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

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 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

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.

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.

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

This is the first part of the module Time Series Models for Macroeconomic Analysis. The goal of the module is to present and discuss the most popular time series models, as well as recent advances, that can be used to study the propagation mechanisms of macroeconomic shocks and evaluate the effects of macroeconomic policies.

Course overview

The objective of this first 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 extension like Smooth transition VARs, Threshold VAR, Time-Varying Coefficients VAR and FAVARs. 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.

Requirement: basic knowledge of univariate time series models (ARMA models).

Contents

I. Structural VAR (SVAR)

a) The model: Representation, estimation.
b) Tools: Impulse response functions, variance decomposition, historical decomposition.
c) Identification: short and long-run zero, sign restrictions, penalty function approach, mixed restrictions, external instruments, narrative approach.
d) Applications: Monetary and fiscal policy shocks, technology shocks, news shocks, uncertainty shocks.
e) Local Projections

II. Nonlinear SVAR

a) Threshold VAR, Smooth Transition VAR.
b) Applications: Fiscal policy shocks in booms and recessions.
c) Nonlinear MA and local projections.

III. Time-Varying Coefficients VAR

a) The model: representation and estimation.
b) Applications: the Great Moderation, monetary  policy and stock market
bubbles.

IV. An Introduction to VAR in a Data-rich environment

FAVAR: Representation, estimation. Application: Credit market shocks.

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

This is the continuation of the first part ‘’Time Series Methods for Macroeconomic Analysis: Part I’’ but can be taken independently. The course represents an advanced course in Time Series Methods for Macroeconomic Analysis. The starting point of the course is to discuss potential pitfalls arising in VAR models. More specifically, the issue of non-fundamentalness and non-invertibility, a problem that arises because of the typical gap between the information set of the econometrician and that of the agents. We will cover both theoretical and empirical procedures to detect non-fundamentalness and discuss models to tackle non-fundamentalness. In particular we will present and discuss models for large-N, including Factor models and FAVARs. In this context, we will review several applications, among others the news-driven business cycles debate and the fiscal foresight literature.

Next, we will study the implications of relaxing the assumption of perfect shocks observability for structural analysis with empirical models. We will see how to perform macroeconomic and policy analysis under the assumption that economic agents only observe a noisy signal of the structural shocks by means of dynamic identification. As an application, we will review the ongoing debate about news versus noise as the source of business cycle fluctuations. Matlab programs to implement the theoretical methods and replicate the applications studied in class will be made available to students.

Requirement: good knowledge of time series econometrics, in particular VAR analysis. The attendance to the Part I is recommended, but not required.

Contents

I. Pitfall in SVAR models: Non-fundamentalness and non-invertibility

a) Preliminaries

i. MA representations
ii. Blaschke factors
iii. Nonfundamentalness noninvertibility.

b) VAR and DSGE models

i. Poor man’s condition
ii. Partial fundamentalness and partial invertibility.

c) Examples of nonfundamental shocks in VARs.

II. Large-N models

a) Factor Models

i. Principal components estimator.
ii. Small N, i.i.d. and dynamic, EM algorithm, Kalman filter.
iii. Large N, i.i.d. and dynamic.
iv. Applications: Commonality in European regions, new Eurocoin, monetary policy in real time, nowcasting, measuring macroeconomic uncertainty.

b) Structural Factor model (SFM)

i. Specification and estimation.
ii. Tools: Impulse response functions, variance decomposition, historical decomposition.
iii. Identification: Short and long-run zero, sign restrictions, penalty function approach, mixed restrictions, external instruments, narrative approach.
iv. DSGE and Factor models.
v. Applications: Monetary policy shocks, house prices, disaggregated prices.

c) Factor augmented VAR (FAVAR).

i. Applications: Monetary Policy, news shocks, credit shocks.
ii. Testing noninvertibility.

III. Time series models under imperfect information

a) Theory

i. Imperfect information as agents’ nonfundamentalness.
ii. News noise VAR representation.
iii. Dynamic identification with Blaschke factors in SVARs and Structural Factor Models.
iv. Structural estimation and the Kalman filter.

b) Applications: Noise bubbles, noise-driven business cycles.

About the Instructors

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.

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)