Economies of Scale and Economies of Scope in Multiproduct Financial Institutions: A Study of British Columbia Credit Unions

Abstract

This paper investigates the production technology facing computerized credit unions in Canada. A full system of translog cost equations is estimated in order to test for economies of scale, economies of scope, and other production characteristics in a multiproduct context. The regression results indicate that most of the credit unions in our sample experience significant increasing returns to scale as they expand their level of output. There is also evidence of cost complementarity or economies of scope in their mortgage and other lending activities. As a result, legislation which limits the ability of credit unions to grow and diversify will likely raise the operating costs of this important group of financial institutions. Additional structural tests of the most general translog specification suggest that none of the restrictive production conditions commonly imposed by other researchers using Cobb-Douglas and CES specifications provide a valid representation of credit union technology. The results of many earlier studies are therefore open to question. THIS PAPER PRESENTS A number of structural tests of the production technology facing large computerized credit unions in Canada. A full system of translog cost equations is estimated using detailed cross-sectional data on British Columbia credit unions. The parameter estimates obtained from our multiproduct specification allow us to test for economies of scale, economies of scope, and factor substitution.Unlike many earlier studies, the present paper introduces the various outputs as separate variables instead of crudely proxying them with a single output measure such as total assets, the total number of loans, or the number of depositors. By explicitly recognizing the multiproduct nature of the intermediation process, we are able to address more interesting production questions and remove some of the bias caused by misspecification and measurement error in simpler Approaches. The flexible translog specification allows us to estimate the sensitivity of costs to proportionate increases in all outputs (economies of scale), as well as the cost savings firms realize by producing several outputs jointly rather than specializing in the production of one (economies of scope).The test results reported in the latter part of the paper suggest that increasing returns to scale exist in almost all of the credit unions in our sample. Though

Scale and Scope Economies in the Canadian Property and Casualty Insurance Industry

“…Murray and White (1983) obtain similar results when including or excluding the input share equations.…”

“…We accomplished this by using the definitions of Panzar and Willig (1977) and BPW (1982), and the estimation techniques described by Murray and White (1983) and Kim (1987). Panzar and Willig (1977) demonstrate that a local measure of overall economies of scale (SL) for a multiproduct firm is the scale elasticity: 3 inC SL=c(Yw)IfYiMci=lI.…”

“…A negative cross-marginal elasticity implies a cost complementarity between two products. Following Murray and White (1983), we used an approximate test of this condition, which is: a,a1+a<O…”

Cost Functions, Efficiency, and Quality in Day Care Centers

“…Assume there are two categories of output: infant-toddlers, and older children. Following Gyimah-Brempong (1987), Murray and White (1983), and Denny and Pinto (1978), economies of scope exist, if…”

Assessing output and productivity growth in the banking industry

“…The intermediation approach (Sealy and Lindley, 1997, Murray and White, 1983, Favero and Papi, 1995 emphasizes the intermediating role of banks, i.e. the fact that they collect deposits and buy capital, which they convert into loans and other assets.…”