Econometrics with Unobserved Heterogeneity

Learn unobserved heterogeneity-robust causal inference methods — heterogeneous coefficients, nonparametric models, and quantile and distribution regression
Author

Vladislav Morozov

Published

2025

Econometrics with Unobserved Heterogeneity

Course Information

Short Description

Unobserved heterogeneity is pervasive in economics, driven by heterogeneous parameters and treatment effects, unobserved characteristics of agents, missing variables, etc. This class introduces methods for estimating parameters of interest in settings with such unobserved heterogeneity.

The course is structured into three main parts:

  1. Linear models with heterogeneous coefficients
  2. Nonparametric models with unobserved heterogeneity
  3. Quantile and distributional treatment effects and quantile and distributional regression methods.

This class focuses on observational cross-sectional and panel data settings.

Instructor: Vladislav Morozov 

Level: Second-year Master’s and PhD students; accessible to sufficiently prepared upper-level undergraduate students 

Course Materials

Textbook: None. This course is based on lecture notes and background articles, which are listed in the references.

Recommended Readings: Please see the bibliography for a detailed reading list.

About These Notes

These lectures notes are based on a topics course I delivered at the University of Bonn. They are currently being uploaded in blocks as I organize and transform my notes. These notes are a work in progress. If you find any typos or have suggestions, please open an issue on GitHub using the link on the right!

Current version (March 20, 2025): Includes material on average effects in linear models with heterogeneous coefficients.

Learning Outcomes

By the end of this course, students will be able to:

  • Identify and explain different sources of unobserved heterogeneity in economic data.
  • Apply econometric methods, such as heterogeneous coefficient models and quantile regression, to account for unobserved heterogeneity.
  • Evaluate the trade-offs and assumptions underlying different modeling approaches in empirical research.

Syllabus

Block 0: Introduction to Unobserved Heterogeneity

  • Definition and a brief classification
  • Examples in applied econometrics
  • Overview of key methodological challenges

Block 1: Linear Models with Heterogeneous Coefficients

  • Linear models and their applicability
  • Heterogeneity in linear models
  • Average effects:
    • Issues with the within estimator under heterogeneity
    • Interlude: Dynamic panels with random intercepts
    • Issues with dynamic panel IV estimators under heterogeneity
    • Robust estimation with the mean group estimator
  • Variance of coefficients
  • Distribution of coefficients:
    • A primer on deconvolution
    • Identification of the distribution
    • Estimation with discrete covariates

Block 2: Nonparametric Models with Unobserved Heterogeneity

  • A partial classification of nonparametric models with unobserved heterogeneity
  • Introduction to nonseparable models
  • Heterogeneity bias and issues with identification in cross-sectional settings
  • Identification and estimation of average marginal effects in fully nonseparable models with panel data:
    • Identification for stayers under strong stationarity
    • Extending identification results beyond stayers
    • Accommodating changes in the structural function
  • Variance of marginal effects in nonseparable models

Block 3: Quantile and Distribution Treatment Effects:

  • Background: Quantiles and their properties
  • Causal framework: Quantile and distributional treatment effects and their interpretation
  • Identification of QTEs and DTEs under unconfoundedness
  • Methods:
    • Quantile regression:
      • General formulation
      • When is quantile regression correctly specified?
      • Quantile crossing and rearrangement techniques
    • Distribution regression:
      • General formulation
      • Rearrangement for distribution regression
  • Estimation of QTEs and DTEs
  • What can quantile regressions tell us about nonseparable models?