Intermediate Econometrics (10620843)

Instructor

  •   Prof. Giuseppe Ragusa
  •   Sapienza, University of Rome
  •   Department of Economics and Law
  •   Viale del Castro Laurenziano, 9
  •  
  •   Office Hours

Course details

  •   TBA
  •   20 February, 2025 - 31 May 2025
  •   TBA
  •   TBA

Course descriptions

Intermediate Econometrics (10620843) is a master’s-level course that provides students with a rigorous foundation in both theoretical and applied econometric analysis. It covers tools used in modern empirical research in economics, finance, and other social sciences.

Part I covers the theoretical foundations of cross-sectional and panel data econometrics, with a focus on asymptotic theory and the potential outcomes framework that underlies causal inference. Building on these fundamentals, we study the classical linear regression model—including estimation, inference, and the challenges that arise when key assumptions fail. We then extend these ideas to instrumental variables and linear panel data models, emphasizing identification, estimation, and inference. Throughout this first part, the focus is primarily on data generated by independent random variables.

Part II covers time series econometrics. We begin with ARIMA models, which provide a foundation for understanding stochastic dynamics, persistence, and forecasting. We then turn to Vector Autoregressions (VARs) as a flexible framework for modeling the joint dynamics of multiple time series, followed by Structural VARs (SVARs)—one of empirical macroeconomists’ most widely used tools for identifying causal relationships and conducting policy analysis. The course continues with an introduction to state-space models and the estimation of their parameters through the Kalman filter. It concludes by applying these techniques to Dynamic Factor Models (DFMs), which are commonly employed to summarize information from large panels of time series and underpin virtually all contemporary approaches to high-dimensional forecasting and macroeconomic analysis.

Software and Computing

This course includes hands-on programming work using Julia, a high-performance language well suited to numerical and statistical computing. Through coding exercises and empirical applications, students will implement the techniques presented in lectures—from OLS and instrumental variables estimation to Kalman filtering and dynamic factor models.

Programming is an invaluable way to understand the details of econometric methods: writing code forces clarity about each step of an estimation procedure and reveals how theoretical assumptions translate into practical choices. By building estimators from first principles, students develop a deeper intuition for the techniques and gain experience bridging the gap between theory and application.

Prior experience with Julia is not required, but familiarity with programming fundamentals (in any language) is helpful. Introductory materials on Julia will be provided at the start of the course.

Textbooks

The course draws primarily on four textbooks:

  1. Wooldridge, Jeffrey M. Econometric Analysis of Cross Section and Panel Data. MIT Press, 2010.

  2. Angrist, Joshua D., and Jörn-Steffen Pischke. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton University Press, 2009.

  3. Hamilton, James D. Time Series Analysis. Princeton University Press, 1994.

  4. Brockwell, Peter J. and Richard A. Davis. Introduction to Time Series and Forecasting, Springer, 2002.

These are advanced references, but selected chapters and sections will be accessible at the level of this course. Where appropriate, supplementary lecture notes will be provided to present the material in a more intuitive and accessible manner.

Prerequisites

Students are expected to have a solid background in introductory econometrics at the level covered by standard undergraduate textbooks such as Introductory Econometrics: A Modern Approach by Jeffrey Wooldridge or Introduction to Econometrics by James Stock and Mark Watson.

Successful completion of the Econometrics course offered in the Laurea Triennale in Economics and Finance—or an equivalent undergraduate course—satisfies this prerequisite.

Students who have not previously taken a formal course in econometrics are strongly encouraged to review the foundational material before the start of the semester. Independent study using Wooldridge or Stock and Watson is highly recommended to ensure adequate preparation for the advanced topics covered in this course.

Syllabus

Part I: Cross-Sectional and Panel Data Econometrics

Week 1–2: Foundations of Econometric Theory

  • Review of probability and statistical inference
  • Asymptotic theory: convergence in probability, convergence in distribution, laws of large numbers, central limit theorems
  • The potential outcomes framework for causal inference

Readings

  • Wooldridge, Ch. 3 (Basic Asymptotic Theory)
  • Angrist & Pischke, Ch. 1–2 (Questions about Questions; The Experimental Ideal)

Week 3–4: The Classical Linear Regression Model

  • Identification and estimation under exogeneity
  • Finite-sample and asymptotic properties of OLS
  • Hypothesis testing and confidence intervals
  • Violations of classical assumptions: heteroskedasticity, serial correlation, measurement error

Readings

  • Wooldridge, Ch. 4–5 (The Single-Equation Linear Model; Instrumental Variables)
  • Angrist & Pischke, Ch. 3 (Making Regression Make Sense)

Week 5: Instrumental Variables

  • Endogeneity and omitted variable bias
  • The IV estimator: identification, consistency, and inference
  • Two-stage least squares (2SLS)
  • Weak instruments and diagnostics
  • Local average treatment effects (LATE)

Readings

  • Wooldridge, Ch. 5 (Instrumental Variables Estimation)
  • Angrist & Pischke, Ch. 4 (Instrumental Variables in Action)

Week 6: Linear Panel Data Models

  • The structure of panel data
  • Pooled OLS, fixed effects, and random effects
  • Within and between variation; the Hausman test

Readings

  • Wooldridge, Ch. 10 (Basic Linear Unobserved Effects Panel Data Models)
  • Angrist & Pischke, Ch. 5 (Parallel Worlds—Fixed Effects, Differences-in-Differences)

Part II: Time Series Econometrics

Week 7–8: Univariate Time Series Models (ARIMA)

  • Stationarity and ergodicity
  • Autoregressive (AR), moving average (MA), and ARMA processes
  • Unit roots, integration, and ARIMA models
  • Invertibility and forecasting
  • Model selection and diagnostic testing

Readings

  • Hamilton, Ch. 3–4 (Difference Equations; Lag Operators)
  • Hamilton, Ch. 5 (Stationary ARMA Processes)
  • Brockwell-Davis, Ch. 2-3 (Sattionary Processes and ARMA Models)

Week 9: Vector Autoregressions (VAR)

  • Multivariate time series and the VAR representation
  • Estimation and lag selection
  • Granger causality
  • Impulse response functions and forecast error variance decomposition

Readings

  • Hamilton, Ch. 10–11 (Covariance-Stationary Vector Processes; Vector Autoregressions)
  • Brockwell-Davis, Ch. 7 (Multivariate Time-Series)

Week 10: Structural Vector Autoregressions (SVAR)

  • From reduced form to structural form
  • Identification strategies: short-run restrictions, long-run restrictions, sign restrictions
  • Policy analysis and counterfactual simulations
  • Applications in macroeconomics

Readings

  • Hamilton, Ch. 11 (Vector Autoregressions), selected sections
  • Supplementary lecture notes

Week 11: State-Space Models and the Kalman Filter

  • The state-space representation
  • Filtering, smoothing, and prediction
  • Maximum likelihood estimation via the Kalman filter
  • Applications: trend-cycle decomposition, time-varying parameters

Readings

  • Hamilton, Ch. 13 (The Kalman Filter)
  • Brockwell-Davis, Ch. 8 (State-Space models)
  • Supplementary lecture notes

Week 12: Dynamic Factor Models (DFM)

  • Dimensionality reduction and latent factors
  • Principal components and maximum likelihood estimation
  • State-space representation of DFMs
  • Forecasting in high-dimensional environments
  • Applications to macroeconomic monitoring and nowcasting

Readings

  • Supplementary lecture notes