Macroeconometrics Summer School

Course Overview

This is a course in introductory Bayesian econometrics with a focus on models used in empirical macroeconomics. It begins with a brief introduction to Bayesian econometrics, describing the main concepts underlying Bayesian theory and seeing how Bayesian methods work in the familiar context of the regression model. Computational methods are of great importance in modern Bayesian econometrics, and these are discussed in detail.

Subsequently, the course turns to state space models and discusses estimation of several state space models popularly used in macroeconomics. These include time series models where parameters change over time, models with autocorrelated disturbances, and stochastic volatility models.

The models and methods covered in this course are of direct use in many macroeconomic applications. But they also represent the groundwork that underlies popular multivariate macroeconomic models such as Vector Autoregressions (VARs), time-varying parameter VARs (TVP-VARs), factor and Dynamic Stochastic General Equilibirum (DSGE) models.

Prerequisites

Basic knowledge of time series econometrics.

Course Outline

1. Introduction: Review of the classical linear regression model. Maximum likelihood estimation. The Bayesian approach to the classical linear regression model. Bayes formula. The likelihood principle. James – Stein result. Ridge regression. 
2. Bayesian estimation of the CLRM: Theil mixed estimator. Prior selection via the marginal data density. The independent Normal-Inverse Gamma prior. Treatment of the error variance. The chi-square, gamma, and inverse gamma distributions. Gibbs sampling. Convergence and mixing. The Natural – Conjugate prior. Marginal data density. The Normal-diffuse and Jeffrey’s prior. 
3. The Generalized Linear Regression Model: Autocorrelation and Heteroskedasticity. Stochastic volatility models. Metropolis Hastings algorithms. Independence Metropolis. Random Walk Metropolis. 
4. Linear and Gaussian state space models: Forward filtering/backward sampling algorithms. Carter-Kohn algorithm. Models with time varying coefficients. 
5. Non-linear non-Gaussian state space models: The Kim, Shepard, and Chib algorithm for stochastic volatility models. Sequential Monte Carlo methods. 

List of References

• Koop, G. (2003). Bayesian Econometrics, published by Wiley.
• Koop, G. (2016). Bayesian Methods for Fat Data.
• Chan, J., Koop, G., Poirier, D. and Tobias, J. (2019). Bayesian Econometric Methods, second edition, published by Cambridge University Press.

Software/Hardware

LAPTOP REQUIRED. In order to participate in practical sessions, you must bring your own portable computer.

About the Instructor

Andrea Carriero is Professor of Economics at Queen Mary University of London and at the University of Bologna. He has been a consultant for the UK Treasury Debt Management Office, and has previously worked in the Monetary Policy Strategy division of the European Central Bank. He has been a research visitor at the Federal Reserve Banks of New York and a visiting scholar at the University of Pennsylvania.

Andrea has an extensive experience in teaching a variety of hand-on courses on applied and financial econometrics in universities and central banks.

His research focuses on empirical macroeconomics and forecasting, with a particular emphasis in Bayesian methods and large datasets. He has published in several peer-reviewed international journals including the Journal of Econometrics, Review of Economics and Statistics, Journal of Business and Economics Statistics, International Economic Review, Journal of Applied Econometrics, and the Journal of the Royal Statistical Society.

Course Overview

Introduced to econometrics by Nobel laureate Chris Sims and his students, Bayesian VAR methods have recently become the workhorse models for forecasting macroeconomic variables and are routinely used by central banks to inform policy decisions.

The two key characteristics of these methods is the possibility of handling very large cross-section of data –thereby including a large information set to base forecasts on- and the possibility of specifying a-priori beliefs on the behavior of macroeconomic time series. More recent developments extended these models to account for time variation in the coefficients and volatilities, which dramatically improve the accuracy of density forecasts and now-casts.

This course aims at introducing state of the art methods for structural analysis and forecasting with Bayesian Vector Autoregressions. The course has a hands-on philosophy and Matlab code will be provided for each of the topics covered.

At the end of the course students will be able to specify and estimate a variety of multivariate linear models featuring drifting coefficients and volatilities, to produce real-time forecasts and now-casts, and to assess forecast uncertainty via fan charts.

Prerequisites

Basic knowledge of multivariate time series econometrics.

Students should be familiar with the concept of linear regression models, the least squares estimator, and the definition of the likelihood function.

Good knowledge of basics of Bayesian computation and linear regression using conjugate priors would be beneficial. It is not necessary to have a deep understanding of asymptotic theory, test statistics, GMM, EM algorithms or other classical concepts before attending this course.

We will need to rely heavily on distributions such as the Normal, Gamma, and Wishart, so students should be familiar with the concept of a p.d.f., a c.d.f., and their basic functional forms. Computations are in MATLAB. I will provide all the code in a very accessible form, so that even students with no knowledge of programming can attend this class. Nevertheless, students who are serious about using Bayesian macroeconometrics are expected to have some basic MATLAB skills (e.g. know how to estimate a VAR with OLS using basic commands).

Course Outline

1. Introduction to Vector Autoregressions. Forecasting formulae. Classical estimation of VAR models. Curse of dimensionality. Bayes formula. The likelihood principle. Common misconceptions about unit roots and cointegration. The Minnesota prior.
2. Bayesian Vector Autoregressions. The independent Normal-Inverse Wishart prior. Gibbs sampling. The conjugate Normal-Inverse Wishart prior. Monte Carlo sampling. Marginal likelihood. Hierarchical priors. Priors from DSGE models.
3. VARs with time varying coefficients. Forward filtering/backward sampling algorithms. Carter-Kohn algorithm.
4. VARs with time varying volatilities. Metropolis Hastings algorithms. The Jacquier-Polson-Rossi approach. Volatility in mean model. Leverage model.
5. Large Bayesian VARs. Homoskedastic VARs with conjugate prior. Triangularization. Large Bayesian VARs with drifting volatilities and non- conjugate priors. Density forecasting and fan charts.

List of References

1. Banbura, M., Giannone, D., and Reichlin, L., 2010. Large Bayesian Vector Autoregressions, Journal of Applied Econometrics 25, 71-92.
2. Carriero A., Clark, T. and Marcellino, M., 2019. Large Bayesian VARs with time varying volatility and non-conjugate priors. Journal Econometrics, forthcoming.
3. Cogley, T., and Sargent, T., 2005. Drifts and Volatilities: Monetary Policies and Outcomes in the post-WWII US, Review of Economic Dynamics 8, 262-302.
4. Del Negro, Marco, and Schorfheide Frank, Priors from General Equilibrium Models for VARS, International Economic Review, Volume 45, Number 2, p.643–673, (2004).
5. Jacquier, E., Polson, N.G., Rossi, P. E., 1994, Bayesian Analysis of Stochastic Volatility Models. Journal of Business & Economic Statistics 20(1), 69-87.
6. Kadiyala, K., and Karlsson, S., 1997. Numerical Methods for Estimation and Inference in Bayesian VAR-Models, Journal of Applied Econometrics 12, 99-132.
7. Kim, S., Shephard, N. and S. Chib, 1998. Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models. Review of Economic Studies 65, 361-393.
8. Litterman, R., 1986. Forecasting with Bayesian Vector Autoregressions-Five Years of Experience, Journal of Business and Economic Statistics 4, 25-38.
9. Primiceri, G., 2005. Time Varying Structural Vector Autoregressions and Monetary Policy, Review of Economic Studies 72, 821-852.

Software/Hardware

LAPTOP REQUIRED. In order to participate in practical sessions, you must bring your own portable computer.

About the Instructor

Andrea Carriero is Professor of Economics at Queen Mary University of London and at the University of Bologna. He has been a consultant for the UK Treasury Debt Management Office, and has previously worked in the Monetary Policy Strategy division of the European Central Bank. He has been a research visitor at the Federal Reserve Banks of New York and a visiting scholar at the University of Pennsylvania.

Andrea has an extensive experience in teaching a variety of hand-on courses on applied and financial econometrics in universities and central banks.

His research focuses on empirical macroeconomics and forecasting, with a particular emphasis in Bayesian methods and large datasets. He has published in several peer-reviewed international journals including the Journal of Econometrics, Review of Economics and Statistics, Journal of Business and Economics Statistics, International Economic Review, Journal of Applied Econometrics, and the Journal of the Royal Statistical Society.

Course Overview

The objective of the course is to teach student how to use state-of-the-art Bayesian methods to estimate and analyze modern macroeconomic models. The course will cover the most popular methods to construct posterior estimates of structural model parameters and probability intervals for arbitrary model outputs (such as impulse response functions and variance decompositions). Special attention will be given to recent advances in empirically analyzing the role of news, noise and imperfect information in business cycle models. The course aim to give students a good understanding of both advantages and limitations of the current generation of DSGE models.

Matlab programs to implement the theoretical methods and replicate the applications studied in class will be made available to students.

Course Outline

1. Macro models as data generating processes
   • Models for forecasting and for policy making
   • The building blocks of modern macro models
   • Linearized macro models as state space systems
   • Limitations of empirical models
2. State Space Models and Likelihood based estimation
   • The Kalman filter
   • The likelihood function for linear Gaussian models
   • Numerical maximization of the likelihood
3. Bayesian Estimation of DSGE models
   • Bayesian and frequentist methods
   • Priors, data, posteriors
   • Choosing priors for macro models
   • Estimating DSGE models using the Metropolis-Hastings algorithm
4. Bayesian analysis of DSGE models
   • Constructing probability intervals
   • Prior predictive analysis
   • Bayesian model comparison
5. Structural empirical models of news, noise and imperfect information
   • News and noise: Identifying the effect of sentiment shocks
   • Using survey data in likelihood based estimation
   • The Kalman simulation smoother

List of References

• Canova, F. 2007, Methods for Applied Macroeconomic Research, Princeton University Press.
• Geweke, J. 2005, Contemporary Bayesian Econometrics and Statistics, Wiley-Interscience.
• Hamilton J. D. 1994, Time Series Analysis, Princeton University Press.
• Koop, G. 2003, Bayesian Econometrics, Wiley.

In addition to the text book references above, a list of the relevant research articles will be provided.

Software/Hardware

LAPTOP REQUIRED. In order to participate in practical sessions, you must bring your own portable computer.

About the Instructor

Kristoffer Nimark is Professor of Economics at Cornell University. Before this he was Researcher at the Center for Research on International Economics (CREI), Adjunct Professor at Universitat Pompeu Fabra, and Affiliated Professor of the Barcelona School of Economics. He has also been a Visiting Assistant Professor at New York University and Senior Research Manager at the Reserve Bank of Australia.

Course Overview

This course deals with factor models for large cross-sections of time-series (large N environment). We build the argument in steps, starting from the simplest multivariate technique, principal components.

We then discuss “small N” factor models for cross-sectional data and study how to estimate factor models with the EM algorithm.

We then review dynamic “small N” models for time-series, the associated state-space form and the Kalman filter and smoother, which are typically used to estimate those models.

Moving to the “large N” environment, first with cross-sectional data and then with time-series data, we discuss the link between factors and principal components. We clarify the distinction between static and dynamic factors and highlight how “large N” dynamic factor models can be used to perform structural analysis by using techniques similar to those used in Structural VAR models.

In this context, we review several applications, among others, factor augmented VAR models (FAVAR), the construction of business cycle indicators, how to handle the jagged nature of macroeconomic data releases in nowcasting and forecasting exercises, the analysis of monetary policy in real time, the identification of the monetary transmission mechanism, the identification of news shocks to technology.

If time permits, we will discuss non-invertibilities and the relation to factor models.

Matlab programs to implement the theoretical methods and replicate the applications studied in class will be made available to students.

Prerequisites

Good knowledge of time series econometrics, in particular VAR analysis.

Course Outline

1. Factor Models
   • Principal components estimator.
   • Small N, i.i.d. and dynamic, the EM algorithm, Kalman filter/smoother.
   • Large N, i.i.d. and dynamic. Consistency at large: a law of large numbers in the cross-section.
   • Applications: Commonality in European regions, new Eurocoin, monetary policy in real time, nowcasting, measuring macroeconomic uncertainty.
2. Structural Factor model (SFM)
   • Specification and estimation.
   • Tools: Impulse response functions, variance decomposition, historical decomposition.
   • Identification: Short and long-run zero, sign restrictions, penalty function approach.
   • DSGE and Factor models.
   • Applications: Monetary policy shocks, house prices, disaggregated prices.
3. Factor augmented VAR (FAVAR)
   • Applications: Monetary Policy, news shocks.
   • Testing non-invertibility.

Software/Hardware

LAPTOP REQUIRED. In order to participate in practical sessions, you must bring your own portable computer.

About the Instructor

Luca Sala is Associate Professor at the Ettore Bocconi Department of Economics and Research Fellow of IGIER (Innocenzo Gasparini Institute for Economic Research). He took part in the Graduate Research Program of the European Central Bank and was Visiting Student at Tel Aviv University. He has been a visiting scholar at the Department of Economics, New York University. He taught at the Università Nova de Lisboa and University of Oslo. He did research at the European Central Bank and Norges Bank. He has a PhD from the European Center for Advanced Research in Economics and Statistics (ECARES), at the Université Libre de Bruxelles (ULB).

Course Overview

The course provides an introduction to the state-of-the-art econometric and statistical techniques used for the analysis of large panels of economic and financial time series.

The course begins by reviewing the properties of the classic linear regression model in a large dimensional environment. It then introduces some of the most popular methodologies used to carry out estimation in such a setting, namely regularized estimation techniques such as Ridge, LASSO and Elastic-net. The course then focuses on showing how this methodology can be used for forecasting economic and financial time series using large panels. These techniques are applied to carry out forecasting using the FRED-MD dataset.

The second topic of the course is covariance matrix estimation in large dimensions. It is shown that the performance of the classic sample covariance estimator is poor when the dimensionality of the covariance is large. This motivates a large literature that proposes to regularize the sample covariance using a number of different strategies. In particular, the course focuses on the class of shrinkage estimators proposed by Ledoit and Wolf. These methods are illustrated with an application to asset allocation.

The third and final topic of the course is the estimation of large dimesional network models. It is shown how the estimation of these models can be cast as either a large covariance or a large Vector Autoregression estimation problem subject to appropriate sparsity constrainst. These network techiniques are then applied to estimate the CDS credit risk network of the European financial system as well to estimate the Granger volatility risk network of the US financial system.

Prerequisites

Basic knowledge of matrix algebra, econometrics and time series econometrics.

Course Outline

1. Estimation and Regularization of Large Dimensional Regression Models
   • Linear regression model estimation and regularization in large dimensions, Ridge regression, LASSO regression, Elastic-net.
2. Forecasting Using Large Dimensional Panels of Time Series
   • Forecasting using factor, shrinkage and hybrid methods.
   • Application: Forecasting using the FRED-MD dataset
3. Large Dimensional Covariance Estimation
   • Covariance matrix estimation in large dimensions, the Marchenko–Pastur law, Ledoit & Wolf shrinkage estimators.
   • Application: Asset allocation for large dimensional panels of assets
4. Large Dimensional Network Estimation
   • Network models, contemporaneous Network models and covariance estimation, Granger Network models and VAR estimation.
   • Application: Estimation of the CDS credit risk network of the European financial system, Estimation the Granger volatility risk network of the US financial system.

List of References

• Bai, J. and Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70, 191-221.
• Bai, J. and Ng, S. (2008). Forecasting economic time series using targeted predictors. Journal of Econometrics, 146, 304-317.
• Bai, J. and Ng, S. (2009). Boosting di¤usion indices. Journal of Applied Econometrics, 24, 607-629.
• Barigozzi, M. and Brownlees, C. NETS: Network Estimation for Time Series. Journal of Applied Econometrics, 2019, 34, 347-364
• Brownlees, C. Nualart, E. and Yucheng, S. Realized Networks. Journal of Applied Econometrics 2018, 33, 986-1006
• Bühlmann, P. and S. van de Geer (2011). Statistics for High–Dimensional Data: Methods, Theory and Applications. New York: Springer.
• Dahlhaus, R. (2000). Graphical Interaction Models for Multivariate Time Series. Metrika 51, 157–172.
• De Mol, C., D. Giannone, and L. Reichlin (2008). Forecasting Using a Large Number of Predictors: Is Bayesian Shrinkage a Valid Alternative to Principal Components? Journal of Econometrics 146, 318–328.
• Diebold, F. and K. Yilmaz (2009). Measuring financial asset return and volatility spillovers, with application to global equity markets. Economic Journal, 158–171.
• Diebold, F. and K. Yilmaz (2015). Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring. Oxford University Press.
• Fan, J., Fan, Y., and Lv, J. (2008). High Dimensional Covariance Matrix Estimation using a Factor Model. Journal of Econometrics, 147, 186-197
• Friedman, J., T. Hastie, and R. Tibshirani (2008). Sparse Inverse Covariance Estimation with the Graphical Lasso. Biostatistics 9, 432–441.
• Hautsch, N., J. Schaumburg, and M. Schienle (2012). Financial Network Systemic Risk Contributions. Technical report, Discussion Paper 2012-053, CRC 649, Humboldt-Universität zu Berlin.
• Kock, A. B. (2012). On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions. CREATES Research Papers 2012-05, School of Economics and Management, University of Aarhus.
• Ledoit, O. and Wolf, M. (2004). A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices. Journal of Multivariate Analysis, 88, 365-411
• Ledoit, O. and Wolf, M. (2012). Nonlinear Shrinkage Estimation of Large-Dimensional Covariance Matrices. Annals of Statistics, 40, 1024-1060
• Stock, J. H. and Watson, M. W. (2002). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97, 1167–1179.
• Stock, J. H. and Watson, M. W. (2004). Combination forecasts of output growth in a seven-country data set. Journal of Forecasting, 23, 405–430.

Software/Hardware

LAPTOP REQUIRED. In order to participate in practical sessions, you must bring your own portable computer.

About the Instructor

Christian Brownlees is Associate Professor in the Department of Economics and Business at Universitat Pompeu Fabra and BSE Affiliated Professor. He obtained his PhD in Statistics in 2007 from the University of Florence and was a Post-Doc Research Fellow at NYU Stern until 2011. Christian’s research focuses on time-series analysis for financial and macro applications. His research has been published among others in the Journal of Econometrics, Annals of Statistics and the Review of Financial Studies.

Course Overview

The course is an introduction to time series analysis. The goal of the course is to provide students with the foundational concepts of time series econometrics and the knowledge of some popular time series models. The course, open to anyone, can be especially useful to participants of the Barcelona Macroeconometrics Summer School who want to acquire the necessary knowledge or strengthen their skills in this field, before starting the more specialized courses.

The course includes 10 hours of theory lectures and 10 hours of practical sessions. 

Course Outline

1. Preliminary Concepts.
2. Autoregressive (AR) and Moving Average (MA) models.
3. Likelihood function and the estimation of AR and MA models.
4. Introduction to Vector Autoregressive (VAR) and Vector Moving Average (VMA) models.
5. Likelihood function and the estimation of VAR models.
6. Bayesian econometric preliminaries.

Software/Hardware

MATLAB

About the Instructor

Konstantin Boss is a doctoral researcher at UAB and BSE. His research interests include non-linear dynamics in time series econometrics, structural factor models and migration forecasting. His research is funded by the Spanish Ministerio de ciencia e innovación (FPI) grant.

Course Overview

The objective of this course is twofold: 

First, to present some of the most popular time series models designed to analyze the propagation mechanisms and measure the effects of economic shocks. In particular, we will cover in details Structural Vector Autoregressive models with a special focus on several identification schemes used in the literature. We also present several extensions like and FAVARs and Time-Varying Coefficients VAR.

The second objective is to discuss some recent applications of these models in economics. The focus will be on monetary and fiscal policy shocks, news shocks, technology shocks and stock market bubbles.

Matlab programs to implement the theoretical methods and replicate the applications studied in class will be made available to students.

Prerequisites

Basic knowledge of univariate time series models (ARMA models).

Course Outline

1. Structural VAR (SVAR)
   1. The model: Representation, estimation.
   2. Tools: Impulse response functions, variance decomposition, historical decomposition.
   3. Identification: short and long-run zero, sign restrictions, penalty function approach, mixed restrictions, external instruments, narrative approach.
   4. Applications: Monetary and fiscal policy shocks, technology shocks, news shocks, uncertainty shocks.
   5. Local Projections
2. Factor Augmented (FAVAR)
   1. Representation, estimation, identification of structural shocks. Application: Monetary Policy.
3. Time-Varying Coefficients VAR
   1. The model: representation and estimation.
   2. Applications: the Great Moderation and monetary policy.

Software/Hardware

LAPTOP REQUIRED: In order to participate in practical sessions, you must bring your own portable computer.

About the Instructor

Luca Gambetti is Associate Professor of Economics at UAB and BSE Associate Research Professor. He is a research fellow of MOVE (Markets, Organizations and Votes in Economics) and an external member of RECent. He obtained his PhD in Economics from Universitat Pompeu Fabra in 2006. Luca's research focuses on quantitative macroeconomics and applied time series analysis. His research has been published among others in the Journal of Monetary Economics, the Economic Journal, the Journal of Applied Econometrics and the American Economic Journal: Macro.

Course Overview

After covering the most popular linear time series models designed to analyze the propagation mechanisms of policy measures and the dynamic effects of economic shocks during the course Time Series Methods for Macroeconomic Analysis I, we now open to the possibility of non-linearities. Building on the lessons learned during that course (or from your own previous knowledge of the topic), we allow for the fact that the same measures or the same shocks might have different, non-proportional, impact on the main macroeconomic variables, depending on the size, moment and sign of the measures and shocks.

Understanding these features implies the need to properly infer the state of the economy in real time, in order to provide timely valuable information to rapidly design and implement the necessary policy responses. This is especially important in the deep COVID-19 recession that we have recently experienced.

Prerequisites

Basic knowledge of time series econometrics.

Course Outline

1. Markov Switching Models
   • Univariate Specification
   • Dynamic factor MS models. Use of high frequency data
   • Dynamic factor models with time varying parameters
   • MS VAR models
   • Applications: Real time turning point detection. Generalized Impulse response, Monetary policy effects across the business  cycle. Financial and real cycles. The role of credit.
2. Threshod and Smooth Threshold Models
   • Univariate Specification
   • Threshold VAR, Smooth Transition VAR
   • Applications: Fiscal policy shocks in booms and recessions.
   • Nonlinear MA and local projections

List of References

• Canova, F. 2007, Methods for Applied Macroeconomic Research, Princeton University Press.
• Geweke, J. 2005, Contemporary Bayesian Econometrics and Statistics, Wiley-Interscience.
• Hamilton J. D. 1994, Time Series Analysis, Princeton University Press.
• Koop, G. 2003, Bayesian Econometrics, Wiley.

In addition to the text book references above, a list of the relevant research articles will be provided.

Software/Hardware

LAPTOP REQUIRED. In order to participate in practical sessions, you must bring your own portable computer.

About the Instructor

Gabriel Pérez-Quirós (PhD, University of California San Diego) is the Unit Head of Macroeconomic Research in the Research Department of the Bank of Spain. He previously worked on business cycle research at the United States Federal Reserve Bank of New York and the European Central Bank.

Gabriel also worked as an advisor in the Economic Bureau of the Spanish Prime Minister and has been consultant for the European Commission, the European Central Bank, United Nations and the World Bank. He was a member of the Scientific Committee of the Euro Area Business Cycle Network. He is a Research Affiliate of the Centre for Economic Policy Research (CEPR) and was co-editor of SERIES, Journal of the Spanish Economic Association.

He has published extensively on applications of non-linear models to the analysis of economic and financial variables over the business cycle. He teaches PhD courses at the Universidad de Alicante where he has supervised several dissertations on these topics.