A Cost System Approach to the Stochastic Directional Technology Distance Function with Undesirable Outputs: The Case of us Banks in 2001–2010

Abstract

This paper offers a methodology to address the endogeneity of inputs in the directional technology distance function (DTDF) based formulation of banking technology which explicitly accommodates the presence of undesirable nonperforming loans -an inherent characteristic of the bank's production due to its exposure to credit risk. Specifically, we model nonperforming loans as an undesirable output in the bank's production process. Since the stochastic DTDF describing banking technology is likely to suffer from the endogeneity of inputs, we propose addressing this problem by considering a system consisting of the DTDF and the first-order conditions from the bank's cost minimization problem. The first-order conditions also allow us to identify the "cost-optimal" directional vector for the banking DTDF, thus eliminating the uncertainty associated with an ad hoc choice of the direction. We apply our cost system approach to the data on large U.S. commercial banks for the 2001-2010 period, which we estimate via Bayesian MCMC methods subject to theoretical regularity conditions. We document dramatic distortions in banks' efficiency, productivity growth and scale elasticity estimates when the endogeneity of inputs is assumed away and/or the DTDF is fitted in an arbitrary direction.

A novel model of costly technical efficiency

“…These relate to FDIC insured commercial banks, where the data vary widely by size, capitalization, regulatory environment, and so on. To ameliorate the potential for heterogeneity in production, Malikov, Kumbhakar and Tsionas (2016) select a sub-sample of larger banks, so giving an unbalanced panel of 2,397 bank-year observations for 285 banks. Metrics for the outputs of a bank's production process are: consumer loans (y 1 ); real estate loans (y 2 ); commercial and industrial loans (y 3 ); securities (y 4 ) and off-balance-sheet income (y 5 ).…”

A hedonic-output-index-based approach to modeling polluting technologies

“…1 We estimate the hedonic-output-index-based IDF in (3.4)-(3.5) subject to the Slutsky symmetry as well as the theoretical monotonicity and curvature restrictions in order to ensure that our results are economically meaningful, as emphasized by Barnett et al (1991), Barnett (2002) and Malikov et al (2015b). 2 Specifically, the monotonicity of D i x, h(y, b) in inputs and hedonic output index, respectively, requires that the log-derivatives satisfy the following conditions:…”

The profit function system with output- and input-specific technical efficiency

“…We also include total assets, to control for bank size, and a time trend. For general studies of the banking industry we refer to Mester (1997, 2003), Hughes and Mester (1993, 1998), Feng and Serletis (2009), and Malikov, Kumbhakar and Tsionas (2016.…”