My research focuses on unobserved heterogeneity in network and panel data.
Tractable Estimation of Nonlinear Panels with Interactive Fixed Effects
(with Andrei Zeleneev)
Abstract: Interactive fixed effects are routinely controlled for in linear panel models. While an analogous fixed effects (FE) estimator for nonlinear models has been available in the literature (Chen, Fernández-Val and Weidner, 2021), it sees much more limited use in applied research because its implementation involves solving a high-dimensional non-convex problem. In this paper, we complement the theoretical analysis of Chen, Fernández-Val and Weidner (2021) by providing a new computationally efficient estimator that is asymptotically equivalent to their estimator. Unlike the previously proposed FE estimator, our estimator avoids solving a high-dimensional non-convex optimization problem and can be feasibly computed in large nonlinear panels. Our proposed method involves two steps. In the first step, we convexify the optimization problem using nuclear norm regularization (NNR) and obtain preliminary NNR estimators of the parameters, including the fixed effects. Then, we find the global solution of the original optimization problem using a standard gradient descent method initialized at these preliminary estimates. To make our method readily applicable in practice, we also propose specific numerical algorithms for solving the involved optimization problems, establish their convergence, and provide their efficient implementation in our R package NNRPanel.
Flexible Imputation of Incomplete Network Data
(with Ge Sun)
Abstract: Sampled network data are widely used in empirical research because collecting complete network information is costly. However, empirical analyses based on sampled networks may lead to biased estimators. We propose a nonparametric imputation method for sampled networks and show that empirical analyses based on imputed networks yield consistent estimates. Our approach imputes missing network links by combining a projection onto covariates with a local two-way fixed-effects regression. The method avoids parametric assumptions, does not rely on low-rank restrictions, and flexibly accommodates both observed covariates and unobserved heterogeneity. We establish entrywise convergence rates for the imputed matrix and prove the consistency of generalized method of moments (GMM) estimators based on imputed networks. We further derive the convergence rate of the corresponding estimator in the linear-in-means peer-effects model. Simulations show strong performance of our method both in terms of imputation accuracy and in downstream empirical analysis. We illustrate our method with an application to the microfinance network data of Banerjee et al. (2013).