Simultaneous Equations Models With Higher-Order Spatial or Social Network Interactions

Abstract

This paper develops an estimation methodology for network data generated from a system of simultaneous equations, which allows for network interdependencies via spatial lags in the endogenous and exogenous variables, as well as in the disturbances. By allowing for higher-order spatial lags, our specification provides important flexibility in modeling network interactions. The estimation methodology builds, among others, on the two-step generalized method of moments estimation approach introduced in Kelejian and Prucha (1998, Journal of Real Estate Finance and Economics 17, 99–121; 1999, International Economic Review 40, 509–533; 2004, Journal of Econometrics 118, 27–50). The paper considers limited and full information estimators, and one- and two-step estimators, and establishes their asymptotic properties. In contrast to some of the earlier two-step estimation literature, our asymptotic results facilitate joint tests for the absence of all forms of network spillovers.

Bayesian estimation of multivariate panel probits with higher‐order network interdependence and an application to firms' global market participation in Guangdong

“…Such an approach is desirable, for example, with structural models, where several outcomes influence each other, and where some or each of these outcomes feature network or spatial interdependence. For example, Kelejian and Prucha (2004) studied such a case with continuous outcomes in a cross‐sectional model, and Drukker et al (2021) generalized it and derived the joint variance‐covariance matrix of all model estimates. Other studies analyzing systems of—simultaneous as well as seemingly unrelated—equations with continuous outcomes include Cohen‐Cole et al (2018), Liu (2014), and Yang and Lee (2017) for cross‐sectional data and Baltagi and Bresson (2011), Baltagi and Pirotte (2011), and Baltagi and Deng (2015) for panel data.…”

“…We permit multiple sources of interdependence of the cross‐sectional units. For instance, the various sources could reflect different rings (or orders) of neighbors or they could reflect conceptually different sources of interdependence (such as geography and input‐output relationships); see, for example, Badinger and Egger (2013), Drukker et al (2021) for such considerations in the context of continuous outcomes with single‐equation panel and systems‐cross‐sectional data, respectively. We will introduce the weights matrices $$$ {W}_{st} $$$ to capture interdependence with respect to the source $$$ s $$$ at time $$$ t $$$, whose characteristics will be specified below.…”

Estimating Dynamic Spillover Effects along Multiple Networks in a Linear Panel Model

“…Egami (2021) developed methods of sensitivity analysis when there are unobserved networks that capture part of the spillover effects. Drukker, Egger, and Prucha (2022) proposed asymptotic analysis of estimation and inference procedures in a linear spatial model, which accommodates multiple networks.…”

Bayesian Estimation of Multivariate Panel Probits with Higher-Order Network Interdependence and an Application to Firms' Global Market Participation in Guangdong

“…Such an approach is desirable, for example, with structural models, where several outcomes influence each other, and where some or each of these outcomes feature network or spatial interdependence. For example, Kelejian and Prucha (2004) studied such a case with continuous outcomes in a cross-sectional model, and Drukker et al (2021) generalized it and derived the joint variance-covariance matrix of all model estimates. Other studies analyzing systems of-simultaneous as well as seemingly unrelated-equations with continuous outcomes include Cohen-Cole et al (2018), Liu (2014), and Yang and Lee (2017) for cross-sectional data and Baltagi and Bresson (2011), Pirotte (2011), andDeng (2015) for panel data.…”