Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity

TL;DR

This paper develops advanced GMM estimators for dynamic spatial panel models that incorporate endogenous network formation, common shocks, and interactive effects, broadening the applicability to social networks and complex dependencies.

Contribution

It introduces a flexible estimation framework for models with endogenous spatial weights and complex dependence structures, including identification strategies and asymptotic properties.

Findings

Estimation method accommodates endogenous spatial weights.

Identification of social interaction parameters via combined moment conditions.

Asymptotic distribution of estimators is mixed normal, test statistics are chi-square.

Abstract

This paper considers a class of GMM estimators for general dynamic panel models, allowing for weakly exogenous covariates and cross sectional dependence due to spatial lags, unspecified common shocks and time-varying interactive effects. We significantly expand the scope of the existing literature by allowing for endogenous spatial weight matrices without imposing any restrictions on how the weights are generated. An important area of application is in social interaction and network models where our specification can accommodate data dependent network formation. We consider an exemplary social interaction model and show how identification of the interaction parameters is achieved through a combination of linear and quadratic moment conditions. For the general setup we develop an orthogonal forward differencing transformation to aid in the estimation of factor components while maintaining orthogonality of moment conditions. This is an important ingredient to a tractable asymptotic distribution of our estimators. In general, the asymptotic distribution of our estimators is found to be mixed normal due to random norming. However, the asymptotic distribution of our test statistics is still chi-square.