Are All U.S. Credit Unions Alike? A Generalized Model of Heterogeneous Technologies with Endogenous Switching and Correlated Effects

Credit unions differ in the types of financial services they offer to their members. This paper explicitly models this observed heterogeneity using a generalized model of endogenous ordered switching. Our approach captures the endogenous choice that credit unions make when adding new products to their financial services mix. Failure to do so is likely to yield biased and inconsistent estimates. The model that we develop also allows for the dependence between unobserved effects and regressors in both the selection and outcome equations and can accommodate the presence of predetermined covariates in the model. We use this model to estimate returns to scale for U.S. retail credit unions from 1996 to 2011. We document strong evidence of persistent technological heterogeneity among credit unions offering different financial service mixes, which, if ignored, can produce quite misleading results. Employing our generalized model, we find that credit unions of all types exhibit substantial economies of scale.