Macroeconometrics Summer School

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 7.5 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

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

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

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

This is the first part of a course focusing on the identification of causal relationships in macroeconomics, a key step to understand economic fluctuations, design sound economic policies, and assess economic theories. The course provides a variety of models and methods to identify macroeconomic shocks and estimate their propagation mechanisms. 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 detail Structural Vector Autoregressive models with a special focus on several identification schemes used in the literature and also present several extensions.

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

Prerequisites

Knowledge of univariate time series models (ARMA models) and basic knowledge of multivariate ARMA.

Course Outline

1. Structural VAR
2. Large information
   • FAVAR
   • Factor Models
   • Common Components SVAR
3. Nonlinear SVAR
   • Smooth Transition SVAR
   • Nonlinear Moving Averages

List of References

A reading list will be provided at the beginning of the course.

Software/Hardware

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

About the Instructor

Luca Gambetti is and Associate Professor of Economics at Universitat Autònoma de Barcelona (UAB) and an Affiliated Professor of the Barcelona School of Economics (BSE). He is also an external member of RECent. His research focuses on Quantitative Macroeconomics and Applied Time Series Analysis. He has published articles in journals such as the Journal of Monetary Economics, the Economic Journal, the Journal of Applied Econometrics and the American Economic Journal: Macro, among others.

Course Overview

The course focuses on the identification and estimation of causal relationships in macroeconomics. The course represents a continuation of Time Series Models for Macroeconomic Analysis I but can be taken independently.

The goal of the course is to discuss and present a variety of advanced time series methods to estimate causal relationships in macroeconomics, identify macroeconomic shocks and estimate their propagation mechanisms. Special emphasis will be put on Bayesian analysis.

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

Prerequisites

Knowledge of univariate and multivariate time series models (ARMA and VARMA models) and basic knowledge of Bayesian Econometrics.

Course Outline

1. Local projections (LP)
   • Frequentist LP
   • Bayesian LP
2. Bayesian VAR (BVAR)
   • Small scall BVAR
   • Large Bayesian SVAR
3. Noninvertible models
   • Blaschke factors
   • Generalized SVAR-IV

List of References

A reading list will be provided at the beginning of the course.

Software/Hardware

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

About the Instructor

Giovanni Ricco is an Assistant Professor in Economics at the University of Warwick, and a Chercheur Associé at OFCE-SciencesPo. His research interests include Empirical Macroeconomics, Monetary and Fiscal Policy, and Time Series Econometrics. Giovanni holds a Ph.D. in Economics from the London Business School and a Ph.D. in Physics from the University of Pisa.

Course Overview

The objective of the course is to teach student how to use state-of-the-art Bayesian methods to estimate and analyze structural business cycle models. The course covers the foundations of Bayesian inference, model solution methods, MCMC posterior sampling methods and the key components of Bayesian analysis and model evaluation.

Students will (i) learn how to formulate, solve and estimate both representative (RANK) and heterogeneous (HANK) New Keynesian models, (ii) learn how to construct posterior probability distributions for model outputs, (iii) learn how to evaluate the relative role of prior information, the data and model structure for model outputs,and (iv) gain an understanding of the challenges and opportunities involved with solving and estimating HANK models relative to RANK models.

Prerequisites

Basic knowledge of time series econometrics.

Course Outline

Lecture 1: Introduction to Bayesian inference and Representative Agent New Keyensian (RANK) models.

• Introduction to Bayesian analysis
• Macro models as data generating processes
• Formulating and solving a representative agent New Keynesian business cycle model

Lecture 2: State space models and likelihood based estimation.

• State space models
• The Kalman filter
• Likelihood based estimation
• Numerical maximization

Lecture 3: Bayesian Estimation of linearized RANK models.

• Bayesian computation and sampling from a target distribution
• Formulating priors for a macroeconomic model
• Simulating from the posterior distribution of a business cycle model

Lecture 4: Bayesian Analysis of structural model.

• Efficient and robust posterior simulation
• Constructing probability intervals of model outputs
• Prior predictive analysis
• Bayesian model averaging

Lecture 5: Bayesian Estimation of Heterogeneous Agent New Keynesian (HANK) models.

• Specifying, solving and estimating heterogeneous agent models. What are the key differences and challenges compared to RANK models?
• Solving HANK models
• Evaluating the likelihood function for a HANK model
• Formulating priors and sampling from the posterior

List of References

1. Acharya, S., Chen, W., Del Negro, M., Dogra, K., Gleich, A., Goyal, S., Matlin, E., Lee, D., Sarfati, R. and Sengupta, S., 2023. Estimating HANK for Central Banks.
2. Ahn, S., Kaplan, G., Moll, B., Winberry, T. and Wolf, C., 2018. "When inequality matters for macro and macro matters for inequality." NBER macroeconomics annual, 32(1), pp.1-75.
3. Auclert, A., Rognlie, M. and Straub, L., 2020. Micro jumps, macro humps: Monetary policy and business cycles in an estimated HANK model (No. w26647). National Bureau of Economic Research.
4. Auclert, A., Bard ́oczy, B., Rognlie, M. and Straub, L., 2021. "Using the sequence-space Jacobian to solve and estimate heterogeneous-agent models." Econometrica, 89(5), pp.2375-2408.
5. Berger, J.O., 2013. Statistical decision theory and Bayesian analysis. Springer Science & Business Media.
6. De Finetti, B., 2008. Philosophical Lectures on Probability: collected, edited, and annotated by Alberto Mura (Vol. 340). Springer Science & Business Media.
7. del Negro, M. and Schorfheide, F., "Bayesian Macroeconometrics." In The Oxford Handbook of Bayesian Econometrics.
8. Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. and Rubin, D.B., 2013. Bayesian data analysis. CRC press.
9. Koop, G. and Korobilis, D., 2009. "Bayesian multivariate time series methods for empirical macroeconomics." Foundations and Trends in Econometrics, 3(4), pp.267-358.
10. Robert, C., 2007. The Bayesian choice: from decision-theoretic foundations to computational implementation. Springer Science & Business Media.
11. Robert, C. and Casella, G., 2013. Monte Carlo statistical methods. Springer Science & Business Media.
12. Winberry, T., 2018. "A method for solving and estimating heterogeneous agent macro models." Quantitative Economics, 9(3), pp.1123-1151.

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 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

Factor Models

1. Principal components estimator.
2. Small N, i.i.d. and dynamic, the EM algorithm, Kalman filter/smoother.
3. Large N, i.i.d. and dynamic. Consistency at large: a law of large numbers in the cross-section.
4. Applications: Commonality in European regions, new Eurocoin, monetary policy in real time, nowcasting, measuring macroeconomic uncertainty.

Structural Factor model (SFM)

1. Specification and estimation.
2. Tools: Impulse response functions, variance decomposition, historical decomposition.
3. Identification: Short and long-run zero, sign restrictions, penalty function approach.
4. DSGE and Factor models.
5. Applications: Monetary policy shocks, house prices, disaggregated prices.

Factor augmented VAR (FAVAR)

1. Applications: Monetary Policy, news shocks.
2. 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

Recent economic events, financial crises, the COVID crisis, the Ukraine war, rising inflation, etc., have sparked a great interest in understanding the real-time economic situation. Optimal investment decisions and economic policy choices in this rapidly shifting environment require a careful analysis of the real-time economic landscape, which is often characterized by scant, unbalanced, revised, non-seasonally adjusted, and noisy data.

In the midst of this whirlwind, analysts responsible for deciphering these complex dynamics often find themselves overwhelmed by the sea of available techniques and information, as well as the pressure to produce reliable forecasts. There's no easy guide for comparing methods, understanding data filtration, determining the number of variables for forecasting, or gauging the complexity of the models. It's within this challenging space that our course finds its purpose.

Starting from the bedrock of undergraduate econometrics, this course steers students through a spectrum of techniques. It commences with fundamental ARIMA models and concludes with advanced state-of-the-art models that introduce non-linear and machine learning concepts.

The course includes computer codes written in both Matlab and Python languages. No previous knowledge of these languages is needed although some basic notions in any of them are welcomed.

Prerequisites

Basic econometrics notions at the undergraduate level.

Course Outline

1. Basic concepts and definitions
2. Forecasting Models
   • ARIMA Models and VARs
   • Local Projection
   • Static and Dynamic factor models
   • Non-linear specifications: Smooth threshold and Markov switching
   • Introduction to Machine Learning
3. Special Issues
   • Filtering, data mining and model selection
   • Forecast evaluation
   • Forecasting with Prophet (Python)

List of References

There will be specialized readings in each of the topics covered in the course, but some basic books recommended are

1. James Hamilton. “Time Series Analysis” Princeton. (1994).
2. Chang-Jin Kim, Charles R. Nelson. “State-Space Models With Regime Switching: Classical and Gibbs-Sampling Approaches With Applications”. MIT Press (1999).
3. Andrew Blake and Haroon Mumtaz. “Applied Bayesian Econometrics for Central Bankers” (2007). Bank of England.
4. Helmut Lütkepohl “New Introduction to Multivariate Time Series Analysis” (2005).
5. Fabio Canova.” Methods for Applied Macroeconomic Research” (2007)
6. Frank Diebold. “Elements of forecasting” (2007)
7. Juana Sanchez. “Time series for data scientists: data management, description, modeling and forecasting (2023)

Software/Hardware

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

About the Instructor

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 a 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.