Uncertainty and total factor productivity in the Taiwanese banking industry

Abstract

In this article, we formulate a behavioural model under uncertainty to estimate Total Factor Productivity (TFP) in the Taiwan banking industry. In particular, the article provides a model based on the safety-first rule under uncertainty to measure the risk premium in banking operations that are subject to loan default and other investment risks. With panel data of 40 banks in 1981–1996, a translog cost function and the associated share equations are used to estimate the dual rate of Total Cost Diminution (TCD), the dual Returns To Scale (RTS) and the derived primal rate of TFP. A constant elasticity of transformation output function is employed to construct an aggregated output index of loan and investment activities. The empirical results indicate zero productivity growth and a highly risk-averse banking industry. Government-owned banks are generally more risk-averse than privately owned banks. As expected, the Taiwan banking industry became more risk-venturesome after the deregulation and liberalization of the industry and during the stock market boom of the late 1980s.

Notes

¹ In the second half of 1997, the value of the currencies in Thailand, Indonesia, South Korea, Malaysia and the Philippines plunged. The drop ranged from 35 to 56% and the stock markets declined almost as much, in the range of 32–52%. During the same second half of 1997, the value of Taiwanese currency fell by 15.2%, while the stock market index fell by 9.5%.

² In November 1998, a NT$55 billion (US$1.7 billion) cash run on the Taichung Business Bank was bailed out by the government.

³ The Central Bank in Taiwan was criticized for a series of actions taken in May 1998 to stabilize currency devaluation and prevent foreign capital flight. It suspended the trading of nondelivery forward contracts for foreign exchange hedging. It persuaded banks not to lend any local currency to foreign banks.

⁴ Other nonbanking industry studies have also come to the same conclusion when the nonneutrality towards risk is linked to the measurement of productivity and efficiency. Appelbaum (1991) studies the effects of uncertainty on TFP in the US textile industry. Huang et al. (1986) link risk-averse behaviour to the allocative inefficiency measure in Indian agricultural production. Ballivian and Sickles (1994) estimate the shadow cost of farmer-specific risk attitudes in terms of foregone profit.

⁵ We shall later consider the aggregation issues in a multi-product case.

⁶ This approach of imputing the output price to include loan default and investment loss differs from other studies on banking productivity and efficiency. For example, Hughes and Mester (1993) treat the output quality as an additional argument in the production function, while Huang et al. (1999) measure the output in quality-adjusted units.

⁷ The worst enemy in banking operations is not the low expected profit or utility but its high variation. A risky real estate loan may yield higher expected returns, but it might instead end in bank failure as is evident in the Asian financial crisis.

⁸ This result is similar to the first-order condition of maximizing the expected utility of profits, E( U (π)), without a probability constraint on the threshold utility. Appelbaum (1991) refers to the condition 11 as the output equation.

⁹ We follow Ohta (1974) and Berndt and Khaled (1979) in establishing the relation between primal TFP and dual cost diminution.

¹⁰ There has been much discussion in the literature about whether bank deposits should be treated as input or output in bank operations. One might argue that the deposits should be considered as input since they provide loanable funds for loans and investments. On the other hand, it is an output since the bank provides transaction services to depositors and causes operating expenses to be incurred. Since the purpose of this article is to measure the effect of risk and uncertainty in a bank's loans and investment portfolio on productivity, we adopt the loanable funds argument of treating deposits as input. Furthermore, the specification of two aggregate outputs is reasonably parsimonious in estimation and is subject to data limitation. Disaggregated data on real estate loans, commercial and industrial loans and consumer loans are not available.

¹¹ In their study of scale economies in banking, Benston et al. (1982) adopt a Divisia index on demand deposits, time and savings deposits, real estate loans, installment loans and commercial and industrial loans.

¹² For the pre-reform banks (Bank 1–22), t = 1 for 1981 and for the post-reform new privately owned banks (Banks 23–40), t = 1 at the first year of operation.

¹³ An alternative measure of p is the geometric mean, p = ( p _{y L} ) ^{y _L/y} ( p _{y I} ) ^{y _I/y} .

¹⁴ Only 60% of the reserve requirement is subject to interest payment at an average rate of 2.4% annually. Thus, the effective rate on the reserve requirement is R_s = 1.44%.

¹⁵ This definition of total costs is viewed as the intermediation approach of cost function specification since both operation costs and interest costs are included. See Humphrey (1985) for the discussion of the approach and the alternative production approach. The adoption of the intermediation approach is more appropriate here as the purpose of the article is to address the overall productivity and risk management of a bank.

¹⁶ Professor Bih-Shiou Chen of Soochow University provided the panel data in this study. We acknowledge and appreciate her generosity.

¹⁷ Prior to 1991, the Taiwan banking system consisted of 24 domestic commercial banks, 35 foreign banks and roughly 400 credit cooperatives, the credit departments of farmers’ and fishermen's associations. By the end of 1996, 18 new privately owned banks and six more foreign banks were chartered. Except for two specialized banks, the Export–Import Bank of China and the Central Trust of China, all 40 domestic banks in Taiwan are included in this study.

¹⁸ The Overseas Chinese Bank the Shanghai Commercial and Savings Bank, and the United World Chinese Commercial Bank were granted charters by the government and founded by overseas Chinese in the 1970s as a means of attracting investments from overseas Chinese to Taiwan. The International Commercial Bank of China was founded in 1912 as the government-owned Bank of China and was privatized in 1971.

¹⁹ For comparison, the full-information maximum likelihood method was also used to estimate the simultaneous system of cost and share equations. The results on the coefficient estimates and the derived estimates on RRP, TFP, TCD, RTS and SCOPE are almost identical to the results obtained from the seemingly unrelated method. Only the latter estimates and results are reported here.

²⁰ To facilitate the nonlinear computation, the output transformation function 20 is linearized using Kementa's approximation, ln y = δln y _L + (1 − δ) ln y _I + 1/2 δ(1 − δ)λ(ln y _L − ln y _I )².

²¹ The simple correlation coefficient between the portfolio ratio, y _L /y_I , and the growth rate of the stock index is −0.49.

²² The Cathay Investment and Trust Company was taken over by a group of banks after a huge loss on its speculative investment in real estate. Triggered by financial problems in the Cathay Group, a cash run on the Tenth Credit Cooperative Association in Taipei occurred when its excessive credit to the conglomerate was questioned. The Association was later taken over by the Taiwan Cooperative Bank. In late 1985, the Overseas Investment and Trust Company was taken over by the United World Chinese Commercial Bank after accruing substantial losses due to illegal speculation and trading in foreign exchange.

²³ The Taiwan stock index rose 585% from 2135 in 1987 to a peak of 12 495 in February, 1990. After the Central Bank of China tightened its money supply in 1989 and 1990, the stock index slumped to a squeaky halt at 2560 in October 1990.

²⁴ TCD is not tabulated since it is directly related to TFP and RTS by the identity, TFP = (TCD)(RTS).

²⁵ Statistically, the sample mean TFP of 2.58% for the privately owned banks is significantly higher than the sample mean TFP of 0.41% for the government-owned banks during the post-reform period with the asymptotic t-value of 5.613.

²⁶ The likelihood ratio test on the hypothesis that α _tD = α _ttD = α _tLD = α _tFD = α _tyD = 0 is rejected. When the full-information maximum likelihood method is used to estimate the cost and share equations, the log-likelihood values for the unrestricted and the restricted models are 1958.193 and 1867.279, respectively. With the chi-square values of 181.828, i.e. χ² = 2 (1958.193 − 1867.279), the null hypothesis of zero coefficients is rejected at the 1% level, based on the asymptotic likelihood ratio test.

²⁷ An international survey by Berger and Humphrey (1997) has found mixed results across countries on the impact of deregulation on the productivity and efficiency of financial institutions. For example, Norwegian and Turkish banks experienced improved efficiency and productivity after deregulation. However, banking efficiency in the US was relatively unchanged after the deregulation of the early 1980s. Bank productivity fell due to the rising cost of attracting deposits in an increasingly competitive market.

²⁸ A multiple regression of the RTS on the logarithmic values of asset size (ASSET) and the number of a bank's branches (B) is

where the SEs are in parentheses. The estimates are all significantly positive at the 1% level.