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. The model that we consider 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 model, we find that credit unions of all types exhibit substantial economies of scale.Keywords: Credit Unions, Correlated Effects, Ordered Choice, Panel Data, Production, Returns to Scale, Switching Regression JEL Classification: C33, C34, D24, G21 * Email : emalikov@stlawu.edu (Malikov), drestr16@eafit.edu.co (Restrepo), kkar@binghamton.edu (Kumbhakar).We would like to thank the editor, the associate editor and two anonymous referees for many insightful comments and suggestions that helped improve this article. We are also thankful to Alfonso Flores-Lagunes, Thierry Magnac, Dave Wheelock, Jeff Wooldridge and seminar participants at Syracuse University, University at Albany, Federal Reserve Bank of Dallas and the 2013 Midwest Econometrics Group Meeting at Indiana University Bloomington for many helpful comments and suggestions. Any remaining errors are our own. We also gratefully acknowledge the technical assistance from the Center for Scientific Computation APOLO at EAFIT University in setting up the cluster we used for the estimation. Restrepo-Tobón acknowledges financial support from the Colombian Administrative Department of Sciences, Technology and Innovation, Colombian Fulbright Commission and EAFIT University. The original version of this paper was circulated under the title "Are All U.S. Credit Unions Alike? A Generalized Model of Heterogeneous Technologies with Endogenous Switching and Correlated Effects".
Credit risk is crucial to understanding banks' production technology and should be explicitly accounted for when modeling the latter. The banking literature has largely accounted for risk by using ex-post realizations of banks' uncertain outputs and the variables intended to capture risk. This is equivalent to estimating an ex-post realization of bank's production technology which, however, may not reflect optimality conditions that banks seek to satisfy under uncertainty. The ex-post estimates of technology are likely to be biased and inconsistent, and one thus may call into question the reliability of the results regarding banks' technological characteristics broadly reported in the literature. However, the extent to which these concerns are relevant for policy analysis is an empirical question. In this paper, we offer an alternative methodology to estimate banks' production technology based on the ex-ante cost function. We model credit uncertainty explicitly by recognizing that bank managers minimize costs subject to given expected outputs and credit risk. We estimate unobservable expected outputs and associated credit risk levels from banks' supply functions via nonparametric kernel methods. We apply this framework to estimate production technology of U.S. commercial banks during the period from 2001 to 2010 and contrast the new estimates with those based on the ex-post models widely employed in the literature.
We derive new measures of returns to scale based on input distance functions (IDFs) and estimate them using nonparametric regression methods. In contrast to the cost function approach, the IDF does not require input prices which are usually unavailable or measured imprecisely. In addition, we can account for equity and physical capital in the IDF. These variables are either excluded from the analysis (especially in a cost function approach) or treated as quasi-fixed inputs, because their prices are not readily available. In our application, we use data for bank holding companies and large commercial banks in the U.S. from 2000 to 2010. We find that although some of these institutions enjoy increasing returns to scale, scale economies are economically small. Thus, concerns about potential cost increases arising from breaking up large banking organizations seem exaggerated, especially from the scale economies point of view. KeywordsNonparametric regression • Returns to scale • Distance functions • Banks JEL Classification D24 • G21 • L13 • C14 Restrepo acknowledges financial support from the Colombian Fulbright Commission; the
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