An examination on the cost efficiency of the banking industry under multiple output prices’ uncertainty

Abstract

This article formulates a behavioural model of profit maximization, which explicitly incorporates both multiple output prices’ risk and safety-first practice. This theoretical model is specifically suitable for investigating financial institutions, whose output prices frequently encounter a variety of risks, such as loan defaults/arrears. The sample banks are empirically found to be highly risk-averse. Furthermore, risk preferences exert little effect on the technical efficiency estimates, whereas the same estimates obtained by the standard fixed-effect model under certainty tend to be overestimated. Evidence is found that a specialized bank offering a single product with a larger scale of production will be preferable in an uncertain atmosphere.

Notes

¹ In the context of risk-reducing inputs, proposed by Just and Pope (1978) under production uncertainty, several empirical studies have emerged recently; for example, Kumbhakar (1993), Battese et al. (1997) and Tveteras (1999). These papers unanimously investigate agricultural data, possibly pervasive of production risk.

² Roy (1952) provided a brief history of the safety-first attitude.

³ Between the second quarter of 1997 and the first quarter of 1998, the value of the currencies in Thailand, Indonesia, South Korea, Malaysia and the Philippines dropped substantially, ranging from 57.46 to 228.95%, and their stock markets also fell by a scope of 26.59–50.89%. During the same period, the value of Taiwan's currency decreased 21.79%, while its stock market index declined 13.24%.

⁴ Note that term MRP _i is now equal to and Equation A4 reduces to Π₁₂ .

⁵ In fact, two out of the three cost share equations, implied by the translog cost function, can also be estimated simultaneously in order to improve the accuracy of the estimates. Unfortunately, this implies that all inefficiencies are technical in essence, excluding the possibility of allocative inefficiency, see Berger (1993).

⁶ At the end of 2002, there were 53 domestic banks in Taiwan. We preclude the two industrial banks and two specialized banks from the sample, since their activities differ dramatically from commercial banks.

⁷ Note that we have tried to put an extra term of a quadratic trend in Equation 5.1. However, its coefficient estimate is insignificant due possibly to the fact that the sample period spans only 7 years. Notation T* can also be formulated as firm-specific, which implies that 48 additional parameters (one of these firm-specific parameters has to be normalized to be zero) have to be estimated. We fail to make the likelihood function converge using many sets of initial values for the parameters.

⁸ The linear time trend is originally included in the cost function of Model I to capture the effect of technical progress. Since its coefficient estimate is found to be insignificant, it is removed from all models.

⁹ If we re-run Model I under the assumption of a ₁ = 0, then we come up with an estimate of 0.023 for a ₀, which is significant at the 1% level and smaller than 0.5.

¹⁰ The individual estimates of 's are not shown to save space, but are available upon request to the authors.

¹¹ In particular, their TE scores derived from the fixed-effect and the random-effect models are about 65.4 and 67.1%, respectively.

¹² It is important to note that Model II is still affected by the joint probability distribution of random prices P ₁ and P ₂.

¹³ We also compute the measures of cost complementarities, proposed by Baumol et al. (1982). Similar implications to the estimates of scope economies can be drawn and hence, are overlooked to save space.

¹⁴ The commonly-used Allen-Uzawa partial elasticity of substitution between inputs i and j is defined as:

where and . If S_ij is greater (less) than zero, then the two inputs are said to be substitutes (complements). The own price elasticities S_ii , i = 1, 2, 3, …, must be negative in congruent with standard theory.