An Overlapping Generations Model of Bank Failures and Taxpayer Bailout Oz Shya a MIT

Rune Stenbackab

Sloan School of Management School of Economics

b Hanken

Payments Research Conference–Charles Kahn Festschrift Banff Conference Centre, Canada , June 17–18, 2016 The views expressed in this presentation are those of the presenter and do not necessarily represent the views of the affiliated institutions.

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Introduction

Bank failures and financial crises

Bank failures and financial crises Fractional-reserve banking system collapses and bailed out by taxpayers every 10 to 30 years (for over 700 years). Banks create money (Alchemy). Banks lend out 90% of deposits made into transaction accounts, and, often, 99% of deposits made into saving accounts. Depositors do not have control over the risk taken with their money. ⇒ Banks “bundle” account services with risk! Thereby creating a standard “moral hazard” conflict, associated with “managing other people’s money,” Assets and significant amount of leverage = Equity (see balance sheet):

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Introduction

History of bank failures

Early history of large bank failures and taxpayer bailout In 1345, world’s biggest banks failed, led by the Bardi & Peruzzi companies of Florence (preceded by 30 years of fictitious financial practices) ⇒ total financial disintegration in Europe. Most was trade stopped. In 1361, Venice’s Senate prohibits lending out depositors’ money (repealed later on). In 1584, Venice’s largest bank (House of Pisano & Tiepolo) closed because of inability to refund depositors. State gov’t turned it into a state bank that also failed 1619. In 1790 The Bank of Amsterdam was taken over by the City after depositors discovered that it broke its promise to maintain reserves. 1813 Napoleon takes possession of the Bank of Hamburg and finds 7.5m silver Marks in excess over deposits. Later on, French gov’t returns securities ⇒ bank fails. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Introduction

History of bank failures

Modern history of large bank failures and taxpayer bailout London bank failures and bailouts: 1825, 1836, 1847, 1866, and 1914. 1986–1995: Collapse of 1,043 savings and loan (S&L) associations.

In 1992 the Swedish gov’t guaranteed all bank deposits of the nation’s 114 banks and assumed some of bad debts. 2008: Total collapse of financial systems in the U.S. and Europe

2012–2013 Cyprus’ banks collapse (some depositors eventually get 80 cents on a Euro). Bitcoin price rises sharply.

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Introduction

History of bank failures

Major failure waves of U.S. banks

In 1792, the first bank bailout by the U.S. government (Alexander Hamilton, Treasury Secretary). O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Introduction

Taxpayer cost

A sample of taxpayer cost of bailing out banks By 1995, the S&L crisis had cost taxpayers $124 billion, plus additional $29 billion on the thrift industry. The most recent 2008 crisis cost the taxpayer $750b (TARP). The cumulative bailout commitment (asset purchases plus lending by Federal Reserve during 2007–2009 was $7.77 trillion to 407 banks (Bloomberg) and over $29 trillion (Felkerson). In March 2013, a e10 billion international bailout of Cyprus’ banks. U.K.’s 2009 gov’t support for the top 5 banks exceeded £100 billion: Therefore, lending (credit) to banks is equivalent to lending to governments (that will bail banks out).

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Introduction

Deposit insurance

Deposit insurance during financial crises Currently, the FDIC’s deposit insurance fund has $67.8 billion, which translates to 1.06% reserve ratio (of total U.S. deposits). JPMorgan Chase total deposit is $1.33 trillion (=$1,330b). Bank of America $1.24 trillion. Wells Fargo $1.22 trillion. Citibank $0.94 trillion. Each of the 24 largest U.S. banks holds deposits more than the entire FDIC fund.

Conclusion: Deposit insurance is not a feasible solution to large bank failures! O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Introduction

Lobbying

Lobbying expenditure by U.S. banks

which, in 2015, was over $1.2 million per week.

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Introduction

Purpose and motivation

Purpose and motivation What this paper is NOT about We do not criticize the fractional-reserve banking system. In fact, we assume that this system will continue to prevail forever. We do not analyze proposals for banking reforms such as “equity financing,” “narrow banking,” or TBTF regulations.

Our analysis Construct an OLG model with banks that may fail and lose deposits Introduce government bailout policies (taxpayer funded, equity bailout, no bailout) into the model. Taxpayer bailouts and bank failures are generally missing from existing models of banks! Our goal: To investigate the effects of the different bailout policies on banks’ incentive to take risks with depositors’ money. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Introduction

A “typical” academic model of banks

A “typical” three-period model of banks

t = 1: Two savers deposit $1 each. t = 1: The bank keeps $1 (reserves) and invests $1 in risky projects, maturing in t = 3. t = 2: Each saver has an urgent liquidity need to withdraw $1 with probability 12 . t = 2: Expected total withdrawals = 12 $1 + 12 $1 = $1 = bank reserves. ⇒ Prob.{ bank run } = 14 (not the main reason for bank failures). t = 3: Each saver has an urgent liquidity need to withdraw $1 with probability 12 . Discussion 1. Academia “likes” fractional-reserve banking because banks perform maturity transformation (key concept). 2. However, the above model does not analyze a failure of the bank’s investment project in t = 3, which create financial crises. This motivates our paper: We analyze “t = 3” bank investment failures and evaluate a variety of taxpayer bailouts. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Introduction

Literature

Related literature Bagehot (1873): Incentives for risk-taking could be reduced with enforcement of bank closures. Acharya & Yorulmazer (JFI, 2007), Diamond & Rajan (JPE, 2012), Farhi & Tirole (AER, 2012): Bailouts create severe moral hazard problems leading to excessive risk-taking. However, a commitment not to bail out generates a time-inconsistency problem (depositors are held hostage). Keister (RES, forthcoming): Combining bailouts with prudential policy would outperform complete bailout and no bailout. Dell’Ariccia & Ratnovski (IMF, 2013) introduce risk externalities among banks and demonstrate that bailouts may mitigate contagion. Kareken & Wallace (JOB, 1978) show that bank liabilities are free of default if creditors know banks’ portfolios and bankruptcy is costly. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Introduction

Literature con’d

Related literature con’d Rosas (AJPS, 2006) empirically estimates government propensities to engage in bailouts. Green (FRB, 2010) and Bernardo, Tally, & Welch (WP, 2014) analyze the design of corporate bailout policies in general. Overlapping generations (OLG) models of the banking industry Qi (RFS, 1994) extends Diamond & Dybvig (JPE, 1983) and finds potential improvement in banks’ ability to supply liquidly based on intergenerational transfers. However, runs can be generated by withdrawals or lack of new deposits. Gersbach & Wenzelburger (Macroeconomic Dyn, 2008): Competitive risk premia are low to prevent bankruptcy. Question: Why do we choose to work with an OLG framework? Answer: To generate tradeable bank equity (as one form of savings) O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Introduction

Our approach and main results

Our approach and main results

We analyze an OLG model where banks’ equity is sold from old to young. (a) Explore 4 bailout policies: No bailout, taxing young or old generation to finance bailout, and equity bailout. (b) Analyze how each bailout policy affects banks’ incentive to take excessive risks. (c) Equity bailout (if feasible) is shown to suppport optimal risk-taking. (d) The effects of tax-financed bailouts depend on bank owner’s objective function and deposit market structure.

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The model

The economy

The economy: Overlapping generations model Discrete time, t = 0, 1, . . . model, with two-period lived agents. in each t = 0, 1, . . ., the economy consists of one representative old generation τ = t − 1 agent and one young generation τ = t agent. One representative bank (old eventually sell it to the young). The young at t is endowed with ω units of a real resource (money). Young at t allocates ω according to resource constraint: dt + bt + TtY = ω. dt = amount deposited in the bank (savings for t + 1 to be consumed in period t + 1, if available). bt = value of bank equity (shares) acquired from the old agent. TtY = bailout tax (if imposed on the young agent at t). Assumption: Young depositors posses a technology for one-period storage of money at no cost. If indifferent, they will deposit with the bank. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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The model

Timeline

Modelling method: Timeline The sequence of events within each period t is as follows: Stage 1: Realization of the bank’s period t − 1 investment (success or failure). Realized profit πt (if any) is collected by the owner of the bank (the old agent). Stage 2: Potential bailout implementation (none, tax, equity bailout). Note that only deposits and interest (if promised) may be bailed out, whereas lost profit cannot be bailed out. Stage 3: The bank is sold to the young agent for a price bt (discounted sum of future profit). Stage 4: Young uses remaining resources to make a new bank deposit dt .

O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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The model

The bank

A representative bank, deposits, and profit A new (young) bank owner selects between 2 investment projects: Safe investment: with return ρS hence, dt =⇒ dt (1 + ρS ) in t + 1. Risky investment (ρR > ρS ): ( dt (1 + ρR ) dt =⇒ 0

prob. λ prob. 1 − λ

in period t + 1.

Note: The entire investment is lost with probability 1 − λ. Expected one-period (t + 1) bank profit from $dt deposited at t: ( S πt+1 = dt ρS (safe investment) Et πt+1 = R = λdt ρR (risky investment). Et πt+1 Note: Initially, assume that the bank does not pay interest on deposits. Interest-bearing accounts will be introduced later on. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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The model

The bank

Steady-state value (price) of the bank Let 0 < δ < 1 denote the time discount factor. bt = Expected discounted sum of future bank profit starting t + 1. b S = value of the bank when all generations of bank owners make safe investments (with d dollars). b R = value of the bank when all generations of bank owners make risky investments (with d dollars). The value (price) of the bank when sold from old to young at t is: bt = b S =

δdρS 1−δ

and bt = b R =

δdλρR . 1−δ

bt = O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Safe investment

Charaterization

Characterization of steady-state safe investment path Solving 3 equations with 3 variables (d S , π S , b S ): 1. Young’s resource allocation: d S + b S = ω (no bailout, no tax needed) 2. One-period bank profit: π S = d S ρS , and 3. Price (value of shares) of buying the bank b S = dS =

ω(1 − δ) , 1 − δ(1 − ρS )

πS =

ω(1 − δ)ρS , 1 − δ(1 − ρS )

δd S ρS 1−δ

yields:

and b S =

δωρS . 1 − δ(1 − ρS )

δ ↑=⇒ b S ↑=⇒ d S ↓=⇒ π S ↓ (Higher discount factor, higher bank value (price), leaves less for deposits) ρS ↑=⇒ π S ↑=⇒ b S ↑=⇒ d S ↓ (Higher investment return, higher bank profit and value, less for deposits)

O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Government bailout policies

Terminology

Government bailout policies No bailout (N): The government lets the bank fail, depositor loses the deposit amount (d) and the bank owner loses one-period bank profit (π). Equity bailout (E ): The owner of the bank distributes shares of the bank to the depositor before the bank is sold to the young agent. Bailout with a tax on the old (O): The government levies a tax T O on the old agent at the time the bank fails. Bailout with a tax on the young (Y ): The gov’t levies a tax T Y on the young agent before the young agent buys the bank and makes a deposit. Note on terminology: We examine bailout policies from a depositor’s perspective. Bailout of corporations use different terminology. (N) could be called “equity bailout” b/c bank owners keep their equity. (E ) could be called “bankruptcy” (priority for depositors). O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Social optimum

Definition and characterization

Social optimum Definition: Safe investment is socially optimal if it yields a higher expected gross return than risky investment. Formally, if 1 + ρS | {z }

≥

safe return on $1

λ(1 + ρR ) , | {z }

or

def

ρR ≤ ρR∗ =

1 + ρS − λ . λ

risky return on $1

Note: Risky investment may result in total loss (not only interest)



0 ρ

More risky than optimal

S

O. Shy, R. Stenbacka (MIT Sloan, Hanken)

Less risky ρR∗ =

Bank Failures and Taxpayer Bailout

1+ρS −λ

- R ρ

λ

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Strategic investment decisions

Objective functions

Strategic investment decisions: Young Bank owner’s objective We analyze (separately) two different young bank owner’s objectives: (a) Maximize shareholder value (future bank profits): A bank owner works on behalf of shareholders and maximizes expected future discounted profits: def Vt = δ (Et πt+1 + Et bt+1 ) [= profit + sale value]. Bank owners act “professionally” and separate their roles as bankers and depositors. (b) Maximize old-age consumption A (young) bank owner at t maximizes expected old-age consumption: Et ct+1 . Bank owners act “unprofessionally” and combine their own interests as bankers and depositors. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Strategic investment decisions

Equilibrium

Equilibrium concept Players: Each generation of young new bank owners t = 0, 1, . . . . Action: Selected in period t by the young new bank owner. Payoff: Realized in period t + 1 (when old). def

Let the action (strategy) set of each new of bank owner be A = {S, R} (safe or risky investment). Safe investments constitute a Nash equilibrium if, given that all generations t = −1, 0, 1, 2 . . . choose at = S, then (a) There is no generation t¯ (t¯ = 0, 1, 2, . . .) so that either: (i) Vt¯(R) > Vt¯(S) [maximizing bank value], or (ii) Et ct+1 (R) > Et ct+1 (S) [maximizing old-age consumption] .

(b) Young depositors believe that no bank owner will deviate from at = S. We examine one-time deviation from safe investments. W.O.L.G, we focus on generation t = 0 incentives to deviate from “S”. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Strategic investment decisions

Bank owner maximizes shareholder value

Bank owner maximizes shareholder value: No bailout (N) If the young bank owner at t = 0 chooses a safe investment: Shareholder value is:   δωρS ω(1 − δ)ρS S S S + , V0 = δ(π + b ) = δ 1 − δ(1 − ρS ) 1 − δ(1 − ρS ) If the young bank owner at t = 0 chooses to deviate to risky investment: Under no-bailout policy (N), expected shareholder value becomes: V0R,N = δ(Et π R,N + b S ) = δ(λd S ρR + b S ). ρS < ρR∗ . λ Hence, even with no bailout, bank owners take excessive risk relative to social optimum (even for relatively low ρR ). Why? Because the possible loss of deposit d S is not internalized by bank owners (limited liability). V0R,N ≤ V0S

if and only if λρR ≤ ρS

O. Shy, R. Stenbacka (MIT Sloan, Hanken)

or

Bank Failures and Taxpayer Bailout

def

ρR ≤ ρR,N =

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Strategic investment decisions

Bank owner maximizes shareholder value

Bank owner maximizes shareholder value Equity bailout (E)

If the young bank owner at t = 0 chooses to deviate to risky investment: Under equity bailout policy (E), expected shareholder value becomes:     V0R,E = δ Et π R,E + b S − (1 − λ)d S  | {z } equity bailout

1 + ρS − λ = ρR∗ . λ Hence, with equity bailout, bank owner’s risk incentives are aligned with social optimum. Intuition: Equity bailout reduces the value to shareholders, hence the price the old shareholder receives for selling the bank to the young. V0R,E ≤ V0S

def

if and only if ρR ≤ ρR,E =

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Strategic investment decisions

Bank owner maximizes shareholder value

Bank owner maximizes shareholder value Bailout by taxing the young (Y)

Suppose the young bank owner at t = 0 chooses to deviate to risky investment and the bank fails in t = 1. =⇒ Young at t = 1 will be taxed T1Y = d S , =⇒ will have less money to deposit in t = 1, =⇒ lower t = 2 bank profit =⇒ Lower t = 1 bank sale value (b1R,Y < b S ).   d1R,Y = ω−b1R,Y −T1R,Y = ω−b1R,Y −d S and b1R,Y = δ d1R,Y ρS + b S . h i =⇒ V0R,Y = δ Et π R,Y + λb S + (1 − λ)b1R,Y   S S R,Y S R R,Y def 1 + δ(1 + ρ − λ) ρ . V0 ≤ V0 if and only if ρ ≤ ρ = λ(1 + δρS ) Hence, a bailout tax on the young generates excessive risk but not the strongest incentive as under no bailout. Why? Because the tax burden on the young reduces bank activity, next-period profit, and hence the bank’s shareholder value (b1R,Y < b S ) O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Strategic investment decisions

Bank owner maximizes shareholder value

Bank owner maximizes shareholder value: Results Which bailout policies reduce risk-taking behavior? Equity bailout (E) =⇒ implements optimal (low) risk-taking Taxing the young (Y) =⇒ “medium” risk-taking No bailout or taxing the old (O) =⇒ “strong” risk-taking behavior ρR,N = ρR,O < ρR,Y < ρR∗ = ρR,E . 

0

ρ

S

More risk than optimal ρR,N = ρR,O =

O. Shy, R. Stenbacka (MIT Sloan, Hanken)

ρS λ

ρ

R,Y

Bank Failures and Taxpayer Bailout

- R ρ

ρR,E = ρR∗ =

1+ρS −λ λ

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Strategic investment decisions

Bank owner maximizes old-age consumption

Bank owner maximizes old-age consumption If the young bank owner at t = 0 chooses a safe investment, the owner’s consumption when old would be (3 sources of income): S ct+1 = d S + πS + bS =

ω(1 + ρS − δ) . 1 − δ(1 − ρS )

If the young bank owner at t = 0 chooses a risky investment, the owner’s R = consumption when old would be: ct+1  S R S  bank does not fail in t + 1 d + π + b   S   bank fails and is not bailed out (N) b S S O d + b − Tt+1 bank fails and is bailed out using a tax on the old (O)    d S + (b S − d S ) bank fails and is bailed out using shareholder equity (E)     S d + b R,Y fails and is bailed out using a tax on the young (Y). A young bank owner in period t would not deviate from safe investments if R < cS . Et ct+1 t+1 O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Strategic investment decisions

Bank owner maximizes old-age consumption

Bank owner maximizes old-age consumption: Results Which bailout policies reduce risk-taking behavior? Equity bailout (E), taxing the old (O), or no bailout (N) =⇒ implement optimal (low) risk-taking Taxing the young (Y) =⇒ “medium” risk-taking ρR,Y < ρR,E = ρR,N = ρR,O = ρR∗ .

More risk than optimal



0

ρ

S

ρ

R,Y

O. Shy, R. Stenbacka (MIT Sloan, Hanken)

- R ρ

ρ

R,E

=ρ

R,N

R,O

=ρ

Bank Failures and Taxpayer Bailout

=ρ

R∗

=

1+ρS −λ λ

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Competitive banking industry with interest-paying banks

Extension

Perfect competition with interest-paying banks

The bank now pays interest rate i on one-period deposit Promises to credit period t depositors with dt (1 + i) in t + 1 Expected t + 1 bank profit: ( S πt+1 = dt (ρS − i) Et πt+1 = R Et πt+1 = λdt (ρR − i)

(safe investment) (risky investment).

S Perfect competition =⇒ i = ρS =⇒ πt+1 = 0.

=⇒ one-period deviation from safe investment is always profitable R because Et πt+1 = λdt (ρR − ρS ) > 0.

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Competitive banking industry with interest-paying banks

Bank owner maximizes shareholder value

Perfect competition with interest-paying banks Bank owner maximizes shareholder value (discounted sum of future profits)

Excessive risk-taking cannot be prevented! ρR,N = ρR,O = ρR,E = ρR,Y = ρS < ρR∗ .

More risk than optimal



0 ρ

R,N

=ρ

R,O

R,E

=ρ

=ρ

R,Y

=ρ

S

ρR∗ =

1+ρS −λ

- R ρ

λ

Intuition: Bailout does not affect one-period profit from risky investments. E and O are infeasible because the old does not have any assets if the bank fails (equity has no value). Y bailout does not affect profit (only lost deposit and interest). O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Competitive banking industry with interest-paying banks

Bank owner maximizes shareholder value

Perfect competition with interest-paying banks Bank owner maximizes her old-age consumption

Bank owner’s t + 1 old-age consumption if selects safe investment in t: S ct+1 = dt (1 + i) = dt (1 + ρS ).

t + 1 old-age consumption if  R πt+1   }| { z    R S S  dt (1 + ρ ) + dt (ρ − ρ )     0  0      0     dt (1 + 0!)

R = selects risky investment in t: ct+1

if the bank does not fail in t + 1 if the bank fails and is not bailed out (N) fails and bailed out by a tax on the old (O) fails and bailed out by shareholder equity (E) fails and bailed out by a tax on the young (Y).

Intuition: (E) and (O) are infeasible b/c old does not have assets. (Y) bailout transfers some of the old’s loss to the young (intergeneration transfer). Young does not sufficient funds to bailout the lost interest. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Competitive banking industry with interest-paying banks

Bank owner maximizes shareholder value

Perfect competition with interest-paying banks Bank owner maximizes her old-age consumption: Results

Except for policy (Y), owner’s incentives are aligned with social optimum. ρR,Y =



0 ρ

S

ρS < ρR,N = ρR,O = ρR,E = ρR∗ . λ

More risk than optimal  ρ

R,Y

=

ρS λ

- R ρ

ρR,N = ρR,O = ρR,E = ρR∗ =

1+ρS −λ λ

Intuition: (E) and (O) are infeasible b/c old does not have assets (equity has no value). (Y) transfers some of the old’s loss to the young =⇒ promotes risk-taking

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Summary

The effects of 4 bailout policies

Summary: The effects of 4 bailout policies Non-competitive banks: No deposit rates Owner’s objective

N

O

E

Y

Bank’s future profit

Strong

Strong

Optimal

Medium

Consumption when old

Optimal

Optimal

Optimal

Strong

Competitive banks: High deposit rates Bank’s future profit

Strong

Infeasible

Infeasible

Strong

Consumption when old

Optimal

Infeasible

Infeasible

Strong

Equity bailout (E), if feasible, supports optimal risk-taking. Tax bailout on the young (Y) generates strong incentives for risk-taking. No bailout (N) is optimal only if owners’ objective is to maximize their own old-age consumption. O. Shy, R. Stenbacka (MIT Sloan, Hanken)

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Conclusion: What should we do now?

Policy recommendation

Is there any hope? No! Taxpayer is still on the hook! Some hope on the horizon: Non-banks providing bank-like services. Policy recommendation: Federal Reserve provide services to FinTech on a “pre-funded” basis (storage of money, ACH, FedWire, etc.) Why? Removes the uncompetitive advantage of banks over FinTech.

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Conclusion

Recommended books

Recommended books

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