Missing dependent variables in fixed-effects models

Area of Science:

• Econometrics
• Statistics

Background:

• Linear fixed-effects models are widely used but can be challenging when data is missing.
• Traditional methods may lose efficiency with missing dependent variables.

Purpose of the Study:

• To propose a novel estimation method for linear fixed-effects models with missing dependent variables.
• To enhance estimation efficiency by leveraging all available covariate data.

Main Methods:

• A classical minimum distance (CMD) estimator, building on Chamberlain's work, is developed.
• The estimator is shown to be consistent under missing-at-random (MAR) assumptions.
• The approach is extended to autoregressive fixed-effects models with lagged dependent variables.

Main Results:

• The CMD estimator offers efficiency gains compared to complete-data methods.
• Identification of model parameters is possible even without 'within' variation in certain cases.
• Monte Carlo simulations demonstrate the CMD approach's performance against existing methods.

Conclusions:

• The CMD estimator provides a robust and efficient solution for fixed-effects models with missing data.
• The method is applicable to static and dynamic (autoregressive) models.
• Further extensions address sequential exogeneity and missing covariates.