Strategic Interaction and Spatial Econometrics

Analysis of strategic interaction among decision makers has recently become a major focus of economists and other social scientists. An example of such interaction includes interdependent choices of policy instruments by local or state governments. In this case, the optimal level of a jurisdiction's policy instrument depends on the levels chosen by other (perhaps neighboring) jurisdictions. Another example of strategic interaction might include fashion decisions. One individual's preferred choice of clothing style might depend on what other people are wearing. In both cases, an agent's optimal choice depends on the choices of others. The equilibrium set of decisions in such a setting must be mutually consistent, with all agents making choices that are optimal given what others are doing. Spatial econometrics provides an ideal tool kit for empirical analysis of strategic interaction. The \spatial lag" model in particular closely captures the behavior described above, where di®erent, spatially distinct agents make interdependent decisions. The model allows the analyst to test for the presence of strategic interaction and, if present, to determine its nature. The purpose of the ensuing discussion is to sketch a general theoretical model for the analysis of strategic interaction, and to discuss the use of the spatial lag framework in estimating its parameters. In the economics literature, two principal types of strategic-interaction models can be identi ̄ed. Despite their di®erences, these models ultimately lead to the same empirical speci ̄cation, which can be estimated with spatial lag methodology. The ̄rst approach can be referred to as the \spillover" model. In this framework, each agent chooses the level of a decision variable, or \instrument," with ti denoting the level of agent i's instrument. In addition to being a®ected by the level of his own instrument, agent i is a®ected by the instrument levels of other agents as well. Thus, i's objective function is written