and is multiple times more efficient than existing accept/reject algorithms for sign restrictions.
This paper proposes a new Bayesian sampling scheme for VAR inference using sign restrictions. We ... more This paper proposes a new Bayesian sampling scheme for VAR inference using sign restrictions. We build on a factor model decomposition of the reduced-form VAR disturbances, which are assumed to be driven by a few fundamental factors/shocks. The outcome is a computationally efficient algorithm that allows to jointly sample VAR parameters as well as decompositions of the covariance matrix satisfying desired sign restrictions. Using artificial and real data we show that the new algorithm works well and is multiple times more efficient than existing accept/reject algorithms for sign restrictions.
This paper evaluates alternative indicators of global economic activity and other market fundamen... more This paper evaluates alternative indicators of global economic activity and other market fundamentals in terms of their usefulness for forecasting real oil prices and global petroleum consumption. We …nd that world industrial production is one of the most useful indicators that has been proposed in the literature. However, by combining measures from a number of di¤erent sources we can do even better. Our analysis results in a new index of global economic conditions and new measures for assessing future tightness of energy demand and expected oil price pressures.
This Chapter reviews econometric methods that can be used in order to deal with the challenges of... more This Chapter reviews econometric methods that can be used in order to deal with the challenges of inference in high-dimensional empirical macro models with possibly "more parameters than observations". These methods broadly include machine learning algorithms for Big Data, but also more traditional estimation algorithms for data with a short span of observations relative to the number of explanatory variables. While building mainly on a univariate linear regression setting, I show how machine learning ideas can be generalized to classes of models that are interesting to applied macroeconomists, such as time-varying parameter models and vector autoregressions.
This paper proposes a mean field variational Bayes algorithm for efficient posterior and predicti... more This paper proposes a mean field variational Bayes algorithm for efficient posterior and predictive inference in time-varying parameter models. Our approach involves: i) computationally trivial Kalman filter updates of regression coefficients, ii) a dynamic variable selection prior that removes irrelevant variables in each time period, and iii) a fast approximate state-space estimator of the regression volatility parameter. In an exercise involving simulated data we evaluate the new algorithm numerically and establish its computational advantages. Using macroeconomic data for the US we find that regression models that combine time-varying parameters with the information in many predictors have the potential to improve forecasts over a number of alternatives.
This paper proposes a simulation-free estimation algorithm for vector autoregressions (VARs) that... more This paper proposes a simulation-free estimation algorithm for vector autoregressions (VARs) that allows fast approximate calculation of marginal parameter posterior distributions. We apply the algorithm to derive analytical expressions for independent VAR priors that admit a hierarchical representation and which would typically require computationally intensive posterior simulation methods. The benefits of the new algorithm are explored using three quantitative exercises. First, a Monte Carlo experiment illustrates the accuracy and computational gains of the proposed estimation algorithm and priors. Second, a forecasting exercise involving VARs estimated on macroeconomic data demonstrates the ability of hierarchical shrinkage priors to find useful parsimonious representations. We also show how our approach can be used for structural analysis and that it can successfully replicate important features of news-driven business cycles predicted by a large-scale theoretical model.
This paper develops methods for estimating and forecasting in Bayesian panel vector autoregressio... more This paper develops methods for estimating and forecasting in Bayesian panel vector autoregressions of large dimensions with time-varying parameters and stochastic volatility. We exploit a hierarchical prior that takes into account possible pooling restrictions involving both VAR coefficients and the error covariance matrix, and propose a Bayesian dynamic learning procedure that controls for various sources of model uncertainty. We tackle computational concerns by means of a simulation-free algorithm that relies on analytical approximations to the posterior. We use our methods to forecast inflation rates in the eurozone and show that these forecasts are superior to alternative methods for large vector autoregressions.
This paper proposes two distinct contributions to econometric analysis of large information sets ... more This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous predictors, as an equivalent high-dimensional static regression problem with thousands of covariates. Inference in this specification proceeds using Bayesian hierarchical priors that shrink the high-dimensional vector of coefficients either towards zero or time-invariance. Second, it introduces the frameworks of factor graphs and message passing as a means of designing efficient Bayesian estimation algorithms. In particular, a Generalized Approximate Message Passing (GAMP) algorithm is derived that has low algorithmic complexity and is trivially parallelizable. The result is a comprehensive methodology that can be used to estimate time-varying parameter regressions with arbitrarily large number of exogenous predictors. In a forecasting exercise for U.S. price inflation this methodology is shown to work very well.
Machine learning methods are becoming increasingly popular in economics, due to the increased ava... more Machine learning methods are becoming increasingly popular in economics, due to the increased availability of large datasets. In this paper I evaluate a recently proposed algorithm called Generalized Approximate Message Passing (GAMP), which has been popular in signal processing and compressive sensing. I show how this algorithm can be combined with Bayesian hierarchical shrinkage priors typically used in economic forecasting, resulting in computationally efficient schemes for estimating high-dimensional regression models. Using Monte Carlo simulations I establish that in certain scenarios GAMP can achieve estimation accuracy comparable to traditional Markov chain Monte Carlo methods, at a tiny fraction of the computing time. In a forecasting exercise involving a large set of orthogonal macroeconomic predictors, I show that Bayesian shrinkage estimators based on GAMP perform very well compared to a large set of alternatives.
We develop a novel, highly scalable estimation method for large Bayesian Vector Autoregressive mo... more We develop a novel, highly scalable estimation method for large Bayesian Vector Autoregressive models (BVARs) and employ it to introduce an "adaptive" version of the Minnesota prior. This flexible prior structure allows each coefficient of the VAR to have its own shrinkage intensity, which is treated as an additional parameter and estimated from the data. Most importantly, our estimation procedure does not rely on computationally intensive Markov Chain Monte Carlo (MCMC) methods, making it suitable for high-dimensional VARs with more predictors that observations. We use a Monte Carlo study to demonstrate the accuracy and computational gains of our approach. We further illustrate the forecasting performance of our new approach by applying it to a quarterly macroeconomic dataset, and find that it forecasts better than both factor models and other existing BVAR methods.
ABSTRACT We use Bayesian factor regression models to construct a financial conditions index (FCI)... more ABSTRACT We use Bayesian factor regression models to construct a financial conditions index (FCI) for the U.S. Within this context we develop Bayesian model averaging methods that allow the data to select which variables should be included in the FCI or not. We also examine the importance of different sources of instability in the factors, such as stochastic volatility and structural breaks. Our results indicate that ignoring structural breaks in the loadings can be quite costly in terms of the forecasting performance of the FCI. Additionally, Bayesian model averaging can improve in specific cases the performance of the FCI, by means of discarding irrelevant financial variables during the estimation of the factor.
In this paper we develop methods for estimation and forecasting in large time-varying parameter v... more In this paper we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computa-tional constraints with likelihood-based estimation of large systems, we rely on Kalman filter estimation with forgetting factors. We also draw on ideas from the dynamic model averaging literature and extend the TVP-VAR so that its dimension can change over time. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting fac-tor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output, and interest rates demonstrates the feasibility and usefulness of our approach.
This paper proposes a mean field variational Bayes algorithm for efficient posterior and predicti... more This paper proposes a mean field variational Bayes algorithm for efficient posterior and predictive inference in time-varying parameter models. Our approach involves: i) computationally trivial Kalman filter updates of regression coefficients, ii) a dynamic variable selection prior that removes irrelevant variables in each time period, and iii) a fast approximate state-space estimator of the regression volatility parameter. In an exercise involving simulated data we evaluate the new algorithm numerically and establish its computational advantages. Using macroeconomic data for the US we find that regression models that combine time-varying parameters with the information in many predictors have the potential to improve forecasts over a number of alternatives.
In this paper we develop methods for estimation and forecasting in large time-varying parameter v... more In this paper we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computa-tional constraints with likelihood-based estimation of large systems, we rely on Kalman filter estimation with forgetting factors. We also draw on ideas from the dynamic model averaging literature and extend the TVP-VAR so that its dimension can change over time. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting fac-tor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output, and interest rates demonstrates the feasibility and usefulness of our approach.
We forecast quarterly US ination based on the generalized Phillips curve using econometric method... more We forecast quarterly US ination based on the generalized Phillips curve using econometric methods which incorporate dynamic model averaging. These methods not only allow for coe ¢ cients to change over time, but also allow for the entire forecasting model to change over time. We nd that dynamic model averaging leads to substantial forecasting improvements over simple benchmark regressions and more sophisticated approaches such as those using time varying coe ¢ cient models. We also provide evidence on which sets of predictors are relevant for forecasting in each period.
The evolution of monetary policy in the U.S. is examined based on structural dynamic factor model... more The evolution of monetary policy in the U.S. is examined based on structural dynamic factor models. I extend the current literature which questions the stability of the monetary transmission mechanism, by proposing and studying time-varying parameters factor-augmented vector autoregressions (TVP-FAVAR), which allow for fast and efficient inference based on hundreds of explanatory variables. Different specifications are compared where the factor loadings, VAR coefficients and error covariances, or combinations of those, may change gradually in every period or be subject to small breaks. The model is applied to 157 post-World War II U.S. quarterly macroeconomic variables. The results clearly suggest that the propagation of the monetary and non-monetary (exogenous) shocks has altered its behavior, and specifically in a fashion which supports smooth evolution rather than abrupt change. The most notable changes were in the responses of real activity measures, prices and monetary aggregat...
We develop efficient Bayesian estimation algorithms for dynamic factor models with time-varying c... more We develop efficient Bayesian estimation algorithms for dynamic factor models with time-varying coefficients and stochastic volatilities for the purpose of monitoring and forecasting with possibly large macroeconomic datasets in the presence of structual breaks. One algorithm can approximate the posterior mean, and the second algorithm samples from the full joint parameter posteriors. We show that our proposed algorithms are fast, numerically stable, and easy to program, which makes them ideal for real time monitoring and forecasting using flexible factor model structures. We implement two forecasting exercises in order to evaluate the performance of our algorithms, and compare them with traditional estimation methods such as principal components and Markov-Chain Monte Carlo.
This paper should not be reported as representing the views of the European Central Bank (ECB). T... more This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB.
This paper proposes a new Bayesian sampling scheme for VAR inference using sign restrictions. We ... more This paper proposes a new Bayesian sampling scheme for VAR inference using sign restrictions. We build on a factor model decomposition of the reduced-form VAR disturbances, which are assumed to be driven by a few fundamental factors/shocks. The outcome is a computationally efficient algorithm that allows to jointly sample VAR parameters as well as decompositions of the covariance matrix satisfying desired sign restrictions. Using artificial and real data we show that the new algorithm works well and is multiple times more efficient than existing accept/reject algorithms for sign restrictions.
This paper proposes a new Bayesian sampling scheme for VAR inference using sign restrictions. We ... more This paper proposes a new Bayesian sampling scheme for VAR inference using sign restrictions. We build on a factor model decomposition of the reduced-form VAR disturbances, which are assumed to be driven by a few fundamental factors/shocks. The outcome is a computationally efficient algorithm that allows to jointly sample VAR parameters as well as decompositions of the covariance matrix satisfying desired sign restrictions. Using artificial and real data we show that the new algorithm works well and is multiple times more efficient than existing accept/reject algorithms for sign restrictions.
This paper evaluates alternative indicators of global economic activity and other market fundamen... more This paper evaluates alternative indicators of global economic activity and other market fundamentals in terms of their usefulness for forecasting real oil prices and global petroleum consumption. We …nd that world industrial production is one of the most useful indicators that has been proposed in the literature. However, by combining measures from a number of di¤erent sources we can do even better. Our analysis results in a new index of global economic conditions and new measures for assessing future tightness of energy demand and expected oil price pressures.
This Chapter reviews econometric methods that can be used in order to deal with the challenges of... more This Chapter reviews econometric methods that can be used in order to deal with the challenges of inference in high-dimensional empirical macro models with possibly "more parameters than observations". These methods broadly include machine learning algorithms for Big Data, but also more traditional estimation algorithms for data with a short span of observations relative to the number of explanatory variables. While building mainly on a univariate linear regression setting, I show how machine learning ideas can be generalized to classes of models that are interesting to applied macroeconomists, such as time-varying parameter models and vector autoregressions.
This paper proposes a mean field variational Bayes algorithm for efficient posterior and predicti... more This paper proposes a mean field variational Bayes algorithm for efficient posterior and predictive inference in time-varying parameter models. Our approach involves: i) computationally trivial Kalman filter updates of regression coefficients, ii) a dynamic variable selection prior that removes irrelevant variables in each time period, and iii) a fast approximate state-space estimator of the regression volatility parameter. In an exercise involving simulated data we evaluate the new algorithm numerically and establish its computational advantages. Using macroeconomic data for the US we find that regression models that combine time-varying parameters with the information in many predictors have the potential to improve forecasts over a number of alternatives.
This paper proposes a simulation-free estimation algorithm for vector autoregressions (VARs) that... more This paper proposes a simulation-free estimation algorithm for vector autoregressions (VARs) that allows fast approximate calculation of marginal parameter posterior distributions. We apply the algorithm to derive analytical expressions for independent VAR priors that admit a hierarchical representation and which would typically require computationally intensive posterior simulation methods. The benefits of the new algorithm are explored using three quantitative exercises. First, a Monte Carlo experiment illustrates the accuracy and computational gains of the proposed estimation algorithm and priors. Second, a forecasting exercise involving VARs estimated on macroeconomic data demonstrates the ability of hierarchical shrinkage priors to find useful parsimonious representations. We also show how our approach can be used for structural analysis and that it can successfully replicate important features of news-driven business cycles predicted by a large-scale theoretical model.
This paper develops methods for estimating and forecasting in Bayesian panel vector autoregressio... more This paper develops methods for estimating and forecasting in Bayesian panel vector autoregressions of large dimensions with time-varying parameters and stochastic volatility. We exploit a hierarchical prior that takes into account possible pooling restrictions involving both VAR coefficients and the error covariance matrix, and propose a Bayesian dynamic learning procedure that controls for various sources of model uncertainty. We tackle computational concerns by means of a simulation-free algorithm that relies on analytical approximations to the posterior. We use our methods to forecast inflation rates in the eurozone and show that these forecasts are superior to alternative methods for large vector autoregressions.
This paper proposes two distinct contributions to econometric analysis of large information sets ... more This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous predictors, as an equivalent high-dimensional static regression problem with thousands of covariates. Inference in this specification proceeds using Bayesian hierarchical priors that shrink the high-dimensional vector of coefficients either towards zero or time-invariance. Second, it introduces the frameworks of factor graphs and message passing as a means of designing efficient Bayesian estimation algorithms. In particular, a Generalized Approximate Message Passing (GAMP) algorithm is derived that has low algorithmic complexity and is trivially parallelizable. The result is a comprehensive methodology that can be used to estimate time-varying parameter regressions with arbitrarily large number of exogenous predictors. In a forecasting exercise for U.S. price inflation this methodology is shown to work very well.
Machine learning methods are becoming increasingly popular in economics, due to the increased ava... more Machine learning methods are becoming increasingly popular in economics, due to the increased availability of large datasets. In this paper I evaluate a recently proposed algorithm called Generalized Approximate Message Passing (GAMP), which has been popular in signal processing and compressive sensing. I show how this algorithm can be combined with Bayesian hierarchical shrinkage priors typically used in economic forecasting, resulting in computationally efficient schemes for estimating high-dimensional regression models. Using Monte Carlo simulations I establish that in certain scenarios GAMP can achieve estimation accuracy comparable to traditional Markov chain Monte Carlo methods, at a tiny fraction of the computing time. In a forecasting exercise involving a large set of orthogonal macroeconomic predictors, I show that Bayesian shrinkage estimators based on GAMP perform very well compared to a large set of alternatives.
We develop a novel, highly scalable estimation method for large Bayesian Vector Autoregressive mo... more We develop a novel, highly scalable estimation method for large Bayesian Vector Autoregressive models (BVARs) and employ it to introduce an "adaptive" version of the Minnesota prior. This flexible prior structure allows each coefficient of the VAR to have its own shrinkage intensity, which is treated as an additional parameter and estimated from the data. Most importantly, our estimation procedure does not rely on computationally intensive Markov Chain Monte Carlo (MCMC) methods, making it suitable for high-dimensional VARs with more predictors that observations. We use a Monte Carlo study to demonstrate the accuracy and computational gains of our approach. We further illustrate the forecasting performance of our new approach by applying it to a quarterly macroeconomic dataset, and find that it forecasts better than both factor models and other existing BVAR methods.
ABSTRACT We use Bayesian factor regression models to construct a financial conditions index (FCI)... more ABSTRACT We use Bayesian factor regression models to construct a financial conditions index (FCI) for the U.S. Within this context we develop Bayesian model averaging methods that allow the data to select which variables should be included in the FCI or not. We also examine the importance of different sources of instability in the factors, such as stochastic volatility and structural breaks. Our results indicate that ignoring structural breaks in the loadings can be quite costly in terms of the forecasting performance of the FCI. Additionally, Bayesian model averaging can improve in specific cases the performance of the FCI, by means of discarding irrelevant financial variables during the estimation of the factor.
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Papers by Dimitris Korobilis