Applying theCubic Spline Approach on Merger Effects of Credit Departments of Farmers’ Associations in Taiwan
Pai-Lung Chou(1)Chun-AnLu (2)
Wei-Chun Chen(3) Rhung–Jieh Woo(4)
(1)Department of Risk Management and Insurance, National Kaohsiung First University of Science and Technology
(2)Ph.D. Student, Institute of Management, National Kaohsiung First University of Science and Technology
(3)Department of Risk Management and Insurance, National Kaohsiung First University of Science and Technology
(4)Deportment of Agricultural Economics, National Taiwan University
** Corresponding author: Pai-Lung Chou
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Applying theCubic Spline Approach on Merger Effects of Credit Departments of Farmers’ Associations in Taiwan
Abstract
In the past, most research studies were based on translog costfunction models when discussing benefits of merging of financialinstitutions. In this paper, we use spline functions, whichare more flexible, to reconsider benefits of merging of creditdepartments of farmers’ associations in Taiwan. This is the first timethat such functions are used in related research studies inside Taiwan. The results show that, after considering all possibilities ofconsolidation of these institutions using counties as basic units,there are cost savings among almost all counties, which ranges from -0.865%to 33.4%. This shows that these merging activities are deeply affectedby regions where the institutions are. If we further classifysavings by output levels after merging, institutions will getmore benefits if total output levels are less than 5 or greater than 15billion dollars. The best benefits are seen if total output levels are over20 billion dollars, with an estimated 26% of cost savings.
Keywords: Spline function、Operation performance、Merger effects、Credit Departments of Farmers’ Associations.
JEL：G21；G34；L11
Induction
Since 1980, under the trend of financial liberalization and internalization, main countries in the world started to relax control regulations over financial institutions. Open financial environment made huge changes to the world financial services distribution. However, due to the immaturity of regulatory and withdraw mechanisms, overgrowth and competition, inferior operating schemes occurred in the financial market. These were reasons why many too-small or bad-structured financial institutions confronted with serious instability after the Asian Financial Crisis in 1997. In order to respond to challenges of the new era and to achieve the goal of business continuity, global financial institutions have been expanding their breadth of services by mergers and acquisitions in recent years. They expect that they can lower costs and diversify risks.
With this world upsurge trend of consolidation, there have been active financial reforms and innovations in Taiwan to improve self-competitiveness. Under the pressure of trade liberalization after joining WTO, local financial institutions will be confronted with more intense international challenges. In view of the situation that financial institutions in Taiwan are generally too small, have too low a market share, and have too many kinds, it is really necessary to get a step further by integrating the services in order to develop financial organizations which are more sound and fit to world trends. To this end, the government published “The Financial Institutions Merger Act” in 2000 for the first financial reform in Taiwan, with the focus on eliminating bad debts and encouraging consolidation of the financial industry with similar or different industries. Scales of financial institutions in Taiwan have improved ever since, although a gap to international standard still exists. The government issued a second financial reform to declare future directions of enlarging mergers and improving market shares.
Credit departments of farmers’ associations are a part of the community-level financial system. They played an important role in early stages of the agricultural economy in Taiwan. Their main responsibility was to provide members and members’ family with production-marketing and career funds, and funds needed for daily life; they also deposited unnecessary funds to upper-level professional banks of farmers’ associations. Other than that, most business practices that farmers’ associations performed were of service nature, such as supply-marketing, insurance and agricultural extension. However, the profits generated by these services were limited, thus sixty percent of surplus coming from credit departments must be used to run farmers’ associations, and these credit departments became important sources of funds for farmers’ associations. With financial liberalization, services and operating regions for these credit departments had been losing competitiveness and facing excessively high management risks due to regulation constraints. Governments saw the need to propose solutions for these financial institutions after lots of running on banks, excessive outstanding loans and increasing ratio of non-performing loans had occurred, therefore recently many competent authorities have been planning for reforms of these credit departments, with main issues including regional agricultural bank transformation, merging of farmers’ associations inside counties, merging credit departments into banks, and upper-level institution setting-up, etc. In November 2002, the largest-scaled protest demonstration of farmers and fishers in Taiwan history occurred; over 100 thousand farmers and fishers went on street, opposing against taken over of the credit departments and cheap selling of farmers’ assets. This stirred up governments’ awareness of community-level financial systems and what farmers and fishers thought. This also expedited the passing of “Agricultural Finance Law” in 2003, and national agricultural banks officially started to run in 2005. However, too-small-a-size is still a characteristic of the credit departments. To get a more positive solution, the credit departments still have to strengthen its competitiveness in order to combat the pressure brought by many large financial banks and treasuries. In summary, consolidation within the system will be the most laudable approach to enhancing community-level financial systems in our country.
In general, approaches to discussing merging efficiency of financial institutions include the following. 1. Financial Ratio Analysis. Through the selection of merging cases, the choosing of many financial ratios according to characteristics of companies before and after merging, we can analyze the differences and find out changes in operating efficiency brought by consolidation. 2. Event Study Method. This is mainly based on analysis of variability of stock prices, or changes in company market values, to see if there are abnormal returns in merging cases. 3. Econometric Model. Apply models on the research topic and estimate parameters using econometric methods to analyze benefits of merging.
Since credit departments of farmers’ associations are not listed or over-the-counter institutions, we cannot use Event Study Methods here. Besides, Financial Ratio Analysis is deeply affected by the chosen financial variables; also there are no cases of consolidation inside the system for analysis. Considering all these factors, we decide to use Econometric Models in this research study. We discuss the problem from cost aspects, using cubic spline functions to construct cost functions of credit departments of farmers’ associations in Taiwan, overcoming the structural problem inherent in using translog cost functions to estimate costs in the financial industry in many recent research studies. We also use the approximated cost functions to do simulation analyses of merging of the credit departments in the system. We expect that by using a more flexible cost estimation to analyze operating conditions and feasibility of merging of the credit departments realistically, we can make an effort to the reform of community-level financial systems in Taiwan. Overall, this is the core purpose of this research study.
1Review of literatures
The earliest usage of cost functions on financial systems should be attributed to Alhadeff (1954) and McGee (1961), where they used multivariable regression analysis to estimate costs of banks. Since these cost functions lacked theoretical bases, Benston (1965) and Bell and Murray (1968) set production functions of banks to be of Cobb-Douglas forms, and estimated such cost functions by assuming profit maximization in banks using dual theory. Schweitzer (1972) set cost functions to be of CES forms and got similar results. However, whether Cobb-Douglas or CES forms are used, the default value of the substitution elasticity of the input factor is assumed to be a constant. This strong assumption is not consistent with the real world and leads to a conclusion of constant return to scale. To overcome the shortcoming of the previous model, Benston, Hanweek and Humphery (1982) used translog cost functions as a model. Due to the fact that these functional forms have advantages of variable substitution elasticity for factors and production elasticity, allowing the existence of inter-substitution among factors, and the ability to calculate price elasticity directly from partial elasticity formula, translog functions have become the most widely used model for cost functions of financial institutions.
Recently, many related research studies about consolidation of credit departments of farmers’ associations in Taiwan used translog cost functions as a model. For example, Chang, Yan and Wang (2000) used panel data from years 1995 to 1997 to analyze the consolidation from aspects of cost structures and economy of scale. The research results showed that benefits of consolidation among different counties were better than within the same county. Benefits are not significant among Taipei Area or Eastern Part of Taiwan, but are very good in Southwestern Taiwan and Kaohsiung-Pingtung Area.Chen and Fu (2004) used panel data from 279 credit departments from farmers’ associations during 1998 and 2000, in combination with thick efficiency frontier and a priori combined simulation design in Shaffer (1993) to measure cost benefits of consolidation among different cost groups. The results showed that the benefits were better for consolidation among different cost groups than for consolidation in the same group, and benefits of scales had significant effects on merging of these departments in Taiwan.Recently, there is a related research study about merging activities in the financial industry outside the country. Valverde and Humphery (2004) used panel data from savings banks in Spain during years 1986 and 2000 to compare translog, Fourier and spline cost functions in the model, and did simulation analyses on benefits of merging. They used their results to compare with 22 sample banks during the sample period, when there were merging activities among them, and observed that spline functions are more accurate than the other two when predicting directions of cost variation after merging.Humphery and Vale (2004) used panel data from 130 banks in Norway between 1987 and 1998 to compare translog, Foureir and spline functions in the model with the same analysis method and an additional consideration of marginal costs. They observed that spline functions predicted average cost savings to be 3.09%, which was closest to 2.81% in the real case among the three functions. Obviously spline functions performed better than the other two.
From the above analyses, Fourier functions and spline functions are really flexible, which can be used as cost functions in the model. Among these two, spline functions are more accurate in predicting benefits of merging of financial institutions in the real world. Therefore, in this research study, we will focus on spline cost functions proposed by Valverde and Humphery (2004) in doing simulation analyses of merging of credit departments in farmers’ associations in our country.
2Research methods and models
Spline functions were first seen in mathematical literatures by Schoenberg (1946) and evolved to have many different types. Research of these functions became a branch in numerical approximation theory. The main purpose of cubic spline functions that will be used in this research study is to interpolate in different sections separated by many knots in a group of scattered data points. This is similar to the way piecewise polynomial functions are used, therefore cubic spline functions can be seen as a species in piecewise polynomial functions. When used with constraints of smoothness on knots, we can approximate many kinds of trends in data points using a smoothed cubic curve.
Suit, Mason and Chan (1978) used regression methods to approximate spline functions, as shown in Figure 1. The functional form can be expressed as
(1)
where is the minimum value in the data points; and are separating knots; ’s are separating dummy variables in that when =1, the observed value is between and , and when =0, the observed value is in other sections, etc.; is the random error term. Obviously, in formula (1), the function is not continuous in different sections, so we have to add smoothness constraints
(2)
In formula (2), constraints of are for equality of values left and right to knots, constraints of are for equality of slopes left and right to knots, and constraints of are for equality of second order differentials left and right to knots. For convenience, set
(3)
Substitute formula (2) and (3) into formula (1) and combine terms with the same coefficient, we can get
(4)
Until now the fitted spline function can be seen as a combination of multivariable regression functions in five composite variables, with , , , , , and to be estimated. To further simplify formula (4), set new dummy variables and to
and
Substitute those into formula (4), we can get
(5)
This is the functional form of a spline function with two knots and three sections. It can be extended to a general functional form with k knots and (k+1) sections
(6)
From the above, we can get a basic idea of the principle of cubic spline functions and how to derive such functions.
Most often used spline functions in business and economic areas are B-spline functions. They are used to approximate yield curves and do related research of interest term structure. Examples are McCulloch(1975), Deacon and Derry(1994), Lin(1999) and Chou, Yu and Chang(2004). Diewert and Wales(1993) used linear and square spline functions to measure consumer demand system. They discovered that using income levels as knots to get fitted Engel curves was better than traditional methods. It was also more fitted to real data properties. Horowitz, Loughran and Savin (1996) used cubic spline functions to model listed companies in NYSE. They set nine knots according to deciles in the data to get ten sections, and then used those sections to see the relationship between expected returns and the size of companies. In the aforementioned research studies of Valverde and Humphery (2004) and Humphery and Vale (2004), cubic spline functions were used to construct multiple production cost functions to analyze economic benefits.
We used approximated spline cost functions as a model to do simulation analyses on benefits of merging between credit departments of farmers’ associations in Taiwan. We tried to get insights of cost saving effects categorized by counties and output levels after merging. Besides, areas after consolidation with lower benefits were analyzed again and the best output level for merging was estimated too.
According to Stone (1986), the best number of knots for cubic spline functions was between 3 and 7. Borrowing concepts from Horowitz, Loughran and Savin (1996) and considering structures of data of those departments, we partitioned the two output levels using quartiles to get three knots. Data positions in this research were at=13.948, =14.502, =15.004, =13.404, =14.016 and =14.574. In combination with cubic spline functions from Humphery (2004) to estimate cost share functions, where costs and input prices are standardized variables, we got the following as our empirical model
(7)
where TC* represents standardized total costs; is the total amount of outstanding loans; is total savings in banks and treasuries; represents standardized price of funds and standardized price of capital, respectively; T is time trend; represents the Jth knot value of different outputs; is a special dummy variable, whose value is 1 when the ith output value exceeds the Jth knot value, otherwise its value is 0; is the cost share function; are random error terms.
3Data sources and variable definitions
We used panel data from credit departments of 279 farmer’s associations during 1997 and 2000 in Taiwan as empirical data to construct models in this study and did analyses of benefits of merging using data from year 2000. The main data source were from “Operating service analysis of community-level credit departments of farmers’ associations in Taiwan” published by agricultural finance department of Taiwan Cooperative Bank and “Annual report of financial services in all levels of farmer’s associations in Taiwan” published by Taiwan Provincial Farmers’ Association.
Since there were many ways to define input and output variables for financial institutions, we considered financial institutions as intermediaries of capital demand and supply, as was commonly used in the intermediate approach. Therefore capital supply, such as savings, and other liabilities were seen as input terms. Operating expenses for loan management and interest expenses were seen as inputs, too. On the other hand, savings in these departments that were put to loans and deposits to other banks and treasuries, respectively, were output terms. Input terms were further classified as funds price, capital price and labor price. Descriptive statistics and definitions of all the variables are listed in Table 1.