Dynamic spatial interaction models for a leader's resource allocation and followers' multiple activities

This paper introduces a novel spatial interaction model to explore the decision-making processes of two types of agents-a leader and followers-with central and local governments serving as empirical representations. The model accounts for three key features: (i) resource allocations from the leader to the followers and the resulting strategic interactions, (ii) followers' choices across multiple activities, and (iii) interactions among these activities. We develop a network game to examine the micro-foundations of these processes. In this game, followers engage in multiple activities, while the leader allocates resources by monitoring the externalities arising from followers' interactions. The game's unique NE is the foundation for our econometric framework, providing equilibrium measures to understand the short-term impacts of changes in followers' characteristics and their long-term consequences. To estimate the agent payoff parameters, we employ the QML estimation method and examine the asymptotic properties of the QML estimator to ensure robust statistical inferences. Empirically, we investigate interactions among U.S. states in public welfare expenditures (PWE) and housing and community development expenditures (HCDE), focusing on how federal grants influence these expenditures and the interactions among state governments. Our findings reveal positive spillovers in states' PWEs, complementarity between the two expenditures within states, and negative cross-variable spillovers between them. Additionally, we observe positive effects of federal grants on both expenditures. Counterfactual simulations indicate that federal interventions lead to a 6.46% increase in social welfare by increasing the states' efforts on PWE and HCDE. However, due to the limited flexibility in federal grants, their magnitudes are smaller than the proportion of federal grants within the states' total revenues.