Analysing scale and scope specialization efficiencies of US agricultural and nonagricultural banks using the Fourier flexible functional form

Abstract

This study presents results of cost estimation and efficiency analyses of various size categories of agricultural and nonagricultural commercial banks using the Fourier Flexible (FF) function model. The traditional cost estimation model is expanded in this study with the inclusion of loan quality and financial risk indexes often ignored in empirical efficiency models. The FF model produced more intuitive scale efficiency results than the standard translog model owing to its greater global approximation capability. Scale efficiency measures provide evidence of increasing returns to scale for small and medium-size banks. Agricultural banks demonstrated a stronger tendency to maximize the potentials of increasing returns to scale as a result of output expansion. The translog cost model, however, remains a reliable tool in scope efficiency analyses that, in this study, produced results suggesting that agricultural banks are more likely to thrive more efficiently under specialized lending operations.

Keywords:

• expansion path sub-additivity
• Fourier flexible functional form
• ray scale economy
• translog cost

JEL Classification::

• Q14
• G21

Notes

¹ This study refers to ‘agricultural banks’ as deposit-taking commercial banks with agricultural loan ratios exceeding the designated cutoff ratio for categorizing agricultural and nonagricultural commercial banks. These farm lenders are therefore not to be confused with other agricultural lending institutions, such as the Farm Credit System and the federal government's Farm Service Agency.

² Ellinger and Neff (1994) and Neff et al. (1994) all used the translog cost function; Featherstone and Moss (1994) estimated an indirect multi-product (normalized quadratic) cost function.

³ For more details on the derivation of the FF function, please see Chalfant and Gallant (1985) and Gallant and Souza (1991).

⁴ Gallant (1982) claimed that rescaling the data within [0, 2π] is important for accurate Fourier series to compensate the so-called Gibb's phenomenon.

⁵ The choice of the cost share equation to be dropped will not significantly influence the results of the estimation.

⁶ The period of study covered qualifies as part of the bubble period when rising land prices have driven the market to engage in significant land investment transactions and consequently pose as an impediment to implementing cost minimization strategies. Ogawa (2008) points out that since concavity condition on cost functions is based on the implicit assumption that firms are indeed minimizing costs. Thus, analysing firm's cost decisions during bubble periods with an imposed concavity condition will lead to model misspecification.

⁷ Branch banking data would ideally provide more sources of variability than consolidated banking data. However, it can be argued that consolidated banking data could have adequately captured important operating decisions on output expansion and product/service diversification as these decisions are usually made at the main headquarters. Nonetheless, the reader is cautioned to interpret this study's results as accruing only to consolidated banking parameters.

⁸ The FDIC criterion for defining agricultural banks provides a compromise between the Federal Reserve System approach (periodically changing agricultural loan ratios ranging from 10% to 15% based on actual financial conditions of all commercial banks) and the methods used by the American Banking Association (based on either the absolute dollar volume of agricultural loans or an agricultural loan ratio of 50%).

⁹ 

The reason for using z ₁ instead of NPL is because ln z ₁ is a monotonic transformation of NPL which will only change the magnitude of the NPL but still will keep all other properties of NPL. In addition, after the transformation, ln z ₁ will be all positive numbers with less extreme values.

¹⁰ 

The justification for developing z ₂ is the same as the rationale used for calculating z ₁.

¹¹ For the sake of brevity, the coefficients of Fourier series are not presented in Table 3. These results may be available from the authors upon request.

¹² Microeconomic theory requires that the cost function should satisfy: (i) nondecreasing in input prices, (ii) homogeneity of degree one in input prices, (iii) concavity in input prices and (iv) nondecreasing in outputs.