Economies of Scale

Much of the TBTF literature is premised on the notion that large banks take excessive risks because of the implicit guarantee and carries an im­plicit policy recommendation that bank size should be held below a TBTF threshold.

Wheelock and Wilson (2012) find that across the size spectrum, US banks faced increasing economies of scale in the period 1984-2006. They argue that early studies that had found an exhaustion of economies of scale once banks reach $100 million to $200 million in assets were flawed because they applied “parametric cost functions that fail basic specification tests” (p. 172). The nonparametric method they develop shows pervasive returns to scale. They identify output categories (consumer loans, business loans, real estate loans, securities, and other) and input categories (purchased funds, core deposits, and labor services). This formulation begs a question they do not address: If because of TBTF the price of purchased funds declines above some large-size threshold, is lower unit cost from an implicit subsidy being conflated with greater efficiency?

Using quarterly data for a period in which the number of US banks fell from about 14,000 to about 7,000 but average size rose fivefold in real terms, their sample has about 900,000 observations. Their technique, however, applies estimates in clusters of only about 6,000 observations each. The framework obtains “local” estimators for a “k-nearest-neighbor bandwidth” (p. 184). They find that the elasticity of costs with respect to output size is systematically only about 0.96 across nearly the full size distribution (p.

Hughes and Mester (2013) argue that most studies of economies of scale in banking fail to take into account bank managers' taste for risk taking. They maintain that better diversification resulting from larger scale can generate not only scale economies but also incentives to take on more risk, which can add to cost and obscure the underlying scale economies. They use the “almost ideal (AI) demand system” approach from consumer theory to estimate utility-maximizing profit and input demand functions. This ap­proach allows for the possibility that managers trade off profit for reduced risk, incurring higher cost to reduce risk. If instead they simply maximize profit, the AI formulation reduces to the more usual translog production function often used in banking sector scale economy estimates.^[159]

Their main estimates are for 842 US bank holding companies in 2007. They consider five outputs (liquid assets, securities, loans, trading assets, and off-balance-sheet activities) and six inputs (labor, physical capital, large time deposits, all other deposits, all other borrowed funds, and equity capital). They first test their managers' preferred model. They find that they can statistically reject maximization of profit alone (validating the hypoth­esis that managers also take account of risk in their utility function).

In their first simple test for economies of scale (the “economic cost func­tion”), the coefficient for returns to scale (analog to the sum of output elas­ticities with respect to inputs) is in the range of 1.03-1.06 across the full size spectrum—about the same outcome as the nearly uniform cost elasticity of 0.96 identified by Wheelock and Wilson (2012). However, in their test using the AI-based managers' most preferred function, the scale economy coeffi­cient reaches about 1.13 for banks under $2 billion in assets, rising with size to reach 1.34 for banks with more than $100 billion in assets. Although the authors do not quite say so, this degree of returns to scale is extraordinary. It implies that a bank with $1.6 trillion in assets would have unit costs of less than half those of a bank with $50 billion in assets.^[160]

Hughes and Mester (2013) do illustrate the importance of economies of scale by showing that breaking in half each of the 17 banks with more than $100 billion in assets in 2007would increase their aggregate costs from $410 billion to $506 billion.^[161] They carry out an important test to separate out the influence of possible TBTF subsidy effects as opposed to under­lying economies of scale. They do so by rerunning their estimates replacing the large banks' actual cost rates for deposits and borrowed funds with the median rates of banks with less than $100 billion in assets. They find a scale economies coefficient for banks larger than $100 billion that is almost un­changed from that in their main test, indicating that the scale economies are not a misleading artifact of TBTF subsidies. Overall, their study pro­vides important evidence that scale economies probably do exist in banking. Their relatively circuitous and opaque method gives pause, however, as does the extreme degree of economies of scale found for banks over $100 billion in size.

Davies and Tracey (2014) examine whether estimates of economies of scale hold up even after controlling for the TBTF subsidy.

The authors apply a translog cost function, with the logarithm of total cost specified as a function of logarithms of output, input prices, and control variables (such as per capita growth and nominal interest rates). Scale economies are identified as the inverse of the sum of derivatives of the logarithm of cost to the logarithm of each of the outputs. Output includes liquid assets, securities, loans, other assets, and off-balance-sheet activities; inputs include debt (including deposits), labor, and physical capital. Cost is obtained by estimating an average price for each input.

The authors first estimate a “standard model,” which shows an econo­mies of scale coefficient of 1.07 for the full sample and 1.15 for banks over $2 trillion (meaning costs rise only 0.93 percent or 0.87 percent, respec­tively, when output rises 1 percent). These coefficients are highly signifi­cant. They then rerun the model repricing debt at the social cost (adding back the ratings uplift advantage). When they do so, the scale coefficients are about unity for each of five size groups, and none is significantly dif­ferent from unity.

A potentially important problem with the estimates is that they use a single parametric (translog) function across all observations.

Including banks from all regions may also distort the diagnosis, despite the attempt to include controls.^[163] Rather than providing definitive evidence that economies of scale are not present except for TBTF cost advantages, the study would thus seem to serve as a caution regarding the new domi­nant finding of returns to scale in banking.

McAllister and McManus (1993, 397) emphasize that “the most impor­tant source of financial returns to scale in banking is the fact that asset diversification reduces the amount of costly financial capital that an inter­mediary must hold in order to function.” This fundamental point poses a problem of identification of causality and interpretation for the current debate on capital requirements and TBTF-induced risk taking. If larger banks with more diversification are best at dealing with risk, the fact that they take on more risk could reflect their natural comparative advantage rather than moral hazard from TBTF. Indeed, the diversification argument would tend toward the implication that larger banks need to hold less, not more, equity capital against a properly risk-weighted portfolio of assets.

A caveat to the various studies of economies of scale is that empirical work on this issue is constrained by the fact that neither the inputs nor the outputs can be expressed in straightforward physical units.^[164] For example, in Wheelock and Wilson (2012), “output” comprises five categories of loans and securities and “inputs” comprise two categories of financing as well as a third input (labor). They examine scale economies along a “ray” on which the ratio of each output to the other factors remains constant. This ap­proach is far from a test in which, for example, tons of steel are the output and capital and labor are the inputs. Nonetheless, analysis of economies of scale almost always requires some form of aggregation.^[165] This strand of the literature would thus seem to warrant at least cautious attention. Ideally, case studies could provide a supplementary qualitative analysis of what ef­ficiencies have been gained (or lost) from the fact that the largest five US banks now have an average size of 10 percent of GDP each (see figure 5.3 later in chapter), whereas the corresponding measure in 1995 was only 2.4 percent (according to 10-K data).