Product mix, transactions and cost behaviour: a study of South African bank branches

Abstract

This paper utilizes microeconomic theory and a panel data set to assess the impact of product mix and transactions on cost behaviour of bank branches in South Africa over the short and long‐term. Estimates of properties of concavity and monotonocity indicate that the cost functions of typical bank branches in South Africa are neither consistent with short‐term nor long‐term cost‐minimizing behaviour. This corroborates earlier findings which indicate that South African banks have low production efficiency and high market power. In addition the cost functions and two production‐output type indices indicate that overall, the intermediation‐output type mix (foreign exchange and custodial services) has a more significant effect on cost behaviour than the production‐output type mix (cheque and deposit accounts). The variety of production‐output type services provided by a branch appears to have limited effect on costs. However the financial value of production‐output type transactions has an impact on costs while the financial value of intermediation type products does not. Branches that provide intermediation‐output type products tend to have higher variable costs – the key determinant of costs is the number of transactions.

Keywords:

• banking
• product mix
• cost behaviour
• South Africa

JEL classifications:

• D01
• D23
• G21

Acknowledgements

This paper is part of the Southern Africa Financial Institutions Industry Structure (SAFIIS) Project funded under BARDA – Grant 017/2002–2008. I wish to acknowledge Econometrix (Pty) Ltd, South Africa for allowing me access to their various commercial database products. I am grateful to Michael Adeyemo, Fabian Ogbonna and Bongiwe Kanzi for able research assistance particularly in the cleaning and cross‐validation of the branch input cost data. They are not responsible for any errors or omissions which may remain.

Notes

1. The exchange controls in South Africa are governed by the 1961 amendments to section 9 of the Currency and Exchange Control Act, Number 9 of 1933. Enforcing compliance of the exchange controls regime has spawned other legislation such as the Financial Intelligence Centre Act (FICA) of 2003 and Exchange Control Amnesty and Amendment of Taxation Bill 2004.This has increased the regulatory and compliance burden. As Strausz (2006) indicates, this buries organizations in paperwork and influences their cost behaviour. Retail banks have attempted to invest in computer equipment and other quasi‐fixed inputs to automate the compliance process or but are still highly reliant on variable inputs.

2. From an epistemological perspective, the studies that are perhaps most related to this one, are that of Steward (1998), who uses bank data to illustrate the pros and cons of the Varian weak axiom of cost minimization (WACM) methodology, and Ray and Bhadra (1993) and Bilodeau, Cremieux and Ouellette (2000), who test for evidence of cost minimization in farming and hospitals respectively. If they preserve the given order, functions that are between ordered sets have properties of monotonicity. If every line segment which joins two points on a graph does not lie above the graph at any point then a function of a single variable is concave.

3. Ray and Bhadra (1993) and Bilodeau, Cremieux and Ouellette (2000) illustrate such an approach can be applied to farms and hospitals respectively. Indeed their approach greatly influences the approach taken herein.

4. There are two major non‐parametric approaches – data envelope analysis and the free disposal hull analysis. There are three major parametric approaches – the distribution free approach, the thick frontier approach and the stochastic frontier approach.

5. So as Wang (2003) illustrates, attempts are underway to get the best of both methods by applying other techniques such as neural networks to the estimation of production frontiers.

6. One of the few studies that has applied the production approach and the intermediation approach is the study by Berger, Leusner and Mingo (1997).

7. The data did not allow for meaningful differentiation of the labour and capital inputs of these two types of branches. Therefore we assume that the branches are lending and borrowing branches.

8. There is a fairly long‐standing debate in the applied econometric literature regarding the relative performance of the translog, Fourier and other functional forms. Although developed over three decades ago by Christensen, Jorgenson and Lau (1973), more recent studies confirm that the performance of the translog justifies its continued use. For example, Ivaldi et al. (1996) find that Fourier and translog cost functions provide similar information. However, tests tend to favour the Fourier cost function because it is able to represent a wider range of technological structures than the translog function, particularly where there are significant trigonometric terms in the empirical specification. Allied to this Stern (1994) also finds that the translog is as reasonably accurate as most other functional forms – however, this is data and application dependent. So the consensus would appear to be that a number of semi‐parametric and non‐parametric functions are (possibly) more accurate – but dependent on the application, the translog is still capable of quite robust estimates. Also see Adams, Berger and Sickles (1999) for more discussion on the choice of an appropriate functional issue with relevance to banking.

9. See Takayama (1990) for a full explanation of how concavity can be imposed on the translog by ensuring that the relevant matrix is negative–semi‐definite.

10. There has been some criticism that translog cost models do not effectively assess the characteristics of the underlying production technology. Driscoll and Boisvert (1991) use Monte Carlo experiments and second and third‐order cost and production models to overcome this. They illustrate that the primary cause of ineffectiveness and low performance is errors in variables bias and not the translog specification per se.

11. See Judge et al. (1982) and Wiens (2007).

12. For more details on steps to do this, see Joreskog (1970) who developed one of the earliest general models for the analysis of covariance structures and applied this to behavioural and social science data.

13. An earlier version of the BCSA data base contains observations for 61 branches from all of the nine provinces of South Africa and was used in Okeahalam (2006).

14. This method has a drawback in that, strictly speaking, the funds deposited at the SARB cover license costs for retail, corporate and commercial bank activity. Given the focus of the study on retail banking, it is not entirely accurate to allocate all of this capital cost to retail banking.

15. While we did not explore this issue in our analysis, ‘deposit’ branches provide funds to ‘lending’ branches at market related costs. Therefore, given that it can increase the profits of a deposit branch, the volume of excess funds at a deposit branch can be considered to be a product output. Conversely the lending branches utilize the funds derived from the deposit branches as inputs. Since all branches receive funds at constant prices, this leads to a reduction in the operating profit of branches.

16. This is an improvement on the measure – number of available tellers/open teller hours (NAT/OTH) – as has been used in some studies, for example Okeahalam (2005). Indeed, while it can be specified as an output, the open teller hours (NAT/OTH) variable is more clearly an input than it is an output.

17. Bilodeau et al. (2000) develop this type of index in their study of hospitals and Nautiyal and Singh (1985) applied a similar approach in a study of timber plants.

18. Cebenoyan (1990) estimated a hybrid Box–Cox function coefficient and applied this to scope economies in banking. The same technique has been used in this study to estimate an iterated Box–Cox coefficient and measure second‐order cost derivatives. Although second‐order terms are used, we are also aware of Hayes' (1986) illustration of theoretical and empirical advantages of estimating third‐order rather than second‐order translog utility function and terms. In theory the rigor of tests for the appropriate functional form is improved as a result of the increase in the order of approximation.