Empirical Economics

, Volume 48, Issue 1, pp 143–168 | Cite as

Nonparametric estimation of returns to scale using input distance functions: an application to large U.S. banks

  • Diego Restrepo-TobónEmail author
  • Subal C. Kumbhakar


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.


Nonparametric regression Returns to scale Distance functions Banks 

JEL Classification

D24 G21 L13 C14 



We thank Christopher F. Parmeter, Emir Malikov, James Byder, Jimmy Saravia, and three anonymous referees for their helpful comments which substantially improved the quality of the article. We, alone, are responsible for any remaining errors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.EAFIT UniversityMedellínColombia
  2. 2.Binghamton UniversityBinghamtonUSA

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