Bank capital buffers in a dynamic model

• Published date: 01 June 2020
• Date: 01 June 2020
• Author: Jochen Mankart,Spyros Pagratis,Alexander Michaelides
• DOI: http://doi.org/10.1111/fima.12253

DOI: 10.1111/fima.12253

ORIGINAL ARTICLE

Bank capital buffers in a dynamic model

Jochen Mankart1Alexander Michaelides2Spyros Pagratis3

1Deutsche Bundesbank, Frankfurt,Germany

2Department of Finance, Imperial College

London,South Kensington Campus, London, UK

3Department of Economics, Athens University of

Economics and Business, Athens, Greece

Correspondence

SpyrosPagratis, Department of Economics,

AthensUniversity of Economics and Business,

Athens10434, Greece.

Email:spagratis@aueb.gr

Abstract

We estimate a dynamic structural banking model to examine the

interactionbetween risk-weighted capital adequacy and unweighted

leveragerequirements, their differential impact on bank lending, and

equity buffer accumulation in excess of regulatory minima. Tighter

risk-weighted capital requirements reduce loan supplies and lead to

an endogenous fall in bank profitability, reducing bank incentives to

accumulate equity buffers and, therefore, increasing the incidence

of bank failure. Alternatively,tighter leverage requirements increase

lending, preserve bank charter value, and incentives to accumulate

equity buffers leading to lower bank failure rates.

1INTRODUCTION

Policy makersrecognize the importance of developing quantitative models to assess both microprudential and macro-

prudential risks in the financial system. These tools seek to improve the identification and assessment of systemically

important risks from high leverage,credit growth, or money market freezes.1Moreover,quantitative structural models

can be used in real time to perform counterfactual experiments and inform policy making.

Given the need for such applied, quantitative models, we construct a dynamic structural model of bank lending

behavior and capital structure choices with the following features. Banks transform short-term liabilities into long-

term loans (a maturity transformation function) and premature liquidation of loans is costly in the spirit of Diamond

and Dybvig (1983), Gorton and Pennacchi (1990), Diamond and Rajan (2001), and Holmström and Tirole (1998). One

key departure from Modigliani and Miller (1958) arises because banks are run bymanagers who maximize bank char-

ter value, defined as the utility from consuming current and future dividends accruing to shareholders for as long as the

bank remains a going concern. Another departure from Modigliani and Miller (1958) is the existence of deposit insur-

ance implying that depositors do not respond to bank riskiness. Banks also operate in an incomplete markets setup in

c

2018 Financial Management Association International

1Kiyotakiand Moore (1997) and Bernanke,Gertler, and Gilchrist (1999) are seminal examples where leverage interacts with asset prices to generate ampli-

fication and persistence over the business cycle, whereas Gertler and Kiyotaki (2010) and Gertler and Karadi (2011) illustrate the importance of banking

decisions in understanding aggregate business cycle dynamics. Adrian and Shin (2010) provide empirical evidencefurther stressing the importance o f lever-

agedbank balance sheets in the monetary transmission mechanism. Bernanke and Blinder (1988) provide the macrotheoretic foundations of the bank lending

channel of monetary policy transmission. Using aggregate data, Bernankeand Blinder (1992), Kashyap, Stein, and Wilcox (1993), and Oliner and Rudebusch

(1996) provide evidence that supports the existence of the bank lending channel. Brunnermeier (2009) discusses the freeze of money marketsduring the

recentrecession in the United States.

Financial Management. 2020;49:473–502. wileyonlinelibrary.com/journal/fima 473

474 MANKART ETAL.

the spirit of Allen and Gale (2004) and face uninsurablebackground risks in funding conditions and asset quality. Banks

raise equity capital internally through retained earnings, while we abstract from seasoned equity issuance.2

In such an environment, the limited liability option of bank shareholders may lead to incentives to shift risks to

creditors and to the deposit insurance fund. Excessive risk-taking in good times could lead to high losses when the

cycle turns, as documented in Beltratti and Stulz (2012) and Fahlenbrach and Stulz (2011), especially for banks whose

charter value is low. Bank capital regulations exist to contain excessive risk-taking and limit potential losses to the

deposit insurance fund.3

Using individual US commercial bank data, we first establish empirical regularities similar to the ones emphasized

in Kashyap and Stein (2000) and Berger and Bouwman (2013) who also use disaggregated data to understand bank

behavior. Wecomplement their approach by building a quantitative structural model to replicate the cross-sectional

and the time series evolutionof bank financial statements. We consider a relatively rich balance sheet structure where

illiquid loans and liquid assets are funded by short-term insured deposits, unsecured wholesale funds, and equity.

Toperform counterfactual experiments, we estimate the quantitative model using a method of simulated moments,

as in Hennessy and Whited (2005). The model replicates the wide rangeof cross-sectional heterogeneity in bank finan-

cial ratios through the endogenous response to idiosyncratic risks emanating from deposit flows and loan write-offs,

as well as the motive to hedge liquidity risk arising from maturity transformation. Consistent with the data, smaller

banks are estimated to face a higher cost of accessing the wholesale funding market and therefore rely more heavily

on deposit funding. Small banks also havea more concave objective function associated with more severe financial fric-

tions (Hennessy & Whited, 2007). Alternatively, larger banks are more highly levereddue to the additional flexibility

provided by easier access to wholesale funding.

Loan growth is strongly procyclical and peaks at the onset of expansions leading to an increase in leverageduring

the first few quarters of an expansion (Adrian & Shin, 2010, 2014). However,over the course of the expansion, banks

retain part of their higher earnings to replenish their equity, leading to a reduction in leverage(Brunnermeier & San-

nikov,2014; He & Krishnamurthy, 2013). During recessions, banks curtail new lending and shrink their balance sheets

reducing reliance on wholesale funding. The model also generates strongly countercyclical bank failures induced by

a deterioration in asset quality and the associated reduction in the bank charter value. Consistent with the empirical

results in Berger and Bouwman (2013), banks that fail tend to have higher (lower) average leverage(equity capital)

than surviving banks, regardless as to size.

We interpret these findings as consistent with quantitative features of the data. Thus, we use the model to analyze

the effect of changing capital requirements, a major issue of policy concern. We assume that regulatory intervention

takes the form of a prudential limit on bank leverage(henceforth, the leverage requirement) measured as the ratio of

total assets to equity.In addition to the leverage constraint, banks face regulatory restrictions with respect to the ratio

of risk-weighted assets to equity (henceforth, the capital adequacy requirement), a proxy for the Tier 1 capital ratio.

Tighter capital requirements could increase bank resilience to shocks and reduce the likelihood of bank failure.

Higher equity capital could mechanically increase an individual bank’s survival probability, whereas greater equity

capital can also alleviate other frictions thereby increasing the likelihoodof survival (Allen, Carletti, & Marquez, 2011;

Mehran& Thakor, 2011). But tighter capital requirements could also reduce financial flexibility.Limited flexibility could

increase the likelihood of bank failure byeither reducing the bank charter value or increasing the likelihood of breach-

ing a tighter limit or both (Besanko & Kanatas, 1996; Koehn& Santomero, 1980). Thus, setting capital requirements at

an appropriate level is a balancing act (De Nicolo, Gamba, & Lucchetta, 2014; Freixas& Rochet, 2008; Van den Heuvel,

2007, 2008).

2Banks’limited access to equity markets could be due to a debt overhang problem as in Myers (1977) and Hanson, Kashyap, and Stein (2011). It could also be

due to adverse selection problems à la Myersand Majluf (1984) and the information sensitivity of equity issuance. That problem might be particularly acute

in a situation where a bank faces an equity shortfall due to loan losses. In that case, information sensitivities may prevent the bank from accessing external

equitycapital from private investors as discussed in Duffie (2010).

3Fahlenbrachand Stulz (2011) find evidence that better alignment of incentives between bank managers and shareholders implies poorer performance during

a crisis supporting the idea of risk shifting moral hazards due to limited liability.Jiménez, Ongena, PeydrÓ, and Saurina. (2014) also find that banks with less

“capitalin the game” are susceptible to excessive risk-taking.