  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.
