Estimation of scale and scope economies in multiproduct banking: evidence from the Fourier flexible functional form with panel data

Abstract

An empirical study is conducted on scale and scope economies for Taiwan's banking industry with panel data using a Fourier flexible cost function developed by Gallant and a translog cost function, both of which take economic efficiency into account. It is found that the Fourier form is more appropriate than the traditional translog form in fitting the data, and that various efficiency measures computed using the Fourier function are compatible with each other, while those computed using the translog function are not. The Fourier evidence shows that sample banks continue to enjoy economies of scale, and exhibit scope diseconomies, which indicates that greater product diversification can reduce banking costs through product-mix economies. Banks may benefit from further diversifying their line of financial services.

Notes

 It is noteworthy that coefficients of the second order terms in the translog function are derived from the Fourier series (to be discussed in Section II). Therefore, the two parts of the FF function are not independent of each other, which may have been overlooked by Mitchell and Onvural (1996), Berger and DeYoung (1997), Berger et al. (1997), Berger and Mester (1997), and DeYoung et al. (1998).

 Mitchell and Onvural (1996) defined their μ _j 's using 6 as the numerators, which differs from Gallant (1982).

 For the restrictions and hypotheses about the characteristics of a firm's production function, see Appendix B.

 Although matrix ψ is a 6 × 6 square matrix with 36 elements (parameters), it actually contains only 15 free parameters to be identified in estimation after imposing homogeneity and symmetry restrictions required by microeconomic theory. Therefore, only 15 of the 43

s can be estimated by the particular FF cost function.

 According to microeconomic theory, a cost function must be (i) nondecreasing in input prices, (ii) homogeneous of degree one in input prices, (iii) concave in input prices, and (iv) continuous in input prices.