Estimating Strategic Complementarities in Credit Union’s Outsourcing Decisions

We examine the choice between internal or external provision of information technology (“IT†) services for US credit unions. Credit unions may provide their own systems for tracking loans and deposit accounts or they may choose to outsource these systems from external providers. Empirically, the likelihood that a credit union outsources its system is increasing in the number of other credit unions in the same geographic market who outsource. This empirical regularity may be due to common characteristics of credit unions in close proximity that make them more or less likely to outsource. It may also be due to complementarities whereby one credit union’s decision to outsource affects the relative costs associated with outsourcing for the other credit unions in the market. Anecdotal evidence suggests that the credit unions communicate with one another at the local level due to their non-profit status and lack of significant competitive overlap. This level of communication may give rise to strategic complementarities present in models of social interactions as well as network effects. In this study, we estimate a structural model in which credit unions outsource if doing so achieves a cost savings relative to maintaining their own systems. The decision to outsource is modeled as a game in which the simultaneous outsourcing decisions of the other credit unions in the market are contained as an argument in the relative costs associated with outsourcing. Ours is an example of a game with strategic complementarities in the sense that a given agent’s payoff is increasing in the number of other players who take the same action. The problems arising from multiple equilibria which are endemic to these games have received significantly less attention, in large part because interest in the economics of social interactions and network externalities (two leading examples involving complementarities among agents’ actions) has been a relatively recent phenomenon. To estimate the extent of complementarities in credit union outsourcing decisions, we adapt the intuition in recent work by Ciliberto and Tamer (2004) and propose a method for estimating payoff parameters that places no restrictions on which outcome obtains when the model is consistent with multiple equilibria. Unlike previous work, however, we are able to overcome the curse of dimensionality that makes estimation of the model impossible for markets with more than five or so firms. We present an algorithm to find the fixed points of the best reply correspondence using known properties of the set of pure strategy Nash equilibria. Our model is also powerful enough to assess coordination failures in different sized markets. Our main empirical finding is that the probability that the observed outcome is pareto dominated by another outcome, when the observed outcome is consistent with multiple PSNE, is U-shaped reaching its minimum at five credit unions.