Fixed-Effect Regressions on Network Data


Martin Weidner
Martin Weidner
  • Speaker
Faculty of Social & Historical Sciences, University College London

Event Information

Type
Research Seminar
Programme
Finance
Date
Tue. 30 May. 2017
Contact
Wing Wah Tham
Time
16:00 - 17:00
Location
H10-31


Abstract

This paper studies inference on fixed effects in a linear regression model estimated from network data. An important special case of our setup is the two-way regression model, which is a workhorse method in the analysis of matched data sets. Networks are typically quite sparse and it is difficult to see how the data carry information about certain parameters. We derive bounds on the variance of the fixed-effect estimator that uncover the importance of the structure of the network. These bounds depend on the smallest non-zero eigenvalue of the (normalized) Laplacian of the network and on the degree structure of the network. The Laplacian is a matrix that describes the network and its smallest non-zero eigenvalue is a measure of  connectivity, with smaller values indicating less-connected networks. These bounds yield conditions for consistent estimation and convergence rates, and allow to evaluate the accuracy of first-order approximations to the variance of the fixed-effect estimator. The bounds are also used to assess the bias and variance of estimators of moments of the fixed effects.

Andreas Pick
Associate Professor of Econometrics
  • Coordinator
Wing Wah Tham
Wing Wah Tham
  • Coordinator