Limited Deposit Insurance Coverage and Bank Competition Oz Shya

Rune Stenbackab

Vladimir Yankovc

a Federal

Reserve Bank of Boston School of Economics c Board of Governors of the Federal Reserve System b Hanken

System Committee Meeting on Financial Structure and Regulation FRB Dallas, Houston, TX 9 - 10 October 2014 The views expressed here are those of the authors and do not necessarily represent the views of the Federal Reserve Bank of Boston or the Federal Reserve System

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Introduction

Observations and motivation

Observations and motivation

Deposit insurance (DI) schemes place a limit on the covered amount deposited in each bank However, there is no limit on the number of accounts held with different banks Therefore, some depositors open accounts with different banks to take advantage of full FDIC coverage Consequently, a new industry has emerged: The Certificate of Deposit Account Registry Service (CADR) that splits a customer’s deposit into several banks (possibly, 3,000 banks)

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Introduction

Deposit insurance: Facts

Deposit insurance: Facts

78 countries have explicit DI, 68 of them have limited DI, 10 have unlimited DI [IMF survey, see Garcia (2000)] In the U.S. the FDIC established with the Banking Act of 1933 The “logic” behind the DI limit is to allow protection of small investors, but not to large sophisticated investors who can “impose” market discipline Note: It is not clear how any investor can impose discipline on banks without knowing their exact investment portfolio In addition, depositors can spread their deposits among multiple banks thereby disregarding any risk

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Introduction

Our goals and methodology

Goals and methodology of the paper

1

2

Document stylized facts on the demand for multiple deposit accounts to achieve higher or full deposit insurance Model of deposit competition 1. 2. 3. 4.

assume an imperfectly-competitive market structure where banks compete in deposit rates (interest on deposits and CDs) depositors bear a cost of opening and maintaining a second bank account We compare 3 regimes of deposit insurance (DI): (a) No DI (b) Unlimited DI (c) Limited DI (observed policy)

with respect to equilibrium interest rates, depositors’ welfare, banks’ profit, and total welfare

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Empirical facts on the demand for multiple deposit accounts

Empirical facts on the demand for multiple deposit accounts under limited deposit insurance

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Empirical facts on the demand for multiple deposit accounts

Deposit insurance limits (table)

Deposit insurance limits over time (table) Year 1934 1935 1950 1966 1969 1974 1980 2008

Limit (nominal) 2,500 5,000 10,000 15,000 20,000 40,000 100,000 250,000

Limit (real) 40,218 78,434 89,460 99,497 117,384 174,658 261,263 250,000

Fin.wealth (real) NaN NaN 119,581 184,555 194,933 181,028 208,522 370,674

Deposits (real) NaN NaN 20,439 37,293 39,321 47,361 49,177 69,176

Real values are in 2008 USD. Financial wealth and deposits are averages per U.S. household Current limit per bank: $250,000 (single account), $500,000 (joint), with some additional allowed permutations 1980 marks the maximum real coverage O. Shy, R. Stenbacka, V. Yankov (2014)

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Empirical facts on the demand for multiple deposit accounts

Deposit insurance limits (graph)

Deposit insurance limits over time (graph) Deposit insurance limit Avg. fin. assets Avg. deposits

500

250

100

40

30

20

1935

1950

O. Shy, R. Stenbacka, V. Yankov (2014)

1966 1969

1974

1980

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2008

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Empirical facts on the demand for multiple deposit accounts

Cumulative density of average balance

Cumulative density of average balances exceeding $100,000 in 2008 (before the limit was raised to $250,000) 1 0.9 0.8 0.7 0.6

57.9 % of accounts below $ 250,000 ← $ 235,000 median account balance

0.5 0.4 0.3 0.2 0.1 0 100

150

200

250 300 350 Average account balance in thousands

400

450

500

60% of these large deposits were below $250,000 Almost all accounts were below 2 × $250, 000 O. Shy, R. Stenbacka, V. Yankov (2014)

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Empirical facts on the demand for multiple deposit accounts

Share of insured brokered deposits

Share of insured brokered deposits Share of insured brokered deposits 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

Small banks: below 75 pctile Medium large banks: 75-99 pctile Large banks: Top 99 pctile

0.1 0 Jan80

Jan85

Jan90

Jan95

Jan00

Jan05

Jan10

Jan15

A substantial increase in the demand for insured brokered deposits at the onset of the Financial Crisis of 2008 O. Shy, R. Stenbacka, V. Yankov (2014)

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Empirical facts on the demand for multiple deposit accounts

Deposit Account Allocations and Household Wealth

1 2 4 6 8 10 12 14 16 18 20 Number of CD contracts (top coded at 20)

Number of banks: CD contracts (top coded at 10) 1 2 4 6 8 10

Deposit Account Allocations and Household Wealth

10

Number of CD contracts

Wealthy households maintained multiple deposit accounts with different banks (SCF, 2007)

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Empirical facts on the demand for multiple deposit accounts

Pricing of Large Denomination Retail Jumbo CDs (≥ $100, 000)

Pricing of Large Denomination Jumbo CDs (≥ $100, 000) 2.5 3−month 6−month 12−month 2

1.5

1

0.5

0

−0.5 Jan96

Jan98

Jan00

Jan02

Jan04

Jan06

Jan08

Jan10

Jan12

Spread between matched maturity LIBOR and Jumbo CD rates Banks paid significantly lower interest rates on Jumbo CDs with minimum balance of $ 100,000. (Source: RateWatch) O. Shy, R. Stenbacka, V. Yankov (2014)

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Empirical facts on the demand for multiple deposit accounts

Summary of facts

Summary of facts Fact 1. For the period 1986–2008, the average balance of most of the large (> $100k) partially insured denomination accounts was within two or three times the deposit insurance limit. Fact 2. For most of the period 1986–2008, smaller banks attracted a larger share of brokered insured deposits compared with medium and large size banks. Fact 3. According to the Survey of Consumer Finances, a large fraction of wealthy households maintain multiple deposit accounts with multiple deposit institutions. Fact 4. There is a strong positive correlation between the average number of CD accounts, the average amount deposited, and the number of banks these accounts are held with. Fact 5. Banks charged a large monopoly mark-up on retail Jumbo CDs over the period 1997-2011 O. Shy, R. Stenbacka, V. Yankov (2014)

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A Model of Bank Competition

A Model of Bank Competition for Deposits

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A Model of Bank Competition

Banks’ Asset Returns

Banks’ Asset Returns There are two competing banks: bank A and bank B Each bank invests in a risky project  ρ (1 − φ) ρ˜ = 0 φ Banks fund their investments with deposits (no equity) For each bank i ∈ {A, B}, $ 1 of deposits earns (1 − φ)(ρ − ri ) in expected profits if a bank promises to pay a deposit rate of ri Bank defaults are perfectly correlated and occur with probability φ (we will relax this assumption)

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A Model of Bank Competition

Depositors

Depositors Initially, each depositor has $2 deposited in either bank A or B We call them type A depositors and type B depositors (i = A, B) σ · s = cost of opening a 2nd account (with the competing bank) where, 0 ≤ s ≤ n, and “n” measures the # depositors of each type Depositors with “low” s may open a 2nd account. “High” s will not

0 Open a second bank account si

Do not

-s

n

sA and sB are depositors who are indifferent between sticking to their original bank and opening a 2nd bank account Note: σ · s is the cost of opening a 2nd account which is independent of how much money is transferred to the new account O. Shy, R. Stenbacka, V. Yankov (2014)

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Limited Deposit Insurance

Deposit Insurance Design: Limited Deposit Insurance

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Limited Deposit Insurance

Limited Deposit Insurance Design

Deposit insurance is limited to $ 1 per bank (half of depositors’ wealth) Deposit insurance covers both the principal and promised interest payment Deposit insurance fund is funded through non-distortionary taxes (on either banks or depositors)

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Limited Deposit Insurance

Depositors

Limited Deposit Insurance: Depositors Depositors are insured up to $1 per bank The expected utility of a type i ∈ {A, B} depositor s ∈ [0, n] : ui (s) =  uninsured insured  }| {  z}|{ z   1 r + (1 − φ)1 r − φ 1 i i  1 ri + 1 r−i − σs    1 r−i + (1 − φ)1 r−i − φ 1 − σs

does not open a 2nd bank account opens 2nd account and transfers $1 to −i opens 2nd account and transfers $2 to −i

Given deposit rates rA , rB , type i ∈ {A, B} depositors with switching costs lower  than a threshold si open a second account: +φ 0 if ri ≥ r−i   1−φ  def r−i − (1 − φ)ri + φ +φ si = if r−i +φ−σn < ri < r−i 1−φ 1−φ  σ   n if ri ≤ r−i +φ−σn 1−φ O. Shy, R. Stenbacka, V. Yankov (2014)

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Limited Deposit Insurance

Depositors

Limited Deposit Insurance: Deposit market segmentation

0

Primary bank account A ($1) Secondary bank account B ($1)

0

Primary bank account B ($1) Secondary bank account A ($1)

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sA Bank A only ($2) n s sB Bank B only ($2) n s

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Limited Deposit Insurance

Banks and equilibrium

Limited deposit insurance: Banks

Banks compete for deposits by posting deposit interest rate offers o n rAL = argmaxrA |rB (1 − φ)(ρ − rA ) (2(n − sA ) + sA + sB ) | {z } Deposit demand of bank A

o n rBL = argmaxrB |rA (1 − φ)(ρ − rB ) (2(n − sB ) + sB + sA ) | {z } Deposit demand of bank B

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Limited Deposit Insurance

Equilibrium

Limited insurance: Equilibrium Equilibrium interest rates, banks’ profit, and # of new accounts are: rAL = rBL = ρ −

2σn 2−φ

4(1 − φ)σn2 2−φ 2σn 

and πAL = πBL =

sAL = sBL = s L ≡

φ 1+ρ− σ 2−φ

Consumer welfare  2nσ 2 2nσ  φ2  1+ρ− + 2n(2 − φ) 1 + ρ − − 4n cw L = σ 2−φ 2−φ Expected cost to the deposit insurance fund   di L = φ (sAL + sBL )(2 + rAL + rBL ) +φ (n − sAL )(1 + rAL ) + (n − sBL )(1 + rBL ) {z } | | {z } Depositors with two accounts

Depositors with one accounts

2

 φ 2σn 2 2σn  =2 1+ρ− + 2φn 1 + ρ − . σ 2−φ 2−φ O. Shy, R. Stenbacka, V. Yankov (2014)

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Limited Deposit Insurance

Equilibrium

Limited insurance: Equilibrium welfare Equilibrium welfare: w L =cw L + πAL + πBL − di L = 2σn 2 φ2  1+ρ− =4n((1 − φ)ρ − φ) − σ 2−φ | {z } SL

Aggregate cost of maintaining multiple accounts SL =

Z

sAL

Z σs ds +

0

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sBL

σs ds = 0

φ2  2σn 2 1+ρ− σ 2−φ

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No Deposit Insurance

Deposit Insurance Design: No Deposit Insurance

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No Deposit Insurance

Depositors

No deposit insurance: Depositors The expected utility of a type i depositor s ∈ [0, n] initially invested in bank i ∈ {A, B} is given by: ( (1 − φ) 2 ri − φ 2 ui (s) = (1 − φ) 2 r−i − φ 2 − σs

if does not open a second bank account opens a second account and transfers $2 to B.

Switching thresholds:   0     2(1 − φ)(r−i − ri ) def si = σ     n

if ri ≥ r−i σn < ri < r−i 2(1 − φ) σn if ri ≤ r−i − . 2(1 − φ) if r−i −

No incentives for multiple accounts - either (sA > 0, sB = 0) or (sA = 0, sB > 0) O. Shy, R. Stenbacka, V. Yankov (2014)

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Unlimited Deposit Insurance

Deposit Insurance Design: Unlimited Deposit Insurance

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Unlimited Deposit Insurance

Unlimited Deposit Insurance: Depositors All deposit accounts insured in full The expected utility of a type i depositor s ∈ [0, n] initially invested in bank i ∈ {A, B} is given by: ( 2ri ui (s) = 2 r−i − σs

if does not open a second bank account opens a second account and transfers $2 to B.

Switching thresholds:   0    2(r − r ) def −i i si = σ    n

if ri ≥ r−i σn if r−i − < ri < r−i 2 σn if ri ≤ r−i − . 2

No incentives for multiple accounts - either (sA > 0, sB = 0) or (sA = 0, sB > 0) O. Shy, R. Stenbacka, V. Yankov (2014)

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Comparing the three regimes of deposit insurance

Comparing the three regimes of deposit insurance

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Comparing the three regimes of deposit insurance

Equilibrium Summary

Equilibrium Summary Equilibrium interest rates, segmentation thresholds, profits, consumer welfare (cw ), aggregate switching costs (S), expected deposit insurance costs (di)

(rA , rB ) (sA , sB ) (πA , πB )

No DI

Unlimited DI

σn ρ − 2(1−φ) 0

ρ − σn 2

σn

0

2

(1 − φ)σn

2

− φ) 4n((1 − φ)ρ − σn 2

4n(ρ − σn ) 2

S

0

0

di

0

) 4nφ(1 + ρ − σn 2

w

4n((1 − φ)ρ − φ)

4n((1 − φ)ρ − φ)

cw

Limited DI 2σn ρ − 2−φ φ 2σn ) (1 + ρ − 2−φ σ 4(1−φ)σn2 2−φ     φ2 2nσ 2 + 2n(2 − φ) 1 + ρ − 2nσ 1 + ρ − 2−φ σ 2−φ φ2 2nσ )2 (1 + ρ − 2−φ σ     φ2 2σn 2 + 2φn 1 + ρ − 2σn 2 σ 1 + ρ − 2−φ 2−φ 2 2nσ )2 4n((1 − φ)ρ − φ) − φσ (1 + ρ − 2−φ

A mean-preserving spread comparative statics analysis shows that higher credit risk leads to higher equilibrium deposit rates and non-increasing profits. No risk-shifting incentives of banks even in the presence of limited or unlimited deposit insurance

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−

Comparing the three regimes of deposit insurance

Deposit insurance and bank competition

Limited Deposit Insurance and Bank Competition A system with limited DI coverage weakens competition among banks: Banks pay lower interest, formally rkL < rkN < rkU , k = A, B Banks earn higher profit, formally πkL > πkN > πkU , k = A, B Why is that? Because under limited insurance (relative to no or unlimited insurance), 1. banks gain some monopoly power over depositors with low cost of opening a 2nd bank account (low “s”), therefore 2. able to extract some of depositors’ surplus gain from obtaining 100% coverage via a 2nd account A limited deposit insurance design is equivalent to a tax on depositors and a subsidy to banks

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Comparing the three regimes of deposit insurance

Deposit insurance and welfare

Limited Deposit Insurance and Welfare

A system with limited DI coverage lowers total welfare: Under the assumption on the funding of deposit insurance, limited deposit insurance redistributes surplus from depositors to banks by softening competition for deposits Total welfare is lowest under limited deposit insurance due to the aggregate switching costs which are a deadweight loss: wL + SL = wN = wU

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Independent Bank Failures

Independent Bank Failures

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Independent Bank Failures

An extension

Extension: Independent Bank Failures Dependent failures B fails B not A fails θ 0 A not 0 1−θ

Independent failures B fails B not 2 A fails θ θ(1 − θ) A not (1 − θ)θ (1 − θ)2

Expected benefit to a type A depositors: uA (s) =  if does not open a 2nd account;  (1 − φ) 2 rA − 2φ   no defaults B fails  z }| { z }| { 2 (1 − φ) (rA + rB ) + (1 − φ)φ(rA − 1) if opens a second bank account     + φ(1 − φ)(rB − 1) + φ2 (−2) −σs and transfers $1 to bank B.   | {z } | {z } A fails

both fail

Reworking all the computations yields no change in results O. Shy, R. Stenbacka, V. Yankov (2014)

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Conclusion

Conclusion

Limited DI coverage may have emerged as a tradeoff between: 1. Stability via elimination of a bank run equilibrium (Diamond & Dybvig) 2. Increased risk-taking by banks (moral hazard)

Our model analyzes a 3rd factor (associated with limited DI): The competition-softening effect In addition, we identify some social loss caused by opening and maintaining multiple bank accounts Next step: Estimating total welfare effects associated with all the above 3 factors

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