Macroeconometrics Summer School

* Laptop required In order to participate in practical sessions, you must bring your own portable computer.

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

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.

About the Instructor

Kristoffer Nimark was Researcher at the Center for Research on International Economics (CREI), Adjunct Professor at Universitat Pompeu Fabra, and Affiliated Professor of the Barcelona GSE until 2014. Previously he was a Visiting Assistant Professor at New York University and Senior Research Manager at the Reserve Bank of Australia.

* Laptop required In order to participate in practical sessions, you must bring your own portable computer.

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 re- gression model. Computational methods are of great importance in modern Bayesian econometrics and these are discussed in detail.

In macroeconomics, we often have Big Data and work with models where the number of parameters to be estimated is large relative to the number of observations in the data set. A range of Bayesian methods have been derived for dealing with Big Data including Bayesian model averaging (BMA), stochastic search variable selection (SSVS) and the least absolute shrinkage and selection operator (LASSO). The second part of the course covers these methods and shows how they are applied in the context of the regression model. 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 regime change 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 Autoregres- sions (VARs), time-varying parameter VARs (TVP-VARs), factor and Dynamic Stochastic General Equilibirum (DSGE) models. 

Background

The course assumes that participants have some background knowledge of econometrics (e.g. obtained from a graduate level or senior undergraduate level econometrics course), but will assume no prior knowledge of Bayesian methods. I will assume that participants have a basic knowledge of probability (i.e. definitions and rules relating to conditional, marginal and joint probabilities and definitions and properties of common distributions such as the Normal and t- distributions). In addition, the participant should have a knowledge of basic matrix algebra. The Appendices to Koop (2003) provide a summary of the probability theory and matrix algebra used in this course.

Course Content

Code for references: K = Koop (2003), KPT = Koop, Poirier and Tobias (2007), Ko = Korobilis (2013)

Topic 1: Bayesian Basics


i) An Overview of Bayesian Econometrics (Reading: K, Chapter 1).


ii) Bayesian inference in the Normal linear regression model. Computational topic: Monte Carlo integration
Reading: K, Chapters 2 and 3.


iii) Bayesian treatment of the regression model with general error covariance matrix (Reading: K, pages 117-121 and 130-137)
 Computational topic: Gibbs sampling (Reading: K pages 62-68) and the Metropolis-Hasting algorithm (Reading, K pages 92-99).

Topic 2: Bayesian Model Averaging and Model Selection

i) Bayesian Model Averaging (BMA) (K, Chapter 11 and KPT, pages 281- 287) Computational topic: Markov Chain Monte Carlo Model Composition (MC3)

ii) Prior shrinkage: empirical Bayes and training sample priors (Ko)


iii) Stochastic Search Variable Selection (KPT, pages 287-289)


iv) The Bayesian Lasso (Ko)

Topic 3: Bayesian State Space Modelling

Reading: KK, section 3 and K, chapter 8.


i) The Normal linear state space model


ii) Linearized DSGE models as state space models


iii) Dynamic mixture models for modelling breaks and regime change


iv) Stochastic volatility


v) Forecasting with TVP regression models (including dynamic model averaging)

Reading 

Most of the material is taken from the textbook: Koop, G. (2003). Bayesian Econometrics. I also have a book of solved exercises that I will draw on occasionally: Koop, G., Poirier, D. and Tobias, J. (2007). Bayesian Econometric Methods, Cambridge University Press, (Volume 7 in the Econometrics Exercises Series edited by Karim Abadir, Jan Magnus and P.C.B Phillips). A good reference for the Big Data material covered in the course is: Korobilis, D. (2013). "Hierarchical shrinkage priors for dynamic regressions with many predictors," International Journal of Forecasting, 29, 43-59.

I end the course with an application to inflation forecasting based on:

Koop, G. and Korobilis, D. (2012). Forecasting inflation using dynamic model averaging, International Economic Review

About the Instructor

Dimitris works in the fields of applied econometrics, macroeconomics and finance. He has a wide range of publications in economics and econometrics journals, such as the European Economic Review, International Economic Review, and the Journal of Econometrics. He is currently in the top 3% of authors in the world according to the website RePEc, collecting data for over 45,000 economists worldwide. Among a rich list of professional activities, Dimitris has been a visitor of the Deutsche Bundesbank; visiting assistant professor at Universite de Rennes 1; and has worked as an external consultant for the European Central Bank, the South African Reserve Bank, and the Scottish Government. He has a vast teaching experience, having delivered specialized courses and summer-schools in ECB, Bundesbank, Queen Mary, and Barcelona GSE, among others.

* Laptop required In order to participate in practical sessions, you must bring your own portable computer.

Course overview

The main aim of this course is to help students develop an understanding of Bayesian methods in the analysis of multivariate macroeconomic time series. The emphasis throughout this course is on Bayesian estimation and computation, and specication of exible models. Several topics will be covered including static and dynamic factor models, Bayesian shrinkage priors, multivariate stochastic volatility, vector autoregressions, panel vector autoregressions, and estimation of multivariate models for Big Data. This short course will introduce a very large spectrum of time series models used in macroeconomics and nance. Instead of focusing on the theoretical time-series properties of these popular models, we will delve deeply into estimation issues which are of practical importance for PhD students and applied researchers. As an illustration, students will learn how to estimate Bayesian linear static factor models for the mean of a time series, as well as univariate stochastic volatility models using the Gibbs sampler. Then enough guidance and hints will be given so that students can independently combine this knowledge to estimate state-of-the-art econometric models such as the factor stochastic volatility model to test Asset Pricing Theory. The focus of this course will be on estimation and computation. We focus on the Gibbs sampler which allows us to estimate a large class of models (e.g. Markov Switching models, time-varying parameter VARs, dynamic factor models, stochastic volatility models). I also make references to estimation of Bayesian DSGE models using Metropolis-Hastings algorithm without, however, getting into details (this is a separater topic that cant be covered in detial in this course).

Who should attend this course

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

Deep understanding of asymptotic theory, test statistics, GMM, EM algorithms or other classical concepts is NOT needed for this course. However, good knowledge of basics of Bayesian computation and linear regression using conjugate priors would be benecial. 

We will need to rely heavily on distributions such as the Normal, Bernoulli, 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).

Readings and resources

1. Bauwens, L. and Korobilis, D. (2013). Bayesian Methods, in Handbook of Research Methods and Applications on Empirical Macroeconomics.
2. Koop, G. and Korobilis, D. (2010). Bayesian Multivariate Time Series Methods for Empirical Macroeconomics, Foundations and Trends in Econometrics, 3, pp. 267-358.
3. Koop, Gary (2003) Bayesian Econometrics, Wiley.
4. Koop, G., Poirier, D. and Tobias, J. (2007) Bayesian Econometric Exercises, Cambridge University Press
5. Further references will be given during the course

Lecture Outline

1. Lecture I: Multivariate models; Bayesian Vector Autoregression; Static Factor Model
2. Lecture II: State-space models and Bayesian ltering; Dynamic Factor Model; Multivariate Stochastic Volatility models; Generic estimation of DSGE systems
3. Lecture III: Special Topics 1:panel VARs; Bayesian Global VARs; Factor augmented VARs; Hierarchical Dynamic Factor Models
4. Lecture IV: Special Topics 2: Models with time-varying parameters; Markov Switching VARs
5. Lecture V: Special Topics 3: Estimating models for Big Data

About the Instructor

Gary Koop is a Professor in the Department of Economics at the University of Strathclyde. He received his PhD from the University of Toronto in 1989. He has held university posts in the UK, the US and Canada. His research interests lie in the field of Bayesian econometrics with a particular focus on macroeconometrics. He has a wide range of publications of theoretical and empirical work within this field. He has written several textbooks including Bayesian Econometrics and Bayesian Econometric Methods (co-authored with Dale Poirier and Justin Tobias). He is co-editor (with John Geweke and Herman van Dijk) of the Oxford Handbook of Bayesian Econometrics.

* Laptop required In order to participate in practical sessions, you must bring your own portable computer.

Course overview

The objective of the 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 macroeconomic shocks. In particular we will cover Structural Vector Autoregressive models as well as several extensions like the Factor Augmented VAR, Smooth transition VAR, Threshold VAR and Time-Varying Coefficients VAR. The second objective is to discuss some recent applications of these models in macroeconomics. The focus will be on monetary and fiscal policy shocks, news shocks and technology shocks among others. Matlab programs to implement the theoretical methods and replicate the applications studied in class will be made available to students.

Requirement: basic knowledge of econometrics and time series econometrics.

Course Outline

I. Structural VAR (SVAR) models
Preliminaries. Representation. Estimation. Identification: short run restrictions, long-run restrictions, sign restrictions, penalty function approach, mixed restrictions, the Stock and Watson approach, narrative approach.

II. Structural VAR (SVAR) models 
Applications. Monetary and Fiscal policy shocks. Technology shocks and News shocks. Uncertainty shocks

III. Factor Augmented VAR (FAVAR)
Representation. Estimation. Infefence. Applications: Monetary policy shocks and the price puzzle. Monetary policy and state-level house prices. Credit market shocks. Micro-level bank behavior and aggregate shocks.

IV. Threshold VAR (TVAR) and Smooth Transition VAR (STVAR)
Application: Fiscal policy shocks in booms and recessions.

V. Time-Varying Coefficients Models
Theory. Applications: the Great Moderation, monetary policy and stock market bubbles

References

1. Auerbach, A. and Y. Gorodnichenko, 2012. "Measuring the Output Responses to Fiscal Policy," American Economic Journal: Economic Policy, American Economic Association, vol. 4(2), pages 1-27, May.
2. Bernanke, B. S., Boivin, J. and Eliasz, P., 2005, Measuring monetary policy: a factor augmented autoregressive (FAVAR) approach, The Quarterly Journal of Economics 120, pp. 387-422.
3. Blanchard, O.J. and R. Perotti (2002). An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output, The Quarterly Journal of Economics: 1329-1368.
4. Boivin, J.,. M. P. Giannoni and I. Mihov, 2009. "Sticky Prices and Monetary Policy: Evidence from Disaggregated US Data," American Economic Review, American Economic Association, vol. 99(1), pages 350-84,
5. Boivin, J., M. P. Giannoni,, and D. Stevanovic, 2013. "Dynamic Effects of Credit Shocks in a Data-Rich Environment,"CEPR Discussion Papers 9470, C.E.P.R. Discussion Papers.
6. Buch, C. M., S. Eickmeier, and E. Prieto, 2014. "Macroeconomic Factors and Microlevel Bank Behavior," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 46(4), pages 715-751,
7. Burnside, C., M. Eichenbaum, and J. D. Fisher (2004). Fiscal Shocks and Their Consequences. Journal of Economic Theory 115, 89-117.
8. Canova F, and Gambetti L. 2009. Structural Changes in the US Economy: Is There a Role for Monetary Policy?. Journal of Economic Dynamics and Control, 33(2):477-490.
9. Cogley T, and Sargent T. J. (2001). Evolving Post WWII U.S. Ination Dynamics. In Macroeconomics Annual, 331-373. MIT Press.
10. Cogley T, and Sargent T. J. (2005). Drifts and Volatilities: Monetary Policies and Outcomes in the Post WWII US. Review of Economic Dynamics, 8: 262-302.
11. Edelberg, W., M. Eichenbaum, and J. D. Fisher (1999). Understanding the Effects of a Shock to Government Purchases. Review of Economic Dynamics 2 (1), 166-206.
12. Eichenbaum, M. and J. D. Fisher (2005). Fiscal Policy in the Aftermath of 9/11. Journal of Money, Credit and Banking 37 (1), 1-22.
13. Fatas, A. and I. Mihov (2001). The E_ects of Fiscal Policy on Consumption and Employment: Theory and Evidence. CEPR Discussion Paper No. 2760.
14. Fisher J.D.M. and R. Peters (2010). Using Stock Returns to Identify Government Spending Shocks. The Economic Journal 120, 414-436.
15. Gali, J., D. Lopez Salido, and J. Valles (2007). Understanding the Effects of Government Spending on Consumption. Journal of the European Economic Association 5, 227-270.
16. Gali J, and Gambetti L. (2009). On the sources of the Great Moderation. American Economic Journal: Macroeconomics, 1(1):26-57.
17. Gali J, and Gambetti L. The Effects of Monetary Policy on Stock Market Bubbles: Some Evidence. Forthcoming American Economic Journal: Macroeconomics, 1(1):26-57.
18. Gilchrist, S., V. Yankov, and E. Zakrajsek (2009): “Credit Market Shocks and Economic
19. Fluctuations: Evidence From Corporate Bond and Stock Markets,” Journal of Monetary Economics, 56, 471–493.
20. Granger, Clive W., and Timo Terasvirta. 1993. Modelling Nonlinear Economic Relationships.
21. New York: Oxford University Press.
22. Hamilton J. D. 1994, Time Series Analysis, Princeton University Press: Princeton.
23. Koop, Gary, M. Hashem Pesaran, and Simon M. Potter. 1996. “Impulse Response Analysis in Nonlinear Multivariate Models.” Journal of Econometrics 74(1): 119-147.
24. Lutkepohl, H. 2005, New Introduction to Multiple Time Series, Springer-Verlag: Berlin.
25. Mertens and M. O. Ravn, (2010). "Measuring the Impact of Fiscal Policy in the Face of Anticipation: A Structural VAR Approach," Economic Journal, Royal Economic Society, vol. 120(544), pages 393-413, 05.
26. Mertens, K and M. O Ravn, (2011). "Understanding the Aggregate Effects of Anticipated and Unanticipated Tax Policy Shocks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(1), pages 27-54.
27. Mertens, K. & M.O. Ravn, 2014. "A reconciliation of SVAR and narrative estimates of tax multipliers," Journal of Monetary Economics, Elsevier, vol. 68(S), pages S1-S19.
28. Mountford, A. and H. Uhlig (2002). What Are the Effects of Fiscal Policy Shocks. CEPR Discussion Paper No. 3380.
29. Perotti, R. (2007). In Search of the Transmission Mechanism of Fiscal Policy. NBER Macroeconomics Annual.
30. Perotti, R. (2011). Fiscal Policy and Expectations: An Empirical Investigation.
31. Primiceri, Giorgio E. (2005): "Time Varying Structural Vector Autoregressions and Monetary Policy," Review of Economic Studies, 72, pp. 821-852.
32. Ramey, V.A. (2009). Identifying Government Spending Shocks: It's All in the Timing, NBER Working Papers no. 15464.
33. Romer, C.D., and D. H.. Romer. 2010. “The Macroeconomic Effects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks.” American Economic Review 100: 763–801.
34. Schmitt-Grohe, S. and Uribe, M., 2008, What's news in business cycles", NBER Working Paper no. 14215.
35. Sims, C. A. 1980. Macroeconomics and Reality. Econometrica, 48 (1), 148.
36. Sims, E., 2011, News, non-invertibility, and structural VARs, mimeo, University of Notre Dame.
37. Stock, J. H. and Watson, M. W., 2002, Macroeconomic forecasting using diffusion indexes", Journal of Business and Economic Statistics 20, pp. 147-162.
38. Stock, J. H. and Watson, M. W. , 2005, Implications of dynamic factor models for VAR analysis", NBER Working Paper no. 11467.
39. Stock, James H. and Mark W. Watson, 2012, “Disentangling the Channelsof the 2007-2009 Recession”, Brookings Panel on Economic Activity, Conference Paper March 22-23
40. Uhlig, H. (2005). What are the e_ects of monetary policy on output? Results from an agnostic identifycation procedure. Journal of Monetary Economics 52, 381-419.

About the Instructor

Luca Gambetti is Associate Professor of Economics at UAB and Barcelona GSE 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.

* Laptop required In order to participate in practical sessions, you must bring your own portable computer.

Overview

Most time series in economics and finance display a large degree of persistence. Also, since economic and financial systems are known to go through both structural and behavioral changes, many of them exhibit characteristics that are not compatible with linearity.

The goal of this course is to introduce some popular non-stationary and non-linear time series models that have been found to be effective at modeling macroeconomic and financial time series data.

The course is mainly designed for practitioners and students who will use time series data in empirical analysis.

Topics Covered

1. Linear models for nonstationary data. Integration and fractional integration. Univariate and panel unit root tests, non-stationary dynamic factor models.
2. Cointegration and Fractional cointegration.
3. Measuring persistence. Impulse response functions and related methods. Aggregation and persistence.
4. Non-linear methods. Markov Switching and Threshold models.
5. Univariate and multivariate analysis
6. Dynamic non linear factor models
7. Real time assessment of recession probabilities

Prerequisites

Statistics and econometrics at an advanced undergraduate level are recommended. Computer applications will be based on MATLAB so some knowledge of basic programming will be useful although not necessary.

About the instructors

Laura Mayoral is a Barcelona GSE affiliated professor and works at the Institute for Economic Analysis (IAE) since 2006. Before joining the institute she was Assistant Professor and Ramón y Cajal Felow at Universitat Pompeu Fabra and Universitat Autonoma de Barcelona. She has also been visiting professor at New York University (Abu Dhabi), the Paris School of Economics and the Department of Economics of the University of Gothenburg.

Gabriel Pérez-Quirós has a B.A. in Economics from Universidad de Murcia (1989), Master in Economics and Finance from CEMFI (1991), and PhD in Economics from the University of California San Diego (1996). He is currently the Unit Head of Macroeconomic Research at the Research Department of the Bank of Spain. He previously worked on business cycle research at the Federal Reserve Bank of New York and the European Central Bank. He 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 b usiness cycle. He teaches PhD courses at the Universidad de Alicante where he has supervised several dissertations on these topics.

* Laptop required In order to participate in practical sessions, you must bring your own portable computer.

Overview

The course provides an introduction to the state-of-the-art techniques for the analysis of financial time series. The first part of the course introduces univariate time series models used for the analysis of time-varying volatility (GARCH models) as well as multivariate timeseries models for the analysis of time-varying correlations (DCC models). The second part of the course presents empirical applications of GARCH-DCC models. The first application shows how GARCH-DCC models can be used for Value-at-Risk forecasting. In the second application, GARCH-DCC models are used to construct a number of different systemic risk measures recently proposed in the literature. These measures will then be employed to study the US financial system in the 2007–2009 financial crisis. During the practice session students will replicate the methodology as well as the empirical findings documented in the lectures using Matlab.

Requirement: basic knowledge of econometrics and time series econometrics.

Course Outline

1. Modeling and Forecasting Time-Varying Volatility using GARCH Models (part I) Stylized facts of financial time series. GARCH Models: Properties, Inference and Prediction.
2. Modeling and Forecasting Time-Varying Volatility using GARCH Models (part II) Beyond GARCH Models: Asymmetric Effects, Long-Memory and Realized Volatility. Volatility Forecast Evalution.
3. Modeling and Forecasting Time-Varying Correlations using DCC Models Stylized facts of financial time series. DCC Models: Properties, Inference and Prediction. Covariance Forecast Evalution.
4. Applications: Value-At-Risk Modeling fat tails using GARCH models. Value-at-Risk forecasting. Value-at-Risk forecast evaluation.
5. Applications: Systemic Risk CoVaR, MES and SRISK prediction using GARCH-DCC models with an application to the 2007-2009 financial crisis

About the Instructor

Christian Brownlees is Assistant Professor in the Department of Economics and Business at the Universitat Pompeu Fabra and Barcelona GSE Affiliated Professor. He obtained his Ph.D. degree 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.