ECONOMIES OF SCALE IN THE MANAGEMENT OF OCCUPATIONAL SUPERANNUATION SCHEMES BY D. M. KNOX, B.A., F.I.A., 1. INTRODUCTION

Transcription

1 ECONOMIES OF SCALE IN THE MANAGEMENT OF OCCUPATIONAL SUPERANNUATION SCHEMES BY D. M. KNOX, B.A., F.I.A., F.I.A.A. 1. INTRODUCTION THE level of benefits paid to members of occupational superannuation schemes will depend on the level of contributions made by the employer and employee, the investment earnings received by the accumulated assets and the expenses incurred in the management of the scheme. However, this third factor has been ignored by previous studies into occupational superannuation, even though higher expense levels will naturally cause reduced benefits for a given level of contributions and investment return. In this respect, cost efficiency within the superannuation industry is an important criterion in assessing the efficacy of employer-sponsored occupational superannuation. One method of revealing the degree of efficiency within any industry is through an investigation into the existence of economies of scale within its operation. Yet it must be borne in mind that the existence of scale economies per se does not make an industry cost-efficient. Indeed, the simultaneous existence of high-cost small firms and low-cost large firms might suggest an undesirable situation. However, as will be discussed later, there are many features of the superannuation (or pension) industry which provide significant contrasts to other industries. In essence, superannuation schemes are not concerned with maximizing profits, but rather with providing valuable benefits to its members. With this in mind, the expenses incurred in the management of individual superannuation schemes are assessed in this paper, such that the extent of any economies of scale may be found. As a result, some action will be suggested which may decrease future expenses so that benefits may increase. No previous study has analysed the overall cost structure of the Australian superannuation management industry. Management of superannuation schemes comprises many aspects and may involve the activities of life offices, professional investment managers, merchant banks, superannuation consultants, actuaries and lawyers, as well as the sponsoring employer. In view of this variety of management activities. it is essential that any study into management costs is as broad as possible and not limited to a particular component of the superannuation management industry. This is the major problem of the earlier Australian studies which bear upon this subject as they have been restricted to life offices. For instance, Praetz (1978) estimated cost curves for the superannuation business of Australian life offices while Rutledge and Tuckwell (1974) and Praetz (1981) studied economies of scale within the life office industry. These studies have not considered the overall cost structure of individual superannuation 337

2 338 Economies of Scale in the Management of scheme management but rather the cost structure for life offices. Hence in contrast to the above-mentioned studies, this investigation will analyze the cost structure for individual superannuation scheme management, including schemes with a wide variety of management practices. This new approach, taking into account all the costs incurred in superannuation management, enables cost curves to be estimated for this industry. These estimates show that significant economies of scale exist and that contrasting cost curves may apply for life office and self-administered schemes. However, possible shortcomings of these estimates must also be recognized as they are based on a sample of schemes, and not the whole population, due to the unavailability of comprehensive data. Nevertheless, the results suggest that there are significant cost implications for the sponsoring employer in the choice of the most appropriate management structure for their superannuation scheme. It should also be added that whilst this study has been restricted to Australian schemes, it is possible that similar results may occur elsewhere, if comparable studies were carried out. The next section reviews the variety of superannuation management arrangements operating within Australia, while 3 discusses the factors that may contribute to the existence of economies of scale within the industry. The following section develops a model based on appropriate economic theory that reflects these influences and discusses the most appropriate definition for each factor. In 5, the available data are evaluated and three possible definitions of total cost are analysed whilst the subsequent section presents the results of the investigation, and discusses the preferred form of management for schemes of various sizes. Finally 7 summarizes the findings and comments upon the implications of the results for the efficiency of Australian occupational superannuation. 2. THE MANAGEMENT OF OCCUPATIONAL SUPERANNUATION SCHEMES The management of an occupational superannuation scheme involves a wide range of activities which may be classified into five broad categories. The following list briefly describes some of the tasks which can be involved within each category: 1. Administration: record keeping, reports to members, entry of new members, benefit payments. 2. Investment: purchase and sale of assets, analysis of current and prospective investments, investment policy. 3. Legal: trust deed arrangements and amendments, implications of current and proposed legislation. 4. Actuarial: regular review of scheme s financial progress, costing advice with respect to possible changes in benefit design. 5. Consulting: general or specific advice concerning trends within the superannuation industry.

3 Occupational Superannuation Schemes 339 Naturally each of these activities generates a cost that is borne by either the accumulated assets of the fund or directly by the sponsoring employer. In toto, these are the costs incurred in the management of a superannuation scheme. Although there are five major areas of management costs, there exists an enormous variety of management structures amongst occupational superannuation schemes. One major cause for this diversity is that each management activity may be performed by either in house staff members or by an external organization. Indeed, in some instances, a particular task may be shared between these two parties. Figure 1 illustrates six examples of various combinations of in house and external management. In the first case, the total management of the scheme, except for some basic administrative records kept by the employer, is carried out by an external organization. This arrangement is very common amongst small and medium-sized superannuation schemes fully administered by life offices. The second example is similar. though in this case the sponsoring employer is also partly involved in the investment decisions. Many medium-sized superannuation schemes adopt this position in which the employer selects an investment policy for the investing organization to follow. The remaining four examples are all instances of schemes completely administered by in house staff, but with varying levels of in house involvement in the other categories of management. In general, these situations are restricted to larger employers, although the third case may be observed in respect of some smaller organizations. In this example, the investment activities are shared whilst all the legal, actuarial and consulting work is completed by an outside body. The fourth figure illustrates a case where in house legal advice is available whilst the fifth instance represents a scheme where the actuary is also an employee. Finally, Figure l(6) shows the extreme position where all the management activities are carried out by in house employees. This possibility is restricted to large financial institutions, such as banks and life offices, and public sector schemes. It should also be added that, whilst Figure 1 represents six examples based on some current Figure 1. Six examples of superannuation management practice.

4 340 Economies of Scale in the Management of practices, it should not be considered comprehensive. Rather, these graphs are indicative of the variety of superannuation management practices that may be adopted. A second factor that is important in understanding the variety of existing management structures for superannuation schemes is the wide range of organizations which offer services. For instance, a scheme represented by Figure 1(1) may be administered by a superannuation broker, invested with more than one financial institution, receive professional advice from independent actuaries and lawyers and conduct regular discussions with a superannuation consultant. In this case, the management is spread over several organizations external to the sponsoring employer. On the other hand, the same graph also illustrates the common situation for smaller schemes where all the management tasks are completed by one body, say a life office. The management of an occupational superannuation scheme is shared between the sponsoring employer and at least one external organization, except in the extreme case illustrated by Figure l(6). Hence the total costs of managing a scheme are the sum of the relevant in house costs and the fees charged by these external organizations. This paper will investigate changes that occur in these total costs as the size of the scheme increases. It will not consider the cost structures and the existence or otherwise of scale economies in the institutions that operate within the superannuation management industry. After all, most of these organizations (for example, life offices and merchant banks) are involved in a wide range of activities that includes, but also extends much beyond, the management of occupational superannuation schemes. It is essential that this distinction is recognized in any study of the costs of superannuation management. It should also be noted that this investigation must be restricted to schemes where expenses can be identified as a separate cost. Hence, the study relates to managed funds or self-administered schemes and excludes schemes based on insurance policies. 3. IMPORTANT FACTORS AFFECTING A STUDY INTO ECONOMIES OF SCALE IN THE SUPERANNUATION MANAGEMENT INDUSTRY An analysis of the costs incurred by firms operating within any industry, and hence whether economies of scale exist or not, provides important information to managers within that industry, firms considering an entry into the industry, as well as legislators, politicians and researchers. However, two requirements are always needed for an accurate study into the costs incurred within a particular industry. These are a homogeneous product, so that individual firms may be compared accurately, and a standardized measurement of costs. The first requirement (which may be difficult to obtain due to diversification), is usually present within industries providing financial services due to their similar products, often caused by the significant impact of legislation. In

5 Occupational Superannuation Schemes 341 particular, within the superannuation industry there is a high level of product homogeneity as the benefits are only provided upon the happening of certain contingencies. However, the second requirement is much more difficult to obtain due to differing accounting methods, and inconsistent definitions of output.* Nevertheless, several studies have been conducted into the industries providing financial services, as these difficulties are often reduced with the legislative requirements of annual returns. Hence the cost structures in banking, life insurance, credit unions and trust departments have been investigated. However, almost no work has been carried out on the cost structure within the superannuation management industry. These previous studies have considered several industries providing financial services to the public and it may be suggested that occupational superannuation provides a similar financial service. Yet there are significant differences which exist and these require emphasis so that any cost structures derived, together with implications, are clearly distinguished from the earlier studies. These distinctive characteristics include: 1. The importance of the employer-employee relationship. All employersponsored occupational superannuation schemes are based on this relationship so that the size of a particular scheme (as measured by membership) is primarily determined by the number of employees eligible to join and is not affected by the cost or structure of the scheme s management. In essence, the scheme s size is a by-product of a large number of economic, social and political factors which influence the demand for the company s product. 2. The absence of direct competition between individual firms (schemes) producing the industry s output (namely superannuation benefits). This is in contrast to almost all other industries offering financial services wherein the individual firm competes directly against other firms and is thereby able to attract customers. In this normal competitive environment, market forces ensure that firms with an excessive average cost (that is, those who are unable to offer competitive products) either withdraw from the market or merge with other firms to reduce their costs and hence improve the competitiveness of the resulting product. This direct competition, with the related requirement to reduce average costs, does not occur within the superannuation industry due to the employer-employee relationship. The results of this study suggest that significant economies of scale occur within the superannuation management industry and consequently, if direct * For a more detailed discussion on this matter, refer to Benston (1972), Friedman (1955) and Johnston (1960). North American examples include Benston (1972), Houston and Simon (1970) Murray and White (1980) and Murphy (1969) respectively. British data published by the National Association of Pension Funds (1975) suggest limited economies of scale although a detailed investigation into the matter was not conducted.

6 342 Economies of Scale in the Management of competition existed, many smaller schemes would be forced to close or merge due to their higher expenses per unit contribution. It should be noted that whilst the presence of economies of scale suggests that an element of inefficiency operates within the total industry, given the tens of thousands of small schemes that exist, this does not imply that the current managers are inefficient in the administration of the schemes. Indeed, given the variety of organizations offering management services and the intense competition between them, it is unlikely that inefficient organizations would continue. Rather, the results suggest that the existing structure (with its tens of thousands of schemes) is an inefficient mechanism to provide superannuation benefits. One small area of direct competition that is beginning to exist within Australia is between union-based and employer-sponsored schemes. The extent of this competition is very limited as the benefit levels of most union schemes are fairly low and primarily assist those union members without access to an employer-sponsored scheme. Nevertheless, some firms in particular industries have chosen to join the union schemes. Although these decisions have been determined by a number of factors, one potential influence is the lower expense rate that applies to the union scheme due to its size. 3. The restrictions placed on the actions of scheme members. The consumers of an occupational superannuation scheme (namely the members) are unable to receive any benefit from the scheme until the employer-employee relationship is broken. This differs from other financial service industries where the consumer is able to receive the benefit (for example, the interest paid on a deposit) at regular dates. Similarly, the superannuation consumer is unable to elect to change schemes without choosing to resign. These restrictions remove many of the choices that consumers of other financial service industries enjoy. 4. The luck of substantial entry or exit requirements. Unlike most industries, no initial capital is required for entry into the superannuation industry. All employers may establish a scheme and, where appropriate, may close a scheme, with few additional costs. This ease of entry and exit means that employers are able to change their attitudes towards superannuation as circumstances alter and so enter or leave the industry, almost at will. However, winding-up a scheme is not a regular event due to the significant industrial relations problem that is normally associated with it. 5. The luck of annual returns. In contrast to most other financial institutions, many occupational superannuation schemes are not required to submit annual returns. Further, the returns that are completed are primarily concerned with the guidelines affecting the taxation status of the scheme and not the costs incurred in scheme management. This means that uniform accounting data, which are available for many other financial institutions, do not exist for occupational superannuation schemes in Australia.

7 Occupational Superannuation Schemes The effect of legislation. Primarily, the major legislative impact on occupational superannuation is through the Income Tax Assessment Act. The receipt of the taxation concessions are subject to the format of superannuation benefits provided by the scheme. This restriction means that there is limited product differentiation between schemes, thereby removing the problem of heterogeneity to a significant extent. 7. The variety of management structures. As explained in the previous section, there exist considerable differences between the various management structures that may be adopted by the schemes. This diversity, together with the lack of annual returns, produces significant difficulties in compiling accurate uniform data on the costs of superannuation management. The above features are important characteristics to be considered in any study into the cost structure of managing occupational superannuation schemes. Two advantages which result from them are the easy identity of the firm (i.e. the scheme) within the industry and a high level of homogeneity in the output market. On the other hand, the lack of available data and the mixture of in house and external costs produce substantial difficulties in the accurate measurement of the cost required. But given the above characteristics, are economies of scale likely to occur? The major activity of superannuation scheme management is the day-to-day administration associated with record-keeping, benefit payments, etc. It is suggested that this activity offers considerable scope for scale economies, as a component of this cost will be fixed, irrespective of the size of the scheme. Examples would include the establishment of a system of records and/or the purchase of computing equipment. Additional sources for scale economies include regular activities that are normally completed irrespective of scheme size such as actuarial reviews and trust-deed documentation or amendments, where the costs of the service are relatively stable. A further area of probable scale economies concerns the investment of the individual scheme s accumulated assets with a decreasing level of average transaction costs as the size of some investment parcels rises. In addition, larger funds may have increased power within the capital markets due to the size of their accumulated assets, and this may result in preferential treatment. In summary, there are a number of factors which are likely to cause reducing average costs as the size of the scheme increases. Prior to establishing the relevant model for this study, it is appropriate to outline some of the benefits that may accrue from the ensuing results. Firstly, the major factors that influence the total cost of scheme management will be identified. This will provide both sponsoring employers and the variety of organizations providing the services with a better understanding of their cost structure and should lead to greater efficiency in the management industry. Secondly, the investigation will assist sponsoring employers in the choice of the appropriate management structure for their individual superannuation scheme

8 344 Economies of Scale in the Management of although there may be factors other than cost, such as business associations, which are also important. Nevertheless, the cost differentials between the various forms of management structures available for superannuation schemes should, in most circumstances, be a major criterion in the choice. Thirdly, identifying the management costs will permit employers without a scheme to assess the total costs incurred in introducing a scheme, which normally include both their level of contributions and the costs of scheme management. Finally, the existence of economies of scale may cause employers to reconsider their strong desire for a single-employer scheme in lieu of a multi-employer arrangement. This latter alternative, which is increasingly popular in the United States of America,* could cause a decline in the average management costs, if larger multi-employer or union-based schemes are able to benefit from any economies of scale present within the superannuation management industry. 4. A MODEL TO MEASURE MANAGEMENT COSTS 4.1. The form of the cost function A generalized cost function, which requires further specification in line with the unique characteristics of the Australian superannuation management industry, is C = f (Q, H, P, O) (1) where C represents the operating costs per period; Q represents the level of output per period; H represents factors which cause heterogeneity in the output; P represents differences in factor prices and/or management structure; and O represents other unspecified factors. However, before this estimation of the cost function can proceed it is necessary to clarify the objective of the individual firm (or scheme). Bell and Murphy (1968) have shown that if the firm s output is determined exogenously, and if firms seek to minimize costs, for that pre-determined level of output, then unambiguous estimates of the parameters of the cost function may be obtained where the underlying production function is Cobb-Douglas. But are these assumptions appropriate for the superannuation industry? First, the output level of an occupational superannuation scheme is determined primarily by the sponsoring employer through the adoption of a particular benefit design. This decision is not a function of the costs of scheme management but is influenced by a large number of factors. Hence the first assumption that the output level is determined exogenously may be accepted. Second, the costs of scheme management are either paid directly by the employer * Munnell (1982) notes that multi-employer plans covered 9% of private plan participants in 1950, 16% in 1959 and 22% in 1980.

9 Occupational Superannuation Schemes 345 (in addition to its normal contributions) or from the accumulated funds of the scheme. In both instances, it is reasonable to assume that there is an attempt to minimize them as they reduce either the employer s profits or the level of members benefits. Further, the direct competition that exists between the organizations offering the various management services provides schemes with the option of changing their management structure, should excessive costs occur. It is therefore reasonable to assume that individual schemes endeavour to minimize their management costs and, indeed, are able to do so. Third, the Cobb-Douglas production function is relatively unimportant as the model remains valid, provided certain statistical requirements are met and these will be tested in a subsequent section. Thus. based on the above assumptions, that each scheme endeavours to minimize its management costs for an exogenously determined level of output. the cost function becomes: Economies of scale exist where there is a declining average cost per unit of output as the level of output increases. Dividing equation (2) by Q and taking logs, the following equation results: where AC repesents the average cost per unit output; b* equals b1-1; and b1, b2, b3 and b4 represent the elasticities for each input factor in respect of the total cost. Hence, scale economies will be confirmed if b* is significantly less than zero whilst diseconomies occur if the reverse is found. The specification of the variables in the equation is now necessary before empirical results can be considered The definition of output The occupational superannuation industry does not produce one item of output each year. Instead, a range of benefits of varying size are provided to scheme members, following the happening of a contingency during their employment. This variety. together with the lack of any detailed statistics, means that a scheme s output cannot be easily and accurately assessed. A proxy measure for the level of output is required. Previous studies of the cost functions of life insurance offices (for instance Houston and Simon (1970), Rutledge and Tuckwell (1974), Praetz (1978) and Praetz (1981)) considered that premiums received were the most appropriate measure of output. In all cases except Praetz (1978) additional variables were added to the model to allow for the non-homogeneity of the output from different life offices. Geehan (1977) also used premiums, although he redefined premium per unit of output by using a weighted sum of activities. However, as (2) (3)

10 346 Economies of Scale in the Management of discussed earlier, there are important differences between superannuation schemes and other financial institutions (including life offices) such that there may exist a better proxy for superannuation output than the level of contributions (or premiums). Two alternative proxies for output that require consideration are the value of accumulated assets held by an individual scheme and the level of benefits paid to scheme members within a particular period. The use of asset-values to measure output is unsatisfactory as it is a volatile measure subject to market movements. Further, the variety of funding levels between schemes of similar membership and benefit scales means that asset-values are not a good measure of present or future output levels. The omission of asset-values as a measure of output due to these unsatisfactory features is unfortunate as some economies of scale may be based on the size of the fund s assets. For instance, schemes with large investible funds may receive investment opportunities that are not available to the smaller funds. Nevertheless the removal of asset-values is necessary due to the uncertainty of its meaning as a measurement. The second alternative is to measure scheme output by the level of benefits paid to members during a particular period. Whilst this approach appears to measure the ultimate purpose of superannuation (namely, the provision of benefits), it is not necessarily indicative of the overall level of output for a particular scheme, due to the variations in the number of benefit payments that may occur from year to year. The Australian context of predominantly lump sum benefits further accentuates these yearly fluctuations. Hence, the measurement of output by benefit payments is unsatisfactory. The rejection of these two alternatives leaves the level of total contributions per unit period as the only available proxy for the output of a scheme. But is the level of output (i.e. benefits paid) proportional to the level of contributions? In almost all cases, the ultimate level of benefits is dependent on the contributions received and the investment earnings. Whilst the level of investment earnings will fluctuate between schemes and so could influence the level of output, it is reasonable to assume that the long-term variations between schemes will be relatively small and that the benefits provided will not be significantly affected. In other instances, the level of contributions will also reflect additional contributions in respect of unfunded past service. However, as this is normally a minor proportion of the total contribution, its effect will also be minimal. Hence it is reasonable to assume that the level of contributions is the major factor determining the size of benefits provided and thus, the best proxy for output. Other advantages of using this measure are: (i) it is readily identified in respect of all schemes; (ii) it is reasonably stable for an individual scheme from year to year; and (iii) the average cost will then be expressed as a percentage of contributions which is readily understood by all sponsoring employers and scheme managers.

11 Occupational Superannuation Schemes Definitions of the other variables The remaining variables in equation (3) reflect the non-homogeneous output within the industry and differences in factor prices (such as wage rates), scheme design, management structure, and other unspecified factors. One of the characteristics of the occupational superannuation industry mentioned earlier was that the existing legislation ensured a fair degree of homogeneity between the output of various schemes. In practice, this means that most schemes provide retirement, death, disablement and resignation benefits only. However, even within this uniform set of benefits, there is considerable diversity in the benefit formulae used by schemes in the determination of benefits. This means that individual members in different schemes but with similar salary experience and service may receive benefits of varying size. The best measure of this non-homogeneity would be the benefit design but due to the diversity of formulae used these are not directly comparable. Instead, the level of total contributions per member will be used as a proxy to represent the variety of benefit levels provided. It is expected that in most cases there will be a correlation between this measure and the benefit scale as larger benefits require higher total contributions per member. However it should be realized that contributions per capita may also vary due to the age structure of the scheme members, even if benefit levels are the same. This problem may be overcome through the introduction of an age variable or by assuming that the age structure is similar for the membership of most superannuation schemes. This latter alternative will be adopted here due to reasonableness of the assumption in respect of most schemes and the difficulty in obtaining an objective variable measuring the age structure of the membership. A priori reasoning suggests that higher contributions per member would cause a reduced average cost for the same level of output (or total contributions) due to fewer members, and hence a reduction in the level of administration required. The next variable in equation (3) indicates differences in management structure and/or factor prices. As discussed in 2 there is a wide variety of management structures in operation. However, as the major cost is incurred in the administration component of management it is appropriate to restrict this consideration to the two major forms of scheme administration: namely life office administration, or self-administration. To assess the effect of these two forms of administration a dummy variable will equal one for life office schemes and zero for self-administered schemes. It will be assumed that no variation occurs in wage levels (the dominant factor price) as these are primarily determined by exogenous influences within the economy and should have a similar impact for all schemes. The final variable relates to unspecified factors which may influence the cost structure of superannuation management. Murray and White (1980) suggest that higher unit costs are associated with growth while Benston (1970) believes that additional growth causes an initial reduction in average cost as existing staff work more intensively. Within the Australian superannuation industry, growth

12 348 Economies of Scale in the Management of in the scheme s output (as measured by total contributions) may cause an initial reduction in average cost in line with Benston s reasoning, as the existing management structure is likely to remain unchanged. That is, a lagged effect in respect of growth could exist, such that any necessary changes do not occur for some time. Hence, it would be expected that recent growth could cause a reduction in the average cost. However, this does not imply that the reduction will be permanent. In line with the above reasoning, equation (3) may be re-written as: log, AC = B0 + b* loge Q + b2 logc, C + b3d + b4 loge, G (4) where Q represents the level of total contributions per unit period (as a proxy for output); C represents the average contribution per member (as a proxy for benefit levels); D represents the dummy variable equalling 1 for life office and 0 for self-administered schemes; and G represents the ratio of the latest period s contribution level to the preceding period s contribution level. Prior to utilizing this model with empirical data, it is first necessary to review the available data. It should be added that there may exist other factors or priorities which interact with the management of a superannuation scheme and so affect the level of costs for an individual scheme. However, in the absence of quantifiable data, these have been omitted from this initial study into the topic. 5. THE BASIS OF THE EMPIRICAL INVESTIGATION 5.1. The sample An empirical investigation into the existence of economies of scale within the cost structure of managing occupational superannuation schemes based on the model developed above requires data pertaining to costs, output, membership and the management structure of individual schemes. This information is unavailable, so that it is necessary for data relating to a sample of individual schemes to be obtained. Further. it is desirable that any sample represents a cross-section representing superannuation schemes of all sizes and management structures. In view of this requirement, questionnaires (similar to Appendix 1) were forwarded in August 1981 to 453 companies publicly listed on Australian Stock Exchanges. The companies chosen were those with details in the Stock Exchange Research Handbook Table 1 indicates the response to the questionnaires. Although the response rate is low, with no response from 83% of the companies, two factors need to be borne in mind.

13 Occupational Superannuation Schemes Table 1 No. Responses received 45 Reply indicating unwillingness to respond 15 Reply indicating inappropriate superannuation scheme 2 Reply indicating no superannuation scheme 5 Questionnaire returned-incorrect address 11 No reply As discussed earlier, total costs include some in house costs for all sponsoring employers. This item. which was requested, may be particularly difficult to determine for some schemes and may have deterred many companies from replying. 2. Many companies may have no superannuation scheme or one based on individual insurance policies, for which the questionnaire was unsuitable. Before assessing the information obtained, it is useful to note the diversity amongst the responses received. In total there were 49 superannuation schemes included in the sample (4 companies responded with respect to 2 schemes) with total scheme membership of 56,183 (ranging from 28 to 7,541 members) and total fund assets of $631.0 million (ranging from $260,000 to $82.1 million)* for the respective scheme years which ended in These total assets represent approximately 5% of all assets held by superannuation schemes in the private sector. Twenty-three of the schemes were managed by the individual employer, twenty-two by life offices and four were administered by other organizations. This variety within the sample is an advantage as the results may then be interpreted with reference to a much broader cross-section of the industry than any previous study. There is also the chance of bias within this small sample. This is impossible to check accurately as no population statistics are available. However, the distribution of membership size for the sampled schemes shows no significant difference from the much larger 1980 survey of superannuation schemes carried out by the Association of Superannuation Funds of Australia. Although this result is not conclusive. it suggests that no significant bias exists within the sample The definition of total cost Section 2 identified five major components of cost in the management of superannuation schemes, each of which is fully or partly incurred by the sponsoring employer or an external organization. Hence the questionnaire * It should be noted that the scheme with the largest membership did not have the highest fund value.

14 350 Economies of Scale in the Management of requested data concerning costs paid to external organizations involved in each of the five management categories as well as in house costs relating to any or all of the individual cost categories. Thus the most comprehensive definition of the total cost for management of a superannuation scheme would be the summation of all costs shown in the returned questionnaire in respect of the scheme year ending in For this purpose, the sample size has been reduced to 44 as four respondents did not complete this question and one scheme was excluded due to extreme data.* This first definition of total cost, which uses all the information given, provides inconsistent data due to the different methods used in assessing the investment cost by organizations involved in this component of superannuation management. For instance, some organizations charge a fee which is clearly identified and payable by the sponsoring employer (or the scheme) whilst others provide the scheme with a net yield, after the deduction of investment costs. In these cases, the sponsoring employer may be unaware of the investment cost as the gross yield (i.e. before deduction of the fee) is never shown. This practice resulted in some schemes showing no investment costs. Hence to provide a greater consistency within the data, it is necessary to exclude investment costs from the total costs. This requirement means that any economies of scale due to investment costs will not be shown. One further problem remains. Many respondents did not show any in house costs. As mentioned earlier, all sponsoring employers will incur an element of these costs which should be included in any measurement of total costs. Hence, replies which excluded any in house costs were removed from the sample as they were considered incomplete, with two exceptions. These are (i) self-managed schemes which included in house costs in their administration costs; and (ii) life office schemes with less than 100 members. It is considered that in house costs in these cases will be fairly small and so may be ignored without removing the validity of their inclusion within the sample. Although it must be acknowledged that this procedure is not ideal, it improved the quality of the sample through the removal of nine schemes. The above comments provide three definitions for the total costs involved in the management of an occupational superannuation scheme which are: (i) Total costs-all costs shown: (ii) Non-investment costs-all costs shown with the exclusion of investment costs; and * In this case, the plan was declining and, according to the data provided, the annual superannuation contribution per member (excluding expenses) was only $66. The effect of removing investment costs from this investigation is difficulto assess though there is little doubt that some economies occur within the investment markets. For example, many transaction costs involve a sliding scale of charges. Further, the monoposonistic power of the larger funds within the market may also reduce their investment costs.

15 Occupational Superannuation Schemes 351 (iii) Best estimate of costs-all non-investment costs with the exclusion of nine schemes due to the omission of any in house costs. In view of the above reasoning, the third definition is to be preferred, even though the sample size is smaller. 6. THE EMPIRICAL STUDY 6.1. The overall results Economies of scale imply a decreasing average cost per unit of output. Hence before considering the regression results based on the model developed earlier, it is relevant to consider the average costs incurred by schemes of various sizes. Table 2 summarizes these results, using the third definition of costs.* A strong inverse relationship between the average cost and the level of contributions is Table 2. Average costs ( as a percentage of contributions/ grouped by scheme size Total Average cost contributions as a percentage per annum of contribution No. of ($ million) (%) schemes <¼ ¼ l > suggested, although it is clearly non-linear. The logarithmic functions used in the model appear appropriate. The coefficients in equation (4) will now be estimated using ordinary least squares regression. Two important assumptions required for this approach are that the residuals have a constant variance and are independent from each other. These may be tested by: (a) counting peaks in the actual residuals, shown as k, and (b) using the signs of the residuals and counting the number of runs within the residuals with the standarized test statistic shown as r. Together with these two tests, the Durbin-Watson statistic (shown as d) will assist in the diagnosis of any mis-specification within the model. To enable these three tests to be carried out, the sample has been ordered by the level of total contributions paid in the individual scheme year ending in * Similar results are produced if the other two cost estimates are used. This is the Goldfeld-Quandt peak test as defined in Goldfeld and Quandt (1972), pp , The standardized test statistic is calculated using the expected number of runs and its variance, as developed by Kane (1968), p. 365.

16 352 Economies of Scale in the Management of Table 3 shows the regression results in respect of equation (4) for each of the three definitions of costs described earlier. Similar results were obtained in each case with the significant test statistics for the output and contribution per member variables strongly suggesting the existence of scale economies. In addition, in respect of the third cost definition, both the dummy and growth variables were significant. As expected, this definition provided the best results, due to the better data, and for these reasons the ensuing discussion will be Table 3. Ordinary least squares regression results for equation (4) Variable Constant logeq logec D logeg Cost definition used (ii) (iii) (i) Non-investment Best estimate Total costs costs of costs (1 190) (1 061) ( 901) ( 069) ( 151) 205 ( 188) (1 187) ( 061) ( 135) 309 ( 168) (1 059) ( 054) ( 120) 407 ( 159) ( 891) Sample size k r d Notes: 1. Standard errors are shown in parenthesis. 2. The sample size is reduced when the growth variable is used due to the incomplete returns for two schemes. restricted to this definition of costs. It should also be noted that none of the tests for model mis-specification produced significant results. These regression results, which confirm the existence of scale economies, may now be used to estimate elasticities within superannuation scheme management and thereby assess the causes and impact of the existing cost structures. Using the estimated co-efficients from the third column in Table 3, equation (4) may be estimated as: log, AC = log, Q log, C D loge, G. (5) Recalling that Q represents total contributions and C contributions per member, then this equation may be re-expressed as AC = K (Contributions)- 555 (Membership) 403 G (6)

17 Occupational Superannuation Schemes 353 where K is a constant. As AC represents management costs divided by the total contributions, this result suggests a contribution elasticity of 445. That is, a 10% rise in contributions (which is the measure of output used) is associated with a cost increase of only 4 45%. This result provides empirical evidence for the existence of substantial economies of scale within superannuation scheme management. Equation (6) highlights two other results. Firstly, an increase in membership, without an increase in total contributions, causes a higher proportion of the total contributions to be paid for management costs. This result is in line with the earlier reasoning and is due to the greater membership requiring additional records, etc. Secondly, the regression results suggest that growth has a negative impact on average cost which supports Benston s suggestion of the lagged effect of growth. However, it is possible that while a substantial growth may not cause a corresponding rise in costs in the short term, the costs in the longer term will rise proportionately. This possibility w-as not able to be tested with the available data. The significance statistic in respect of the life office dummy variable also suggests that a different cost curve may exist for schemes with contrasting management structures. If this is the case, it may have significant implications for employers in their choice of the appropriate scheme manager Who should manage the scheme? Some writers, in discussing the management of occupational superannuation or pension schemes, imply that there are cost advantages for small schemes to be wholly administered by an external organization (say, a life office) and for larger schemes to be self-administered. For instance, Lee (1973) suggests that life office management is particularly attractive for small schemes in terms of costs and uses British experience to confirm this idea. The argument has been supported within the Australian context by Knight et al. who state that the services provided by life offices can be a great help to the employer, especially in the case of smaller funds, where the work involved does not justify the employment of a full-time secretary.* The truth of this reasoning has never been tested in an objective study, although it has been accepted by many employers, as borne out in the study discussed by Baker (1973). Table 4 shows that Australian schemes with larger membership are more likely to be self-administered than smaller schemes. If this behaviour of changing the management structure of a superannuation scheme as it increases in size is rational, then it is reasonable to expect two distinct cost curves for life office and self-administered schemes. With this in mind, the ordinary least-squares regressions for equation (4) were completed separately in respect of the third cost definition for life office and non-life office administered schemes. The results are shown in Table 5 and whilst they should be treated with * Knight et al., Superannuation Planning in Australia, Second edn, CCH Australia Limited. 1979, p. 194.

18 354 Economies of Scale in the Management of Table 4. Scheme size and self-administration % of schemes with non-investment Size of scheme administration carried (as measured by out by the company number of employees) or trustees Source: Baker (1973), Appendix 1. Table 5. O.L.S. regression results for life office and non-life office schemes Life office administration Non-life office administration Constant (2.233) (1 340) (1.311) LogeQ ( 101) ( 082) ( 097) LogeC ( 235) ( 183) LogeG ( 979) ( 795) Sample size k r d (1.112) ( 067) ( 144) ( 481) Notes: 1. Standard errors are shown in parenthesis. 2. None of k, r or dare significant (1 227) (1 123) ( 074) ( 080) ( 168) ( 620) caution due to the small samples, it is nevertheless appropriate to express the two average cost functions that are suggested. They are: For life office administration: Average costs = e- 8/4 (Contributions)- 208 (Membership) 045 G 357 (7.1) For non-life office administration: Average costs=e1 475 (Contributions)- 605 (Membership) 511 G (7.2) These two estimated cost functions are illustrated in Figure 2. This depicts the diminishing average costs for increasing size (as measured by total contributions), for three levels of contributions per member, based on a no-growth assumption. The co-efficients in the above equations suggest that economies of scale may be more pronounced amongst schemes not administered by life offices.

19 Occupational Superannuation Schemes 355 Figure 2. Illustrations of equations (7) Notes: 1. The figure in parentheses is the average contribution per member. 2. In all cases, growth is assumed to be zero. Yet the graphic illustration clearly shows that both types of schemes experience the effects of scale economies, but that the costs incurred by non-life office schemes are also affected by the number of members and hence the level of contributions per member. These results, which do not wholly conform to conventional wisdom, may be explained by a combination of the following two factors: 1. Expenses incurred in the management of a superannuation scheme are, in part, determined by the number of members. However, many life offices calculate the expense charge as a percentage of contributions only. Hence they may be undercharging schemes with a high number of members but a low level of contributions per member. 2. The costs incurred by life offices may be less subject to the number of scheme members due to the computerized data management systems operating within these institutions. If these results are indicative of practice, then there is an implication that schemes with a relatively low level of contributions per member should be administered by life offices and not by the sponsoring employer. On the other hand, most other schemes should be self-administered. Figure 2 has highlighted this result whilst Table 6 shows the estimated average cost for both cost functions in respect of the data for each scheme within the sample. By listing the schemes in order of increasing contributions per member, the contrasts between the two estimated cost functions are clearly illustrated.