Dyadic Regression with Sample Selection

Abstract: This paper addresses the sample selection problem in panel dyadic regression analysis. Dyadic data often include many zeros in the main outcomes due to the underlying network formation process. This not only contaminates popular estimators used in practice but also complicates the inference due to the dyadic dependence structure. We extend Kyriazidou (1997)'s approach to dyadic data and characterize the asymptotic distribution of our proposed estimator. The convergence rates are $\sqrt{n}$ or $\sqrt{n^{2}h_{n}}$, depending on the degeneracy of the H\'{a}jek projection part of the estimator, where $n$ is the number of nodes and $h_{n}$ is a bandwidth. We propose a bias-corrected confidence interval and a variance estimator that adapts to the degeneracy. A Monte Carlo simulation shows the good finite sample performance of our estimator and highlights the importance of bias correction in both asymptotic regimes when the fraction of zeros in outcomes varies. We illustrate our procedure using data from Moretti and Wilson (2017)'s paper on migration.