CEMFI Summer School

Local Projection Methods for Time Series and Panel Data


11-15 September 2023


9:30 to 13:00 CEST


In person

Intended for

Academic researchers and policy analysts who are interested in modern multivariate time series methods to compute the dynamic effect of policy interventions and the method of local projections in particular.


Some basic knowledge of probability or statistics is expected. Individuals with undergraduate degrees in economics, statistics or related disciplines should be able to follow the course. The emphasis will be on applications and practical aspects rather than on deep theory. The applications will primarily use the statistics software package STATA.


It is often of interest to empirically evaluate how an intervention will affect an outcome over time. What makes such an exercise difficult? First, there are confounding factors that make isolating the intervention difficult. A variety of identification methods have proliferated over time to deal with this confounding. Second, economies are dynamic. It is rare to find one-off interventions. Rather, they are usually implemented in the form of treatment plans. Such plans are not set in stone, they get adjusted as the effects of the outcome (and other variables) materialize over time. This feedback between treatments, outcomes, and other factors requires methods in time series analysis to sort out the contribution of each channel.

Exploring these questions requires a tiered approach, from the most to the least structural approach. The course will start with a discussion of state-space models. This platform accommodates most macroeconomic models and permits a rigorous discussion of issues of identification, invertibility, and fundamentalness. In addition, the state-space representation accommodates a wide class of time series and macroeconomic models that can then be estimated by maximum likelihood using the Kalman filter and iterative algorithms or with Bayesian methods.

Moving from the state space models to a less structural viewpoint, vector autoregressions (VARs) are the next natural step. Not surprisingly, they have enjoyed a prominent place in the past few decades. VARs serve two main functions. They are a natural forecasting tool, and they serve to conveniently estimate dynamic multipliers. VARs facilitate the construction of impulse responses by integrating alternative methods of identification from a time series perspective. Given their prominence, the course will review the basic features of this method.

The main emphasis of the course is on local projections (LPs), the final step in the journey toward the least structural approach. LPs depart from VARs in a number of dimensions. First, LPs do not restrict the dynamics of the response from one period to the next, thus accommodating potentially complex and long-lasting outcome effects. Second, it is a single equation method, which is at the same time simpler to implement, but also simpler to extend into nonlinear settings. Third, because LPs are explicit about the goal of estimating counterfactual policy effects, one can quickly draw the connections with the applied microeconomics literature on potential outcomes, policy evaluation, and their implications.

Over the past few years, there have been numerous extensions to LPs that will be discussed. These include new results on impulse response inference; a decomposition of the impulse response into direct, indirect, and composition effects with the Kitagawa decomposition; simple linear methods to estimate time-varying impulse responses based on the economic setting; stratification of impulse responses as a function of economic conditions and other nonlinear extensions, to name a few.

More recently, it has become more common to analyze panel data in macroeconomics. Panel data structures allow for richer options, especially on identification. The course will take advantage of these new developments, particularly in the area of difference-in-differences (DiD) identification. It turns out that LP-DiD methods accommodate a wide range of recently proposed estimators of staggered, heterogenous treatment effects.

The breadth of topics covered limits the rigor with which each result will be discussed, though appropriate references will be provided for those interested. The goal of the course is to guide practitioners to appropriate methods for their problems, and to elicit fruitful extensions and avenues for new research.


Introduction to the main questions of interest: where do VARs and LPs fit in the discussion?
State-space models: implications of macroeconomic models for identification, invertibility, and fundamentalness. Maximum-likelihood estimation with the Kalman filter
Vector autoregressions: discussion of the basic concepts. Estimation and inference of impulse responses. Identification
Local projections, their connection to VARs, and their points of departure. Basic estimation and new inferential results
Smoothing methods and economic interpretation
Local projections and nonlinearities. The Kitagawa decomposition. Stratification, decomposition, and time-varying impulse responses
Staggered, heterogenous treatment effects in difference-in-difference studies using LPs. Panel data applications

Òscar Jordà is Senior Policy Advisor at the Federal Reserve Bank of San Francisco and Professor of Economics at the University of California, Davis. He earned his doctorate at the University of California, San Diego. He is the founding Chair of the Spanish Business Cycle Dating Committee and currently serves as a member. In addition, he is a member of the Center for Economic Policy Research. His research focuses on time series econometrics with applications in macroeconomics, economic history, and finance. He has published in international journals such as the American Economic Review, Journal of Political Economy, Review of Economic Studies, Quarterly Journal of Economics, Journal of the European Economic Association, and International Economic Review. He is Co-editor of the International Journal of Central Banking, and Associate Editor of the Journal of International Economics, and the Journal of Applied Econometrics. He previously served in the editorial boards of the Journal of Business and Economic Statistics, the Journal of Econometric Methods, Empirical Economics, and the Journal of the Spanish Economic Association.