Identification and Inference of Strategic and Social Interaction Models

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

The understanding of interactions not mediated via prices is important in many economic phenomena. For example, a firm's decision to enter a market may be affected by other firms' decisions. In the classroom, peer effects may affect outcomes and decisions which may in turn play an important role later in life. There are many other examples. Because of the interplay of decisions and outcomes across actors, the empirical analysis of these phenomena is related to the empirical analysis of individual outcomes and decisions but poses challenges beyond those typically found in the analysis of individual decision making. This research project investigates methodological aspects and substantive applications in the empirical analysis of interaction models. One of the main challenges arises as a given model may be amenable to more than one set of predicted outcomes or behaviors (i.e. "equilibria"). When this is the case it is not clear how to retrieve important model components from observed data. In a first set of studies, the researcher extends previous work where the investigator and a co-author study the identification of interaction models where certain information is private to participants (de Paula and Tang, 2011). Under typical assumptions in this literature they showed that when multiple solutions are possible and different data points correspond to potentially different solutions, whether someone is incentivized or dissuaded from taking an action (when others do) can be inferred even with a very loosely defined model. As a byproduct, the investigators are also able to test for the existence of multiple solutions in the data. This is important since multiplicity is problematic for many estimation techniques currently available. The researcher extends that analysis in several directions. First, whereas the basic insight on the detection of more than one solution remains applicable in dynamic games under standard assumptions, the results on the retrieval of interaction effects is affected since what a person does at present affects the environment in the future. Second, even in the static environment originally investigated, continuously distributed control variables such as prices or income pose practical complications in estimation. Because different values for those variables may induce a different number of solutions in the underlying economy, typical nonparametric estimates of the interaction effect aggregate over covariates that contaminate one's inference on the uniqueness of a solution and, consequently, on the sign of interaction effects. Finally, whereas in many applications one can easily label the relevant players (e.g., husband and wife, Wal-Mart and local stores), in other contexts the labels do not naturally present themselves. The researcher also investigates how this affects the inference of interaction effects and applies the methods to the analysis of peer effects among college roommates, a topic that has been studied extensively in recent years. In a related project, the researcher focuses on empirical models where people choose who to associate with (i.e. "network formation games"). Recently, a lot of interest has developed around network phenomena in Economics and the Social Sciences more generally. It is common, for example, to find multiple equilibria in both environments. Because a network formation model bears many similarities to models usually studied in the empirical Industrial Organization literature, ideas and techniques akin to those previously used in the analysis of that literature can be adapted to the study of social networks. To demonstrate the methodology developed in this research, an illustration using the AddHealth dataset is presented. The techniques proposed in this research will provide an important first step in the subsequent analysis of outcomes which are influenced by how individuals connect to each other. Examples include educational outcomes and information transmission.