# Post-Selection Inference in Three-Dimensional Panel Data

## TL;DR

This paper develops a post-selection inference method for three-dimensional panel data models, improving the accuracy and efficiency of fixed effects estimation after model selection, especially when using lasso techniques.

## Contribution

It introduces a novel post-selection inference approach that accommodates many nonzero fixed effects, enhancing model accuracy and efficiency in three-dimensional panel analysis.

## Key findings

- More precise than under-fitting fixed effect estimators
- More efficient than over-fitting fixed effect estimators
- Achieves inference accuracy comparable to the oracle estimator

## Abstract

Three-dimensional panel models are widely used in empirical analysis. Researchers use various combinations of fixed effects for three-dimensional panels. When one imposes a parsimonious model and the true model is rich, then it incurs mis-specification biases. When one employs a rich model and the true model is parsimonious, then it incurs larger standard errors than necessary. It is therefore useful for researchers to know correct models. In this light, Lu, Miao, and Su (2018) propose methods of model selection. We advance this literature by proposing a method of post-selection inference for regression parameters. Despite our use of the lasso technique as means of model selection, our assumptions allow for many and even all fixed effects to be nonzero. Simulation studies demonstrate that the proposed method is more precise than under-fitting fixed effect estimators, is more efficient than over-fitting fixed effect estimators, and allows for as accurate inference as the oracle estimator.