K Diseconomies and Optimal Structure

This paper explores the effect on costs when firms within an industry must interact with each other in the normal course of business. Such interaction will generally cause the socially optimal scale of each firm to deviate from its minimum average cost scale. In addition, the socially optimal industry structure may be more concentrated than conventional firm-level cost studies would suggest and may also differ from the unregulated (free-entry) equilibrium structure. These concepts, while potentially applicable to several industries, are here made more precise for the banking industry, both theoretically and empirically. NETWORK DISECONOMIES AND OPTIMAL STRUCTURE Public policy toward industrial structure has traditionally adhered to the neoclassical assumption that an industry can efficiently supply a growing market at constant marginal cost through the entry of new, optimal-sized firms over time. However, to the extent that firms within an industry must interact with each other, as is true of many service industries, the costs of that interaction may be an increasing function of the total number of firms in the industry. Such interfirm network diseconomies may have at least three results. First, unit costs will rise as the market grows, even if individual firms are at their efficient scale. Second, the socially optimal scale of each firm may deviate from its minimum average cost scale, once these network diseconomies are taken into account. Third, the socially optimal industry structure may be more concentrated than conventional firm-level cost studies would suggest, and may also differ from the unregulated (free-entry) equilibrium structure. This paper explores these concepts theoretically and empirically in the specific context of the banking industry. Evidence emerges that U.S. banking may exhibit network diseconomies, with important implications for both equilibrium structure and optimal public policy. The empirical results also incorporate what appears to be the first test of agglomeration effects in the banking industry, identifying both localization diseconomies and urbanization economies. 1. Background Previous studies of network effects have focused largely on issues of compatibility, innovation, consumer demand, and competition (see, for example, pathbreaking studies by Farrell and Saloner, 1985; Katz and Shapiro, 1985, 1986; or the survey by Economides, 1996). The aspects of interfirm 2 networking considered here, by contrast, may be essentially transparent to the consumer and primarily affect a firm’s costs. Examples of industries exhibiting interfirm networking in fact or in principle include the postal service, telecommunications, airlines, and banking. A primary characteristic of 1 such industries, relevant to this study and in contrast to many previous studies, is that consumers value coverage (access to all endpoints) of an exogenous network or market, rather than the size of that network (number of endpoints) per se. For example, when mailing a letter, writing a check, or making a telephone call, a consumer needs a service provider that can deliver the letter, effect payment, or complete the call to any potential recipient. Similarly, a traveler wants to be able to reach any desired destination. In the situations considered here, we will assume that the demand for global coverage is either absolute or at least sufficiently inelastic that any equilibrium market outcome will yield global coverage. Given such global access or coverage, the consumer may be indifferent to whether a single 2 provider maintains direct links with all endpoints or instead must interact with one or more other firms to reach a particular endpoint, at least insofar as such interactions are transparent to the consumer. For example, if a traveler must change airplanes en route to a given destination, she may be indifferent to using one airline versus two for the same trip as long as the fare and travel times are the same. Similarly, a consumer mailing a letter may not care whether the postal service chooses to subcontract part of the delivery to third parties, as long as the letter arrives promptly and intact. As long as the industry provides global access by some combination of means, the size of the network and the structure of the industry do not affect consumer demand. Therefore, only cost considerations will influence firms’ choice of scale and scope or (assuming that competitive pricing can be assured) societal preferences regarding industry structure. 3 If a firm in one of these industries hopes to avoid the need for systematic interaction with its rivals as an intrinsic step in the provision of the service, it must establish its own direct links with every endpoint to compete effectively. In this regard, the problem considered here is similar to the interconnected networks problem of Laffont et al. (1996), in which each firm controls a bottleneck (its own customers) to which rivals must have access, and in which the interconnections render a consumer indifferent to the relative sizes of the firms. However, Laffont et al. focus on the pricing equilibria of such cases, whereas this paper--like Radner’s (1992) analysis of hierarchies--focuses on the resulting characteristics of cost. Because it confronts an industry with the need to choose between markets (interfirm linkages) and hierarchies (intrafirm networks) in serving its clientele, the problem considered here also constitutes an application of Williamson’s (1975) analysis and is thereby related not only to Radner’s (1992) study but also to Neave’s (1991) interpretation of financial industry structure in terms of markets and hierarchies. Neave focuses on the costs and capabilities of governance mechanisms in financial firms and, secondarily (as in his Chapter 5), on asset-side transactions; by contrast, although our empirical section can reflect the various contributions to costs of asset, liability, and governance operations, our theoretical banking model focuses on a subset of liability-side transactions. Although the focus of this paper is on the cost effects of interfirm linkages, there may well be competitive or pricing effects as well. Firms that choose to maintain direct connections to each endpoint will face their rivals in each geographic market, with behavioral effects that have been analyzed in the literature on multimarket contacts. The alternative structure of maintaining interfirm linkages can reduce the number of multimarket contacts but may have additional competitive effects that have yet to be studied. 4 Different industries have chosen different structures to solve the linkage problem. UPS and Federal Express have established the capability of delivering to any domestic location, while competing long-distance telecommunication companies must connect with local monopoly switching systems to provide their service. We assume compatibility among interacting firms in such cases, unlike previous studies that treat compatibility as a strategic choice variable. Exogeneity of the relevant network is crucial to our focus. The technology of providing a service may suffer aggregate diseconomies of scale beyond some level; yet, when the total population grows beyond that level, the industry cannot exclude new citizens from its scope, and therefore cannot limit its overall scale to the minimum-cost level. The postal service and telecommunications companies cannot reasonably restrict their coverage to a subset of the population residing in their coverage areas, nor can a commercial bank limit its acceptance of checks to those written by or to a selected few parties. Moreover, these industries face an exogenously growing population over time. Globalization and the erosion of local geographic market boundaries contribute to a further increase in the effective market size. It is realistic to expect that diseconomies of scale may characterize one or more of these industries. Casual observation suggests that the postal service may operate in a region of decreasing returns, comparing service level and costs over the past few decades. In the 1950s, letters traveled coast to coast in a day or two at a cost of 3 or 4 cents, with twice-daily home delivery, without benefit of high-speed jet aircraft or high-speed automated sorting technology, and without the consumer inconvenience of ZIP codes. Today, the cost of a first-class postage stamp is twice as high in real terms, the average transit time longer and more variable, the frequency of delivery lower, and postal codes increasing in length every few years (two digits when introduced, then five, now nine)--despite 5 technological progress and privatization to realign incentives. The main variable driving this apparent deterioration seems to be the sheer volume of mail, occasioned by both the 60 percent growth in U.S. population over the period and the increased use of mail for commercial advertising. In banking, interfirm linkages operate at several levels--on the asset side (for example, loan participations), the liability side (for example, payment transactions), or a mixture of the two (as with interbank lending--the so-called fed funds market). In addition, interbank linkages arise with financial services such as correspondent bank relationships to provide electronic payments, check processing, coin and currency, and securities wire transfer services. On the liability side, the ratio of interbank payment transactions (so-called "transit" transactions) to "on-us" transactions is an increasing function of the number of banks in the market. (This property will be explicitly calculated in the next section under the assumption of isotropic exchange.) To the extent that the receiving bank and the paying bank must duplicate certain steps in the processing of a single transit transaction, the total cost of that transaction will exceed the cost of an otherwise equivalent on-us transaction. Where cost considerations dictate the use of a clearing facility (such as the Federal Reserve or a correspondent bank) rather than direct presentment between the paying and receiving banks, an additional institution is imposed in the chain with its attendant costs. On the asset side, loan participations and loan sales generate comparable interfirm linkages. If participating or acquiring banks or their agents perform independent credit analysis, costly duplication of effort is involved; if not, the participating or acquiring banks are exposed to moral hazard from the originating or lead bank. In addition, Broecker (1990) and Nakamura (1993) have identified an indirect cost of multiple-bank markets in terms of declining credit quality and increased 6 loan losses resulting from loans granted to applicants previously rejected at other banks. Structural consolidation is occurring at a rapid pace among U.S. banks (including the very largest) amid claims of analysts and practitioners of potential cost savings, despite the findings of most empirical cost studies that scale economies are exhausted beyond some smaller scale (Berger and Humphrey, 1992b). The analysis below suggests that network diseconomies may potentially account for at least 4 part of this seeming contradiction. Standard empirical cost studies explore how a firm’s costs change as the firm changes scale or product mix, holding constant the number and other characteristics of rival firms. That approach fails to consider that the entry of new firms may impose higher interfirm networking costs on each incumbent or that the exit of incumbents (whether by merger or by failure) may reduce the interfirm networking costs to each surviving firm. Thus, when conventional studies suggest that a larger market should be supplied by additional firms rather than larger firms, they neglect the possibility that the increased networking costs resulting from entry may outweigh the higher unit costs resulting from increasing the size of a fixed number of firms. That is, in the presence of costly interfirm networking, the socially optimal structure may be more concentrated than the simple firm cost function would suggest and may require each firm to operate in a region of diseconomies of scale. This issue must be explored to establish valid public policy implications of empirical findings of diseconomies of scale in particular industries. 5 This paper broadens the concept of cost structure to incorporate interfirm network effects, demonstrating how they alter the theoretical calculation of the socially optimal and unregulated equilibrium industry structures and presenting exploratory empirical evidence from a sample of U.S. 7 commercial banks. The empirical findings are consistent with the theory and suggest that hitherto overlooked networking costs may have important implications for public policy. Before proceeding to a formal model, we note one property alluded to in the introduction. To expand its aggregate output, an industry must attain larger firms, more firms, or both. If interfirm networking is required and has a positive cost, the average cost will be an increasing function of the number of firms (as explored in the model below). Likewise, if firms have a U-shaped average cost structure, average cost is an increasing function of firm scale beyond some point. Thus, beyond some point, further expansion of an industry’s aggregate output must drive up the average cost, whether that expansion is attained by expanding each firm or by entry. That is, interfirm networking can undermine the neoclassical ability of an industry to maintain constant marginal cost at any aggregate scale by means of entry of optimal-sized firms. This property is related to the decreasing returns to scale previously noted for certain efficient hierarchical networks by Radner (1992). 2. A Model of Payment System Networking Among Banks To illustrate the properties of interest, we depict a simple model of a payment system network comprising n banks. As noted above, banks can or must interact in a variety of ways. Here we focus on just one of these elements to permit precise characterization of the process. Though derived for banks, the model may roughly characterize some other service industries also. For the most part, we shall work with a symmetric structure in which each bank processes identical numbers of accounts and transactions, and in which transactions are uniformly distributed among accounts. This assumption of isotropic exchange parallels that in Laffont et al. (1996) and McAndrews and Roberds (1997). To isolate the network diseconomies per se, we posit a fixed 8 aggregate number of accounts, M, and of net or "endpoint" transactions per unit of time, m. For example, each depositor writes a fixed number of checks per month, some on other accounts in the same bank (commonly called "on-us" transactions) and the rest on accounts in other banks ("transit" transactions), with the mix between on-us and transit transactions determined by the bank’s market share measured by the number of accounts. We shall quantify how networking among banks unambiguously increases the total number of transactions by layering intermediate (i.e., transit) transactions onto the fixed base of m endpoint transactions. The essential feature of the model is an explicit accounting of how m total endpoint transactions are apportioned and linked among the n banks. It will be necessary to distinguish between incoming transit and outgoing transit transactions, even though the banking industry reports only the latter of these components (e.g., in the Functional Cost Analysis survey administered by the Federal Reserve). A check deposited in bank A and drawn on an account in bank B will be considered as both an outgoing transit transaction with respect to bank A and an incoming transit transaction with respect to bank B. Here, "outgoing" and "incoming" refer to the direction in which interbank authorizations-not funds--flow. A distinctive feature of transit transactions is that they each show up at least twice, once at the outgoing bank and again at the incoming bank. If an intermediary such as a clearinghouse, the Federal Reserve, or a correspondent bank is used, such a transaction will move through at least three institutions. The cost function analyzed here does not explicitly model the interbank market and is consistent with any given combination of direct interbank linkages and clearing houses (including endogenously developed combinations, with or without the check clearing role of the Federal Reserve). If banks have capacity constraints on their ability to deal directly with each other, a cost9 minimizing structure will involve multiple vertical layers of interaction among banks, quantitatively exacerbating the network diseconomies analyzed below; we do not model this more extreme case. Numbers of Transactions In the symmetric structure with n banks, each bank holds a(n) = M/n accounts and directly encounters m/n transactions with the public each period, not including incoming transit transactions from other banks. Of these m/n transactions, a fraction 1/n will be on-us and the remainder will be outgoing transit, under the assumptions. The corresponding numbers of transactions per bank are b(n) = m/n on-us and c(n) = (n 1)m/n outgoing transit. At the same time, the bank receives incoming 2 2 transit transactions corresponding to a fraction 1/(n 1) of each other bank’s outgoing transit transactions. As there are (n 1) other banks, the total number of incoming transit transactions for a given bank is therefore (n 1)m/n , the same as the number of outgoing transit transactions. In 2 aggregate, the total number of incoming transactions must equal the number of outgoing transactions; in the symmetric case, this equality must also hold for each bank individually. The total number of transit transactions per bank, including both incoming and outgoing, is 2(n 1)m/n . The number of 2 all transactions, including both transit and on-us, is (2n 1)m/n per bank. In practice, the numbers 2 of accounts and transactions will vary across banks and stochastically over time; we shall shortly relax the assumption of symmetry across banks, but will ignore stochastic variation for clarity of exposition. Aggregated across all banks, the total number of transactions in the industry equals m/n on-us transactions plus 2m(1 1/n) transit transactions, or m(2 1/n) transactions in all. As the number of banks increases from n to n+1, total transactions increase by m/(n + n), which is positive for all n > 2 0. That is, not surprisingly, spreading a given number of endpoint transactions among a larger number 10 of banks will entail additional intermediary (or transit) transactions and thereby increase the total number of transactions processed in the economy. The implications of this elementary networking property for costs and optimal industry structure depend on details of the technology. In a neoclassical industry without networking, the socially optimal structure allows each firm to operate at its minimum average cost, in a region of locally constant returns to scale (except in the case of natural monopoly). With the networking effects characterized above, by contrast, it is straightforward to show that the number of banks at which total industry cost is minimized can require each bank to operate in a region of diseconomies of scale, whenever the cost of processing transit transactions is sufficiently large relative to the cost of processing on-us transactions. This property is explored in the next section. In the (partially) asymmetric case in which firm i processes m (rather than m/n) endpoint i transactions and each other firm i û j processes m endpoint transactions (m = constant for all i û j), j j the number of on-us transactions processed by firm i is m /[m + (n 1)m ]. The number of incoming i i j 2 transit transactions is m m (n 1)/[m + (n 1)m ] and the number of outgoing transit transactions is i j i j the same. In this case, note that changing the number of accounts in bank i directly alters its number of on-us and outgoing transit transactions, but also indirectly changes its number of incoming transit transactions. The share of on-us transactions, as a fraction of all transactions, is m /[m + 2(n 1)m ] i i j for bank i. These results will be needed in the following sections.