More efficient local polynomial regression with random-effects panel data models

ABSTRACT

We propose a modification on the local polynomial estimation procedure to account for the “within-subject” correlation presented in panel data. The proposed procedure is rather simple to compute and has a closed-form expression. We study the asymptotic bias and variance of the proposed procedure and show that it outperforms the working independence estimator uniformly up to the first order. Simulation study shows that the gains in efficiency with the proposed method in the presence of “within-subject” correlation can be significant in small samples. For illustration purposes, the procedure is applied to explore the impact of market concentration on airfare.

KEYWORDS:

• Kernel regression
• Local polynomial regression
• Nonparametric method
• Random-effects panel data model
• Variance reduction

JEL CLASSIFICATION:

• C14
• C23

Notes

¹In the random-effects model the individual-specific effects, α_i, are assumed to be randomly drawn from an underlying population and independent from the regressors, whereas in a fixed-effects model one makes inference conditional on the individual units. See Henderson et al. (2008) for Kernel estimation on a fixed-effects model.

²Summary of the Monte Carlo results on bias, variance, and average squared error ratios over 100 fixed points. Each ratio is calculated with numerator being results from the WI estimator and denominator being results from the proposed estimator (RQL) or the estimator proposed in Wang (2003). The higher values indicate better performance. The means and quartiles are based on 500 simulated samples.