Bank size, returns to scale, and cost efficiency

Journal of Economics and Business 105 (2019) 105842

Contents lists available at ScienceDirect

Journal of Economics and Business journal homepage: www.elsevier.com/locate/jeb

Bank size, returns to scale, and cost efficiency Ayse Sapcia, , Bradley Milesb ⁎

a b

T

Department of Economics and Finance, Utah State University, 3565 Old Main Hill, Logan, UT 84322, United States Department of Economics, Colgate University, Hamilton, NY 13346, United States

ARTICLE INFO

ABSTRACT

JEL classification: C11 C14 G21 G28 L11

Since the Great Recession, government regulators have become more interested than ever in the significant increase of bank size in the US financial sector. We contribute to the literature by studying the dynamic and bidirectional interactions between size, cost efficiency, and returns to scale using a newly constructed bank-level dataset. We first estimate scale economies for 198 US commercial bank holding companies using Fourier flexible form. We find that all banks except the too-big-to-fail banks exhibit increasing returns to scale. Proving the bidirectional relationship, we find that bank size Granger-causes both returns to scale and cost efficiency. On the other hand, cost efficiency also Granger-causes bank size. Taking this endogeneity into account, PVAR and Bayesian PVAR analyses demonstrate that banks enjoy cost efficiency as they grow, but lose scale economies gains even after controlling for bank-level characteristics, macroeconomic factors, and the regulatory environment. Our findings further suggest that regulations help decrease the costs of most banks, potentially encouraging them to grow further.

Keywords: Returns to scale Cost efficiency Bank size Bank regulations

1. Introduction The past 25 years have been characterized by regulations (and deregulations) as well as significant increases in the bank size. Assets of the five largest US banks as a share of total commercial banking assets increased from 23 percent in 1996 to about 48 percent in 2014.1 In this paper, we investigate the consequences of the bank size increase on economies of scale and cost efficiency for individual banks by taking the endogeneity among the variables into account. Using a newly constructed, quarterly, bank-level dataset for the U.S. between 1992:Q3 and 2014:Q2, we further assess the economic costs of the regulatory environment on banks with different sizes. The problem with understanding the effects of bank size increase is that the causality runs both ways. While larger banks may enjoy returns to scale and cost efficiency gains more, they most likely grow because of these factors. For instance, Fernholz and Koch (2017) show that the recent increase in banks size since mid-1990s follows a period with two distinctive characteristics. First, the period coincides to a decrease in idiosyncratic volatility which can be explained by diversification through non-interest activities and thus is reflected in cost efficiency. Second, there is a significant fall in cross-sectional mean reversion in this period, consistent with legislative changes such as Gramm-Leach-Bliley Act and returns to scale gains. Therefore, the proper approach to study the effects of bank size increase should allow the reverse causality from cost efficiency and scale economies to bank size while controlling for the macroeconomic and regulatory environment. Our paper contributes to the literature by solving this endogeneity problem among bank size, cost efficiency and returns to scale.

Corresponding author. E-mail addresses: [email protected] (A. Sapci), [email protected] (B. Miles). 1 Data are obtained from the Global Financial Development Database (GFDD), the World Bank. ⁎

https://doi.org/10.1016/j.jeconbus.2019.04.003 Received 23 May 2018; Received in revised form 1 April 2019; Accepted 3 April 2019 Available online 22 April 2019 0148-6195/ © 2019 Elsevier Inc. All rights reserved.

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

We analyze the dynamic and endogenous relationship between size, returns to scale, and cost efficiency through a Panel and Bayesian Panel Vector Autoregression (VAR) using newly constructed bank level data. The data cover the period from 1992:Q3 to 2014:Q2 for 198 U.S. commercial bank holding companies and include cost decomposition from consolidated bank income statements and bank level characteristics from consolidated bank balance sheets. Panel and Bayesian Panel VARs allow us to study the effects of changes in one variable on others while treating all variables as endogenous. To understand the nature and the direction of the relationship among bank size, cost efficiency, and returns to scale, we use Granger Causality analysis. Since the period of study corresponds to bank regulations, we also explore whether these reforms cause excess costs on banks and therefore discourage (or encourage) them from growing further. The connection between size and cost efficiency, i.e. the reverse of the ratio of total non-interest expenses to total assets, became more pronounced in the recent period with the larger role of non-interest activities.2 In particular, the mean non-interest income to interest income ratio has increased from 0.18 in 1989 to 0.59 in 2007 for the 10 largest banks Brunnermeier, Dong, and Palia (2012) making the cost efficiency an important indicator for management quality.3 While Ferrier and Lovell (1990) does not find a distinct trend between bank size and cost efficiency, more recent works such as Kovner, Vickery, and Zhou (2014) shows that every 10 percent increase in bank size is associated with 42 basis points increase in cost efficiency.4 Reinforcing the existence of the bidirectional relationship, Assaf et al. (2017) argue that cost efficiency during normal times helps reduce bank failure and risk during subsequent financial crisis which leads banks to grow further. Our paper fills this gap in the literature by studying the bidirectional relationship between bank size and cost efficiency.5 Although there is no consensus, the vast literature on scale economies shows that returns to scale gains for banks change with size. For instance, Schweitzer (1972), Noulas, Ray, and Miller (1990) and Hunter, Timme, and Yang (1990) find increasing returns to scale for all but the largest US banks, which exhibit decreasing returns to scale. Similarly, McAllister and McManus (1993) and Wheelock and Wilson (2001) find increasing returns to scale for most banks except the largest banks which exhibit constant returns to scale. On the other hand, Fries and Taci (2005) show that smaller banks operate with significant unrealized economies of scale while mediumsized banks operate closer to constant returns to scale for 289 banks in 15 East European countries. Again for the European banking industry, Beccalli, Anolli, and Borello (2015) find that there are significant economies of scale even for large banks. More recent literature for the US banking sector, such as Wheelock and Wilson (2012) and Hughes and Mester (2013), among others, find significant economies of scale for even the largest banks. Davies and Tracey (2014), however, show that when the too-big-to-fail effects are controlled, there is no evidence of scale economies for larger banks. Our paper contributes to this literature by analyzing the returns to scale for commercial bank holding companies with different sizes while controlling for the regulatory environment and by studying the bidirectional relationship between bank size and scale economies. The regulatory environment has also played an important role in the observed size increase of the banking sector. For example, regulations which gave more freedom to bank holding companies (such as Gramm-Leach-Bliley) likely resulted in cost synergies through an increase in merger activities. The more restrictive Dodd-Frank, however, may have imposed costs on the banks. DemirgucKunt et al. (2004), Barth et al. (2004) and Barth et al. (2013), and Chortareas, Kapetanios, and Ventouri (2016) show that tighter regulations are associated with lower cost efficiency. Wheelock and Wilson (2012) and Kovner et al. (2014) demonstrate that limiting size of banks causes significant increases in bank costs, primarily because banks exhibit increasing returns to scale. Berger and Hannan (1998), however, contradict this point with a discussion of the “quiet life hypothesis”. The Quiet life hypothesis (QLH) predicts that when there is high concentration in the banking industry (with many large banks that have significant market power), banks do not behave efficiently. According to the neoclassical theory, banks with market power should set a price above the marginal cost in order to maximize their profits. However, Hughes, Lang, Mester, Moon, and Pagano (2003) supports QLH and finds that banks might prefer to use their market power to behave systemically inefficiently because of their alternative objectives (such as building an empire). Berger and Hannan (1998) also find supporting evidence to QLH in the US banking industry. They show that large banks with market power do not set a price to maximize their profits and therefore such banks have high cost inefficiencies. As a result, a deregulation, such as GLB, that helps banks to get larger could have negative effects on their efficiencies. More recently, Lozano-Vivas and Pasiouras (2010) argue that the relationship between banking reforms and cost efficiency are non-linear. In particular, while private monitoring and capital adequacy requirements improve cost efficiency, granting broad powers to supervisors poses a negative effect. To contribute to the discussion in the literature and to effectively address whether bank size alters the costs arising from regulations, we use data for 198 US commercial bank holding companies and account for each pertinent regulatory period. Using Fourier flexible form model, we first show that all but the largest banks exhibit increasing returns to scale. Even after controlling for bank level characteristics, macroeconomic factors, bank regulations, and the recessionary periods banks seem to exploit scale economies until they become too large. Granger causality analysis prove the bidirectional relationship among cost efficiency, returns to scale, and bank size. In particular, we find that while bank size Granger-causes both efficiency and returns to

2 Following, Demirguc-Kunt, Laeven, and Levine (2004) and Barth, Caprio, and Levine (2004) and Barth, Lin, Ma, Seade, and Song (2013) we use non-interest expenses/assets as an indicator of cost efficiency. Moreover, Antunes, Cavalcanti, and Villamil (2013) find that reducing non-interest expenses/assets increases consumption, and Ajello (2016) demonstrates that increases in these costs account for about 25% of GDP volatility. 3 Assaf, Berger, Roman, and Tsionas (2017) show that cost efficiency is a good measure of management quality. 4 Radić, Fiordelisi, and Girardone (2012) find similar results for investment banks. 5 Ideally, a Stochastic Frontier Model would have been a more complete approach in finding the cost efficiency. However, since we focus on analyzing the endogenous relationship between cost efficiency, returns to scale, and size in the banking sector, a Stochastic Frontier Model is beyond the scope of this paper.

2

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

scale, cost efficiency also Granger-causes bank size. In other words, both bank size and cost efficiency contain statistically significant information to explain the future values of each other showing the bidirectional relationship between the two variables. We next demonstrate the effects of a bank size increase on cost efficiency and scale economies by using Panel and Bayesian Panel VARs which control for the endogeneity problem among the variables. We find that an increase in bank size leads to higher cost efficiency but to lower returns to scale benefits. We further discover that both restrictive and loose regulations help banks which can be another contributing factor to the bank size increase observed in the period. However, the gains from regulations are heterogeneous across the bank size groups. For instance, while Dodd-Frank decreases overall costs of banking, it helped too-big-to-fail banks more than smaller banks. The rest of the paper is organized as follows. Section 2 reviews the bank regulations since 1990s, and Section 3 introduces our bank-level data. While Section 4 presents our empirical models, Section 5 demonstrates the results along with the robustness checks. Lastly, Section 6 concludes the paper. 2. Bank regulations and their effects on bank costs The literature on the effects of regulations on bank costs is extensive, but many papers focus either on a country's general policies at a given point in time (such as Barth et al. (2004)) or focus on earlier regulatory periods (such as Demirgüç-Kunt and Detragiache (2002)). These discussions help reinforce the connection between bank costs, size, and regulation; however, they provide little in helping to formulate expectations for how costs respond specifically to more recent regulatory periods in the United States. We contribute to the literature by examining the regulatory environment and their effects on bank costs in the last 25 years. In the period of our study we have three regulations: Riegle-Neal Interstate Banking and Branching Efficiency Act, Gramm-Leach-Bliley Act and Dodd-Frank Wall Street Reform and Consumer Protection Act. By focusing on these banking regulations, we can pinpoint the precise regulatory environment that affects bank costs. Enacted in 1994, the Riegle-Neal Act allowed bank holding companies to acquire banks across state lines regardless of individual state laws. For instance, Chronopoulos, Mcmillan, and Wilson (2015) show that bank sizes grew substantially with the help of the Act. Cornett, Mcnutt, and Tehranian (2006) conclude that increases in short-term profitability were higher in mergers that occurred in the period after Riegle-Neal due to cost synergies from consolidating operations. Given these findings, we expect the Riegle-Neal Act to reduce the bank costs in our sample. The Gramm-Leach-Bliley Act was enacted on 1999 and allowed banks to maintain both investment and commercial banking divisions. Unlike the Riegle-Neal Act, Chronopoulos et al. (2015) find that the Gramm-Leach-Bliley Act actually reduced competition, leading to persistent profits and an increase in bank size. Barth, Brumbaugh, and Wilcox (2000) and Barth et al. (2004) argue that bank costs were reduced, primarily from the cost synergies associated with combining investment and commercial banking facilities. Following these studies, we expect the Gramm-Leach-Bliley Act to reduce bank costs in the more recent period that the paper studies. However, it is important to distinguish the effects on costs for different sized banks. It is indeed possible that the inclusion of investment banking activities to banks’ portfolio could increase costs if they take either more risk or are less efficient in these activities. Lastly, the Dodd-Frank Act (2010) aims to limit the risks that banks take and helps minimize the severe results from bank failures as observed in Great Recession. In order to reduce institutional risk, Dodd-Frank focuses primarily on the bank holding companies that are more likely to cause significant economic shocks (those banks with over $50 billion in assets). The regulation imposes an increase in held reserves which creates a significant buffer against liquidity shocks that had previously damaged bank holding companies. Dodd-Frank also prohibits a single bank holding company controlling more than 10 percent of total liabilities of all financial institutions which effectively imposes a limit on the size of banks and restricts bank mergers and acquisitions. While Barth et al. (2004) and Barth et al. (2013) and Chortareas et al. (2016) show that tighter regulations are associated with lower cost efficiency, Dodd-Frank is different as it reduces the bank risks. Therefore, our paper complements the literature by studying the effects of the Dodd-Frank Act on different sized banks using a recent period. 3. Data Our dataset consists of balance sheet, income statement, as well as 15 operating expenses for 198 US commercial bank holding companies from 1992:Q3 to 2014:Q2. Individual consolidated bank income statements and balance sheets are obtained from the Mergent Online database.6 The dataset captures all publicly traded bank holding companies that the cost decomposition data is available. Thus, our sample consists of 198 bank holding companies with real assets valued at over $300 million as of 2007 and it represents 90% of all the commercial banks in the US.7 6 Since some regulations, such as Riegle-Neal Act, encourage mergers and create cost synergies, it is important for our analysis to include them. However, it is unfortunately not possible to observe any mergers in our dataset unless it happens between two bank holding companies. This only happens a few times during the Great Recession throughout our sample. Since we control for the Great Recession along with bank characteristics such as size in our estimations, we do not expect a significant change in costs that can affect our conclusions. In Section 5.5, we conduct two robustness checks on this point. First, we exclude mergers while balancing our panel. Second, we exclude the period after the Great Recession. Even after these robustness checks our conclusions persist. 7 Regardless of the year we pick to select banks according to their asset sizes, it is inevitable that there will be some survivor bias. To minimize the

3

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Some examples to the operating expenses in our sample are occupancy, supplies, printing, software, equipment, personnel and employee benefits, marketing, telecommunications, litigation, data processing, loan processing, and professional fees.8 These operating expenses allow us to measure capital and labor expenses as well as total expenses accurately in the returns to scale analysis. Following Jaremski and Sapci (2017), we control for macroeconomic variables that could affect the bank size. For instance, we control for real GDP, representing the overall health of the economy. We also control for the money supply (M2) to capture the effects of monetary policy. Lastly, we include Dow Jones Industrial Average to control for the health of the financial markets and CaseShiller U.S. National Home Price Index to control for the house prices. We also add dummy variables for the three regulations in our period and for the Great Recession that might affect bank size. Using the average real asset size of a bank compared to their nearest neighbor, we divide the banks into four groups: Too-big-tofail (TBTF henceforth), large, medium and small banks.9 In particular, bank holding companies with an average real asset size (in 2007 dollars) of over $20 billion make up the TBTF group, between $2.5 billion and $20 billion make up the large group, between $500 million and $2.5 billion make up the medium group, and under $500 million make up the smallest bank category.10 Dividing the groups based on their asset sizes compared to their nearest neighbors allows us to detect any structural breaks in the data. For instance, having an asset size difference more than 20% between the nth and (n + 1)th bank would be an indication of a structural break. We divided our sample using such significant breaks in the bank size distribution. This approach prevents having heterogeneous banks in the same group as opposed to other approaches such as using quartiles. Table 1 shows the summary statistics of the cost decomposition data for different bank size groups. To assess the range of cost efficiency over time and across bank groups of different sizes, Fig. 1 plots the average value of total non-interest expenses divided by total assets for the 1992:Q3 to 2014:Q2 period.11 Interestingly, small and medium commercial bank holding companies appear to become less cost efficient over time, whereas the TBTF and large commercial bank holding companies experienced increases in their cost efficiency since mid 1990s. This analysis shows that there is some heterogeneity among banks in terms of cost efficiency gains. 4. Empirical models 4.1. Fourier flexible form The Fourier flexible form represents a semi-nonparametric approach which is useful when the true functional form of the cost function is unknown. Because sine and cosine functions are orthogonal within the 0 to 2π range, an infinite series of sine and cosine with varying frequencies can accurately represent any continuously differentiable function. Because of dimensionality limits, an infinite Fourier series, which would be a fully nonparametric estimate, is not feasible. A finite Fourier series, however, is seminonparametric and, unlike, for instance, the Translog cost function, is a global approximation of the cost function in which the cosine and sine terms can make the approximating closer to the data. Berger and Mester (1997, 1999) show that the Fourier-flexible form fit the data for US banks better than the commonly specified local Translog approximation and that trigonometric terms improve the fit of the model. Wheelock and Wilson (2012) cautions on another advantage of Fourier form over Translog model that Fourier form allows the data to have more freedom to choose shapes for the cost function particularly when there is heterogeneity in the sample. As Berger and Humphrey (1994) explain “Translog model forces large and small banks to lie on a U-shaped (or possibly flat) ray average cost curve and disallows other possibilities, such as an average cost curve that falls up to some output point and remains flat thereafter.” Because of the heterogeneity of bank sizes in our sample and the flexibility of the Fourier estimation, we choose the Fourier form over Translog function.12 The Fourier flexible form used in this paper is presented below:

(footnote continued) number of banks who failed, we picked the peak in 2007 for the economic and financial activity. 8 Please refer to Appendix A.1.1 for a detailed description of the dataset. 9 Since we use average real assets to establish the bank size groups, banks remain in one category throughout the period. Looking at the data, only 2% of the banks in our sample switches groups over time. Our conclusions remain the same, once we allow these banks to change their size groups over time. 10 We also change the definition of TBTF group as a robustness check. In the current analysis, we have 7 banks in TBTF group, however, our conclusions persist once we allow 11 banks to be in this group following Brewer and Jagtiani (2009). 11 It is important to note that total non-interest expenses divided by assets is a measure of cost inefficiency. Throughout the paper, lower values always denote higher cost efficiency. 12 As a robustness check, we also analyze returns to scale of banks using Translog cost function. Both Translog and Fourier analysis provide similar conclusions. Translog cost function results are provided in Section A.2, Table 9. 4

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Table 1 Summary statistics. Variable

Obs

Insurance exp Supp. and print Software exp Occupancy exp Marketing exp Data processing exp Loan processing exp Prof. services exp Litigation exp Telecommunications exp Travel exp Postal and courier exp Card processing exp Personnel exp Other noninterest exp Total noninterest exp Total deposits Gross loans Total assets Number of banks

ln C *

0

+

L

M

S

TBTF

L

M

S

TBTF

L

M

S

0 0 32 412 221 66 0 263 0 301 0 23 0 435 415 526 522 465 546 7

0 205 171 1673 770 315 48 857 0 504 0 68 70 1722 1113 1839 1685 1504 1832 25

108 432 36 3144 1515 885 208 1453 43 632 114 400 71 3469 2694 3665 3553 3389 3565 54

156 886 83 6204 2477 2700 38 2232 189 1052 18 561 268 6709 5237 7140 6872 6461 6944 101

. . 106406 710902 321462 447955 . 492191 . 411710 . 36820 . 3400753 1611499 6437326 3.53e+08 3.22e+08 7.68e+08

. 4779 47077 77899 54175 58086 49583 54415 . 54993 . 47027 115500 324001 116330 662793 4.95e+07 4.87e+07 7.54e+07

2791 2046 5646 12366 3131 5605 4686 4331 4008 3916 2766 3434 5733 42467 14170 81385 7382313 6297472 9973001

637 303 789 2526 657 1052 281 1081 493 1300 191 480 730 10530 35307 19561 1792173 1573544 2332048

. . 31925 612148 246331 223402 . 507096 . 382001 . 13125 . 2671402 44373 5209732 3.48e+08 2.95e+08 6.98e+08

. 2761 54013 67253 79668 53740 21035 73099 . 59672 . 31196 51452 260935 140158 589071 4.49e+07 4.26e+07 6.67e+07

1725 1729 3804 12195 2943 5396 4342 4083 2751 4406 2138 3669 3913 39139 13255 76686 5338367 4576498 7160884

610 154. 239 2616 564 1463 204 1060 353 2970 42 300 582 17476 3500 26843 1289990 1158160 1725824

+

j ln pj

i ln Qi

ik ln Qi ln z k

1 2

k lnzk

+

jk j

km ln z k ln z m m

+

k

k

k

+

j

+ i

Std. Dev.

TBTF

i

+

Mean

+

ln pj ln z k +

k

1 2

ij ln Qi ln pj i

j

1 2

jn ln pj j

ln pn

n N

il ln Qi i

l

ln Ql +

[ i sin(ki V ) +

i cos(k i V )]

i=1

(1)

+ lnAt + ei, t

Where C is total costs (interest expenses + non-interest expenses), Q is the outputs (gross loans and off-balance sheet activities), p is the vector presenting input prices (capital, labor and deposit prices), z is the netputs measuring loan quality and capital equity. ki is a vector of integer values satisfying the homogeneity of degree one of the cost function.13 V is the matrix of the adjusted logged output quantities and input prices and At is the vector containing macroeconomic controls such as GDP, house prices, Dow Jones Index, M2, as well as bank regulations and the Great Recession dummy variables.14 Table 2 provides more details on all the variables. Following Hasan and Marton (2003), Fries and Taci (2005), and Davies and Tracey (2014), we add physical capital of banks as an input and calculate the price of capital from non-interest expenses. For instance, while Hasan and Marton (2003) use total noninterest expenses over total costs, Fries and Taci (2005) use other non-interest expenses, and Davies and Tracey (2014) use total noninterest expenses minus personnel expenses as a ratio to total assets. However, these measures can include expenses that are not related to capital such as marketing, travel and litigation expenses, professional fees and amortization of goodwill. The advantage of our detailed cost decomposition dataset is that we can pinpoint the capital expenses unlike other papers. In particular, while the price of labor input is specified by the ratio of sum of employee benefits and personnel costs to total assets, the capital input price is the sum of supplies and printing, software, occupancy, and equipment expenses per total assets. As Hughes and Mester (1993, 2013) and Hughes, Mester, and Moon (2001) show, it is important to control for capital structure and risk taking behavior of banks in measuring scale economies. Following this literature, we control for capital structure by adding capital equity of banks and we control for risk behavior of banks by including the loan quality as netput to the cost function. Returns to scale measures can be obtained from the Fourier flexible form by taking a partial derivative with respect to the natural log of outputs:

13 We impose usual restrictions for the estimation to ensure that the regulatory conditions of the cost function holds. For the symmetry, we impose αil = αli, βjm = βmj, and γkn = γnk. For the linear homogeneity in input prices, we have ∑jβj = 1, ∑jβjn = 0 ∀ n, jij = 0 j , and ∑kρjk = 0 ∀ k.

14 Note that the dummy variables take the value of zero before a regulation was enacted and one in all periods thereafter. Similarly, the Great Recession dummy variable takes the value one during the recession and zero otherwise.

5

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Fig. 1. Cost efficiency across time for different bank groups. Notes: The lines represent the average non-interest expenses/total assets for each bank group. Notice that since the ratio shows the costs per assets, the reverse of it can be interpreted as cost efficiency.

1 i

ln C * ln Qi

=

i i

+

il i

ln Ql +

l

ij ln pj i

j

+

ik ln z k i

k

N

ki, Q [ i cos(ki V )

i sin(k i V )]

(2)

i=1

This partial derivative gives the change in cost resulting from an increase or decrease in output. If this number is one, then the cost is perfectly correlated with output and commercial bank holding companies exhibit constant returns to scale. Along the same argument, a value higher than one yields increasing returns to scale, and less than one yields decreasing returns to scale. 4.2. Panel Vector Autoregression (PVAR) Given the endogeneity between bank size, cost efficiency and returns to scale, it would be hard to assess the effects of one variable on the other with regular methods. VAR models, however, are particularly useful because all variables are treated as endogenously determined and interdependent. While there are studies that examine the relationship between cost efficiency and bank size (such as Ferrier and Lovell (1990), Kovner et al. (2014), Assaf et al. (2017)) and others that focus on the relationship between returns to scale and bank size (such as Noulas et al. (1990), Wheelock and Wilson (2001) and Wheelock and Wilson (2012), Berger and Mester (2003), among others), none of these studies consider the reverse causality among these variables. Since bank size, cost efficiency, and returns to scale affect each other, and thus endogenous, PVAR is the best estimation model for this dynamic relationship. With panel data, the general equation for a vector autoregressive model can be written as 6

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Table 2 Definitions of the variables. Symbol

Variable name

Calculation

Dependent variable C

Total costs

Interest expenses + non-interest expenses

Variable input prices pl pk pd

Price of labor Price of physical capital Price of deposits

Personnel expenses/total assets Capital Expenses/total assets Total deposits/total assets

Variable output quantities Ql Qo

Total loans Off-balance sheet activities

Total gross loans Non-interest income

Netput quantities zk za

Capital equity Loan quality

Total equity + loan provisions Loan provisions/total assets

Control variables A1 A2 A3 A4

GDP HP Money supply Stock prices

log log log log

Dummy variables A5 A6 A7 A8

Recession DF GLB RN

Great recession dummy variable Dodd-Frank dummy variable Gramm-Leach-Bliley dummy variable Riegle-Neal dummy variable

of of of of

real GDP real house prices real M2 Dow Jones Index average

Notes: All the bank balance sheet variables are obtained from Mergent Online. The control variables are obtained from Jaremski and Sapci (2017). While the price of labor input is specified by the ratio of sum of employee benefits and personnel costs to total assets, the amount of capital input price is the sum of supplies and printing, software, occupancy, and equipment expenses per total assets.

Xi, t =

i,0

+

i,1Xi, t 1

+

i,2 Xi, t 2

+

+

i, m Xi, t m

+

(3)

i, t

Where Xi,t is a matrix of endogenous variables which include bank size, cost efficiency and returns to scale for 198 US bank holding companies for the period of 1992Q:3-2014:Q2. The variables on the right-hand side of the equation represent lagged values of this matrix, while Γs are the coefficient matrices and ϵ is an i.i.d. vector of error terms. The number of lags in the system is equal to m, the value of which is determined by Akaike and Schwartz information criteria. For our purposes, the most useful information from the PVAR comes in the form of impulse response functions and Granger Causality tests. Impulse response functions measure the responses of current and future values of each variable to a shock, defined as a unit increase in the current value of one of the variables. All variables are typically normalized to have a value equal to zero prior to the shock. Because of the interdependencies that characterize a PVAR, any shock will likely affect all variables in Xt. For commercial bank holding companies, PVAR is particularly interesting because the parameters that characterize an impulse response function will show the effects that an increase in assets have on cost efficiency and returns to scale. Moreover, Granger Causality tests will allow us to understand the direction of this relationship. 4.3. Bayesian panel VAR All forms of regression analysis contain bias based on a researcher's prior beliefs. In order to develop a strong model, the researcher selects variables and, in some cases, even the form of the model (when the model is parametric). While this is a typical frequentist approach in estimation, it imposes the researcher's biases on the model. By assuming that the model's parameters are random, Bayesian analysis allows the researcher to incorporate prior knowledge in the estimation process. The prior distributions are then updated in a series of simulations until a final posterior distribution is determined. This form of estimation gives a more robust result than frequentist analysis because Bayesian estimation uses both data on hand and the prior knowledge. Bayesian analysis requires a choice of priors for the variables that are being estimated. One of the most common priors in the literature that we also use in this paper is called “Minnesota Priors”. Minnesota Priors (also known as Litterman priors) are introduced by Litterman (1986) and Doan, Litterman, and Sims (1984). These priors shrink the VAR estimates toward a multivariate random walk model. In particular, in each equation the prior mean of the first lag of the dependent variable is set to one while others are set equal to zero. The prior variance, on the other hand, of ijth element of A is set to: 2

l

2

if i = j,

i

and

if i

j

j

where λ is the prior standard deviation of Aii1 which controls the overall prior variance of all VAR coefficients, 0 < θ < 1 controls 7

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Table 3 Returns to scale measurements from the fourier flexible form. Size

RTS

All banks TBTF banks Large banks Mid-size banks Small banks

1.59 0.50 1.23 1.90 1.89

Notes: RTS higher than one yields increasing returns to scale, and less than one yields decreasing returns to scale.

the relative tightness of the prior variance in different lags than own and σ is the estimate of the error variance. Following Litterman (1986), we choose θ = 0.3 and λ = 0.2, and estimate σ from the data. Despite the differences in their theoretical basis, the form of the Bayesian PVAR is equivalent to that of Eq. (3) used in PVAR. 5. Results 5.1. Measurements of returns to scale Since we are interested in the dynamic relationship between bank size, cost efficiency and scale economies, we first need to find the returns to scale for each bank size group. To do so, we use the Fourier flexible form as described in Section 4.1, and the estimates of the returns to scale are presented in Table 3. After controlling for bank level characteristics, macroeconomic factors, the regulatory environment, and the Great Recession Table 3 shows that there is an increasing returns to scale in the US banking sector, in general. TBTF commercial bank holding companies, however, exhibit decreasing returns to scale while all other banks experience increasing returns to scale. Our results are consistent with the previous research which find increasing returns to scale up to a particular size limit, for instance Schweitzer (1972), Noulas et al. (1990), Hunter et al. (1990), McAllister and McManus (1993), Wheelock and Wilson (2001). In particular, Davies and Tracey (2014) show that when the TBTF effects are controlled, these banks do not exhibit any scale economies. Similarly, Table 3 shows that smaller banks enjoy increasing returns to scale more compared to larger banks. Therefore, our results suggest that banks enjoy returns to scale gains as they grow up until they become too big to fail. 5.2. Effects of regulations on bank costs Next, we turn to assessing the role that the banking regulations play in total bank costs. Table 4 shows that all regulations helped decrease the US bank costs. There are, however, two interesting findings. First, Gramm-Leach-Bliley Act increased the costs for TBTF banks while significantly decreasing the costs for other banks. Second, the Dodd-Frank legislation have decreased the costs for all banks but more so for the smallest banks. We can conclude that restrictive bank regulations, even those which are targeted towards the largest commercial bank holding companies, have spillover effects for the rest of the bank groups. Great Recession, on the other hand, increased bank costs in general. However, the amount of the increase is heterogeneous among banks. For instance, small and medium sized banks had significantly large increase in their costs due to the adverse economic environment created by the Great Recession. However, the negative effects of the Great Recession does not seem to affect large banks as much. Table 4 The effects of different regulations on total costs. Regulations

RN GLB DF Great recession

Fourier flexible form Overall

Small

Medium

Large

TBTF

−0.015 (0.051) −0.067 (0.042) −0.293*** (0.033)

0.054 (0.035) 0.048 (0.029) −0.082*** (0.032)

0.041 (0.039) 0.002 (0.035) −0.062 (0.039)

0.229 (0.169) −0.183 (0.162) 0.098 (0.177)

−0.105 (0.313) 0.534* (0.276) −0.031 (0.347)

0.093*** (0.035)

0.142*** (0.022)

0.160*** (0.028)

0.029 (0.125)

0.396* (0.222)

Notes: Here ***, **, and * denote the 1, 5, and 10 percent levels of significance, respectively. Standard deviations are in parenthesis. RN, GLB, and DF denote the Riegle-Neal Act, Gramm-Leach-Bliley Act, and Dodd-Frank Act, respectively. 8

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

It is possible that regulations might have delayed effects. To detect such delayed effects, we repeated the estimation by steadily reducing the regulatory dummy variables by one quarter each specification. Therefore, we can compare the full dummy variables with the reduced versions to see if (and when) the effect changes from the initial value. For instance, Gramm-Leach-Bliley Act was effective in November 12th 1999. So in the first regression, the dummy variable would take the value zero before the last quarter of the 1999 and would take the value of one afterwards. In the second regression, the dummy variable would be equal to zero until the first quarter of 2000 and would take the value of one afterwards. We kept reducing the dummy variable one quarter at a time for the entire time-period. The original dummy variable for the GLB Act would show the average effects over the entire time the regulation was effective, whereas the second would determine whether the remaining quarters were significantly different from the previous periods, etc. Since we would expect the largest effect to occur initially, an insignificant result for the reduced periods would suggest that there is not a reversal or a strengthening of the original results. We carry out this exercise for each of the three regulations. We found that the regulation effects (or the lack thereof) is very persistent over time. We find, however, some interesting points. The Dodd-Frank Act starts negative for the entire sample, and while it weakens slightly, it continues to be negative and significant in each period following it. The Gramm-Leach-Bliley Act has an insignificant negative effect initially but by the second period it has significantly negative effect that gets stronger over the following five years. Lastly, the Riegle-Neal Act starts insignificant and only becomes temporarily negative and significant during the Asian financial crisis in 1997. We further find that the GLB effect was positive and significant for the TBTF banks only when we include the first three quarters, suggesting its largest effect was upfront and did not grow or decline over time. 5.3. Panel VAR (PVAR) results The variables used in our PVAR are cost efficiency, bank size (measured as total assets), and the returns to scale estimates from the Section 5.1. This analysis is particularly important, as Wheelock and Wilson (2012), among others, find that returns to scale differs for banks of different sizes, while Kovner et al. (2014) conclude similarly for the cost efficiency. We control for bank fixed effects by using Helmert transformation. The use of vector autoregressive models in returns to scale and bank cost efficiency research is novel, and represents our contribution to the literature. 5.3.1. Granger causality results In order to demonstrate the endogenous relationship between bank size, cost efficiency and returns to scale and assess the direction of the relationship, we perform the Granger causality Wald Test. Granger causality results in Table 5 prove the endogeneity of the relationship among bank size, cost efficiency and returns to scale. In particular, while bank size Granger-causes both cost efficiency and returns to scale, cost efficiency also causes bank size. Returns to scale, however, does not Granger-cause bank size or cost efficiency, it seems to be more of a gain from a bank size increase. 5.3.2. Impulse responses After demonstrating the endogeneity problem in the relationship among bank size, cost efficiency, and returns to scale, we next examine how a bank's returns to scale and cost efficiency respond to a growth in their total assets. As Fig. 2 indicates, an increase in bank size leads to a higher cost efficiency (represented by the decrease in cost to asset ratio) over the period. Although, the response of returns to scale is insignificant in the first period, an increase in bank size leads to significantly lower returns to scale in later periods. Therefore we can conclude that an increase in firm size is associated with an increase in cost efficiency but, interestingly, a decrease in returns to scale. Table 5 Panel VAR Granger causality Wald Test H0: Excluded variable does no Granger-cause Equation Variable. H1: Excluded variable Granger-causes Equation Variable. Equation/excluded

chi2

df

Prob < chi2

Assets (In)Efficiency RTS ALL

22.371 9.301 33.140

11 11 22

0.022 0.594 0.060

(In)Efficiency Assets RTS ALL

24.809 12.227 35.143

11 11 22

0.010 0.347 0.037

RTS Assets (In)Efficiency ALL

35.201 16.851 58.808

11 11 22

0.000 0.112 0.000

Notes: In this table, the last column shows the significance of the Granger-causality relationship. 9

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Fig. 2. PVAR impulse responses to a standard deviation increase in assets. Notes: The figure shows the responses of returns to scale (RTS) and cost (in)efficiency (cost/assets) to a standard deviation increase in assets. While lines represent the orthogonalized IRFs, the shaded areas show the 90% confidence levels that is generated by 500 Monte Carlo draws.

5.4. Bayesian panel VAR results We obtain posterior distributions for the Bayesian PVAR using Metropolis-Hastings Markow Chain Monte Carlo sampling. The posterior distribution of these coefficients is then updated through a series of iterations. To deal with the issue of bank fixed effects, we again apply a Helmert transformation to each of the variables used. As explained in Section 4.3, we use Minnesota priors with tightness parameter equal to 0.3 and the parameter controlling the overall prior variance equal to 0.2. The conclusions drawn from the Bayesian PVAR impulse responses are consistent with those of the PVAR IRFs. Fig. 3 demonstrates that an increase in total assets boosts cost efficiency over time. Similar to PVAR results, a size increase have an insignificant effect on returns to scale in the first two periods, however scale economies decrease significantly in the following periods.

Fig. 3. Bayesian PVAR impulse responses to a standard deviation increase in assets. Notes: The figure shows the responses of returns to scale (RTS) and cost (in)efficiency (cost/assets) to a standard deviation increase in assets. While lines represent the orthogonalized IRFs, the dotted lines represent the 90% confidence levels. 10

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

5.5. Robustness checks First, we test our findings using a balanced panel dataset for the period of 1998:Q1-2014:Q2.15 This analysis effectively drops the merged banks, banks that are established late, or banks that failed during the time period and therefore, helps us to understand whether the unbalanced nature of the dataset affects any of our results. We find that PVAR results are very similar under a balanced dataset as seen in Fig. 4. This analysis shows that failed banks or mergers in our period do not seem to skew our findings. Next, we use the recovery period between the 2001 and 2007 recessions, i.e. the period from 2002:Q1 to 2007:Q3, to determine whether the strong economic effects of recessions are leading to any biases in our findings. As Fig. 5 shows, we find similar results for returns to scale and PVAR analyses, indicating that our results are not driven by the recessionary periods. Given that most of the mergers between bank holding companies occurred during the Great Recession, this analysis also shows that mergers do not have any significant effect on our results. Recognizing that our results could be influenced by the lack of macroeconomic controls, we run the PVAR analysis with the macroeconomic controls specified in Section 3 for the full sample. Fig. 6 shows that our conclusions remain even after controlling for the macroeconomic factors. While returns to scale decreases with less significance, efficiency still increases. While our model is based on the most conservative ordering, we changed the Cholesky ordering in our PVAR estimation to account for ordering effects.16 Our results show that a change in the variable order has no significant effects on the IRFs. Next, we consider the possible autocorrelation among the variables. Table 6 shows the correlation matrix of all the variables that we used in our Fourier analysis to estimate the returns to scale of banks. As is expected, the bank level variables are not correlated with each other, however, there is a higher correlation among macroeconomic variables. We ran the returns to scale estimations again without the macroeconomics variables except for the GDP.17 As Table 7 shows, our conclusions from the Fourier analysis does not change which shows that the correlation among macroeconomic variables do not affect our results. We also use an alternative measure for the cost efficiency incorporating net revenue instead of total assets. In particular, instead of non-interest expenses/assets as the measure for cost efficiency, we use non-interest expenses/net revenue where the net revenue is calculated as the sum of net interest income and non-interest income as suggested by De Young (1997). This measure allows the costs to be related to not only traditional activities but also off-balance sheet activities of banks. Fig. 7 shows the impulse responses of this alternative measure of cost efficiency and returns to scale estimates to a standard deviation increase in bank size. The PVAR analysis indicate that our conclusions are identical in that an increase in bank size leads to cost efficiency gains however causes a decrease in returns to scale benefits. Lastly, we estimate the parameters of our Bayesian PVAR model using non-informative priors. We assume that the parameters from each lag lie in a normal and flat distribution about 0. With such flat priors, our conclusions persist. 6. Conclusion This paper sheds light on the effects of bank size increase on cost efficiency and returns to scale in the past 25 years. In particular, we ask the following two questions: If a bank grows larger in size, would it benefit from scale economies and/or cost efficiency gains? Do dissimilar regulatory environments affect banks differently by lessening (or increasing) costs which could in turn encourage (or discourage) banks to grow? To answer these questions, we study the dynamic effects of an increase in bank size on returns to scale and cost efficiency gains. Using the Fourier flexible form, we find that all but the largest (too-big-to-fail) banks exhibit increasing returns to scale even after controlling for bank-level characteristics, macroeconomic factors and the regulatory environment. Next, we analyze the dynamic and bidirectional relationship between bank size, returns to scale, and cost efficiency through Panel VAR and Bayesian Panel VAR analyses. Both methods show that an increase in bank size decreases the chances that a bank can exploit returns to scale. On the other hand, cost efficiency gains increase as size increases. This result suggests that banks create cost synergies as they grow, possibly due to consolidation of bank activities. Thus, policymakers must consider the cost efficiency indicators as one of the most important factors that can sustain larger sizes among banks. We further analyze the role of restrictive and freeing regulatory environments in the observed bank size increase and study whether regulations impose (or lessen) costs on banks. We find that, both restrictive and freeing regulations benefit almost all banks by decreasing costs which then can encourage them to grow more. In particular, the smallest commercial bank holding companies benefit more from the most restrictive regulations, such as Dodd-Frank. This is an interesting result because the most restrictive regulation is generally focused on the largest commercial bank holding companies. Restrictions that policymakers put on TBTF banks to stabilize the banking system seem to have positive spillover effects on other banks. Thus, our results suggest that regulators must consider the auxiliary implications of regulations on commercial bank holding companies that may not be in their target group. This study provides a foundation for understanding the dynamic relationship between cost efficiency, returns to scale, and bank size. For future research, however, it is important to understand how bank size increases affects bank-level characteristics, such as risk taking behavior or the choice of the traditional versus off balance sheet activities, while taking the regulatory environment into account.

15

The year change is necessary to maximize the number of the banks in the sample given that many banks are established in late 1990s. For our model, the most conservative order is total assets, cost efficiency, and returns to scale. 17 The GDP is added to measure the health of the economy, however, the conclusions are identical if we drop it from our estimation. 16

11

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Fig. 4. PVAR robustness checks: balanced dataset using 1998:Q1-2014:Q2. Notes: The figure shows the responses of returns to scale (RTS) and cost (in)efficiency (cost/assets) to a standard deviation increase in assets. While lines represent the orthogonalized IRFs, the shaded areas show the 90% confidence levels that is generated by 500 Monte Carlo draws.

Fig. 5. PVAR robustness check: excluding recessions using 2002:Q1-2007:Q3. Notes: The figure shows the responses of returns to scale (RTS) and cost (in)efficiency (cost/assets) to a standard deviation increase in assets. While lines represent the orthogonalized IRFs, the shaded areas show the 90% confidence levels that is generated by 500 Monte Carlo draws.

12

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Fig. 6. PVAR robustness check: including macroeconomic controls. Notes: The figure shows the responses of returns to scale (RTS) and cost (in)efficiency (cost/assets) to a standard deviation increase in assets. While lines represent the orthogonalized IRFs, the shaded areas show the 90% confidence levels that is generated by 500 Monte Carlo draws. Table 6 Correlation matrix.

Total costs Total loans Non-interest income Price of labor Price of deposits Price of capital Capital equity Loan quality GDP House prices Money supply Stock prices

Costs

Loans

Nonint. Inc.

Labor

Deposits

Capital

Equity

Loan quality

GDP

H. prices

MS

S. prices

1 0.54 0.75 0.25 0.45 0.26 0.77 0.34 0.19 0.19 0.18 0.18

1 0.46 0.19 0.50 0.15 0.63 0.59 0.31 0.29 0.28 0.28

1 0.33 0.26 0.27 0.73 0.22 0.16 0.15 0.15 0.15

1 0.32 0.43 0.09 0.29 0.05 0.05 0.06 0.05

1 0.21 0.34 0.62 0.10 0.10 0.09 0.09

1 0.12 0.21 0.11 0.11 0.12 0.11

1 0.31 0.25 0.23 0.21 0.21

1 0.17 0.17 0.15 0.15

1 0.95 0.93 0.91

1 0.86 0.79

1 0.97

1

Notes: The table shows the correlation matrix for all the variables used in the Fourier Analysis in calculating the returns to scale measures for the banks. All the coefficients are significant at 1% significance level. Table 7 Returns to scale measurements: dropping macroeconomic variables except GDP. Size

RTS

TBTF banks Large banks Mid-size banks Small banks

0.5 1.33 2.04 2.17

Notes: Returns to scale (RTS) higher than one yields increasing returns to scale, and less than one yields decreasing returns to scale. Here, Eq. (1) is used identically except the macroeconomic variables such as money supply, house prices and stock prices. We only left GDP to measure the general health of the economy, however, excluding it does not change any of the conclusions. 13

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Fig. 7. PVAR robustness check: alternative measure of cost efficiency. Notes: The figure shows the responses of returns to scale (RTS) and cost (in)efficiency (non-interest expenses/net revenue) to a standard deviation increase in assets. While lines represent the orthogonalized IRFs, the shaded areas show the 90% confidence levels that is generated by 500 Monte Carlo draws. Table 8 Selected cost decomposition descriptions. Variable

Description

Personnel Occupancy

Salaries and benefits for all officers and employees of the bank and its consolidated subsidiaries. All noninterest expenses related to the use of premises, equipment, furniture, and fixtures. Premises and fixed assets are defined net of rental income. In addition to rental deductions, income from assets that indirectly represent premises, equipment, furniture, or fixtures included in “Premises and Fixed Assets” are also deducted. Advertising, production, agency fees, direct mail, marketing research, public relations, seminars, and customer magazines. sales training by consultants, public accountants’ fees, management services, consulting fees for economic surveys, and other special advisory services. Other noninterest expenses is a category intended to include items not required to be reported individually in Schedule HI, item 7. The Federal Reserve Microdata Reference Manual lists 31 unique costs that should be included in other noninterest expenses. Some of these costs include civil penalties and fines as well as costs of gifts given to depositors.

Advertising and marketing Professional fees Other noninterest expenses

Table 9 Returns to scale measurements from the translog cost function. Size

RTS

TBTF banks Large banks Mid-size banks Small banks

0.5 9.09 10 1.89

Notes: Returns to scale (RTS) higher than one yields increasing returns to scale, and less than one yields decreasing returns to scale. All the RTS measurements except for TBTF Banks are statistically significant at 5%.

14

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

Appendix A A.1 Data A.1.1 Data definition and measurement Mergent Online obtains the consolidated bank balance sheets and income statements from FR Y-9C filings, which must be filled out quarterly by bank holding companies with over 500 million USD in assets (more information on these requirements can be found in the Bank Holding Company Act, Regulation Y, and the Homeowners Loan Act). In FR Y-9C filings, Schedule HI, item 7 contains a list of possible non-interest expenses a bank holding company could incur: salaries and employee benefits, expenses of premises and fixed assets, goodwill impairment, amortization expenses, other non-interest expenses, and total non-interest expenses. In addition, Schedule HI, memoranda item 7 contains several more possible expenses: data processing, advertising and marketing, director's fees, printing and supplies, postage, legal fees and expenses, FDIC deposit insurance assessments, accounting and auditing expenses, consulting and advisory expenses, interchange fees, and telecommunications expenses. Under this memoranda item, bank holding companies are also able to create additional accounts. The Federal Reserve Microdata Reference Manual lays out the definition of costs reported in FR Y-9C filings. Some of the largest operating costs definitions that we use in this paper are shown in Table 8. Since banks do not provide individual financial statements for their fourth-quarters, we obtained fourth quarter non-interest expenses by summing the three available quarters and subtracting the total from the similar cost presented in the annual reports. We paid special attention to matching the quarterly financial statements with annual statements for every bank and each year. When we fail to do so, we obtained missing fourth-quarter values by averaging the preceding third-quarter and following first-quarter values. If this adjustment is made for more than three years, however, we remove the bank from our dataset. The cost decomposition data used in this paper are far more detailed than the reports that are regulated by the SEC. Thus, sometimes, bank holding companies had slightly different methods of reporting their detailed financial information. Two such categories that required the most careful analysis were the personnel and occupancy expenses. For personnel, some banks report only salaries paid (breaking employee benefits into a separate account), whereas other holding companies would report only one general category. Similarly, some companies choose to group their occupancy costs with their equipment costs. Because the personnel and occupancy data were the largest cost categories, we combined the equipment and occupancy into one category and personnel and employee benefits costs into another for each bank holding company in our dataset. Table 1 shows the summary statistics for TBTF, large, medium, and small commercial bank holding companies. A.2 Translog cost function The translog cost function is a second-order approximation to the cost function. The translog specification takes the following form:

ln C *

+

0

i ln Qi

+

i

+

ik ln Qi ln z k i

+

j ln pj

k lnzk

+

km ln z k ln z m m

ij ln Qi ln pj i

jk j

k

+

k

k

1 2

+

j

+

j

1 2

ln pj ln z k +

k

1 2

il ln Qi i

jn ln pj j

ln pn

n

ln Ql + ln A

l

(4)

where Qj, x and p denote outputs, inputs and input prices, respectively. z is the netputs and vector A contains the control variables as specified in Section 4.1. Returns to scale is obtained as follows:

1 i

ln C * ln Qi

=

i i

+

il i

l

ln Ql +

ij ln pj i

j

+

ik ln z k i

k

(5)

This partial derivative gives the change in cost resulting from an increase or decrease in output. If this number is one, then cost is perfectly correlated with output and commercial bank holding companies have constant returns to scale. Along the same argument, a value higher than one yields increasing returns to scale, and less than one yields decreasing returns to scale. The Translog results for the returns to scale in the banking sector as seen in Table 9 are very similar to those of Fourier flexible form as shown in Table 3. We find that all banks exhibit increasing returns to scale. However TBTF banks returns to scale measure is not statistically significant.

15

Journal of Economics and Business 105 (2019) 105842

A. Sapci and B. Miles

References Ajello, A. (2016). Financial intermediation, investment dynamics, and business cycle fluctuations. American Economic Review, 106(8), 2256–2303. Antunes, A., Cavalcanti, T., & Villamil, A. (2013). Costly intermediation and consumption smoothing. Economic Inquiry, 51(1), 459–472. Assaf, A., Berger, A. N., Roman, R. A., & Tsionas, E. G. (2017). Does efficiency help banks survive and thrive during financial crises? Available from SSRN: https://ssrn. com/abstract=2970251. Barth, J., Brumbaugh, R., & Wilcox, J. (2000). Policy watch: The repeal of glass-steagall and the advent of broad banking. Journal of Economic Perspectives, 14(2), 191–204. Barth, J., Caprio, G., & Levine, R. (2004). Bank regulation and supervision: What works best? Journal of Financial Intermediation, 13(2), 205–248. Barth, J. R., Lin, C., Ma, Y., Seade, J., & Song, F. M. (2013). Do bank regulation, supervision and monitoring enhance or impede bank efficiency? Journal of Banking & Finance, 37(8), 2879–2892. Beccalli, E., Anolli, M., & Borello, G. (2015). Are European banks too big? Evidence on economies of scale. Journal of Banking & Finance, 58, 232–246. Berger, A., & Hannan, T. (1998). The efficiency cost of market power in the banking industry: A test of the “Quiet Life” and related hypotheses. Review of Economics and Statistics, 80(3), 454–465. Berger, A. N., & Humphrey, D. B. (1994). Bank scale economies, mergers, concentration, and efficiency: The US experience. Berger, A. N., & Mester, L. J. (1997). Inside the black box: What explains differences in the efficiencies of financial institutions? Journal of Banking & Finance, 21(7), 895–947. Berger, A., & Mester, L. (1999). What explains the dramatic changes in cost and profit performance of the US banking industry? University of Pennsylvania – The Wharton School. Berger, A. N., & Mester, L. J. (2003). Explaining the dramatic changes in performance of US banks: Technological change, deregulation, and dynamic changes in competition. Journal of Financial Intermediation, 12(1), 57–95. Brewer, E., & Jagtiani, J. (2009). How much did banks pay to become too-big-to-fail and to become systematically important? Federal Reserve Bank of Philadelphia Working Paper 09-34, December 2. Brunnermeier, M. K., Dong, G. N., & Palia, D. (2012). Banks non-interest income and systemic risk. AFA 2012 Chicago meetings paper. Available from SSRN: https://ssrn. com/abstract=1786738. Chortareas, G., Kapetanios, G., & Ventouri, A. (2016). Credit market freedom and cost efficiency in US state banking. Journal of Empirical Finance, 37, 173–185. Chronopoulos, D., Mcmillan, F., & Wilson, J. (2015). The dynamics of US bank profitability. The European Journal of Finance, 21(5), 426–433. Cornett, M., Mcnutt, J., & Tehranian, H. (2006). Performance changes around bank mergers: Revenue enhancements versus cost reductions. Journal of Money, Credit, and Banking, 38(4), 1013–1050. Davies, R., & Tracey, B. (2014). Too big to be efficient? The impact of implicit subsidies on estimates of scale economies for banks. Journal of Money, Credit and Banking, 46(s1), 219–253. Demirgüç-Kunt, A., & Detragiache, E. (2002). Does deposit insurance increase banking system stability? An empirical investigation. Journal of Monetary Economics, 49(7), 1373–1406. Demirguc-Kunt, A., Laeven, L., & Levine, R. (2004). Regulations, market structure, institutions, and the cost of financial intermediation. Journal of Money, Credit & Banking, 36(3), S593. De Young, R. (1997). Measuring bank cost efficiency: Don’t count on accounting. Financial Practice & Education, 7(1), 20–31. Doan, T., Litterman, R., & Sims, C. (1984). Forecasting and conditional projection using realistic prior distributions. Econometric Reviews, 3(1), 1–100. Fernholz, R. T., & Koch, C. (2017). Big banks, idiosyncratic volatility, and systemic risk. American Economic Review, 107(5), 603–607. Ferrier, G. D., & Lovell, C. K. (1990). Measuring cost efficiency in banking: Econometric and linear programming evidence. Journal of Econometrics, 46(1–2), 229–245. Fries, S., & Taci, A. (2005). Cost efficiency of banks in transition: Evidence from 289 banks in 15 post-communist countries. Journal of Banking & Finance, 29(1), 55–81. Hasan, I., & Marton, K. (2003). Development and efficiency of the banking sector in a transitional economy: Hungarian experience. Journal of Banking & Finance, 27(12), 2249–2271. Hughes, J. P., Lang, W. W., Mester, L. J., Moon, C. G., & Pagano, M. S. (2003). Do bankers sacrifice value to build empires? Managerial incentives, industry consolidation, and financial performance. Journal of Banking & Finance, 27(3), 417–447. Hughes, J. P., & Mester, L. J. (1993). A quality and risk-adjusted cost function for banks: Evidence on the “too-big-to-fail” doctrine. Journal of Productivity Analysis, 4(3), 293–315. Hughes, J. P., & Mester, L. J. (2013). Who said large banks don’t experience scale economies? Evidence from a risk-return-driven cost function. Journal of Financial Intermediation, 22, 559–585. Hughes, J. P., Mester, L. J., & Moon, C. G. (2001). Are scale economies in banking elusive or illusive?: Evidence obtained by incorporating capital structure and risktaking into models of bank production. Journal of Banking & Finance, 25(12), 2169–2208. Hunter, W., Timme, S., & Yang, W. (1990). An examination of cost subadditivity and multiproduct production in large U.S. banks. Journal of Money, Credit and Banking, 22(4), 504–525. Jaremski, M., & Sapci, A. (2017). Understanding the cyclical nature of financial intermediation costs. Southern Economic Journal, 84(1), 181–201. Kovner, A., Vickery, J., & Zhou, L. (2014). Do big banks have lower operating costs? Economic Policy Review, 20(2), 1–27. Litterman, R. B. (1986). Forecasting with Bayesian vector autoregressions—five years of experience. Journal of Business & Economic Statistics, 4(1), 25–38. Lozano-Vivas, A., & Pasiouras, F. (2010). The impact of non-traditional activities on the estimation of bank efficiency: International evidence. Journal of Banking & Finance, 34(7), 1436–1449. McAllister, P., & McManus, D. (1993). Resolving the scale efficiency puzzle in banking. Journal of Banking & Finance, 17(2–3), 389–405. Noulas, A., Ray, S., & Miller, S. (1990). Returns to scale and input substitution for large U.S. banks. Journal of Money, Credit and Banking, 22(1), 94–108. Radić, N., Fiordelisi, F., & Girardone, C. (2012). Efficiency and risk-taking in pre-crisis investment banks. Journal of Financial Services Research, 41(1–2), 81–101. Schweitzer, S. (1972). Economies of scale and holding company affiliation in banking. Southern Economic Journal, 39(2), 258–266. Wheelock, D., & Wilson, P. (2001). New evidence on returns to scale and product mix among U.S. commercial banks. Journal of Monetary Economics, 47(3), 653–674. Wheelock, D., & Wilson, P. (2012). Do large banks have lower costs? New estimates of returns to scale for U.S. banks. Journal of Money, Credit and Banking, 44(1), 171–199.

16