  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.
