Weighted asymmetric least squares regression with fixed-effects

TL;DR

This paper introduces the expectile regression with fixed-effects (ERFE) model, which effectively captures heteroscedasticity and biases in panel data, providing robust estimators and outperforming existing methods.

Contribution

The paper develops a novel ERFE model that adapts asymmetric least squares to fixed-effects, addressing heteroscedasticity and bias in panel data analysis.

Findings

ERFE is unbiased and outperforms competitors in simulations.

ERFE effectively captures data heteroscedasticity.

The model's asymptotic properties are theoretically derived.

Abstract

The fixed-effects model estimates the regressor effects on the mean of the response, which is inadequate to summarize the variable relationships in the presence of heteroscedasticity. In this paper, we adapt the asymmetric least squares (expectile) regression to the fixed-effects model and propose a new model: expectile regression with fixed-effects $(\ERFE).$ The $\ERFE$ model applies the within transformation strategy to concentrate out the incidental parameter and estimates the regressor effects on the expectiles of the response distribution. The $\ERFE$ model captures the data heteroscedasticity and eliminates any bias resulting from the correlation between the regressors and the omitted factors. We derive the asymptotic properties of the $\ERFE$ estimators and suggest robust estimators of its covariance matrix. Our simulations show that the $\ERFE$ estimator is unbiased and outperforms its competitors. Our real data analysis shows its ability to capture data heteroscedasticity (see our R package, \url{github.com/AmBarry/erfe}).