Trademarks in Banking∗Ryuichiro Izumi

Antonis Kotidis

Paul E. Soto

July 9, 2024

Abstract
One in five banks in the United States share a similar name. This can increase the likelihoodof confusion among customers in the event of an idiosyncratic shock to a similarly named bank.
We find that banks that share their name with a failed bank experience a half percent dropin transaction deposits relative to banks with similar characteristics but different name. Thiseffect doubles for failures that are covered in media. We rationalize our findings via a model offinancial contagion without fundamental linkages. Our model explains that when distinguishingbanks is more costly due to similar trademarks, depositors are more likely to confuse their banks’condition resulting in financial contagion.
Keywords: Trademarks, Banking, Bank Runs, Bank Failures
JEL Classifications: G21; G14; G30∗

Izumi is at Wesleyan University. Kotidis and Soto are at the Federal Reserve Board. We thank Tomaz Cajner,

Todd Keister, Andreas Lehnert and Skander van den Heuvel for helpful comments. The analysis and conclusions set
forth here are those of the authors and do not indicate concurrence by other members of the research staff or the
Board of Governors.

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1

Introduction

A trademark is a sign - logo, sound or color - used by a firm to identify a product or service. Unlike apatent, which is a property interest held by the proprietor, trademarks create distinctiveness. They
convey information about the quality of a product or service, even when quality is not observable.
As such, they help resolve an information asymmetry problem (e.g., Akerlof, 1970). Due to theirability to convey information, the law protects the owners of trademarks from the use of similarmarks. Consumers may also benefit because owners may be incentivized to deliver a higher levelof quality consistent with theories of trademarks as tradeable assets (e.g., Shapiro, 1982, Landes
and Posner, 1987, Aghion and Howitt, 1992, Tirole, 1996).
A firm’s name is the most important trademark (e.g., Tadelis, 1999). Despite extensive legal
protections, it is not uncommon for firms to use similarly sounding names. The use of similarlysounding names, however, can increase the likelihood of confusion among customers if a similarly
named firm experiences stress. This issue is probably more acute in the banking industry, where
spillovers to the system as a whole are more likely due to banks’ role as liquidity providers (e.g.,
Kashyap, Rajan, and Stein, 2002).
Several cases of runs on banks that have similarly sounding names with banks experiencing
stress provide a useful illustration. For example, following the rescue announcement of the San
Francisco-based First Republic Bank on March 17, 2023, the stock of Pennsylvania-based RepublicFirst Bankcorp plunged by nearly 30%. This marked Republic First’s worst single-day performancesince 1994 despite assurances by the president and CEO of the bank that “amid everything goingon, Republic Bank would like to make very clear: we are Republic Bank, Inc. (FRBK-Red/Blue
Logo); we are NOT First Republic Bank (FRC-Green Logo)”.1 Other banks – Signature Bank ofArkansas and Signature Bank Chicago – released similar statements after Signature Bank New
York showed the first signs of stress in March 2023. 2 On July 25, 2008, following the closure of theFirst National Bank of Reno, Nevada, and the First Heritage Bank of Newport Beach, California,
by the Office of the Comptroller of the Currency (OCC), the president and CEO of Heritage Bankof Reno, Nevada, spent days assuring customers who saw the name Heritage in the news that hisbank was financially sound.3
1

Banking Dive, “Republic First Bank CEO to customers, investors: We are not First Republic”.
See Appendix A.
3
Reno Gazette, “Bank reopens with new name”, 29, July 2008.
2

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These episodes are by no means a U.S. or recent phenomenon. On September 4, 2014, in India,
following the news coverage by a Bengali newspaper that the Jalpaiguri Cooperative Bank Limited
did not have the required RBI licence to be an active bank, depositors became confused with thename and turned up at the Jalpaiguri Central Cooperative Bank branches wanting to withdraw
their money.4 In October 1934, depositors ran on the Amoy branch of the National Industrial Bankof China. The reason was a rumour that the bank’s head office in Shanghai was closed and the bankhad gone out of business. The truth, however, was that a similarly sounding bank in Shanghai had
closed on the exact same day.5 In September 1985, as concerns mounted over the health of small
Canadian banks, a run developed at the Continental Bank of Canada. According to its president,“the bank was also hurt by statements in the media confusing it and a troubled trust company witha similar name”, eventually resulting in a support package from a group of financial institutions
and the Bank of Canada.6
These examples have one thing in common: the use of similarly sounding names can increase
the likelihood of confusion among customers in the event of an idiosyncratic shock to a similarly
named bank. Confusion may then lead to runs even on well-managed banks that are not in any
way related to the stressed bank.
Our paper takes a deep dive into this issue. We study the U.S. banking system due to its
structure and historical evolution. When American banking was a local business, the First National
Bank of a small town was distinctive enough and unlikely to be confused by another First National
Bank two towns over. In fact, the National Bank Act of 1864—a landmark piece of legislationthat established the National Banking System in the United States—required banks to include theword “national” in their names and encouraged them to bear numbers (Conley and Hunter, 2007).
These naming conventions have persisted into the 21st century. The deregulation of the banking
industry and the advent of branch banking in the 1990s have led banks with similarly sounding
names chosen in the past to start competing in the same areas, potentially increasing the likelihoodof confusion among customers. Confusion may further exacerbate in the era of the Internet andrapid communications.
4

The Telegraph Online, “Bank licence scare after RBI notice - Depositors panic as officials seek correction on bankname in newspaper”.
5
South China Morning Post, “Run on Amoy Bank. The National Industrial Bank of China. Victim of Rumours”,
7, November, 1934.
6
The Globe and Mail, “Bank receives $2.9 billion in aid Crisis shows few signs of abating”, 1, November, 1985.

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The first part of the paper establishes facts about bank names and how they evolved overtime. We show that the most prevalent words in bank names are “bank” and charter distinctions
such as “state” and “national”. The type of bank is also a common feature with words like“community”, “savings”, and “trust” being widely used. As of December 2022, nearly 14% ofbank names begin with the word “first”, while 11% of bank names begin with one of seven words:“citizens”, “peoples”, “farmers”, “united”, “heritage”, “liberty”, or “american”. Nearly 210 (103)banks begin with “First National (State) Bank”. These two phrases account for almost 7% of allbank names in 2022. Overall, nearly 20% of bank names begin with a phrase or string that could
refer to several banks in 2022. Interestingly, this share has been remarkably stable over the past
three decades despite the massive consolidation in the U.S. banking industry.
The prevalence of name commonalities may lead to customers’ confusion in the face of a negative
event to a similarly sounding bank. We explore this issue next. For identification, we focus on bankfailures and compare deposits of banks that share their name with the failed bank (treatment group)
to other banks with similar balance sheet characteristics but different name (control group). For
example, we compare deposits of Horizon Bank, Nebraska (treatment bank) to Bank of Vernon,
Alabama (control bank) before and after the failure of Horizon Bank, Florida (failed bank). Our
propensity score matching algorithm ensures that Horizon Bank, Nebraska, and Bank of Vernon,
Alabama, have similar balance sheet characteristics, including size, deposits over total assets, loans
over total assets and profitability. We also ensure that that Horizon Bank, Nebraska, and Horizon
Bank, Florida, have nothing in common but a name.7 We then treat the failure of Horizon Bank,
Florida, as an exogenous event that may (or may not) impact deposits of Horizon Bank, Nebraska.
The purpose of the control bank is to inform us what would have happened to the deposits of the
Nebraska bank in the absence of the failure of the Florida bank.
Via difference-in-differences regressions, we find strong effects on transaction deposits.8 . Transaction deposits as a share of total assets fall nearly 0.7% immediately after the associated bankfailure and slowly rise over the following two years. This effect is robust to saturated models complete with bank and time fixed effects, as well as the inclusion of banking demand controls proxiedby corporate investment in the spirit of Gulen and Ion (2016). This effect is further amplified
by the publicity each bank failure receives (akin to a ”media multiplier” (e.g., Besley, Fetzer, and7
8

Most banks in our sample are unit banks, so none are part of the same banking group when we study them.
In contrast to time or savings deposits, transactions deposits can be withdrawn on demand and is a productconsistent with the role of banks as liquidity providers (Kashyap et al., 2002)4

Mueller, in press)). We find that when a bank failure is mentioned in the news, transaction deposits
over total assets are, on average, nearly 0.8% lower after the associated bank failure and can dropby as much as 1% immediately after the associated bank failure. These results are not driven by
specific banks or time periods and indicate that banks that share a similar name with a failed bankexperience a significant decline in transaction deposits.
To better assess the economic impact, quantile estimates across all treatment banks in our
sample reveal striking insights into the plausible range of effects. We find a one-in-ten chancethat the reduction in transaction deposits amounts to 2.14%, or $2.68 million, and a one-in-fourchance of a reduction of 1.17%, or $1.47 million. Given that our sample comprises of relatively
small community banks, roughly $100 million in total assets, these findings underscore a sizeable
economic impact of name-related contagion risk.
We proceed by exploring the effects on lending. We focus on various types of loans using thedifference-in-differences setting, and find generally no effect. While consumer loans slightly reduce(by roughly 0.12%), these results suggest that the effect appears predominantly via banks’ liabilities
and do not significantly hamper credit provisioning.
We rationalize these findings in a model of financial contagion without fundamental linkages.
Our benchmark model is based on Diamond and Dybvig (1983) augmented to have a random
investment return and considers the environment where there are two ex-ante identical DiamondDybvig banks. The banks have no balance sheet linkages, and their asset returns are independent.
The realization of their investment returns reveals before depositors make a withdrawal decision,and each of them receives a private signal about the realization. However, the signal is noisy,in the sense that it may or may not represent their corresponding bank. The focal point of ourmodel is the probability that the drawn signal corresponds to their bank, and we study how theposterior belief, influenced by this signal, shapes the incentive of bank runs. In equilibrium, wefind that bank run risk decreases when depositors are more certain about whether their received
signal corresponds to their bank. When the signal is more precise, those who receive a good signal
believe that their bank is more likely to have a good asset, reducing the incentive to run on thebank. When they do not run on the bank, those receiving a bad signal also have less incentive,
as the first-mover advantage diminishes. However, when the signal is less precise, even those who
receive a good signal still have stronger incentives to run on the bank. Thus, in the sense that anoisier signal makes a bank run more likely to occur, we have contagion through depositors’ beliefs.

5This contagion channel exists if and only if the signal is imperfect.
We extend this model to evaluate how a bank’s trademark affects the bank run risk. In particular, we add an ex-ante choice of attention allocation, which determines the precision of the signal.
Paying more attention requires resource costs, and the cost parameter represents the similarity ofthe banks’ trademarks. In particular, if the banks share similar trademarks, paying more attention
requires more resources. We interpret the effect of this parameter on the equilibrium bank run
risk as trademark risk. When it is costly for depositors to distinguish banks, depositors rationallychoose to pay less attention, making it easier for the private signal to be misidentified, resulting
in higher incentives to run on the bank. In other words, similarity of trademarks amplify financial
fragility. Lastly, we explore the role of a public signal, which we interpret as media coverage. Thispublic signal appears if and only if at least one bank has a bad investment return, and in thisextension, we show how the media can amplify the trademark risk. Our model provides insights
into how financial contagion can manifest itself to increased bank run risk when depositors havethe possibility of misidentifying the bank.
Related literature: Our paper contributes to several strands of the literature. First, it contributes to the literature on trademarks, which are intangible assets that include logos, sounds orcolors (e.g. Milgrom and Roberts, 1992). A large theoretical literature discusses how trademarks
can inform consumers about the quality of a service or product (e.g. Akerlof, 1970; Economides,
1988) and incentivize firms to deliver a higher level of quality consistent with theories of trademarks as tradeable assets (e.g. Shapiro, 1982; Landes and Posner, 1987; Tirole, 1996; Marvel andYe, 2008). The empirical literature on trademarks is considerably smaller and focuses on the relationship between trademarking activity and a firm’s market value. For example, in a sample ofmanufacturing firms between 1995 and 2005, Krasnikov, Mishra, and Orozco (2009) find that afirm’s trademark is positively correlated with its cash flow, Tobin’s Q, return on assets and stock
returns. Similar results are obtained by González-Pedraz and Mayordomo (2012) who study U.S.
banks during the same period. Our contribution to this literature is twofold. First, we document
facts on the prevalence and evolution of names in the U.S. banking industry over the past three
decades. In contrast to sounds, colors or logos, a firm’s name is one of its most important trademarks (Tadelis, 1999). Second, we explore how similarities in trademarks can lead to distortions infinancial markets. While the literature measuring firm trademarks is nascent, a firm’s trademark
provides substantial economic value and can make goods and services more recognizable (Desai,

6

Gavrilova, Silva, and Soares, 2022). We contribute by showing how a bank sharing a name with afailed bank can cause depositors to run on an otherwise healthy bank.
Our paper also relates investors’ attention allocation and financial contagion. Attention is a
scarce cognitive resource (Kahneman, 1973), which investors must choose how to allocate. As
economic agents are resource-constrained by time and processing market news, their attention canaffect stock prices (e.g., DellaVigna and Pollet, 2009, Da, Engelberg, and Pengjie, 2011). Investors
can also misinterpret information, potentially leading to the misvaluation of assets (Hirshleifer,2001). Even when no new information is provided, stock tickers with similar names have been shownto comove and can bring prices further away from their fundamentals (Rashes, 2001; Balashov andNikiforov, 2019). Mondria and Quintana-Domeque (2013) explains contagion between markets
through investors’ re-balancing attention between them when a market experiences a disruption.
Our paper considers contagion through investors’ limited attention in the context of bank runs.
However, neither attention choices nor trademarks have been considered as a contagion channel ofbank fragility. The closest contagion channel that has been considered in the context of bank runs iscorrelation of asset exposures.9 When banks have common asset exposures, information can cause
a bank run. An early model of an information-based bank run is Jacklin and Bhattacharya (1988),
and then Chen (1999) shows that bank runs can be triggered by information about another bankwhen banks have a common exposure. When investors do not know their bank’s asset quality, they
may use signals about the health of another bank to assess the default probability of their bank,which in turn, may cause a bank run. This common exposure channel has been further exploredby Acharya and Yorulmazer (2008b), Acharya and Yorulmazer (2008a), Manz (2010), and Allen,
Babus, and Carletti (2012). More recent papers, Trevino (2020) and Ahnert and Bertsch (2022),
also consider the environment where banks’ fundamentals, and hence asset returns, are correlated.
This paper is the first to examine contagion in the absence of fundamental linkages between banks.
We instead consider how investors’ beliefs, shaped by the noise of signals, drive contagion. The
intensity of this noise is determined by the allocation of attention, which is influenced by trademarks.
Finally, we contribute to the literature studying the effect of media on financial markets (e.g.
Engelberg and Parsons, 2011, Tetlock, 2007, Dougal, Engelberg, Garcia, and Parsons, 2012, Garmaise, Levi, and Lustig, in press). Our results that the media can exacerbate risks related to9Other channels that are considered in the literature include direct linkages of balance sheets (Allen and Gale,

2000,Kiyotaki and Moore, 2002, Dasgupta, 2004) and common investor base (Goldstein and Pauzner, 2004).

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trademarks aligns with recent work by Cookson, Fox, Gil-Bazo, Imbet, and Schiller (2023), whofind that activity on X (formerly known as Twitter) amplified balance sheet risk during the 2023
Silicon Valley Bank run, and Croce, Farroni, and Wolfskeil (2020), who illustrate how social media
and newspapers accentuate contagion risk emanating from the recent COVID pandemic. With therise of social media, the effect of trademarks and misinformed depositors could intensify as investors
interpret repeated information through such “echo chambers” as genuine information (Jiao, Veiga,
and Walther, 2020). Our theoretical framework adds a novel perspective to how media coverageincreases fragility depending on the information set of economic agents, similar in spirit to models
linking endogenous public information to volatility and crisis episodes (Angeletos and Werning,2006).
The remainder of the paper is structured as follows. Section II discusses our data. Section III
presents facts on bank names, and section IV presents our main results. Section V presents themodel, and section VI concludes.

2

Data and Methodology

The two primary data sources are Call Reports for commercial banks in the United States and the
FDIC Failed Bank dataset. Both datasets are publicly available. Call Reports contain completebank names, as well as balance sheet and income statements data on commercial banks. We also
use these data to identify banks with similar names to those in the FDIC Failed Bank dataset.
The FDIC Failed Bank dataset contains information on 564 banks that failed between 2000 and
2023. Since the bank names in the Call Reports data contain abbreviations, the abbreviations areelongated to match the full name of the FDIC dataset.10
Using a fuzzy matching algorithm, we search for matches between the FDIC Failed Bank dataset
and the Call Reports data one quarter after the failure of each failed bank. This process results in
10

After inspecting the individual names, we make the following substitutions to the Call Reports names: County

for CTY; Cooperative for CO-OP; Community for CMNTY; Federal Savings & Loan Association for FS&LA; Savings& Loan Association for S&LA; Building & Loan Association for B&LA; Bank for BK; State Savings Bank for SSB;Bank & Trust Company for B&TC; Federal Savings Bank for FSB; Banking for BKG; Savings for SVG and SVGS;
Commerce for CMRC; Trust for TR; Savings Bank for SB; State for ST; Financial for FNCL; National Association
for NA; National for NAT; National Bank for NB and NBANK; Merchants for MRCH; Company for CO; Trust andCompany for TC.

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107 failed banks sharing the name of a surviving bank. These 107 failed banks are associated with
1,026 banks that share their name with a failed bank (treatment banks). We drop any treatmentbank that does not contain data two years before and after the date of the similarly named failed
bank. This restriction reduces the number of treatment banks to 945.
Next, we create a matched sample for a control group using a propensity score matching algorithm. The control group consists of banks that do not share a name with treatment banks, but
are similar in notable characteristics, which we restrict to size, deposits over total assets, loans overtotal assets and profitability (proxied by ROA). We perform the matching using data two years
prior to the associated bank failure. We ensure that the failed bank is associated with at least two
similarly named banks to ensure an accurate propensity score matching estimate. This restriction
reduces the number of treatment banks to 899 banks. After the matching process, we find 894
control banks that meet the matching criteria. It is important to note that some control banks arematched to multiple treatment banks, resulting in a difference in numbers between the 894 control
banks and the 899 treatment banks.
Summary statistics for the matched sample can be found in Table 1. These statistics reflect
the two years prior to the associated bank failure to ensure that the treatment and control groups
are similar along observables. Overall, the total assets for both banks are around $108 million inboth groups. Given the size of these banks, the majority of their funding comes from deposits(83% of total deposits in total assets). Given the small size of the banks, these are primarily retaildeposits. The table also shows that time deposits over total assets are nearly 39% in both groups.
Transaction deposits are slightly higher in the treatment group by 3%, while uninsured deposits
represent a small portion of assets, averaging around 1%. Banks in both groups have around 23%of deposits below the $250,000 account limit, and 16% over the same limit. On the asset side,
lending in both groups is approximately 60% of their total assets, with the majority of loans being
mortgages (40%) followed by C&I (9%) and consumer loans (5%).

3Facts on U.S. Banks’ Names

The National Bank Act of 1864 was a landmark piece of legislation that established the National
Banking System in the United States. This legislation imposed a number of requirements on

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national banks, including the requirement that they include the word “national” in their name.11
It also encouraged banks to bear numbers in their names. As a result, bank names have been
descriptive rather than distinctive over the history of American banking with a large number ofbanks today having similar sounding names.
Figure 1 shows a word cloud of the most common words in bank names as of December 2022.
The most prevalent words are “bank” and charter distinctions such as “state” and “national”.
The type of bank is also a distinguishing and common feature in bank names, with words like“community”, “savings”, and “trust” with high usage.
Table 2 shows the percentage of banks with common words and phrases in their names. Becausenames are often referred to using their first word or words (e.g. “Citibank National Association”
is often just referred to as “Citibank” or “Citi”), we show frequencies of names that begin withthe specific token, and also names that contain the token anywhere in their bank name. Nearly
14% of bank names begin with the word “first”, while 11% of banks begin with one of seven words:“citizens”, “peoples”, “farmers”, “united”, “heritage”, “liberty”, or “american”. Table 2 also showsthat a select number of phrases used in bank names can refer to a sizable number of banks. “First
National Bank” and “First State Bank” appear in the beginning of 210 and 103 bank names,
respectively. These two phrases account for nearly 6.6% of bank names in 2022. Overall, 18% ofbanks begin with a phrase or string that could refer to several banks.
Next, we explore how this commonality evolves over time. The left panel of Figure 2 showsthat the prevalence of bank names beginning with these common strings has decreased significantly
since the 1990s. In particular, the number of bank names declined by 71%, from 3,500 banks in1990 to 1,000 banks at the end of 2022. Yet, it remained fairly stable at roughly 20% as a share of
all active banks in a given year after we account for the long-term decline in the number of banks
in the United States (right panel). In other words, despite the massive consolidation of the banking
industry over the past three decades, one in five banks have had a similarly sounding name.
11This requirement was intended to distinguish national banks from state-chartered banks.

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4

Risks associated with similar trademarks

4.1

Effects on Deposits

We begin our analysis by studying the effects on deposits of banks that have a similarly sounding
name with a failed bank. We hypothesize that similarities in bank names may lead to confusion
among depositors of a bank in light of the closure of a similarly named bank.
Before turning to our regression specification, we ensure that the sample of banks analyzed
exhibits parallel trends before the failure of the associated banks. This is done by comparing
the evolution of several relevant variables, including deposits, time deposits, insured deposits, andtransaction deposits, all over total assets, as seen in Figure 3. The control group is represented
as a solid line and the treatment group as a dashed line, with the values representing the relative
growth compared to one year before the associated bank failure. The figure suggests that there areno significant differences across deposits, time deposits, and uninsured deposits before the failure.
However, transaction deposits exhibit a significant reduction starting around one quarter before thefailure, likely reflecting negative news associated with the upcoming failure. After the associatedbank failure, transaction deposits in treatment banks grow at around 2% less compared to one
year before and relative to banks belonging to the control group. These results, along with thecomparison of other observables two years before the failure presented in Table 1, help establish thatthe sample of treatment and control banks do not differ significantly along important dimensions
ex-ante.
Next, we test whether the difference in transaction deposits holds while including several relevant
controls in the following regression specification:

T ransactionDeposits= β ∗ SimilarN ameb ∗ Af terF ailuret +Assetsb,t(1)γ ∗ SimilarN ameb + α ∗ Af terF ailuret + δb + δt + ϵb,twhere T ransactionDeposits
is the amount over total assets of transaction deposits reported by bank b
Assetsb,t
at quarter t, SimilarN ameb equals the value of one for banks that share the name of the associatedfailed bank and zero if not, Af terF ailuret equals the value of one including and after the quarterof the associated bank failure, and zero otherwise. The baseline is the period before the associatedbank failure (i.e., each estimated coefficient measures the differential effect after the associated11

bank failure to the period before the associated bank failure). We include bank fixed effects tocontrol for time-invariant observable and unobservable bank variables, and quarter fixed effects tocontrol for time-varying factors affecting all banks in quarter q.
Our results are presented in Table 3. Column 1, including only bank fixed effects, suggeststhat transaction deposits over total assets are nearly 0.5% lower after the associated bank failure.
Column 2 controls for the quarter, while column 3, our preferred specification, includes lagged
controls of the logarithm of total assets, total deposits to total assets, total loans to total assets
and profitability (proxied by ROA). In both cases, we see the coefficient remains stable around-0.4%. The coefficients of the Af terF ailuret and SimilarN ameb variables are not statisticallysignificant in our preferred specification. This suggests that banks with different (similar) namefrom the failed bank did not experience a change in their transaction deposits after (before) the
associated bank failure (coefficients α and γ,respectively). These results indicate that, relative
to banks with different names, banks that share a similar name with a failed bank experience asignificant decline in transaction deposits after the associated bank failure. Additionally, Figure 4
shows the coefficient interaction term for each event time, which indicates that transaction deposits
over total assets fall nearly 0.7% after the associated bank failure and slowly rise over the following
two years.
To better assess the economic impact of our treatment effect, we conducted quantile estimatesacross all treatment banks in our sample, revealing striking insights into the plausible range ofeffects. We find a one-in-ten chance that the reduction in transaction deposits amounts to 2.14%,
equivalent to a decline of approximately $2.68 million (assuming the average sized bank), anda one-in-four chance of a reduction of 1.17%, equivalent to roughly $1.47 million. These findings
underscore the substantial economic consequences of name-related contagion risk on affected banks.
Importantly, our sample comprises of relatively small community banks, roughly $100 million in
total assets. Our treatment effect could intensify if much larger banks (e.g. systemically importantbanks) shared names with failed financial institutions, as their deposit networks are much larger
and the asset-side activities span a broader set of operations that could be hampered if a deposit
run occurred due to trademark risk. Additionally, Martin, Puri, and Ufier (2018) find that both
deposit inflows and outflows occur during times of distress, potentially attenuating the effects wefind as we can only infer the difference in the stock of deposits.
In Table 4, we present several robustness tests to ensure that the results are not driven by

12specific banks or time periods. Column 1 restricts the sample to control banks that are neverconsidered a treated bank (that’s why the fixed effect absorbs the coefficient of the SimilarN amebvariable), and column 2 restricts the sample to bank failures that occurred between January 1,
2007 to December 31, 2010. Columns 3 and 4 omit the treatment and control banks associatedwith the two failures of First National Bank and the three failures of First State Banks. These
two bank names, which as shown in Table 2 share their name with nearly 200 and 100 banks
even in 2022, comprise a large part of the sample. We eliminate them in these robustness tests
to alleviate concerns that our results are driven by these bank failures. Column 5 restricts the
sample to the time period of one quarter around the time of failure. The results of all these tests
suggest that the findings are robust and not driven by specific cases or time periods. In column 6,
we control for the average Tobin’s Q and cash flows of all firms that exist in the headquarter of abank to control for the demand for transaction deposits.12 These variables vary at the bank-quarter
level. In the absence of loan-level data, these variables aim to control for corporate investment,
which has been shown to be an important determinant of demand for banking services (Gulen and
Ion, 2016; Berger, Guedhami, Kim, and Li, 2022)13 . Our results are little changed when thesedemand controls are included. Lastly, in column 7, the dependent variable is replaced with logged
transaction deposits, and indicates that transaction deposits nominally decline 2% relative to thecontrol banks after the similarly named bank failure.

4.2

Effect of Media Coverage

In this section, we put forth and empirically examine one mechanism behind our results – theinfluence of media. We hypothesize that when a bank failure is referenced to in the news, theeffect would be relatively more pronounced due to the publicity. Column 1 (2) of Table 5 includes
observations where the associated bank failure was (not) referenced to in a Reuters headline during
the month of the failure. The results indicate that transaction deposits over total assets are nearly
0.8% lower after the associated bank failure was mentioned in Reuters and 0.3% if it was not.
Figure 5 explores how this effect varies over time. Coefficients are displayed relative to event timeequal to -2. For those failures that were mentioned in Reuters, transaction deposits in treatment
12

The Tobin’s Q is defined as the market value of assets divided by the book value of assets and cash flows are thesum of earnings before extraordinary items and depreciation.
13
Our sample consists of mostly small banks, which provide liquidity locally. As such, the headquarter of a bankis also where the bank raises the vast majority of its deposits.

13

banks dropped by as much as 1% two quarters after the failure. This effect gradually becomes
smaller and finally disappears five quarters after the failure (panel A). The effect is short-lived andsmaller in magnitude for failures that were not mentioned in Reuters (panel B).

4.3

Effects on Lending

In Table 6, we explore the effects on lending. Columns 1, 2 and 3 consider log amounts of mortgages,
consumer and C&I loans, respectively. Although the coefficients are negative, which is indicative ofa reduction in lending, they are not statistically significant with the exception of consumer loans.
While we find significant effects for consumer loans, these are economically insignificant with areduction of nearly 0.12% nominally. These results suggest that the effect manifests itself within abank largely in their liabilities rather than assets. Importantly, the banks we sample in the paper
are relatively small, with nearly $100 million in total assets largely concentrated around lending.
Our results may differ in the event of a large- to mid-sized bank (e.g. above $1 billion) sharing a
name with a failed financial institution, as not only the bank run may be more severe given thelarger network of depositors, but the diverse set of operations that are not typical in the smallerbanks we study (e.g. asset management, securities trading, etc.) could result in hampered activities
on the asset side.

5

The Model

To rationalize the empirical results and explore the mechanism, we build a model of financial
contagion without fundamental linkages. The model is based on Diamond and Dybvig (1983)
augmented to have two ex-ante identical banks, random investment returns, and noisy signals. A
signal is considered noisy in the sense that it may represent one bank or another, depending on
the degree of attention an investor pays. This attention, in turn, depends on the similarity oftrademarks. Our interest is to show how a good bank can experience bank runs and how this effectis exacerbated by the similarity of trademarks. We will also examine the amplification throughmedia coverage.

14

5.1

The Environment

The economy lasts for three periods: 0, 1 and 2. There are two locations indexed by j = 1, 2, andin each location, a unit measure of depositors indexed by i ∈ [0, 1] enters the economy in period
0 with one unit of an endowment good. Depositors have a utility function u (c1 + ωi c2 ), whereu(0) = 0, u′ (0) = ∞, u′ > 0 and u′′ < 0 and ωi ∈ {0, 1} is a random variable. There is a probability
π that ωi = 0 and the depositor is impatient, and a probability 1 − π that ωi = 1 and the depositor
is patient. The type of a depositor is private information and is revealed at the beginning of period
1.
There is a single, constant-returns-to-scale technology for transforming this endowment into
consumption in the later periods, which we call project. It delivers one unit of goods if liquidated
in period 1. If it is instead held until period 2, it delivers Rz units of goods, where z ∈ Z = {b, g}.
Let pg denote the probability of the good return Rg > Rb , and the return is Rb > 1 with thecomplementary probability pb = (1 − pg ). The state z realizes at the beginning of period 1, andreturns at each location are not correlated with each other.
The investment technology is operated at a central location in each location, where depositors
pool and invest resources together in period 0 to insure individual liquidity uncertainty. This
intermediation technology can be interpreted as a financial intermediary or bank, and thus, there
are two banks in this economy. At the beginning of period 1, each depositor learns her typeand either contacts the bank to withdraw funds in period 1 or waits until period 2 to withdraw.
Depositors are isolated from each other in periods 1 and 2, and cannot engage in trade. Upon
withdrawal, a depositor must immediately consume what is given. Repayments follow a sequential
service constraint as in Wallace (1988). We also follow Ennis and Keister (2009) and prohibit
the bank from pre-committing to actions so that a self-fulfilling bank run arises as an equilibriumoutcome.14
Depositors may also condition their withdrawal decisions on a private signal about the asset
returns. There are two signals, each of which corresponds to one of the realizations of the bank’s
asset return. However, a depositor can observe only one of them in period 1, and thus, the signal
she receives may indicate the asset return of the other bank. A depositor cannot identify which
14

Diamond and Dybvig (1983) examine how a suspension of convertibility can eliminate a bank run equilibrium,

but Ennis and Keister (2009) show that such a policy is not time-consistent. We follow the latter approach to havea self-fulfilling bank run as an equilibrium phenomenon.

15

bank her received signal corresponds to. We let θ denote the probability of drawing the signal
about the corresponding bank, and the value of θ is publicly known. Each signal itself is not noisy,
and hence the depositor can correctly learn her bank’s return if θ = 1.
There are four states of the world: {(Rg , Rg ), (Rg , Rb ), (Rb , Rg ), (Rb , Rb )}, where the first element represents the project return of Bank 1 and the second element expresses the project returnof Bank 2. Since a depositor cannot tell whether her received signal corresponds to her bank or
not when θ < 1, she still has to worry about a potential bad state even in (Rg , Rg ). Note thatinvestment returns are independent between banks, and two banks do not have any interactions.
The sequence of events unfolds as follows. In period 0, the bank receives the endowment from its
depositors and invests in the project. In period 1, the preference and the asset return are realized.
A depositor receives a signal that may or may not represent her bank. After receiving the signal,
depositors choose whether to withdraw their deposit in period 1 or in period 2. Finally, in period
2, the bank pays the remaining depositors.

5.2

Banking gameAt each location, the bank and depositors play the simultaneous-move game. Depositors choose
a contingent withdrawal plan at the same time the bank chooses the repayment schedule. Before
a withdrawal action, depositor i observes a signal λi ∈ {b, g}, which influences their evaluationof expected payoffs. We thus solve a Bayesian Perfect Nash equilibrium consisting of depositor’sposterior belief, depositors’ withdrawal strategies, and the bank’s withdrawal plan.
Posterior beliefs: When a depositor receives λi , the signal represents the investment returniof her bank with probability θ. Let µλ denote the posterior belief that her bank has Rg if sheireceives signal λi , µλ ≡ P r(g | λi ). Using Bayes’ rule, we haveµg (θ) ≡ P r(g | g) = θ + (1 − θ)pg
andµb (θ) ≡ P r(g | b) = (1 − θ)pg ,where µg (0) = µb (0), ∂µg /∂θ > 0, and ∂µb /∂θ < 0. When θ is higher, a depositor believes
that the signal is more likely to represent her bank and that her bank is more likely to have thereturn indicated by the signal. However, when θ < 1, the depositor cannot distinguish which bank16

the signal corresponds to. Therefore, even in (Rg , Rg ) or (Rb , Rb ), the depositor still faces theuncertainty about the investment returns in period 1.
Withdrawal strategy: A depositor’s withdrawal plan is conditioned on both her type and an
extrinsic sunspot variable s ∈ S = [0, 1] that is unobservable to the bank. We assume, without lossof generality, that the sunspot variable is uniformly distributed on S ∈ [0, 1]. A standard approachin the literature is to study under what conditions the following strategy profile constitutes anequilibrium.15 Let ŷi (ωi , s; q) denote a cutoff strategy profile such thatŷi (ωi , s; q) =

( )
ωi
0

( )
≥
if s
q for some q ∈ [0, 1], ∀i,<(2)where ŷi (ωi , s; q) = 0 corresponds to withdrawal in period 1 and ŷi (ωi , s; q) = 1 corresponds towithdrawal in period 2. In this strategy profile, impatient depositors withdraw at period 1 andpatient depositors withdraw in period 2 if the sunspot state is s > q, but both types of depositors
withdraw in period 1 if the sunspot state s ≤ q. Notice that, since s is uniformly distributed on[0, 1], the value q can be interpreted as the probability of a run.
Repayment plan: The bank chooses a state-contingent repayment plan to maximize theexpected utility of its depositors.16 The first π depositors in the line of withdrawals receive acommon amount c1 . If there is no run, there will be no more than π withdrawal requests in period
1. The bank will pay cN
2z to the remaining depositors, where N denotes ’No run’ and z represents
the actual return. If there is a run, the bank still receives withdrawal requests after π withdrawals.
Thus, the bank is able to infer whether a run is underway or not immediately after π withdrawals
are made, and by this point of time, all uncertainty has been discerned. In case of a bank run, theR17bank pays cR
1z to the remaining impatient depositors and c2z to the remaining patient depositors.

Given q, the bank solves the following problem:max

N R
c1 ,{cN
1z ,c2z ,c2z }z=b,g
15
16

h
i
R
2
R
πu(c1 ) + Σz pz (1 − q)(1 − π)u(cN
)
+
q[π(1
−
π)u(c
)
+
(1
−
π)
u(c
)]
2z
1z
2z

See, for example, Cooper and Ross (1998), Peck and Shell (2003), and Ennis and Keister (2010).
As is standard in the literature, the bank can be interpreted as a coalition of depositors or a representative bankwith perfect competition in each location.
17
This process can be interpreted as a bank resolution. Ennis and Keister (2009) explain the court intervention as
an example.

17

subject tocN(1 − π) 2z
Rz
R
2 c2z
π(1 − π)cR
1z + (1 − π)Rz

= 1 − πc1 ,= 1 − πc1 , ∀z,

The first resource constraint represents the case of no bank run, or s < q, and the second constraint
corresponds to the case of a bank run, or s ≥ q. Under (2), all patient depositors run on the bankin case of a bank run, and hence, the measure of the remaining impatient depositors is π(1 − π).
The measure of the remaining patient depositors is thus (1 − π)2 . Letting ηzN and ηzR denote theLagrangian multiplier on the first constraint and the second constraint in state z, respectively, thesolution to the problem is characterized by the first-order conditions:ηgN + ηgR + ηbN + ηbR = u′ (c1 ),ηzN= ERz u′ (cN
2z ),

′ R
ηzR = u′ (cR1z ) = Rz u (c2z ), ∀z.
R
The last condition implies cR
1z < c2z . Assuming the CRRA utility function with the coefficient ofrelative risk aversion, γ, being greater than unity, we havec∗1 (q) =∗cN
2z (q) =cR∗
1z (q) =1
1

π + Ω(q) γ
Rz (1 − πc∗1 (q))
1−π(1 − πc∗1 (q))
1−γπ(1 − π) + (1 − π)2 Rz γ
1
γ
R∗
cR∗
2z (q) = c1z (q)Rz , ∀z,


1−γ γ
1−γ
γ
γ
2
where Ω(q) ≡ (1 − q)(1 − π) {ERz } + qE π(1 − π) + (1 − π) Rz. It is straightforward to∗
N ∗ R∗ R∗
show that c∗1 (q) ≤ EcN
2z (q), ∀q, and c1 is decreasing in q while {c2z , c1z , c2z }z=b,g are increasing in q.

If the crisis probability is high, the bank becomes more cautious and thus decreases the short-term
repayment (c∗1 ), which allows the bank to pay more in a later time. For the sake of exposition, we
1

define βz = (

Rzγ

1−γ
π(1−π)+(1−π)2 Rz γ

) , where βz > 1, ∀z. Then, we can express cR∗ = βz (1 − πc∗ ).
2z
1

18

5.3

Equilibrium bank runs

We now study when the strategy profile (2) constitutes an equilibrium. Because impatient depositors always choose to withdraw in period 1, it suffices to study the incentive of patient depositors.
In particular, we study the expected payoffs of withdrawing in period 1 or 2 to guarantee thata patient depositor is willing to withdraw in period 2 if s > q and in period 1 if s ≤ q. Whenq is substantially large, the bank becomes cautious and reduces short-term payments, which inturn, discourages the depositor from running on the bank. We thus study the threshold of q suchthat a depositor is indifferent between withdrawing in periods 1 and 2, which implies the maximum probability of an equilibrium bank run. We use this maximum probability as the measure offragility.18
We first characterize the expected payoffs. Suppose s < q. If a patient depositor arrives at thebank before π withdrawals, she will get c∗1 . Otherwise, she will receive cR
2z . The depositor evaluates
the state of the bank through the posterior belief. Let v(yi , q; µz ) denote the depositor’s payoff
when she chooses yi and observe λi = z. Thus, the expected payoff of choosing to withdraw inperiod 1 is given byzR∗Ev(0, q; µz ) = πu(c∗1 (q)) + (1 − π) µz u(cR∗
2z (q)) + (1 − µ )u(c2z (q)) .
On the other hand, the expected payoff of withdrawing in period 2 iszR∗
Ev(1, q; µz ) = µz u(cR∗
2z (q)) + (1 − µ )u(c2z (q)).

When Ev(0, q; µz ) ≥ Ev(1, q; µz ), a depositor optimally runs on the bank. These expected payoffs
satisfy the following properties.
Lemma 1 If Ev(0, q; µz ) and Ev(1, q; µz ) cross each other, they satisfy the single-crossing property.
This lemma guarantees that, if Ev(0, q; µz ) and Ev(1, q; µz ) cross each other, there exists the uniquevalue of q such that Ev(0, q; µz ) = Ev(1, q; µz ) holds, which we define as q̄. The q̄ is thus the
maximum value of q such that profile (2) constitutes an equilibrium, which we use as the measure offragility. If Ev(0, q; µz ) ≤ Ev(1, q; µz ) for any value of q, we define q̄ = 1. Likewise, if Ev(0, q; µz ) ≥18This approach is based on the robust-control approach as in Gilboa and Schmeidler (1989) because q = q̄corresponds to the worst-case scenario, which has been applied in the sunspot approach to bank runs.

19

Ev(1, q; µz ) for any value of q, we define q̄ = 0. When q̄ ∈ (0, 1), the q̄ is characterized by
Ev(0, q̄; µz ) = Ev(1, q̄; µz ), and by solving it, we haveγ

Γ(µλ (θ)) γ−1 − (1 − π)γ (Σz pz Rz1−γ )γ,q̄(θ, λ) =1−γ
− (1 − π)γ Σz pz Rz1−γ
Σz pz π(1 − π) + (1 − π)2 Rz γ

(3)where Γ(µλ (θ)) ≡ µλ (θ)βg1−γ + (1 − µλ (θ))βb1−γ . Therefore, the value of θ influences the q̄ throughthe posterior belief. If the signal is positive (λi = g), a depositor believes that her bank is more
likely to have Rg , which in turn, motivates her to wait until period 2. If, instead, the signal isnegative (λi = b), a depositor believes that her bank is more likely to have Rb , which in turn,incentivizes her to run on the bank. The following proposition formalizes these discussions.
Lemma 2 The q̄(θ, g) is decreasing in θ, and the q̄(θ, b) is increasing in θ.
For profile (2) to be part of equilibrium, we need q ≤ q̄(θ) ≡ min{q̄(θ, g), q̄(θ, b)}. Because µg (0) =µb (0) and thus q̄(0, g) = q̄(0, b), it is straightforward to show q̄(θ, g) < q̄(θ, b), suggesting that theq̄(θ) is implied by q̄(θ, g). Thus, using the q̄(θ), we characterize the trademark risk.
Proposition 1 Fragility, measured by q̄(θ), is decreasing in θ. The financial contagion throughlimited attention is measured by q̄(θ) − q̄(1), where θ < 1; there is no contagion through limited
attention when θ = 1.
The driving force of our results is how the private signal helps a depositor update their beliefs.
If a signal is good, she believes that her bank is more likely to have Rg and has a smaller incentive
to run on the bank. The value of θ introduces a noise here, which blunts her belief updating. Thus,
a lower value of θ increases fragility.

5.4

Attention choices

We now turn our focus to an ex-ante attention allocation. We assume that θ is now chosen by eachdepositor through her ex-ante efforts. However, a depositor has to pay a cost δC(θ), where δ > 0,
C(0) = 0, and C ′ (θ) > 0. Each of ex-ante identical depositors chooses θ in period 0 to maximize
her expected utility by balancing the trade-off between leaving more resources and increasing theaccuracy of her signal. We first characterize her expected utility by starting with the modified

20

bank’s problem. Taking θ as given, the bank now solves the following problem in period 1.
V (θ, q) ≡

max

N R
{c1 ,{cN
1z ,c2z ,c2z }z=b,g }hπu(c1 (θ)) + Σz pz (1 − q(θ))(1 − π)u(cN
2z (θ))i
R (θ))]+q(θ)(1 − π)[πu(cR
(θ))
+
(1
−
π)u(c
1z
2z

subject to
cN (θ)(1 − π) 2z
Rz
R
2 c2z (θ)π(1 − π)cR
1z (θ) + (1 − π)Rz

= (1 − δC(θ)) − πc1z (θ),= (1 − δC(θ)) − πc1z (θ), ∀z.

The solution to this problem differs from the previous section, but when the utility function ishomothetic, such as the CRRA function, the chosen levels of consumption will be proportional tothe ones in the previous section. We follow the same procedure as Section 5.3 to construct theq̄(θ), and the expression of q̄ is identical to (3) when the utility function follows the CRRA form.
To capture changes in marginal run incentives, we evaluate V (θ, q) at q = q̄(θ). In other words, adepositor chooses θ in period 0 by anticipating the worst-case equilibrium outcome. Assuming the
CRRA function, we can rewrite V (θ, q̄(θ)) asV (θ, q̄(θ)) =(1 − δC(θ))1−γ(π + Ω (q̄(θ))γ
1−γ

In period 0, a depositor solves the following problem
max V (θ, q̄(θ)),θ∈[0,1]

where a depositor chooses θ by considering its resource cost (δC(θ)) and its effect on fragility. When
θ is an interior solution, the optimal value of θ solvesγ∂Ω(q̄(θ))(1 − δC(θ)),δC ′ (θ) {π + Ω(q̄(θ))} =
|
{z
} 1−γ
∂θ
|
{z
}
resource costs(4)

ef f ects on f ragility

The equation above expresses that a depositor balances the marginal benefit through q̄(θ) with theresource cost.
When θ∗ ∈ (0, 1), the cost parameter δ determines the degree of attention. When δ is smaller,
the depositor chooses a higher θ. When δ is instead larger, the depositor chooses a smaller θ. The
following proposition summarizes the results.
21

Proposition 2 The optimal attention is decreasing in δ.
The value of δ can be interpreted in two ways. First, the δ itself is how similar banks’ trademarks
are. When two banks have very similar trademarks, depositors have to pay more attentions todetails and be careful to distinguish information, which entails more costs. Thus, when banks have
similar trademarks, depositors rationally choose to pay less attention, which in turn makes it easierfor depositors to misidentify the signal, resulting in higher fragility. This mechanism explains ourempirical results about financial contagion without fundamental linkage.
∗

∗

) ∂θ
Corollary 1 The trademark risk is represented by ∂ q̄(θ∂θ∗ ∂δ and is increasing in δ.

Second, we can also consider that the δ depends on investors’ profiles. Institutional depositors likely
need to exert less effort to monitor the lending situations of banks compared to retail depositors. If
an institutional depositor is characterized by having a smaller δ than a retail depositor, our results
suggest that banks with deposits predominantly from institutional depositors are less fragile thanthose reliant on retail depositors.

5.5Media coverage

We extend our framework to have a public signal, which we call media coverage. When either bankor both banks draw a bad return (Rb ), a public signal appears, and all depositors observe this signal
in addition to their private signals. For example, under (Rg , Rg ), this signal does not appear, whichallows depositors to infer that all banks have Rg . However, under other combinations of returns, adepositor infers that her or the other bank has Rb . In such a case, the posterior belief is updated
in the following way through Bayes’ rule,µgm (θ) ≡ P r(z = g | λ = g) = θandµbm (θ) ≡ P r(z = g | λ = b) = (1 − θ)pg ,where µgm (θ) ≤ µg (θ) and µbm (θ) = µb (θ). When the private signal is bad, observing the (negative)
public signal does not change the depositor’s belief. However, when the private signal is good,
observing the public signal erodes confidence. We use µλm (θ) to evaluate the expected payoffs andderive q̄(θ, λ). In particular, we replace µλ (θ) with µλm (θ) in (3), which we call q̄m (θ, λ). The
22q̄m (θ, λ) has the same properties with q̄(θ, λ), but its magnitude is different. By comparing them,
we find the following relationship.
 
 
=
=
Lemma 3 q̄m (θ, g)q̄(θ, g) if θ
1, and q̄m (θ, b) = q̄(θ, b), ∀θ.
>
<Thus, when depositors pay enough effort such as θ = 1, media coverage does not affect the fragility.
However, when θ < 1, media coverage can worsen fragility by allowing depositors to update theirbeliefs. Specifically, the difference q̄m (θ, λ) − q̄(θ, λ) captures the media effect:
Proposition 3 Media coverage increases fragility by q̄m (θ, λ) − q̄(θ, λ), orγγ

Γ(µλm (θ)) γ−1 − Γ(µλ (θ)) γ−1

γ
.
1−γ
Σz pz π(1 − π) + (1 − π)2 Rz γ
− (1 − π)γ Σz pz Rz1−γ(5)

The media effect is zero if λ = b and positive if λ = g, and thus, the media effect appears when thefragility is measured by q̄(θ, g), which suggests the following Corollary.
Corollary 2 Media coverage amplifies fragility if and only if θ < 1, and the magnitude of amplification is decreasing in θ.

6Conclusion

Our paper sheds light on trademark risk within the U.S. banking sector over the last two decades.
By analysing the names of U.S. banking institutions, we observe a consistent decline since the 1990sin the number of banks with similar trademarks. Despite this trend, we find that approximately
one in every five banks remains heavily exposed to trademark risk. When banking was primarily
a local business, this exposure might not have posed a significant threat as it did not lead toconfusion with other institutions. However, with the advent of the internet and branch banking,the potential for consumer confusion and the subsequent exposure to trademark risk has increased.
Through difference-in-difference regressions, we show that sharing a trademark with a failed bankresults in a 0.4% decrease in transaction deposits. This suggests that certain depositors exhibit alevel of caution when faced with potential confusion or association with a failed bank.
Our findings are rationalized by exploring depositors’ incentives when the similarity of trademarks increases the cost of distinguishing between banks. When it is costly for depositors to23

differentiate between banks, they choose to allocate less attention, resulting in less precise signals.
In such a case, those who receive a good signal may still retain substantial doubts about theirbank’s asset quality, thus maintaining some incentive to run on the bank. This remaining uncertainty, or confusion, can escalate concerns among those who receive a bad signal, amplifying their
incentive to run on the bank due to a perceived greater first-mover advantage. Thus, the similarityof trademarks creates a contagion channel through depositors’ confusion even in the absence offundamental linkages between banks.
The concept of “likelihood of confusion” in trademark law plays a crucial role in establishingtrademark infringement or harm. With numerous banks sharing similar names, the potential for
confusion among depositors regarding which bank is under distress can be of significant concern.
Indeed, proving “likelihood of confusion” in courts can be an intricate and challenging task. We
hope this paper motivates further research on measuring and mitigating the risks caused by sharednames in the banking industry.

24

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27

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28

Figures
Figure 1: Common Words in Bank Names

This figure shows frequency counts of bank names as of December 2022.

29

Figure 2: Bank Names Beginning with Common Strings
3500
0.20

2500

% of Bank Trademarks
Beginning with String# of Bank Trademarks
Beginning with String

3000

2000
1500
1000

0.15
0.10
0.05

500
0

1994

1999

2004

2009

2014

0.00

2019

1994

farmers state
farmers and merchantfirst national bankfirst state bank

1999

2004

2009

2014

2019

first community bankcitizens|peoples|merchants
united|heritage|american|liberty

This figure shows how common bank names have evolved between 1990 and 2022. The left (right) chart shows the number(percentage) of banks that begin with a common string or phrase listed in the legend.

Figure 3: Pre-Trends and Impact

Growth Relative to Four Quarters before Failure

Deposits over TATime Deposits over TA
Control
Treatment

1.020

Control
Treatment

1.00

1.015

Control Group 14

0.98

1.010
0.96
1.005
0.94

1.000
0.995
3

2

1

0

1

2

3

4

Transaction Deposits over TA

4

3

2

1

0

1

2

3

4

Control
Treatment

1.10

1.08

1.08

1.06

1.06

1.04

1.04

1.02

1.02

1.00

0.92
4

Insured Deposits over TA
Control
Treatment

1.10

1.00
4

3

2

1

0

1

2

3

4

4

3

2

1

0

1

2

3

4

This figure shows the growth in various balance sheet variables of the banks in our sample relative to four quarters before theassociated bank failure. Treatment banks are banks that share the name of a failed bank and Control banks are those that do
not share their name but were matched during the propensity matching.

30

-1

SimilarNameb*EventTimet
-.5
0

.5

Figure 4: Regression Interaction over Time

-7

-6

-5

-4

-3

-1

0

1

2

3

4

5

6

7

This figure shows the coefficients β t resulting from the estimation of equation (1). Coefficients are displayed relative to event
time equal to -2.

31

Figure 5: Media Exposure-2

SimilarNameb*EventTimet
-1
0
1

2

(a) News Headline

-7

-6

-5

-4

-3

-1

0

1

2

3

4

5

6

7

3

4

5

6

7

-2

SimilarNameb*EventTimet
-1
0
1

2

(b) No Headline

-7

-6

-5

-4

-3

-1

0

1

2

This figure shows the coefficients β t resulting from the estimation of equation (1) depending if the associated bank failure wasfeatured in the news. Panel a (b) includes observations where the associated bank failure was (not) mentioned in a Reuters
headline during the month of the failure. Coefficients are displayed relative to event time equal to -2.

32

Tables
Table 1: Bank Name Statistics as of December 2022

(1)

(2)

(3)

Treatment (899 Banks)

(4)

(5)

(6)

Control (894 Banks)

Variable (2 Years Pre-Failure)Mean

Std Dev.

MedianMean

Std Dev.

MedianTime Deposits (over TA)

0.39

0.12

0.39

0.4

0.14

0.41

Transaction Deposits (over TA)

0.25

0.12

0.25

0.22

0.12

0.22

Uninsured Deposits (over TA)

0.01

0.05

0

0.01

0.05

0

Total Deposits (over TA)

0.83

0.1

0.85

0.84

0.1

0.86

Deposits over 250K (over TA)

0.16

0.08

0.15

0.15

0.09

0.15

Deposits under 250K (over TA)

0.23

0.09

0.22

0.24

0.1

0.25

Total Loans (over TA)

0.61

0.17

0.64

0.62

0.18

0.66

Mortgage Loans (over TA)

0.39

0.18

0.38

0.42

0.2

0.42

Consumer Loans (over TA)

0.05

0.05

0.04

0.05

0.05

0.04

C&I Loans (over TA)

0.09

0.06

0.08

0.09

0.06

0.07

ROA (%)

0.93

0.8

0.91

0.81

0.88

0.77

Log Assets

18.51

1.05

18.44

18.48

1.17

18.4

This table reports the summary statistics of the main variables used in the paper. Treatment banks are banks that share thename of a failed bank and Control banks are those that do not share their name but were matched during the propensity
matching. This table was obtained by running a propensity score matching algorithm two years before the associated bankfailure, matching on the logarithm of total assets, deposits to total assets, loans to total assets and profitability (proxied by
ROA). The 107 bank failures from 2000 to 2022 considered for the study were obtained based on i) finding banks that matchthe name of the failed bank ii) at least two similarly named banks were identified iii) data available around the two-year windowof the associated bank failure. All variables, except for Assets, are divided by total assets.

33

Table 2: Bank Name Statistics as of December 2022

(1)

(2)

(3)

(4)

Bank NameBank Name

Starting with String

Containing String# of Banks% of Banks# of Banks% of Banks

citizens

158

3.3%

171

3.6%

peoples

100

2.1%

104

2.2%

farmers

156

3.3%

177

3.7%

merchants

15

0.3%

73

1.5%

state

85

1.8%

863

18.1%

community

105

2.2%

259

5.4%

national

17

0.4%

760

16%

united

43

0.9%

54

1.1%

heritage

15

0.3%

28

0.6%

american

59

1.2%

63

1.3%

liberty

20

0.4%

22

0.5%

first

653

13.7%

711

14.9%

56

1.2%

59

1.2%

Word

List of Words
farmers state
farmers and merchant

50

1.1%

55

1.2%

first national bank

210

4.4%

216

4.5%

first state bank

103

2.2%

103

2.2%

first community bank

20

0.4%

20

0.4%

citizens—peoples—merchants

273

5.7%

347

7.3%

united—heritage—american—liberty

137

2.9%

164

3.4%

This table shows frequency counts of bank names as of December 2022. Columns 1 and 2 show the number and percentage
of bank names that start with the associated string, respectively. Columns 3 and 4 show the number and percentage of banks
that contain the associated string, respectively.

34

Table 3: Deposit Reaction to Bank Failures with Similar Names(1)
Dependent Variable

SimilarN ameb *Af terF ailuret

(2)

(3)

T ransactDep/T Ab,t-0.480***-0.479***-0.423**(0.172)(0.170)(0.167)0.961***

0.238

0.194

(0.115)(0.180)(0.178)0.0690

0.283

0.186

(0.486)(0.357)(0.367)

Observations

12551

12551

12491

R-squared

0.948

0.954

0.955

Bank FEYYY

Quarter FE

N

Y

Y

Controls

NNY

Af terF ailuret
SimilarN ameb

The dependent variable in columns 1 through 3 is the percentage of transaction deposits for each bank b during quarter t.
The regressions incorporate the time period of three quarters around the time of failure for each failed bank. SimilarN ameb
equals the value of one for banks that share the name of the associated failed bank and zero if not; Af terF ailuret equals thevalue of one including and after the quarter of the associated bank failure, and zero otherwise, which leaves the period before
the associated bank failure as the benchmark period (i.e., each estimated coefficient measures the differential effect after the
associated bank failure to the period before associated bank failure). Fixed effects are either included (‘Y’) or not (‘N’). Control
variables include the lagged logarithm of total assets, lagged deposits to total assets, lagged loans to total assets and lagged
profitability (proxied by ROA). Standard errors are clustered at the bank level and reported in parentheses (rounded to thethird decimal). ***: Significant at 1% level; **: Significant at 5% level; *: Significant at 10% level.

35

Table 4: Robustness

(1)

(2)

(3)

(4)

Dependent Variable

SimilarN ameb *Af terF ailuret
Af terF ailuret

(5)

(6)

(7)

+/- 1 Quarter

Banking Demand

Log(T ransactDep)b,t

from Failure

Controls

T ransactDep/T Ab,t

Only Treatment

During GFC

or Only Control(2007-2010)-0.383**-0.415**-0.466**-0.327*-0.337**-0.449***-0.0212**(0.167)(0.194)(0.198)(0.195)(0.156)(0.171)(0.00861)

0.200

0.125

0.162

0.152

-0.02150.232

0.0123(0.178)(0.191)(0.203)(0.285)(0.190)(0.184)(0.00843)

SimilarN ameb

Excluding FNB

Excluding FSB-0.0840-0.3070.0187-0.731

0.296

0.0330(0.564)(0.556)(0.475)(0.487)(0.381)(0.0325)

Observations

11848

9768

8747

8670

5348

12239

12491

R-squared

0.960

0.963

0.949

0.959

0.967

0.954

0.986

Bank FE

Y

Y

Y

Y

Y

Y

Y

Quarter FE

Y

Y

Y

Y

Y

Y

Y

Controls

Y

Y

Y

Y

Y

Y

Y

The dependent variable in columns 1 through 6 is the percentage of transaction deposits for each bank b during quarter t. The
dependent variable in column 7 is the logarithm of transaction deposit amount for each bank b during quarter t. The regressions
incorporate the time period of three quarters around the time of failure for each failed bank. SimilarN ameb equals the valueof one for banks that share the name of the associated failed bank and zero if not; Af terF ailuret equals the value of one
including and after the quarter of the associated bank failure, and zero otherwise, which leaves the period before the associatedbank failure as the benchmark period (i.e., each estimated coefficient measures the differential effect after the associated bankfailure to the period before associated bank failure). Column 1 restricts the sample to control banks that are never considereda treatment bank. Column 2 restricts the sample to bank failures that occurred between January 1, 2007 to December 31,
2010. Column 3 (and 4) omits the two associated treatment and control banks associated with the two (three) failures of First
National (State) Bank. Column 5 restricts the sample to include the time period of one quarter around the time of failure.
Column 6 controls for the average Tobin’s Q and cash flows of all firms that exist in the headquarter of the bank to control forthe demand for transaction deposits. Fixed effects are either included (‘Y’) or not (‘N’). Control variables include the lagged
logarithm of total assets, lagged deposits to total assets, lagged loans to total assets and lagged profitability (proxied by ROA).
Standard errors are clustered at the bank level and reported in parentheses (rounded to the third decimal). ***: Significant at
1% level; **: Significant at 5% level; *: Significant at 10% level.

36

Table 5: Effect of Media Coverage(1)
Dependent Variable(2)
T ransactDep/T Ab,tReuters Headline

No Reuters Headline-0.780**-0.342**(0.361)(0.174)

0.126

0.163

(0.311)(0.212)3.414***-0.0119(0.285)(0.434)

Observations

2581

9910

R-squared

0.960

0.956

Bank FE

Y

Y

Quarter FEYYControls

Y

Y

SimilarN ameb *Af terF ailuret
Af terF ailuret
SimilarN ameb

The dependent variable in columns 1 and 2 is the percentage of transaction deposits for each bank b during quarter t. The
regressions incorporate the time period of three quarters around the time of failure for each failed bank. SimilarN ameb
equals the value of one for banks that share the name of the associated failed bank and zero if not; Af terF ailuret equals thevalue of one including and after the quarter of the associated bank failure, and zero otherwise, which leaves the period before
the associated bank failure as the benchmark period (i.e., each estimated coefficient measures the differential effect after the
associated bank failure to the period before associated bank failure). Column 1 (2) includes observations where the associatedbank failure was (not) referenced to in a Reuters headline during the month of the failure. Control variables include the lagged
logarithm of total assets, lagged deposits to total assets, lagged loans to total assets and lagged profitability (proxied by ROA).
Standard errors are clustered at the bank level and reported in parentheses (rounded to the third decimal). ***: Significant at
1% level; **: Significant at 5% level; *: Significant at 10% level.

37

Table 6: Loan Variables

Dependent Variable

SimilarN ameb *Af terF ailuret
Af terF ailuret

(1)

(2)

(3)

(4)

Log(M ortgages)b,t

Log(Consumer)b,t

Log(C&I)b,t

Log(Loans)b,t-0.0450-0.121**0.0141-0.0134(0.178)(0.0570)(0.107)(0.217)-0.00210

0.0888-0.04880.129(0.169)(0.0622)(0.0941)(0.211)

0.106

0.202

0.210

0.706

(0.410)(0.139)(0.204)(0.610)Observations

12239

12239

12239

12239

R-squared

0.981

0.973

0.941

0.965

Bank FE

Y

Y

Y

Y

Quarter FE

Y

Y

Y

Y

Controls

Y

Y

Y

Y

Controls for Banking Demand

Y

Y

Y

Y

SimilarN ameb

The dependent variables in columns 1 through 4 are the total mortgage, consumer, commercial industrial, and all loans overtotal assets, respectively. The regressions incorporate the time period of three quarters around the time of failure for eachfailed bank. SimilarN ameb equals the value of one for banks that share the name of the associated failed bank and zero if
not; Af terF ailuret equals the value of one including and after the quarter of the associated bank failure, and zero otherwise,
which leaves the period before the associated bank failure as the benchmark period (i.e., each estimated coefficient measuresthe differential effect after the associated bank failure to the period before associated bank failure). Control variables include
the lagged logarithm of total assets, lagged deposits to total assets, lagged loans to total assets and lagged profitability (proxied
by ROA). Standard errors are clustered at the bank level and reported in parentheses (rounded to the third decimal). ***:
Significant at 1% level; **: Significant at 5% level; *: Significant at 10% level.

38

Appendix A
Figure 1: Signature Bank (Chicago) following Signature Bank (New York) Failure March 2023

This figure shows a snapshot of a public announcement by Signature Bank Illinois in response to the 2023 banking turmoil andthe failure of Signature Bank New York.

39

Figure 2: Signature Bank (Arkansas) following Signature Bank (New York) Failure March 2023

This figure shows a snapshot of a public announcement by Signature Bank of Arkansas in response to the 2023 banking turmoil
and the failure of Signature Bank New York.

40

Appendix B: Proofs
Proof of Lemma 1.

We first differentiate Ev(1, q; µz , 1) with respect to q. Because ∂cR∗
2z /∂q >0, ∀z, we always haveR∗∂cR∗
∂Ev(1, q; µz )2g
g ′ R∗ ∂c2b
= µg u′ (cR∗
)
+
(1
−
µ
)u
(c
)
> 0.
2z
2z
∂q
∂q
∂q

Notice that Ev(0, q; µz ) = πu(c∗1 ) + (1 − π)Ev(1, q; µz , 1) and ∂u′ (c∗1 )/∂q < 0, and then the following
relationship always holds:∂Ev(1, q; µz )∂Ev(0, q; µz )
>
.
∂q
∂q

Therefore, if Ev(1, 0; µz ) < Ev(0, 0; µz ) and Ev(1, 1; µz ) > Ev(0, 1; µz ), there exists the unique valueof q such that Ev(1, 0; µz ) = Ev(0, 0; µz ). Otherwise, they never cross each other.
Proof of Lemma 2. Differentiating q̄(θ, λ), defined in (3), with respect to θ, we have∂ q̄(θ, λ)
=
∂θ

1
γ
λ
γ−1
∂Γ(µλ (θ))γ−1 Γ(µ (θ))


,
γ
1−γ
∂θ
1−γ
γ
2
γ
Σz pz π(1 − π) + (1 − π) Rz− (1 − π) Σz pz Rz|{zpositive}and the sign of ∂Γ(µλ (θ))/∂θ depends on λ. Specifically, the latter derivative is expressed aso λΓ(µλ (θ)) n 1−γ1−γ ∂µ= βg − βb
∂θ
|
{z
} ∂θ
negative

Given that ∂µg /∂θ > 0 and ∂µb /∂θ < 0, we have proven that the q̄(θ, g) is decreasing in θ and theq̄(θ, b) is increasing in θ, as desired.
Proof of Proposition 1.

Since µg (0) = µb (0), we have q̄(0, g) = q̄(0, b). Lemma 2 implies

that q̄(θ, g) < q̄(θ, b) for any θ > 0. Since q̄(θ) = min{q̄(θ, g), q̄(θ, b)}, our measure of fragility, theq̄(θ), is determined by q̄(θ, g), which is decreasing in θ.
Proof of Proposition 2. Suppose the first order condition (4) characterizes the optimal levelof θ. Differentiating (4) with respect to δ, we obtain
positivezγ
C ′ (θ∗ )(π + Γ γ−1 ) +

}|
{
1
γ
γ
∗
∗ γ−1
C(θ )(1 − pg )Θ
Γ(θ )
∂θ∗
1−γ
γ−1
=
< 0,
1


∗ )−1
∂δ
γ
γΘΓ(θ∗ ) γ−1γΘΓ(θ
(1 − pg ) δC ′ (θ) +(1 − δC(θ∗ )) (1 − pg ) − δC ′ (θ∗ )(π + Γ(θ∗ ) γ−1 )(γ − 1)2
1−γ|{z}negative41

where Θ ≡ βg1−γ − βb1−γ < 0. Note that, because γ > 1, each term in the numerator is positive
and that each term in the denominator is negative. Therefore, the optimal level of attension (θ∗ )is decreasing in δ.
Proof of Corollary 1. This result is implied by Propositions 1 and 2.
Proof of Lemma 3.

The difference between q̄m (θ, λ) and q̄(θ, λ) comes from the difference

between µλm (θ) and µλ (θ).

Because µλm (θ) = µλ (θ), we have q̄m (θ, b) = q̄(θ, b). When λ = g, wehave q̄m (θ, g) ≥ q̄(θ, g) because µgm (θ) ≥ µg (θ) and the equality holds if and only if θ = 1.
Proof of Proposition 3. Recall that the q̄(θ, λ) is defined byγΓ(µλ (θ)) γ−1 − (1 − π)γ (Σz pz Rz1−γ )γ,q̄(θ, λ) =
1−γ
1−γ
γ
2
γ
Σz pz π(1 − π) + (1 − π) Rz− (1 − π) Σz pz Rz(6)

and the q̄m (θ, λ) is defined byγΓ(µλm (θ)) γ−1 − (1 − π)γ (Σz pz Rz1−γ )γ.
q̄m (θ, λ) =
1−γ
1−γ
γ
2
γ
Σz pz π(1 − π) + (1 − π) Rz− (1 − π) Σz pz Rz(7)

Lemma 3 implies q̄m (θ, λ) − q̄(θ, λ) ≥ 0, and the difference can be rewritten as (5).
Proof of Corollary 2.

The only difference between q̄m (θ, λ) and q̄(θ, λ) is the first termin the numerator. In (5), µλ (θ) − µλm (θ) is decreasing in θ and is zero when θ = 1. Thus, theamplification through media coverage is decreasing in θ and disappears when θ = 0.

42