GMM estimation of the spatial autoregressive model in a system of interrelated networks

This paper considers efficient estimation of spatial autoregressive models in a system of interrelated networks. An example describes a market situation with several chain stores competing against each other. The strategy of a store in the chain does not only involve coordination with the other stores in the same chain, but also competition against opponent stores in other chains. To estimate the system, we extend the generalized method of moments framework based on linear and quadratic moment conditions proposed by Lee (2007) and Lin and Lee (2010). We show that under some regularity assumptions the proposed GMM estimator is consistent and asymptotically normal. We derive the best GMM estimator under normality and propose a robust GMM estimator against unknown heteroskedasticity. Monte Carlo experiments are conducted to study the finite sample performance of the GMM estimation. We also provide an empirical application of the model on the spatial competition between chain stores in the market of prescription drugs.