Abstract
This paper explores the estimation of a panel data model with cross-sectional interaction
that is flexible both in its approach to specifying the network of connections
between cross-sectional units, and in controlling for unobserved heterogeneity. It is assumed
that there are different sources of information available on a network, which can
be represented in the form of multiple weights matrices. These matrices may reflect
observed links, different measures of connectivity, groupings or other network structures,
and the number of matrices may be increasing with sample size. A penalised
quasi-maximum likelihood estimator is proposed which aims to alleviate the risk of
network misspecification by shrinking the coefficients of irrelevant weights matrices to
exactly zero. Moreover, controlling for unobserved factors in estimation provides a
safeguard against the misspecification that might arise from unobserved heterogeneity.
The asymptotic properties of the estimator are derived in a framework where the true
value of each parameter remains fixed as the total number of parameters increases. A
Monte Carlo simulation is used to assess finite sample performance, and in an empirical
application the method is applied to study the prevalence of network spillovers in
determining growth rates across countries.