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Federal Reserve Bank of Chicago
The Cost of Banking Panics in an
Age before “Too Big to Fail”
Benjamin Chabot
WP 2011-15
The Cost of Banking Panics in an Age
before “Too Big to Fail”
Benjamin Chabot
Federal Reserve Bank of Chicago
ben.chabot@chi.frb.org
Nov 28, 2011
Abstract:
How costly were the banking panics of the National Banking Era (1861-1913) ? I
combine two hand-collected data sets - the weekly statements of the New York Clearing
House banks and the monthly holding period return of every stock listed on the NYSE - to
estimate the cost of banking panics in an era before “too big to fail”. The bank
statements allow me to construct a hypothetical insurance contract which would have
allowed investors to insure against sudden deposit withdrawals and the cross-section of
stock returns allow us to draw inferences about the marginal utility during panic states.
Panics were costly. The cross-section of gilded-age stock returns imply investors would
have willing paid a 14% annual premium above actuarial fair value to insure $100
against unexpected deposit withdrawals The implied consumption of stock investors
suggests that the consumption loss associated with National Banking Era bank runs was
far more costly than the consumption loss from stock market crashes.
The existence of too big to fail banks poses a difficult problem for prudential bank
regulation. The only credible way to prevent financial firms from becoming too big to fail
is to convince bank creditors that large banks will actually be allowed to fail. Bank panics
are costly, however, so regulators have a difficult time convincing market participants
that large banks will fail when participants know that “in the midst of the crisis, providing
support to a too-big-to-fail firm usually represents the best of bad alternatives”1.
The regulatory response to the recent crisis attempts to end too big to fail by
minimizing the consequences of a bank failure. The hope is that by increasing capital
buffers and limiting the size, complexity, and interconnectedness of financial firms,
regulators will be free to let banks fail without grave consequences for the rest of the
financial system and economy. If bailouts are seen as unlikely, the argument goes, selfinterested creditors will limit the leverage and risk taking of financial firms by
demanding compensation for behaviors that increase the likelihood of bankruptcy and
equity holders with plenty of their own “skin in the game” will devote more resources to
monitoring risky behavior.
Simple declarations that banks will hereafter be allowed to fail are not credible
unless the costs of bank failures are relatively small. With this in mind, much of the
regulatory overhaul since the 2008 crisis has sought to limit the cost of a bank failure. If
history is any guide, this goal will be difficult to achieve. For more than 50-years the
United States had a regulatory framework that resulted in a banking system remarkably
similar to the “ideal” system proposed in Dodd-Frank and the new Basel Capital Accords.
Banks were small, well capitalized and insulated from counterparty risk, yet bank panics
were extremely costly.
During the national banking era (1861-1913) no bank was too big to fail and the
lenders of last resort seldom intervened to save illiquid banks. Aware that they would
suffer losses if a bank’s balance sheet became too leveraged or risky, creditors and
counterparties monitored risk taking. As a result, banks were less levered, less
1
September 2, 2010 testimony of Federal Reserve Chairman Bernanke before the Financial Crisis Inquiry
Commission
1
interconnected and, when banks failed, losses were largely borne by equity holders.
Contagious failures due to counterparty default were exceedingly rare during the national
banking era2. Nonetheless, bank panics were extremely costly.
How costly were the banking panics of the national banking era? A natural way to
think about this question is to ask how much consumers would have paid to insure
against the consumption loss experienced during banking panics. Panic insurance did not
exist and consumption data is unavailable but it is possible to use balance sheet and stock
return data to draw inferences about the cost of bank panics. I create a measure of bank
funding from hand-collected weekly balance sheet statements of the New York Clearing
House (NYCH) banks. I use these balance sheets to construct a time series of historical
bank funding during the national banking era. I combine this measure of bank funding
with another hand collected data set - the cross section of all monthly NYSE stock returns
- to draw inferences about investor marginal utility during panics of the national banking
era. The results suggest investors cared a great deal about banking panics. Unexpected
changes in bank deposits were far more important to the consumption of stock investors
than changes in the stock market itself. The cross-section of stock returns imply that
national banking era investors would have paid approximately XXX per year to insure
against unexpected withdrawals from NYCH banks.
Why were panics so costly? Many real investments have high expected returns
but are either irreversible or can only be liquidated at a loss. Savers are aware that they
may face unpredictable future liquidity shocks. These two facts combine to create a role
for financial intermediaries to pool savings and offer intertemporal risk sharing through a
demand deposit or overnight lending contract. In such a setting, a well-functioning
intermediary can have a real effect on the level of investment and consumption in the
economy3.
For example, in the classic model of Diamond and Dybvig (1983) agents know
that they may be subject to an unpredictable future liquidity shock. They are endowed
2
The Comptroller of the Currency was tasked with liquidating failed national banks. The Comptroller
appointed investigators to ascertain the reason for bank failures. Of the 586 national banks liquidated
between 1865 and 1917 the Comptroller concluded only 12 (or 2.1%) failed due to a counterparty default.
See 1917 Report of the Comptroller of the Currency p.63
3
Allen and Gale (1997). See Allen and Carletti (2008) for a recent survey.
2
with investment opportunities that, once completed, will yield high real returns but are
costly to liquidate early. In the absence of financial intermediation, risk-averse consumers
may choose to forgo investment in high return but irreversible technologies if the risk of
experiencing a liquidity shock before completion is too high. In such a setting, financial
intermediaries can increase aggregate investment and consumption by offering depositors
liquidity on demand and investing a portion of their deposits in the high return
irreversible technology4. Demand deposits improve total welfare but the promise of
liquidity on demand creates a mismatch between the maturity of the intermediary’s assets
and liabilities. This temporal mismatch exposes the intermediary to the risk of a bank run
and the economy to the risk of lost output if otherwise high return investments have to be
forgone out of fear of a run or liquidated early to satisfy withdrawal requests.
A bank run is characterized by a sudden withdrawal of deposits from the banking
system. Runs may be caused by irrational mob psychology5, a switch between completely
random sunspot equilibria6 or a rational response to a common signal about future
liquidity demands or investment returns7. Regardless of the cause, bank runs lower
welfare by forcing banks to forgo high return investments or liquidate previous
investments at a loss. Traditional remedies like temporary suspension of convertibility,
interbank money markets or lenders of last resort (clearing house certificates) were all
employed during the national banking era. These remedies can lower the risk of an
individual bank failure but create linkages that can result in systematic risks of
contagious liquidity withdrawals8.
Despite the popular folk history, before the great depression, bank runs seldom
resulted in direct losses for creditors or counterparties9. Instead, the cost of panics was
4
Diamond and Rajan (2001), Allen and Gale (2004)
Kindleberger (1978)
6
Bryant (1980), Diamond and Dybvig (1983)
7
Mitchell (1941), Chari and Jagannathan (1988), Gorton (1988), Allen and Gale (1998, 2004)
8
Friedman and Schwatz (1963), Allen and Gale (2000), Diamond and Rajan (2005,2006), Brusco and
Castiglionesi (2007).
9
Although bank failures were common, losses to depositors were rare. Loss estimates come from the 1919
Annual Report of the Comptroller of the Currency. The comptroller’s report noted that 586 national banks
were liquidated between 1865 and 1917. The report concluded depositors and creditors lost an annual 3/10th
of 1% of their assets due to the bank failures between 1865-1913.
5
3
likely due to market freezes and curtailed lending. In the era before too big to fail,
creditors were aware that they would not be bailed out and disciplined banks by
withdrawing funding whenever they feared a sudden change in actual or perceived
solvency10. During panics the liquidity of interbank lending vanished and banks
responded much like today – by curtailing lending, calling outstanding loans and
hoarding excess reserves. The fear of creditor runs disciplined bank risk taking and
leverage but to the extent that this fear forced banks to hoard liquidity and forgo
investments with high social returns, the panics of the national banking era were costly
even in the absence the failure of systemically important banks.
In the sections that follow I 1) describe the regulatory system and runs of the
national banking era, 2) describe unique balance sheet data and 1866-1913 stock market
data, 3) describe the estimation of a stochastic discount factor to draw inferences about
the cost of banking panics, and 4) conclude.
1. The National Banking Act and “Poverty Corner”
The National Banking Acts (NBA) of 1863 & 1864 reorganized the United States
banking system. The NBA unified the national currency, established a national regulator
and through regulation of reserve requirements encouraged a national inter-bank money
market centered in New York City. The NBA established limits on leverage through
reserve requirements, capital requirements including double liability for shareholders,
limits on note circulation and the requirement that national bank notes be backed by US
government bonds deposited with the comptroller of the currency at a 10% haircut.
Finally, the NBA created explicit lenders of last resort by allowing clearing house
certificates issued by reserve and central reserve city clearing houses to be counted as
lawful money toward reserve requirements11.
10
Friedman Schwartz (1963), Gorton (1988), Calomiris and Gorton (1991) and Wicker (2000) each provide
excellent reviews of the facts and theory of late 19th and early 20th century banking panics.
11
NBA or 1864 sec 31. Gorton (1985) argues these are the origin of central banks in the United States.
4
The National Banking Act encouraged an interbank lending market by divided the
nation’s national banks into three groups and providing regulatory incentives to pool
excess reserves in central cities. The NBA divided banks into Central Reserve City banks
(those chartered in New York City, Chicago & St. Louis), Reserve City banks (those
chartered in regional trade hubs) and country banks (those chartered outside of Reserve
and Central Reserve cities). Country banks were required to hold 15% of their deposits
plus notes outstanding as liquid reserves (specie or treasury notes). This 15% reserve
requirement placed a limit on bank leverage but to encourage an interbank market
country banks were allowed to keep 3/5ths of this 15% on deposit in reserve or central
reserve cities. Reserve City banks were required to hold 25% reserves but they could
keep half of their reserves on deposit with Central Reserve City banks. These regulations
encouraged banks to pool excess reserves that could not be employed profitably at home
and deposit them at interest in Reserve and Central Reserve City banks. In practice,
excess reserves migrated to New York City to be employed in the overnight repo market.
Banks have always desired liquid low-risk investments for their excess reserves.
Before the Federal Reserve System and the development of the modern federal funds
market, national banking era banks looked to the New York securities market for lowrisk, overnight lending of excess reserves. Country banks embraced the opportunity to
deposit reserves in New York city banks and gain access to the New York money market.
By holding a portion of their reserves in New York, country banks were able to manage
their reserve ratios by accessing the New York call money market.
Under the National Banking Act the [New York Call] Money Market was the recipient of
all those surplus funds of the country banks which they desired to invest in some liquid form
which they could count upon as a secondary reserve. As a result, in times when the country banks
had very little use for their funds at home, these funds were sent to New York, where they were
either invested in call loans or put on deposit at the New York banks, who in their turn sought
investment for them. – Griffiss ( 1923) The New York Call Money Market p. 65-66
Banks looked to the New York call market because repo loans made against
security collateral offered an attractive combination of high return, liquidity and low
default risk. Brokers and banks could lend or borrow against security collateral at
“poverty corner” and the New York Stock Exchange money post. Depending on the
5
quality of the collateral, a borrower could typically borrow between 80-90% of the
market value of a pledged security12. The rate of interest charged varied with the
volatility and liquidity of the pledged security but the minimum call rate was always
equal to the rate of interest charged on loans with long-term government bonds as
collateral. As the name implies, call loans gave the lender the right to call in the loan at
any time. The borrower of a call loan signed the pledged security into the name of the
lender. If the lender called the loan and the borrower was not forthcoming with the
money, the lender could sell the collateral to satisfy the obligation. If the collateral fell in
value the lender could issue a margin call and demand the borrower raise his collateral
back to the original level. Thus lenders suffered a partial default only when the borrower
defaulted and the collateral declined by more than 10-20% before the lender could
liquidate. Given these margins and the liquidity and the low volatility of the government
bond market, call loans on government bond collateral were, for all practical purposes,
default-risk free13. Despite the right to call for payment at any time a call loan did commit
the lender’s money for a brief period. Even in the event of a collateral sale the lender
would not receive his cash until the sale cleared one day after the trade date. The call loan
rate therefore reflected the marginal opportunity cost of a bank holding excess reserves in
their vault as a defense against unexpected withdraws rather than loaning it risk-free for a
minimum of one day.
Although the NBA allowed for the pooling of reserves in Chicago and St. Louis,
the liquidity offered by the active market in hypothecated NYSE securities attracted
excess reserves from across the nation and made poverty corner in New York the de facto
interbank funding market. The practice of lending excess reserves against collateral in
New York created a single nationwide money market. Banks anywhere in the nation
could safely employ their excess reserves with a simple cable to a New York clearing
12
Stock investors could borrow 90% of the value of a security from their brokers at the prevailing margin
rates. The brokers extended this loan but generally did not carry the whole loan on their books. Instead,
brokers typically financed 10% of the value of the stock from their own capital and financed the remaining
80% by rehypothecating the pledged security at poverty corner.
13
Daily bond prices are unavailable but prices are available on the same 28-day frequency as our stock
sample. The riskiest government bond had a 28-day standard deviation of 1.3% and a maximum 28-day
decline of 4.56% during the panic of 1896.
6
house bank. The call rate prevailing at poverty corner provided a single price that
equalized the opportunity cost of excess reserves across the nation.
“And bankers know that they can always depend to a greater or less extent on the supply
of floating capital in ‘ the street.’ In ordinary times, this supply is enormous, and ample
for all demands. It is made up of the deposits of individuals and corporations from every
section of the civilized world. On " Poverty Corner," as the brokers styled a favorite
gathering-place of borrowers and lenders before the panic, one might see clerks of New
York banking houses which represented similar institutions in various parts of the
country, mingling with the agents of wealthy firms In London, Amsterdam, and Berlin.
But it is dangerous to place too much dependence on this supply. It vanishes when most
needed, and is ever keenly alive to the slightest suspicion of danger.” - “Wall Street and
the Crisis” Old and New Magazine January 1874 p.43
This system required the New York Clearing House (NYCH) banks to expand or contract
their balance sheets with the nationwide demand for currency. The tendency of loaned
reserves to “vanish when most needed” exposed the NYCH banks to liquidity shocks
anywhere in the nation and was often cited as the leading cause of pre-FDIC banking
panics.
“The immediate cause of the money drain which started the[1873] panic was, as before,
the sudden demand by out-of-town banks for their cash reserves on deposit. It was found
that the $60,000,000 of call loans on which the New York banks had relied was ‘entirely
unavailable’ ”- Lainer (1922) A Century of Banking in New York p.238
During panics depositors fled from NYCH banks and the “price” of excess reserves in
New York city reached astronomical levels.
“On the corner of Broad and Exchange, almost any time between the hours of 10 and 3,
can be seen a crowd of men who are especially active. The Gold Board is one thing, the
Stock Exchange is another; but Poverty Corner differs from both … Here men gather out
in the rain and cold, who have money to lend or money to hire. Here the price of money
from day to day is fixed. In a panic the first thing is to get money, and men who have
margins to keep up, or Stocks to carry, make a rush for Poverty Corner. The language of
this locality is peculiar. From 200 to 500 men are assembled, all shouting at the top of
their lungs, making an offer for money, or making offers of a loan. On Thursday the
crash in this locality was fearful. One man shouts out, " I want 10;" another, "I want 20;"
another, "I want 40;" which means, "I want 40 thousand." A hard-looking, banged up
Jewish youth, who would hardly make a respectable ragman, shouts out, " I have got 50
—," and everybody goes for him. He jerks down his hat over his eyes, buttons up his coat,
and prepares for the tussle. " 1 1-2," he shouts, which means that he has $50,000 to loan
at the rate of 450 per cent a year ! This is snapped at, for speculators must have money.
Then comes the question of security. At the high rate named, millions were denied,
because the security was not U.S. Bonds, N. Y. Central, or some other gilt-edged Stock.”
7
- Smith (1875) Bulls and Bears of New York. p. 558
The above quotation requires some translation. In normal times repo loans at
poverty corner were quoted in annual percentage rates by type of collateral. Thus if you
were to read the money section of the New York Times in a period of relative calm the
column would report the annual rates to borrow against US government bond collateral
and mixed collateral. Mixed collateral was a portfolio of non-US government bonds
where the haircut on each security was adjusted in relation to its risk until the basket was
considered homogenous. Therefore, if a broker came with a basket of stocks of varying
quality the “gilt-edged” stocks (Vanderbilt lines etc) would be haircut 20% and lent
against at the mixed collateral rate. Stocks of lower quality would be assigned a larger
haircut for the same interest rate or charged a higher interest rate for the same haircut.
During the panic described in the quote above, the haircut on all but the best collateral
went to 100%. That is, no loan could be obtained except with “U.S. Bonds, N. Y. Central, or
some other gilt-edged Stock” as collateral and even in the case of acceptable collateral the
interest rate was 1.5% per day14!
New York balance sheets were extremely sensitive to strain anywhere in the
country. Contemporaries viewed this as a weakness and one of the impetuses for the
founding of the Federal Reserve. In fact, 1911 The National Monetary Commission report
to Congress, which recommended the establishment of the Federal Reserve, devoted an
entire volume to the topic. The volume’s very first sentence summarized the
contemporary view of the New York centered, finance-led business cycle.
“Attention has been repeatedly called to the vicious circle in which the American money market
moves; how the volume of banking credit is rigidly inelastic, being determined as to circulation
by bond security and as to loans and discounts by a fixed ratio to legal reserve; how the surplus
funds which pile up with seasonal fluctuation in the interior flow inevitably to New York City,
there to stimulate speculation at times when general economic conditions suggest quiescence,
and how, conversely, when returning activity draws back funds to the interior, the recovery is
impeded by the strain and cost of speculative liquidation” – Bank Loans & Stock Exchange
Speculation (1911) p. 3. National Monetary Commission
14
Smith arrives at an annual rate of 450% by taking the stock market convention of 300 trading days a year
and ignoring compounding.
8
The sensitivity of the New York money market to nationwide deposit shocks
makes the NYCH balance sheets an ideal source for this study. Stress anywhere in the
national banking system was quickly reflected in the NYCH statements and the panics of
the national banking era were largely New York City affairs. In fact, “With the single
exception of the 1893 panic, pre-1914 banking panics were restricted mainly to the New
York money market with relatively few bank suspensions in the rest of the country”15.
Although panics inevitably occurred in New York their effects were felt nationwide.
“when they suspended, and by so doing locked up their many millions of deposits, on
which thousands of people in various parts of the country were depending to make their
settlements, it was easy to see that the disturbance was not one of passing moment.” – “Wall
Street and the Crisis” Old and New Magazine January 1874 p.42
Therefore, a measure of excess reserves in New York City is likely to reflect the excess
reserves in the entire national banking system and serve as an excellent proxy for
nationwide bank funding stress.
2. 1866-1913 Bank Balance Sheet and Stock Return Data
I wish to construct a relatively high frequency historical measure of the health of
the banking system that can be used to draw inference about the cost of national banking
era panics. This measure should capture both the overall health of the banking system and
be observable at the same frequency as stock returns. An excellent candidate is the
deposit information contained in the weekly balance sheets of New York City banks.
Contemporaries understood that asymmetric information about the health of individual
banks could transform a run on a single bank into a system-wide panic. The NYCH
attempted to minimize information asymmetries by requiring its member banks to publish
weekly balance sheet statements. These statements appeared in the Saturday morning
New York Times, Wall Street Journal and Commercial and Financial Chronicle. The
condensed balance sheets reported the average weekly and Friday closing values of each
bank's loans, deposits, excess reserves, specie, legal tenders, circulation and clearings.
15
Wicker (2001)
9
Bank statements were carefully scrutinized by investors and unexpected changes in
leverage could set off a stock market rally or decline16.
I use the NYCH balance sheet reports to construct a measure of bank funding
stress. The most natural measure of funding stress is the flow of deposits into and out of
NYCH banks. Define dep t+1 as the percentage change in deposits from time t-1 to time
t.
dep t = {(NYCH aggregate deposits)t/(NYCH aggregate deposits)t-1}-1
(1)
I construct a time series of dep t sampled every fourth Friday between Jan 1866
and December 1913. The series is corrected for entry and exit by computing the growth
rate between time t and t+1 using all banks in existence at both dates. The index therefore
reflects the change in deposits of surviving banks and does not mechanically fall when a
bank fails and exits the clearing house or mechanically increase when a new bank is
chartered.
The 28-day sampling frequency was selected to correspond with dates for which I
have previously collected the price, shares outstanding and dividends of every NYSE
stock. The stock data was hand collected from the NYSE closing quotations published in
the Commercial and Financial Chronicle. In total, I observe 70,014 individual 28-day
holding period returns on 466 unique NYSE equities. The price, share and dividend data
allows me to compute the market value and 28-day holding period return for each stock
trading on the NYSE between 1866 and 1913. The Chronicle’s Investor’s Supplement
also contains information that allows me to correct the returns for stock splits, mergers
and bankruptcy.
3.
Using Stock Returns to Draw Inference about the Cost of Banking
Panics
16
The New York Stock Exchange was open on Saturdays throughout our period of study.
10
We can use the deposit growth series and the restrictions of a factor pricing model
to draw inferences about the marginal utility of national banking era investors during
banking panics. Consider hypothetical insurance contracts that would have allowed
national banking era investors to hedge against deposit consumption loss due to
withdrawals from NYCH banks. If banking panics were associated with consumption loss
and such a derivative existed, risk-averse investors would have paid a premium above the
actuarially fair price to purchase this insurance. The size of the premium above actuarial
fair price is a natural measure of the cost of banking panics. Of course panic insurance
did not exist but we can use the observable returns on other assets to draw inferences
about the marginal utility of stock investors during panic and non-panic states and use
these marginal utility estimates to make inferences about the price a national banking era
investor would have willingly paid had panic insurance been available.
Insurance Contracts:
Consider a simple asset that pays a discrete amount $Xp if a banking panic occurs
next period and $Xnp if no panic occurs. The asset is an insurance contract so $Xp > $Xnp.
If this security trades in a market where investors face the same price to buy or sell the
price of the security must satisfy P = E[mX] or
P p m p X p (1 p ) m np X np
Where p is the expected probability of a banking panic and
(2)
is the investors’
stochastic discount factor – the marginal utility of wealth in each state. (2) is derived
from the first order condition of investors who can purchase or sell the security until the
expected marginal gain from buying E[mX] equals the marginal cost P .
Next consider a nominally risk-free asset that pays $1 in both the panic and no
panic states. This asset will trade at P = E[m] . The gross risk-free rate is therefore equal
to R f
1
E[ m ]
. If we use this definition of the risk-free rate and divide both sides of (2) by
P we can express the expected excess return of the insurance contract as a function of the
covariance between the insurance return and the stochastic discount factor.
11
1 E[mR] E[m]E[ R] cov(m, R)
E[ R] R f R f cov(m, R)
(3)
Insurance contracts pay high returns when times are bad and the marginal utility of
money is high. For an insurance contract, cov( m, R ) is therefore positive and the
expected excess return of an insurance contract is negative. Equation (3) provides a
testable prediction about the cost of banking panics. If R is the return of any asset
positively correlated with banking panics, and banking panics were costly in terms of
marginal utility, then the expected excess return of R should be negative.
Securities based on changes in deposits series dep t appear to be excellent
candidates for insurance contracts. An insurance contract should pay a high rate of return
in the states of nature we wish to insure against and a low return otherwise. Consider the
following hypothetical security: A series of 28-day, cash-settled future contracts that
trade each observation date and have a time t+1 payout of dep t+1 . If such a security
existed a national banking era investor would have been able to bet on or insure against
changes in NYCH balance sheets by buying or shorting these contracts. If this contract
traded at an actuarially fair price but banking panics were associated with consumption
loss, all investors would wish to short it. But in the aggregate we can’t all hedge. For
every investor that shorts the derivative contract another investor must be willing to hold
it. If panics were costly, the derivative contract must trade below actuarially fair value to
clear the market. How far below depends on how costly banking panics were in terms of
marginal utility.
Were banking panics correlated with consumption and the marginal utility of
national banking era investors? In other words, were banking panics costly in a utility
sense cov(mt,dep t ) < 0 , beneficial cov(mt,dep t ) > 0 or neither
cov(mt,dep t ) = 0 ? Had these contracts actually existed for a long enough time series
we could simply compare the sample average price and payout to infer the sensitivity of
national banking era marginal utility to banking panics. Alas, no deposit insurance
contracts existed so we must infer the covariance of historical marginal utility with bank
12
deposits in another way.
Estimating a Stochastic Discount Factor implied by a Factor Model
We wish to measure the covariance between national banking era marginal utility,
m, and the payout to holding an derivative contract settled against deposit growth rates
dep t , and test the null hypothesis that cov(mt,dep t ) = 0. If we could observe a time
series of m and dep t a natural way to test if cov(mt,dep t ) = 0 would be to estimate a
regression of m on dep t and test the null that =0
mt = + dept + t
(4)
The marginal utility of national banking era investors, mt, is unobservable, however. In
most cases an unobservable LHS variable is a considerable burden when estimating a
regression! In our case of many observable asset returns, however, we can estimate and
from the moment restrictions P E[mX ] and the law of one price.
The law of one price requires the same mt price all assets. Therefore the
unobservable mt that prices our hypothetical insurance contract must also price the
observable gilded-age NYSE stock returns. We can estimate the regression of
unobservable marginal utility on our hypothetical futures contracts via GMM by
choosing and to best satisfy P E[mX ] for observable national banking era stock
returns.
Our strategy takes advantage of the fact that observable stock returns contain
information about investors’ aggregate consumption. If aggregate production
unexpectedly and temporarily declines, risk-averse investors will want to smooth
intertemporal consumption by selling claims to future consumption. While any individual
can smooth consumption by borrowing against the future, in the aggregate we cannot all
borrow. If aggregate production is lower someone, somewhere, must consume less. Asset
13
prices must therefore fall (and expected returns rise) until investors are willing to
consume less today. We can use this insight to draw inference about aggregate
consumption from observable stock returns.
Recall that the expected excess return of any asset can be linked to covariance
with marginal utility via equation (3). An asset that does relatively well during good
times pays a lot in states where the marginal utility of extra wealth is low and a little in
states where the marginal utility of extra wealth is high. Holding this asset adds to
consumption volatility. All things equal, this is not an appealing asset for a risk-averse
investor. Of course all things are not equal. Markets must clear and even risky assets
must be held. Therefore the price of a risky asset must fall relative to its expected payout
until its expected return is high enough to compensate investors for the extra
consumption risk.
This link between observable asset returns and cov(mt,dept ) is the key to
measuring the effect of banking panics on marginal utility. Given a cross-section of assets
with different expected returns a true unobservable stochastic discount factor should
explain any cross-sectional differences in these asset returns. Equation (4) constrains the
stochastic discount factor to be a linear function of NYCH deposit growth. If a regression
of a true unobservable discount factor on deposit growth had high explanatory power
then the specification in (4) should do a good job of explaining cross-sectional
differences in observable asset prices. On the other hand, if the true discount factor isn’t
correlated with NYCH deposit growth the candidate discount factor in (4) will have a
hard time explaining cross-sectional differences in gilded-age stock returns.
A test of the null hypothesis that banking panics were costly amounts to a test that
the candidate discount factor in (4) can explain cross-sectional differences in the return of
gilded-age stocks. Many authors have used macroeconomic factors and linear
specifications like (4) to test the null hypothesis that a given macroeconomic measure of
“good times” explains stock returns. Rather than ask if a given measure of “good times”
can explain asset returns I let asset returns tell me when times were good and test whether
changes in our measure of banking panics were correlated with the unobservable utility
of national banking era investors.
14
Estimation:
Suppose we observe N test assets. Let
,
denote the time t gross returns on the n-th
asset and dept denote the time t growth rate of NYCH deposits. The law of one price
implies the moment condition
1 for each of the n assets. Impose the
,
constraint mt = + dept and define the following error model:
,
t
,
1
5
Our goal is to pick the free parameters [ , ] to best price the observable asset
returns. Let g () n denote the average pricing error of n-th asset:
g ( ) n
1
T
T
u ( )
(6)
n ,t
t 1
To estimate via GMM, form the vector of average pricing errors
G () [ g ()1 ...g () n ...g () N ] and choose [ , ] to minimize
for a positive definite weighting matrix W.
Throughout this paper I use the statistically efficient weighting matrix W = S-1,
where S-1 is the inverse of the pricing error spectral density matrix17 (see Cochrane
(2001) Ch10) and employ the traditional GMM two-step procedure to estimate W = S-1.
1. Set W equal to the identity matrix and solve
2. Use the pricing errors from Step 1 to estimate W = S-1
3. Set W = S-1 and solve
17
The results are robust to the use of the pre-specified weighting matrixes such the identity matrix or the
Hansen and Jagannathan (1997) minimum distance matrix.
15
Test Assets: Size-sorted and Seasonally Managed Portfolios
We estimate
via GMM by choosing the regression coefficients to best price 10
size-sorted and five calendar-sorted NYSE stock portfolios. The size-sorted portfolios are
formed by assigning stocks to deciles based on the market-value at the beginning of each
28-day period. Value-weighted returns are computed within each decile and stocks are
reassigned each period based upon updated market values. The resulting 10 size-sorted
portfolios exhibit wide cross-sectional differences in returns. If changes in bank balance
sheets are correlated with changes in unobservable marginal utility, knowledge about the
state of NYCH balance sheets should help explain these cross-sectional differences in
returns.
All of our information about unobservable marginal utility must be inferred from
the behavior of asset prices. We can sharpen our estimates by forming managed
portfolios that follow time-varying investment strategies that are likely correlated with
unobservable marginal utility. Likely correlated is a non-trivial statement when the
correlation we desire is with respect to an unobservable variable. Any time varying
investment rule must be based on information known at the time of portfolio formation
and result in differences in expected return. Even in an informationally efficient market
public information available at time t can predict cross-sectional differences in returns at
time t+1 if the differences in return reflect compensation for risk.
The history of banking panics and national banking era interest rates suggest some
potential managed portfolio strategies. The National Monetary Commision (1911),
Friedman and Schwartz (1963) and Miron (1986) all note the seasonality of interest rates
and banking panics during the gilded-age. Contemporaries were also aware of both the
seasonality of interest rates and the increased likelihood of banking panics during the fall.
If consumption risk varied seasonally, portfolios based on seasonal investment strategies
should contain information about seasonal variation (if any) in m.
I form 5 managed portfolios that reflect seasonal investment strategies. The first
four are long-short strategies based on the calendar quarter. The long QN portfolio shorts
16
the risk free asset and invests the proceeds in the value-weighted stock market portfolio
in the n-th quarter and shorts the market and invests the proceeds in the risk-free asset in
the other 3 quarters. The fifth calendar portfolio which I call “Long Harvest” shorts the
risk-free asset and invests in the stock market portfolio during the harvest months of
August-November and shorts the market portfolio and invests in the risk-free asset
otherwise.
Table I reports the annualized average return and standard deviation for each
size-sorted and calendar managed portfolio used in estimation. The size and calendar
sorted portfolios exhibit wide variation in average returns. If unobservable gilded-age
marginal utility varied with bank deposits, knowledge about the change in bank deposits
should explain the spread in size and calendar sorted average returns.
Seasonally Adjusted Deposit Growth
The seasonality of deposits and interest rates suggest caution is in order. If
cov(mt,dept ) is not equal to zero, changes in the marginal utility of consumption should
reflect only the unexpected changes in deposits. If changes in deposits were predictable
these changes would already be reflected in investor’s consumption decisions and asset
prices. Deposit growth was predictably seasonal during the gilded-age 18. A simple time
series regression on month dummies explains 19% of the time series variation in deposit
growth. Deposits were predictably withdrawn from NYCH banks in the fall harvest
season when the seasonal demand for currency in the interior was high. Failure to
account for the predictable movement in bank balance sheets is equivalent to measuring
our deposit growth variable with error. For example, if New York deposits witnessed a
2% decline in a month when investors expected a 5% decline this is actually an
unexpectedly positive shock to bank balance sheets. In the estimation that follows dept
is defined as the seasonally-adjusted change in NYCH deposits Where seasonally
adjusted change is defined as the residual from the regression of the deposit growth series
on a month dummies.
18
Miron (1986)
17
Results
Tables 2 report the GMM regression coefficients and t-stats for the candidate
discount factor mt = + dept . The table also reports the overidentifying Tjt statistic.
Under the null hypothesis that our estimated m is a valid discount factor the Tjt statistic is
distributed kwhere N is the number of assets used in estimation and k is the number
of estimated parameters.
Table 2 reports six separate regressions corresponding to different specifications
of m or different test assets used in estimation. Specifications (1) & (4) report the
coefficients from a univariate GMM regression of m on deposit growth. Regardless of
test assets, the regression coefficient is negative and significant at the 1% level. Changes
in NYCH deposits were significantly correlated with the marginal utility implied by asset
returns. Furthermore, the negative sign of the coefficient on deposit growth tells us
deposits were withdrawn from NYCH banks in states of the world where implied
marginal utility of wealth was high.
A word of caution is in order. Are we really measuring the CAPM equation in
disguise? Regressions (1) and (4) imply that deposit growth is correlated with the
marginal utility of gilded-age investors. Before we place a price on deposit risk we
should be certain that we aren't simply measuring stock market risk. Deposits leave New
York banks during banking panics. The stock market also declines during banking panics
as well. Both theory and the fact that the observable value-weighted stock market excess
return E[ R sm ] R f is positive suggest the stock market is negatively correlated with
marginal utility as well. When we exclude the stock market from our specification mt =
+ dept we should worry that our estimated beta may be biased due to this omitted
variable. If the true specification is the CAPM equation
estimate the regression with dept in place of
but we
we could find a statistically
significant because changes in NYCH deposits are correlated with stock market returns.
In Table 2 specifications (2) and (5) we estimate the candidate stochastic discount
18
. rm is negative and significant
factor implied by the CAPM:
in both cases. Knowledge about the return on the aggregate market index did help explain
differences in the cross-sectional of gilded-age stock returns19.
To properly test the null hypothesis that banking panics affected marginal utility,
holding the stock market fixed, we require a multiple regression of the stochastic discount
factor on our hypothetical deposit contract and the return on the stock market
mt = + depdept) + Rm(Rtsm – Rf,t )
(7)
The coefficients in (7) have the same interpretation as multiple regression coefficients.
dep tells us the affect of deposit growth on implied marginal utility holding the stock
market fixed. In Table 2 specifications (3) & (6) we estimate eq.(7) via GMM. The
change in NYCH deposits are significantly correlated with implied discount factors even
when controlling for stock market changes. In fact, once one controls for changes in bank
balance sheets knowledge about the stock market return contributes practically nothing to
our understanding of national banking era asset returns!
The last point deserves clarification. Unexpected changes in bank deposits explain
differences in 1866-1913 stock returns even after controlling for changes in the market
portfolio. Figure 1 plots the average annual return of each portfolio against the predicted
return implied by the CAPM and deposit growth factor model specifications. By itself the
CAPM factor does a good job of explaining the cross-section of stock returns, however,
the results in Table 2 demonstrate that the CAPM “works” because the market portfolio is
correlated with bank deposits. Once one controls for changes in bank deposits knowledge
about the aggregate market return adds no information about cross-sectional differences
19
The overidentifying test is rejected in the CAPM specifications (2) & (5) but not in specifications where
the candidate discount factor is a function of deposit growth (1) & (4). The reader should resist the urge to
draw conclusions about the relative merits of the CAPM versus deposit factors based on differences in
overidentifying test statistics. The statistic is a ratio.The deposit overidentifying statistic could be smaller
because the discount factor based on bank deposits better explains stock returns or because the discount
factor blows up the variance of the pricing errors. Each Tjt statistic is computed with a different weighting
matrix rendering cross-specification comparisons unwise.
19
in stock returns.
This result is different (and much stronger) than most findings that “the CAPM
failed”. Many papers have rejected the CAPM specification by finding additional factors
that help explain differences in cross sectional stock returns even after controlling for the
market portfolio. In this case, the additional factor not only explains returns after
controlling for the market return but completely drives out the market index as an
explanatory variable!
Measuring the Cost of Insuring Against National Banking Era Panics
Recall the hypothetical derivative contract that pays dept . Had such a contract
existed a national banking era investor could have used it to insure against utility loss
during banking panics. The question remains, just how costly were these panics? The
regressions in Table 2 provide strong statistical evidence that marginal utility was higher
during times of unexpected deposit withdrawals. With 625 time series observations and
portfolios comprised of more than 70,000 individual stock returns even economically
insignificant utility differences can be statistically significant. Before we draw
conclusions about the economic cost of banking panics we require a price of panics in
terms of forgone consumption.
A natural way to think about the cost of bad outcomes is to ask, what would one pay to
avoid them? Consider the hypothetical insurance contract that pays its holder Xins = -
dept if NYCH deposit growth is negative and zero otherwise. This contract would allow
banks or investors to insure against deposit declines. The contract’s payout increases
during banking panics. If an investor expected his consumption to fall during a banking
panic, he could insure against this panic risk by purchasing insurance contracts. Holding
the insurance would eliminate the downside risk but it would come at a cost if
P E[ mX ]
E[ X ]
Rf
. That is, it would be costly to insure if the expected return to buying
the contract is lower than the return of holding the risk-free asset. From (3) we know that
20
this is equivalent to saying it is costly to insure if cov( m, X ) 0 and our GMM
regressions of m on deposit growth tell us it will be costly to insure with insurance
contracts that pay the -dept . How costly amounts to an empirical question of what price
would our hypothetical insurance contract would trade for if they were offered for sale
during the national banking era?
We can price the contract from the time series of payouts and the moment
condition P E[mX ] . The price depends upon the stochastic discount factor m. What m
implied by our regression mt = +
should we use? An obvious choice is the
depdept) + Rm(Rtsm – Rf,t ). With the realizations of insurance payouts and estimates of
in hand, we can compute P E[mX ] and measure the cost of insurance by comparing
the expected gain (loss) from buying the insurance to the expected gain from buying the
risk-free asset. From (2) we know the expected excess return from buying the insurance
is
,
Plugging in our point estimates from
8
estimates with all test assets and mt = +
depdept) + Rm(Rtsm – Rf,t ) yields the estimated cost of insuring $100 of seasonallyadjusted deposits. The discount factor estimated with seasonally-adjusted deposit growth
assigns a price $1.10 above its actuarially fair value. An investor who wished to insure
against any 28-day decline in seasonal-adjusted deposits would willingly pay an expected
(13 x $1.097) = $14.26 per annum to insure $100!
To place these costs in perspective we can compare the cost of buying our
hypothetical 28-day insurance against national banking era deposit withdrawals to the
cost of buying insurance against stock market declines today. Had an investor purchased
30-day, $100 at-the-money put options on the S&P 500 every month from Jan 1990 to the
present the investor would have lost an average of $13.97 per annum20. This is very close
20
The CBOE reports historical VIX on S&P 500 options from 1990 to the present. I use the VIX, T-bill
rate, and dividend yield on the S&P 500 to compute the time series of 30-day at-the-money S&P 500 put
option prices via the Black Scholes formula. The difference between the average annual cost of at-themoney puts and the annual payout is - $13.97.
21
to the cost of insuring against seasonally-adjusted deposit withdrawals during the national
banking era. The cost of unexpected deposit withdrawals between 1866-1913 was
roughly similar to the cost of modern day stock market declines.
It’s important to remember that this asset based estimate of the cost of deposit
withdrawals is inferred from observable asset returns. This is an estimate of cost rather
than a counterfactual exercise. Had actually insurance existed the observable asset returns
may well have been different. Our deposit based candidate discount factor does a good
job of explaining asset returns because assets exposed to banking panics have high
returns to compensate investors for this exposure. The size of this compensation tells us
banking panics were costly but the equilibrium level of compensation would have likely
been different had credible deposit insurance been available. Our observable return based
estimates should be thought of as the equilibrium price of insurance a small price taking
investor would willingly pay assuming his actions had no affect on the general
equilibrium prices of the other assets.
Conclusion
Bank runs are costly even in the absence of large interconnected too big to fail
institutions. Irreversible investments and risk-averse savers create an environment where
financial intermediaries can increase welfare by pooling savings and smoothing
consumption risk. However, irreversible investments combined with asymmetric
information about the quality of loan portfolios or the patience of other depositors can
expose an intermediary to runs and expose the economy to systematic risk. In the era
before the Federal Reserve and too big to fail, banks looked to the New York money
market for a relatively safe, liquid, high return investment for their excess reserves. By
combining data from the balance sheets of NYCH banks and returns of NYSE stocks one
can estimate the cost of national banking era bank panics.
Unexpected changes in NYCH deposits had a significant impact on investors’
stochastic discount factors. In fact, when tasked with explaining cross-sectional
differences in size and calendar-sorted stock returns, knowledge about NYCH balance
22
sheets was far more informative than knowledge about the return on the value-weighted
market portfolio.
I measure the cost of national banking era bank panics by constructing
hypothetical insurance contracts on NYCH deposits. These contracts would have allowed
a price taking gilded-age investors to insure against changes in NYCH deposits. The price
of these contracts implied by our estimated discount factors suggest banking panics were
quite costly and investors would pay up to an annual 14% premium above actuarially fair
value to insure against deposit losses – approximately the same premium modern day
investors have willingly paid to insure against stock market declines over the past 20
years.
23
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25
Figure 2:
Average
g return versus ppredicted return
10 size-sorted portfolios
10size-sorted and 5 Calendar sorted portfolios
Table 1: Annualized Return and Standard Deviation
Average
Return
Standard
Deviation
1866‐1913
Size Sorted Portfolios
Smallest
Size 2
Size 3
Size 4
Size 5
Size 6
Size 7
Size 8
Size 9
Largest
0.1461
0.111
0.092
0.0607
0.0392
0.0738
0.0801
0.0601
0.0515
0.0695
0.471
0.3357
0.2967
0.2607
0.2319
0.205
0.1877
0.1499
0.1296
0.1192
Managed Portfolios
Long Q1
Long Q2
Long Q3
Long Q4
‐0.0311
‐0.0452
0.004
‐0.0525
0.1316
0.1314
0.1317
0.1312
Long Harvest
‐0.0098
0.1318
Average Ret = geometric annulized return
27
TABLE 2 :
Stochastic Discount Factors Estimated with 1866‐1913 Data
m t = + dep ( dep t )+ Rm (R t sm ‐ R f,t )
Test Assets:
10 size‐sorted portfolios
(1)
(t‐stats)
dep
(t‐stats)
‐15.3444
(‐3.72)***
(3)
(4)
‐16.6722
(‐2.76)**
‐4.3343
(‐2.69)***
(t‐stats)
(p-value)
10 size‐sorted portfolios
4 quarterly portfolios
1 long‐ harvest portfolio
0.9994
1.0167
0.9959
(41.53)*** (72.08)*** (36.13)***
Rm
Tjt ~ N-k)
(2)
Test Assets:
5.56
(0.70)
16.382
(0.04)**
‐15.8727
(‐5.19)***
12.54
(.48)
dept = percentage change in seasonally‐adjusted NYCH deposits
(Rm ‐ Rf) = Excess return on the value‐weighted NYSE portfolio
28
(6)
1.0027
1.0204
1.0051
(54.76)*** (98.71)*** (45.93)***
0.7524
(.30)
5.33
(.62)
(5)
‐14.8695
(‐3.07)***
‐4.7867
(‐4.06)***
‐0.5555
(‐0.30)
26.48
(0.01)**
11.77
(.46)
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Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein
WP-10-10
Prenatal Sex Selection and Girls’ Well‐Being: Evidence from India
Luojia Hu and Analía Schlosser
WP-10-11
Mortgage Choices and Housing Speculation
Gadi Barlevy and Jonas D.M. Fisher
WP-10-12
Did Adhering to the Gold Standard Reduce the Cost of Capital?
Ron Alquist and Benjamin Chabot
WP-10-13
Introduction to the Macroeconomic Dynamics:
Special issues on money, credit, and liquidity
Ed Nosal, Christopher Waller, and Randall Wright
WP-10-14
Summer Workshop on Money, Banking, Payments and Finance: An Overview
Ed Nosal and Randall Wright
WP-10-15
Cognitive Abilities and Household Financial Decision Making
Sumit Agarwal and Bhashkar Mazumder
WP-10-16
Complex Mortgages
Gene Amromin, Jennifer Huang, Clemens Sialm, and Edward Zhong
WP-10-17
4
Working Paper Series (continued)
The Role of Housing in Labor Reallocation
Morris Davis, Jonas Fisher, and Marcelo Veracierto
WP-10-18
Why Do Banks Reward their Customers to Use their Credit Cards?
Sumit Agarwal, Sujit Chakravorti, and Anna Lunn
WP-10-19
The impact of the originate-to-distribute model on banks
before and during the financial crisis
Richard J. Rosen
WP-10-20
Simple Markov-Perfect Industry Dynamics
Jaap H. Abbring, Jeffrey R. Campbell, and Nan Yang
WP-10-21
Commodity Money with Frequent Search
Ezra Oberfield and Nicholas Trachter
WP-10-22
Corporate Average Fuel Economy Standards and the Market for New Vehicles
Thomas Klier and Joshua Linn
WP-11-01
The Role of Securitization in Mortgage Renegotiation
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff
WP-11-02
Market-Based Loss Mitigation Practices for Troubled Mortgages
Following the Financial Crisis
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
and Douglas D. Evanoff
WP-11-03
Federal Reserve Policies and Financial Market Conditions During the Crisis
Scott A. Brave and Hesna Genay
WP-11-04
The Financial Labor Supply Accelerator
Jeffrey R. Campbell and Zvi Hercowitz
WP-11-05
Survival and long-run dynamics with heterogeneous beliefs under recursive preferences
Jaroslav Borovička
WP-11-06
A Leverage-based Model of Speculative Bubbles (Revised)
Gadi Barlevy
WP-11-07
Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation
Sule Alan, Bo E. Honoré, Luojia Hu, and Søren Leth–Petersen
WP-11-08
Fertility Transitions Along the Extensive and Intensive Margins
Daniel Aaronson, Fabian Lange, and Bhashkar Mazumder
WP-11-09
Black-White Differences in Intergenerational Economic Mobility in the US
Bhashkar Mazumder
WP-11-10
Can Standard Preferences Explain the Prices of Out-of-the-Money S&P 500 Put Options?
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein
WP-11-11
5
Working Paper Series (continued)
Business Networks, Production Chains, and Productivity:
A Theory of Input-Output Architecture
Ezra Oberfield
WP-11-12
Equilibrium Bank Runs Revisited
Ed Nosal
WP-11-13
Are Covered Bonds a Substitute for Mortgage-Backed Securities?
Santiago Carbó-Valverde, Richard J. Rosen, and Francisco Rodríguez-Fernández
WP-11-14
The Cost of Banking Panics in an Age before “Too Big to Fail”
Benjamin Chabot
WP-11-15
6
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