Master's Degree in Economics and Finance

Master's Degree in Specialized Economic Analysis

Master's Degree in Data Science

Admissions

Career Services

Alumni Community

Economics Program

Financial Economics Program

PhD Economics Track Program

Go to Master's degrees

Close

Microeconometrics

Estimation in High-Dimensional Linear Models

A course designed for those who deal with large, complex data sets.

17.5h (5 days)

€775 - €1,375

Face-to-face

English

Program date: July 7 - 11, 2025

Early bird deadline: April 15, 2025

Learn more

Estimation in High-Dimensional Linear Models

Applications for 2025 Summer School programs are now open!

Summer school

Microeconometrics

Estimation in High-Dimensional Linear Models

Course Overview

High-dimensional data set are abundant nowadays and this course covers estimation of models with many explanatory variables (potentially more than the sample size). The focus is mainly on the linear model to keep the exposition simple. Here, OLS is problematic in the presence of many explanatory variables. We shall see that if one is willing to impose that the model is sparse (that is only a small subset of the large set of potential explanatory variables is actually relevant) then it is possible to estimate the parameters almost as precisely as if one had implemented OLS only including the relevant variables. Such upper bounds on the estimation error are called oracle inequalities as an estimator possessing it is almost as precise as if an oracle had revealed the true model prior to estimation.

We shall prove that one popular estimator possessing the oracle property is the Lasso (Least Absolute Shrinkage and Selection Operator). We also discuss variable selection and screening via the Lasso. As the Lasso shrinks parameters towards zero, it introduces a shrinkage bias. Thus, one may contemplate running OLS after model selection by the Lasso. We will discuss the properties of such a post-Lasso procedure.

The performance of shrinkage estimators depends crucially on the right choice of a penalty parameter. Thus, it is crucial to have a disciplined way of choosing the penalty parameter with ensuing performance guarantees. We will discuss one such procedure and the ensuing oracle inequalities.

We aim to provide detailed proofs of (most of) the results presented.

The practical sessions will focus on illustrating the theoretical results in R.

Both theory and practical sessions are expected to be interactive.

Faculty

High-dimensional datasets are common, we focus on estimating models with many explanatory variables

At the end of the course, you will:

Grasp the opportunities and challenges associated with high-dimensional data in statistical modeling
Identify the limitations of traditional estimators like OLS and variable selection procedures in high-dimensional contexts
Learn how to utilize shrinkage estimators for effective variable screening and selection.
Understand the Lasso method, including its theory and oracle inequalities, for variable selection in high-dimensional settings
Evaluate post-Lasso methods to address shrinkage bias and improve estimation accuracy
Develop skills in data-driven tuning parameter selection to optimize the performance of the Lasso

Program Syllabus for Estimation in High-Dimensional Linear Models

The course will explore the following topics:

High-dimensional Models: Opportunities and Challenges

Problems with Classic Estimators (e.g. OLS) and Variable Selection Procedures

Shrinkage Estimators: Variable Screening and Selection

The Sparsity Assumption

The Lasso and Theory For it. The focus will be on oracle inequalities

The adaptive Lasso and the oracle property*
Variable selection via thresholding*
Leeb+Pötscher critique on superefficiency and the return of Hodges’ estimator*

*If time allows

Post-Lasso to alleviate shrinkage bias. Theory of post-Lasso (oracle inequalities)

Data-driven tuning parameter selection for the Lasso

If time allows: Square-root Lasso and oracle inequalities for this

If time allows: Applications in time series

List of References

There are no specific references for this course
It is enough to follow the lecture slides, which will be a (largely) self-contained coverage of the material to be covered

Software / Hardware

STATA will be used during the course. Participants will receive a temporary personal license, provided by BSE, a few days before Summer School begins
Participants must bring their own portable laptop to participate fully in this course

Why join our Summer School?

All BSE Summer courses are taught to the same high standard as our Master’s programs. Join us to:

1

Network with like-minded peers

2

Study in vibrant Barcelona

3

Learn from world-renowned faculty

Admissions and Requirements

All BSE Summer School applicants must ensure that they meet the basic entry requirements.

Program date: July 7 - 11, 2025

Early bird deadline: April 15, 2025

Requirements

Summer School applicants normally demonstrate one or more of the following:

A strong background in Economics or a field closely related to the course topic (Statistics, Law, etc.)
Postgraduate degree or current Master’s/PhD studies related to the course topic
Relevant professional experience

Requirements for Estimation in High-Dimensional Linear Models

Participants should have a good background in linear algebra probability
For practical exercises, a little experience with R is recommended

Schedule

Here is your schedule for this edition of BSE Microeconometrics Summer School, Estimation in High-Dimensional Models course.

Time

7

mon

8

tue

9

wed

10

thu

11

fri

11:30 - 13:30

Lecture

16:15 - 17:45

Practical

Credit Transfers (ECTS)

To be eligible for credit transfer, students must complete a final project. Students will deliver a short final project one week after the summer school finishes.

It will consist of completing an assignment that will include the practical and empirical issues worked on in class.

Consult the Summer School Admissions page for more information about this option.

Certificate of Attendance

Participants who attend more than 80% of the course will receive a Certificate of Attendance, free of charge.

Fees

Multiple course discounts are available, see more information about available discounts. Fees for courses in other Summer School programs may vary.

Course

Panel Data and Spatial Panels

Econometrics of Cross-section Data with Applications

Dynamic Structural Models for Policy Evaluation

Quantitative Methods for Public Policy Evaluation

Estimation in High-Dimensional Models

Difference-in-Differences with Panel Data

Dynamic and Non-linear Panel Data Models

Modality

Face-to-face

Total Hours

17.5

ECTS

1

Regular Fee

1,375€

Reduced Fee*

775€

* Reduced Fee applies for PhD or Master’s students, Alumni of BSE Master’s programs, and participants who are unemployed.

FAQ

Here are some commonly asked questions by participants. Any further queries, please contact our Admissions Team.

Can I see the full Summer School calendar?

You can view the full Summer School calendar here.

Is accommodation included in the course fee?

Unfortunately, accommodation is not included in the course fee. Participants are responsible for finding accommodation.

Are the sessions recorded?

Sessions will NOT be recorded; however, the materials provided by the professor will be available for a month after the course has finished.

How much does each Summer School course cost?

Fees for each course may vary. Please consult each course page for accurate information.

Are there any discounts available?

Yes, BSE offers a variety of discounts on its Summer School courses. See more information about available discounts or request a personalized discount quote by email.