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Banks as Secret Keepers (AER, Vol 107, 2017)
Tri Vi Dang Gary Gorton Bengt Holmström
Guillermo Ordoñez
Columbia Yale and NBER MIT and NBER Penn and NBER
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Banks are opaque. Why?
Secrecy surrounds banks. Why?
Banks are regulated. Why?
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Opacity developed over the 19th century.
Free bank note discounts were informative.
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Figure 1: Bank of Virginia Note Discounts in Philadelphia (% from face value)
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Demand deposits grew; don’t have secondary markets
but trade inside clearing houses. Discount information
lost.
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100,000
200,000
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1,000,000
Yea
r
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$ T
ho
usa
nd
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Figure 2: Growth of Demand Deposits
Bank Notes in Circulation
Deposits
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Banks stocks endogenously stop trading; delisted by
banks. So, no information revealed.
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40
60
80
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Nu
mb
er
Sto
cks
Figure 3: New York Stock Market, 1863-1909
Total Number of Stocks in Index
Total Number of Bank Stocks inIndex
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Source: CRSP; SIC = 6010, 602x; EXCHCD = 1; SHRCD = 10, 11
Figure 4: Bank Total Annual Trading Volume(CRSP data, Millions of Shares, 1926 to 1979)
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Listed US bank stocks prior to 1962: Bank of America, 1927-1928
Bank Manhattan, 1927-1928
Bank of New York, 1927-1929 Chase National Bank, 1927-1928 Chatham Phoenix National Bank, 1927-1928 Chemical National Bank, 1927-1928 Commerce Guardian Trust & Savings Bank, 1927-1929 Continental Bank, 1927-1930 Corn Exchange National Bank, 1927-1950 Farmers Loan & Trust, 1927-1928 Hanover National Bank, 1927-1928 National City, 1927-1928 National Park, 1927-1929
Banks delist even after Fed in existence.
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Secrecy and Regulation
Banks have always been regulated; charters required; entry limited.
Banks have always been examined, but the examination reports are always
secret.
Discount window borrowing secret.
Secrecy pervades financial crisis responses.
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Banks as institutions produce debt:
• Diamond and Dybvig (1983): Banks exist to smooth
consumption.
• Gorton and Pennacchi (1990): Banks exist to create safe debt
to be used as a medium of exchange.
Optimal contract for trading:
• Dang, Gorton, Holmström (2012): Debt, backed by debt, is the
optimal security for trade. Info-insensitivesensitive = crisis.
• This paper: information has social value. Banks produce info
but are optimally opaque in order to keep their debt trading at
par.
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Basic Idea
• Banks must produce debt that does not vary in value over
time, even when the banks’ assets are risky and the bank
produces private information about the borrowers.
• To produce this safe liquidity banks will keep detailed
information about borrowers secret.
• Capital markets involve information revelation, so they
produce risky liquidity.
• Trade-off determines where firms fund their projects.
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One storable good. Three periods: 0, 1, 2. Three risk-
neutral agents: a firm (F), one early consumer E, and
N>1 identical late consumers (L).
Preferences
𝑈𝐹 = ∑ 𝐶𝐹𝑡2𝑡=0 𝜔𝐹 = (0, 0, 0)
𝑈𝐸 = ∑ 𝐶𝐸𝑡2𝑡=0 + 𝛼min{𝐶𝐸1, 𝑘} 𝜔𝐸 = (𝑒, 0, 0)
𝑈𝐿 = ∑ 𝐶𝐿𝑡 + 𝛼min{𝐶𝐿2, 𝑘}2𝑡=0 𝜔𝐿 = (0, 𝑒, 0)
E born at t=0. Late born at t=1.
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Preferences for F
Cht
Uh
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Preferences for E (or L)
Cht
UE
UE1
k
UE0, UE2
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The firm has two project; each needs w at t=1 to operate.
-One is a lemon which never generates output.
The “worthy” project generates x>w at t=2 (state g) with
prob λ and 0 otherwise (state b).
Projects are linearly divisible.
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Assumptions about projects and endowments
1. Worthy projects are ex ante efficient: λx>w.
2. E can fully cover w or his liquidity need, but not both:
e>k, and e>w, but e<k+w.
3. However, endowments of E and L can jointly cover
both: 2e≥2k+w.
Notation: k>z≡e-w (Note: e – w is residual.)
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Banks (B) and Markets (M)
These institutions facilitate risk sharing between E and L
so generate investments in the firms.
The firm can go to the bank or to the market.
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Information
If the firm goes to a bank to borrow w to invest in a
worthy project at t=0, the bank receives a file on the
project that contains all financial info needed to verify
that it is a worth project.
If the firm goes to the market, the same file will be
presented to a market agent.
Understanding the file requires expertise.
The bank has a low-tech info production technology.
L has a high-tech production technology.
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Assumption on Info
Based on the file, a bank and a market agent can
determine which of a firm’s two projects is worth.
But only L, who has expertise can learn at t=1 whether the
project will be a success or failure at t=2.
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Assumption on differences between banks and markets
Banks can keep the files of projects secret if they choose
to do so. Markets cannot keep the files secret.
Note that at t=1 when L arrives, the info in the file in L’s
hands will cause variation in the valuation of the project.
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Assumption
All the late consumers interact in the market
simultaneously. Only one late consumer (chosen at
random) interacts with the bank.
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Autarky: Consumers just store endowments.
First Best
Period 0: Use w from E to finance the worthy project.
o Feasible since e > w and E saves z ≡ e-w < k
Period 1
o Transfer k – z from L to E (k>z≡e-w) regardless of
whether the project will succeed or fail.
Assign all social surplus to the firm. I.e., F has the
bargaining power.
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Expected Utilities Comparison
Autarky First Best
E(UF)= 0 UF= λx – w>0
UE= e + αk UE= e + αk
UL= e + αk UL= e + αk
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Capital Markets
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EQ Concept: Subgame Perfect.
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Prop 1: The EQ in capital markets shows fully revealing,
state-contingent prices at t=1 and, when the project is fully
financed, it implements an allocation that generates a
welfare loss relative to the first best of
min{α(1-λ)(k-z),λx-w}.
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Capital markets implement α(1-λ)(k-z) less welfare.
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Banks
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Proposition 2: There is a subgame perfect EQ in which
the bank, by keeping the firm’s file secret, permits first-
best implementation: the firms is fully funded and E’s
liquidity needs are fully covered.
Note: By accepting E’s deposits at t=0 the bank commits
itself to a contract with the L. Bank has nothing to
gain by showing L the firm’s file.
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Main Case: Private Information Acquisition
So far we have assumed that it is impossible to
discover the bank’s secret.
There may be incentives for L to acquire private
information about the bank’s balance sheet.
Assume the cost of information production is γ.
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If L does not acquire information before depositing:
(𝟏 + 𝛂)𝐤 + 𝛌(𝐫𝟐𝐋(𝐠) − 𝐤) + (𝟏 − 𝛌)(𝐫𝟐
𝐋(𝐛) − 𝐤)
If L privately acquires information before depositing:
(𝟏 + 𝛂)𝐤 + 𝝀(𝒓𝟐𝑳(𝒈) − 𝒌) + (𝟏 − 𝝀)(𝒆 − 𝒌) − 𝜸
L acquires information if:
𝒓𝟐𝑳(𝒃) > 𝒆 −
𝜸
(𝟏 − 𝝀)
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Set 𝒓𝟐𝑳(𝒃) as high as possible. Then IC constraint is:
(𝟏 − 𝝀)(𝒌 − 𝒛) ≤ 𝜸.
High k and w and low e, λ and γ makes banks less
feasible.
High γ makes the bank more opaque.
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Distortions when First Best Cannot be Implemented
If late consumers have an incentive to produce
information, then one thing the bank can do is to produce
less money—i.e. promise E less.
On the other hand, the bank could make a smaller loan,
so less of the initial project is financed.
Paper provides condition for the bank to prefer distorting
risk-bearing rather than distorting investment.
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Banks versus Markets
Suppose a continuum of banks, E, L, and F’s characterized
by: (𝝀𝒊, 𝜸𝒊).
A mass 1 of each agent and each bank forms a match with
single early and late consumers and finances a single
project.
The cost of each project is w.
Then the previous analysis allows us to characterize which
projects are financed by banks with first best risk sharing,
those financed by banks that distort risk sharing or
investment, and those financed by capital markets.
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Replication Possibilities
Can markets replicate banks in the region where banks
dominate? The answer is no.
Because detailed information is available publicly at t =
1, late consumers can always interpret the information
and compete for the claims in the project, the market
equilibrium at t = 1 will necessarily feature state-
contingent prices.
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Replication Possibilities
Can banks replicate markets in the region where
markets dominate? This would be possible only if the
bank offers to repay at t = 2 whatever the random late
consumer deposits at t = 1 and if the bank could reveal
the detailed information to the late consumer at no
cost. There would be replication in this case as the late
consumer would only deposit funds in the bank if the
state is good, in which case the bank could compensate
the early consumer at t = 1 and repay the late consumer
with the proceedings of the firm’s claims at t = 2, exactly
as in capital markets.
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This is however a knife-edge situation. As long as there
is at least one “naive” late consumer who is not able to
interpret the file, she would never deposit in the bank,
as the bank would use those funds to pay the early
consumer at t = 1 and then not have enough resources
to repay her in a bad state at t = 2.
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Final Comments
Output of banks is debt.
Efficient transactions require money to be information-
insensitive.
But, information needed for investment efficiency.
Opacity of banks optimal for creation of private money.
Banks keep secrets.
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