A General Method of Deriving the Inefficiencies of Banks from a Profit Function

This article develops a new method of estimating inefficiencies in joint production and shows that unlike the approaches utilized in the previous studies of inefficiency, this method maintains a consistent relationship between the error term of a profit function and the error terms of its price derivatives. A useful by-product of the method is a proof of a Hotelling-like lemma that relates stochastic input demand and output supply functions to stochastic profit functions. While the previous studies fit a single frontier to data on all firms, this paper estimates a frontier unique to every observed firm to allow each one to have a different potential of achieving maximal levels of profit. The new method is applied in the analysis of annual data, 1984–1989, for U.S. commercial banks. Both the analytical and numerical results of the paper show that the residual that the previous studies attribute to inefficiency includes the effects of excluded variables and of inaccuracies in the specified functional forms. Once accurate estimates of these effects are subtracted from the residual, the distortions in the measured inefficiencies should be considerably reduced. Consequently, this article considers how such estimates might be obtained.     

The Effects of Megamergers on Efficiency and Prices: Evidence from a Bank Profit Function

This paper examines the efficiency and price effects of mergers by applying a frontier profit function to data on bank megamergers. We find that merged banks experience a statistically significant 16 percentage point average increase in profit efficiency rank relative to other large banks. Most of the improvement is from increasing revenues, including a shift in outputs from securities to loans, a higher-valued product. Improvements were greatest for the banks with the lowest efficiencies prior to merging, who therefore had the greatest capacity for improvement. By comparison, the effects on profits from merger-related changes in prices were found to be very small.     

Small Banks, Small Business, and Relationships: An Empirical Study of Lending to Small Farms

We examine small banks lending to small farms. We find that relationships, as measured by the length of tenure of farm operators, are positively related to bank lending. We also find that de novo banks have a positive tendency to lend to small farms. When existing relationships between borrowers and incumbent lenders are stronger, de novo banks have greater difficulties in lending to small farms. We further find that, even within the category of small banks, lending to small farms (as a percentage of a banks assets) tends to decrease as the bank increases in size.