The Radio and Bank Runs in the Great Depression

The Radio and Bank Runs in the Great Depression

Nicolas L. Ziebarth∗

February 28, 2013

Abstract

Counties with higher levels of radio penetration rates in 1930 experience higher levels ofbanking stress between 1930 and 1933. A 10 percentage point increase in radio penetrationrates leads to a 5 percentage point decline in bank deposits between 1930 and 1933. Thiscorrelation remains after controlling for a variety of measures for local economic conditions aswell as pre-trends from 1920 to 1930. I build a model with strategic externalities and introducepublic information in the form of the radio. The model highlights how the existence of a publicsignal known to a select group of individuals affects the behavior of those uninformed.

1 Introduction

In a classic episode of The Simpsons, Bart calls out at a local bank, “What do you mean, the bank

is out of money?”, “Insolvent?!”, and “You only have enough cash for the next three customers?”

A bank run (and hilarity) ensue with people rushing to demand their deposits. At the heart of this

bank run induced for the sake of comedy and all other bank runs is an informational asymmetry.

Whether or not depositors are worried about illiquidity or insolvency, depositors must deal with

the nagging suspicion that they will be left out if others demand their deposits. Information about

what other depositors are doing, then, is crucial for making a decision on whether to run. In the

modern day, we are saturated with information. Rumors swirled about the solvency of Bear Sterns

and Lehman often stoked by the financial news media such as CNBC before they collapsed. Yet

it has proven very difficult to identify the causal role of those rumors because it is so hard to

sharply identify information flows. History provides an unique setting to address this difficulty by

identifying major shifts in communication due to the introduction of new technologies. I study one

particular case in one major period of time: the radio during the Great Depression.

∗University of Iowa, [email protected]. I thank Nicholas Pottebaum for help in assembling thedata. I thank Steven Vickers for the reference from The Simpsons. Larry Warren and Chris Vickers provided usefulcomments.

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The radio was a major innovation in mass media providing people with up to the minute updates

on breaking news potentially spreading panic. The power of the radio was well understood even at

the time. Stromberg (2004) reports that “By 1937, 70 percent of the American public reportedly

depended on the radio for their daily news. Radio was also considered a credible media: 88 percent

of the American public thought that radio news commentators made truthful reports.” (pg. 193)

There were, of course, the most famous cases where it was used to calm nerves such as in FDR’s

famous fireside chats. A more prosaic example comes from Philadelphia during 1931. “Rabbi

Fineshriber made a radio address urging the wisdom of leaving deposits in the banks.” (Dewsbury,

1933) The Governor of the Philadelphia Federal Reserve, George Norris, also got on the radio

“pleading with the depositors to allow their funds to remain in the local banks.” (Dewsbury, 1933)

In this paper, I first show that county-level penetration rates of the radio in 1930 is a strong

predictor of subsequent banking outcomes between 1930 and 1933. The major worry in these

regressions is some lurking variable that drives both radio penetration rates in 1930 and subsequent

banking performance. The regressions control for the most obvious lurking variable: the local

economic environment. I attempt to control for conditions in agriculture at the county-level as well

as conditions in the labor market through the inclusion of wage and unemployment controls. Besides

these controls for economics conditions, I also include controls relating to population characteristics

resulting in a final set of controls similar to that of Stromberg.

I go beyond that basic set of controls to control for a second potential lurking varibale in the

form of the pre-trend in economics conditions between 1920 and 1930. A variety of authors have

argued that to understand the outcomes during the Great Depression, it is essential to understand

what happened during the boom. Friedman and Schwartz (1971) Field (1992) argues that the slow

recovery is due to low levels of construction, which themselves are related to an “uncontrolled”

real estate boom during the 1920s. In any case, even after controlling for changes in a number

of variables for manufacturing and agriculture, the basic results remain only slightly changed.1

Even after controlling for these factors, a 10 percentage point increase in radio penetration rates

leads to a 5.1 percentage point decline in deposits between 1930 and 1933. Eliminating the radio

would not have completely staunched the bank runs during the Depression, but it would have

1The effects are also not driven by broad geographic variation in the radio usage and banking outcomes since Iidentify the effect off of within state and Federal Reserve district variation.

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reduced the average decline in deposits by about 10 percentage points. Putting the results in a

different perspective, the effect of the radio is only about 1/6 of the effect of unemployment in 1930

suggesting the effects of the radio are not unreasonably large.

A more direct approach to the issue of lurking variables would be to look for an instrument.

To that end, I have also attempted to employ the instruments suggested by Stromberg (2004):

ground conductivity and share of a county’s surface area covered by woodlands. In the early days

of the radio with the technology still being perfected, local geographic features would have had large

effects on the ability to pick up AM signals and, hence, affected the value of of owning a radio in the

first place. This suggests that these variables will be significant in the first stage. Stromberg argues

that they are also valid in the second stage. While it seems plausible that ground conductivity

would be uncorrelated with unobservables that drive New Deal spending in his case and bank runs

in mine, it seems much less plausible to think this for the woodlands variable. For the banking

case, it is easy to imagine that the share of woodlands is correlated with something like the ease

of transportation in a particular county and that the ability to get from one place to another is

important for being able to run to the local bank. For this reason, I choose to include woodlands as

a control and ground conductivity as the instrument. In this specification, the coefficient becomes

much larger and retains a high degree of statistical significance.2

The debate over the banking crisis during the Depression has centered on the relative importance

of illiquidity and insolvency with Friedman and Schwartz (1971) echoed in Wicker (1996) coming

down strongly on the side of illiquidity. Calomiris and Mason (2003b, 1997) both argue that the

importance of illiquidity and contagion has been exaggerated and that poor fundamentals were at

the heart of the cascading bank failures. Richardson and Troost (2009) and Carlson et al. (2011)

identify examples where Fed interventions were effective in mitigating bank runs even in the face

of worries about insolvency. Now my paper does not take a stand on what the major source of

the banking crisis was. Instead I emphasize a contributing factor in the form of the “information”

spread, be it in the form of information on the solvency of local banks or simply the existence of

long lines of depositors.

While not definitive, it is suggestive that the radio does not have effects on banking outcomes

2If I follow Stromberg’s IV specification exactly, then the point estimate of the effect of the radio remains roughlyunchanged but the standard errors are much larger.

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between 1933 and 1935. In fact, most of the effects are concentrated in the “first” Friedman-

Schwartz banking episode from 1930 to 1931.3 The most obvious explanation for this is that there

are simply very few bank failures to begin with,4 and this would exactly be my point. What the

results imply is that there is no “payback” after 1933 for low bank failure rates in areas with few

radios in 1930. Now again I repeat that I make no assumption about the underlying cause, illiquidity

or insolvency. At the same time, the results do suggest that by limiting public information the

authorities could have “bought time” to fix up the problems in the banks whatever the source,

insolvency or illiquidity.

To interpret these results, I study the simultaneous signal-action model developed by Angeletos

and Werning (2006), and in particular, the sequential form discussed in Angeletos and Werning

(2004) (AW). In this setting, agents must make a decision of whether or not to “attack” some

status quo (“a policy of demandable deposits”). Whether or not the attack is “successful,” in other

words, deposit redemptions are suspended, depends on how many people also run. The number of

people that are required for an attack to be successful depends on some (unknown) fundamental

θ, the financial position of the bank. All agents receive a private signal on θ. At the same time,

agents are divided into two groups: those that own radios (late movers) and those that do not

(early movers). The early movers are required to take an action solely on the basis of their private

signal. The late movers, besides receiving their private signal, also receive a public signal about the

number of early movers that decided to attack. On the basis of both of those signals, they decide

whether or not to attack.

To make sense of the results in AW and this paper, it is necessary to step back and place this

model in the broader literature. The classic result in Diamond and Dybvig (1983) was that even

if a bank was solvent, there existed multiple equilibria where in one equilibrium, the bank faces

few depositors and is able to redeem their requests, and another where the bank is overwhelmed

by requests. In this model, because of symmetry between agents, if it is optimal for a particular

agent to run given the strategies of all other agents, then it will be optimal for everyone to run.

The existence of multiple equilibria in coordination games of this type has been taken as a major

3This is roughly speaking since the data are annual and FS identify multiple distinct episodes during this periodof time.

4Another explanation is that by 1933, the 1930 radio penetration rate is no longer a good predictor of the actualradio penetration rate.

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limitation of this approach as it is difficult to empirically implement a model that is fundamentally

underdetermined. Carlsson and van Damme (1993) offer a solution to the problem by introducing a

small amount of noise in the information of each agent. This breaks the symmetry between agents

and leads to a unique prediction of the model. The (somewhat abstract) insight of Carlsson and

van Damme (1993) found application in thinking about the coordination game models of attacks

on fixed exchange rates, bank runs, and liquidity crises more generally (Morris and Shin, 2000).

While this early literature stressed the importance of private information in assuring uniqueness,

it abstracted from other potentially public sources of information about fundamentals. In two

important works, (Morris and Shin, 2002, 2005) took up the question of the value of these public

sources of information for coordination games.5 The important result of Morris and Shin (2005) was

that better public information was not always welfare improving. To the extent that it led agents

to disregard their private source of information, public information could lead to non-fundamental

volatility6 and lower social welfare.7

With this background in place, I now return to the results derived in this paper and AW. The

key innovation in the AW setup is to link the informativeness on the public signal to the quality of

the private signal. They point out that this idea goes back to Atkeson (2000) commenting on Morris

and Shin (2002). He noted that if prices (the public signal, in that case) were fully revealing, then

the game would collapse to the Diamond-Dybvig world. With this idea in mind, AW show that

under certain circumstances of the simultaneous move game, simply introducing a small amount

of private noise is not sufficient to restore uniqueness. Instead informative private signals lead

to informative public signals and determinacy is related to the ratio of the informativeness of

the signals. The second main result is show the role public information plays in generating non-

fundamental volatility. More informative public signals8 can increase volatility in two separate

ways. First, it can introduce sunspots by moving the economy from the region of determinacy to

one of indeterminacy.9 Secondly, even in the region of indeterminacy, the level of the fundamental

5The general case is studied in Angeletos and Pavan (2007).6This is volatility driven by shocks to the public signal.7In a number of ways, the issues addressed in this literature mirror the issues discussed in a variety of other

settings. For example, the industrial organization literature has discussed the role of information disclosure in tacitcollusion. See Vives (2007) for a good survey. The issues somewhat mirror the informed trader literature in finance(Koudijs, 2011b; Kyle, 1985) and the role of opacity in liquidity provision (Dang et al., 2012).

8What is meant here is decreasing the exogenous component of the public signal.9Note that indeterminacy is not in terms of the aggregate outcome, but in the mapping between signals from

prices and signals on the fundamental.

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required for an attack to be successful is more sensitive to noise shocks.

These results are all for the case of simultaneous move game where all agents receive the public

signal. The sequential form of the game brings the model closer to the empirical results. AW show

that in the limit as the fraction of the late moving group approaches 1, the equilibrium collapses

back to the simultaneous move case. First, I extend the analysis to show that increasing the quality

of public information increases the probability of a run in the case when agents receive information

that many people are attacking. This is one interpretation of the empirical results where the role of

better public information is restricted to the times of “panic.” However, it does not exactly match

the regression specification where I examine the effects of changing the number of people who own

the radio. So I turn to a sequential form of the model where late moving agents, those who own

the radio, also receive a public signal in addition to their private one. In this case, I prove that

analogous to before if the endogenous signal is bad, then having more people hear increases the

probability of a bank run. This again is not too surprising of a result.

There is one subtle difference between the quality of the public signal and the number of people

who receive the signal that drives the different results. It is the fact that those that do not receive

the public signal know this and that another group is receiving that information. They understand

how many people have this information even if they do not know what that information is. The

uninformed agent can attempt to infer the still unrealized public signal and the fundamental itself

by using their private signal (a double forecasting problem). The logic is that the uninformed agents

use their private signal to not only infer the fundamental but also to infer the public signal of the

informed agents. This makes the uninformed agents more sensitive to changes in the fundamentals

than the better informed agents.

What is surprising is the fact that this effect is rather muted. Going from practically no people

owning the radio to nearly universal radio ownership has a trivial effect on the probability of a

run for a whole range of values of the signal. The reason for this comes from the signal crossing

property identified in the simultaneous move game by AW. This SCP can be used to show that the

cutoff for early moving agents is basically independent of the fraction of people that own a radio.

Other work has addressed the role of new media focusing mainly on political outcomes like

voting patterns or spending. In a paper similar to this one, Stromberg (2004) studies the role of

radio in changing the allocation of New Deal spending towards areas that are better informed by

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the presence of the radio.10 The effect of media on other more economic forms of behavior have

focused mainly on one aspect, that of financial markets. On the face of it, this is quite promising.

Not only does the media provide up to the minute reports on breaking macroeconomic news, the

price of stocks, and rumors. In addition to providing this “information,” the financial media also

offers “experts” giving advice on stocks to buy and stocks to sell. For example, Tetlock (2007)

found that investor sentiment reflected in a popular column in the Wall Street Journal predicted

future stock returns.

Again the trick is to identify those information flows in a sea of data. Many authors such

as Cutler et al. (1989) have noted the non-existence of major revelations on many days of large

stock price movements. These papers still leave much to be desired by remaining silent on how

information flows. Koudijs (2011a) studies a case from the 18th century where a particular set of

British stocks were traded in both London and Amsterdam. Information regarding these stocks

all originated in Britain but had to make it across the North Sea literally on packet boats to

be incorporated in the price in Amsterdam. This setup allows for clean identification of what

information is being incorporated into the prices in Amsterdam and when that is occurring. More

recently, Hertzberg et al. (2011) showed the role of public information in coordinating the actions

of lenders using plausibly exogenous variation from a change in the availability of a credit registry.

2 Empirics

2.1 Data and Empirical Specification

To examine the relationship between the spread of information and bank failures, I combine data

from the 1930 Census of Population and the FDIC’s report on bank failures between 1920 and

1936 (Federal Deposit Insurance Corporation, 2001).11 The 1930 Censuses of Population and

Manufactures provides penetration rates of the radio Ri across counties measured as a fraction of

households owning the radio as well as a number of control variables discussed below. Figure 1

shows that there is much variation in county-level penetration rates allowing for the possibility of

10There is a burgeoning literature that has shown how mass media can change beliefs through explicit endorsements(DellaVigna and Kaplan, 2007; Enikolopov et al., 2011; Gentzkow, 2006; Gentzkow et al., 2011) or more subtle meanssuch as increasing the salience of particular political candidates (James M. Snyder and Stromberg, 2010). SeeDellaVigna and Gentzkow (2010) for a fine review of this empirical literature.

11David Stromberg graciously shared the 1930 Census data.

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identifying an effect.

The FDIC data provide bank failure rates and declines in deposits across counties. Figure 2

shows that the distribution of (log) changes in deposits is left skewed, unsurprisingly, but that the

left tail is not particularly heavy. For this reason, I choose to not trim tails in my baseline results

though robustness checks suggest that eliminating some of the bigger changes would not materially

change the results. As noted by Richardson (2008), the failure rates must be handled with care as

the FDIC did not attempt to separate out such things as separate versus permanent closures as well

as failed banks that were actually taken over by competitors. Figure 3 shows that an additional

problem with using bank failures as the dependent variable is the mass point at no change. This

makes linear models potentially unattractive. For these reasons, I choose to focus on the decline in

deposits and consider the decline in number of banks as a robustness check.

I estimate the following regression

∆ logDepi = αRadioi +Xiβ + εi

where ∆ logDepi is the log change in deposits between 1930 and 1933 and Xi is a set of controls

that include both state and Federal Reserve district fixed effects. I include both sets of fixed effects

since I do not want to identify the effect of radios off the large variation in bank failures across states

stemming from different bank branching restrictions (Carlson and Mitchener, 2009) nor across Fed

districts stemming from different discount policies (Richardson and Troost, 2009). Note that all

the control variables Xi and the penetration rate Ri are from 1930 while the banking variables are

for subsequent years. I use only 1930 radio data for the basic reason that it is the only year for

which I have this information. Using 1930 data also has the feature of using variables that are

predetermined relative to the bank runs. This lends plausibility to the claim that I am estimating

a causal effect though surely does not establish it. At the same time, clearly, radio penetration

rates will not be constant over this period. Instead the underlying assumption is that relative ranks

of counties in terms of radio penetration rates remain the same over this period. I will consider a

robustness check where I use the rank as the dependent variable rather than the absolute level of

radio penetration rates.

Following Stromberg (2004), I control for a number of variables reflecting local economic condi-

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tions. These include the per capita value of agricultural crops and land, as well as unemployment

and average retail wage.12 I also control for some characteristics of the county including total

population, population density, and two measures of urbanization: (1) an indicator if there are no

urban areas and (2) the fraction of urbanized areas in a county. Standard errors are robust, in

other words clustered at the level of randomization, the county. I do not weight the observations

because I am interested in aggregate outcomes at the county-level rather than per capita or per

bank outcomes though I consider weighting the regressions by the number of deposits in 1930 as a

robustness check later.

2.2 Baseline Results

The basic results for the log change in deposits, ∆ logDepi, are presented in Table 1. As noted

above, my preferred specification in column 1 does not trim tails. It shows that a 10 percentage

point increase in the fraction of families in a county owning a radio leads to a .0523 log points greater

decline in deposits, which is about 5.1 percentage points. This is also statistically significant at

the 1% level. To get a sense of the magnitude of this effect, moving from the 25 percentile to the

75th percentile of the radio penetration distribution would entail an approximately 27 percentage

point increase. Hence, it would imply a roughly .14 log points larger decline in deposits relative

to the mean decline in deposits of .58 log points. This is a fairly sizable effect. At the same time,

if we compare this coefficient relative to another control such as unemployment, I submit that the

effect does not seem too large. In fact, the coefficient on radios is about 1/6 of the coefficient

on unemployment in 1930. Interestingly, the coefficients on the other controls for local economic

conditions are rather insignificant. Columns 2 and 3 show that this result is basically unchanged if

we trim tails of the change in deposits distribution. Column 4 shows that the result is also present

in the unconditional sense after taking out state and Federal Reserve fixed effects.

This attempts to address obvious worry of endogeneity in the basic OLS specific. Stromberg

(2004) suggests using the fraction of area covered by woodlands and ground conductivity measures13

as variables that are correlated with radio penetration rates and, for his case, uncorrelated with

New Deal Spending. Since the initial technology of radios used AM signals, ground conductivity

12To be clear, the “average” wage is, in reality, the per capita amount of total retail wages in a county.13See the original paper by Stromberg (2004) for background on where these variables come from.

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was an important way through which the signals were transmitted. Woodlands and other physical

“impediments” such as mountains would also tend to obstruct the signal. In Table 2, I report

the first stage regression. It is reassuring that many of the other variables have sensible signs

such as higher wages predict higher degrees of radio penetration. Both of Stromberg’s instruments

are statistically significant predictors of radio penetration. The economic effect of woodlands is

quite large with an effect of a one standard deviation shock about double a one standard deviation

shock to ground conductivity. The problem is that the woodlands variable is probably not a valid

instrument even after controlling for, say, urbanization rates. The reason is that woodlands is proxy

for road networks, which potentially affect the ability of people to run. With this potential worry

in mind, Columns 5 of Tables 1 reports the result of an IV regression where I only include ground

conductivity as a valid instrument. The point estimate for the effect of the radio is 5 times larger

and now the other “instrument” of the share of woodlands enters significantly in the second stage.

In results not reported here, I run the IV regression with both instruments. Point estimates are

roughly unchanged with only larger standard errors on the radio coefficient.

2.3 An Accounting Exercise

To get a sense of the magnitude of the effects, I consider a counter-factual where the radio had

never been invented. This exercise makes no assumption about what the source of bank runs are

and should not be interpreted to suggest that radio stations were airing scurrilous stories of panicky

depositors. The results also do not attempt to take into account contagion effects. Calomiris and

Mason (2003b) suggest that contagion effects were quite small. In a regression of hazard rates of

individual banks on fundamentals and aggregate failure rates at the state-level, they find very little

effect from the latter. They are careful to point out that the existence of a correlation would not

necessarily imply contagion but rather just correlated fundamentals. This is the famous reflection

problem noted by Manski (1993) in identifying social effects. That being said, there are cases

suggesting spillovers from runs in one region to another adjacent region. For example,Richardson

and Troost (2009) argue that many of the bank runs in Mississippi in 1931 stemmed from the

collapse of a bank in Tennessee that had no direct connections to the banks in Mississippi.14

14Part of the reason why Calomiris and Mason (2003b) find no contagion effects may be due to simple fact thatthe reference group has not been correctly specified. A state is a fairly large group to use as the relevant on. Whybank failures in one part of a state as large as say California should effect those in another part is rather difficult to

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Taking the baseline OLS effect from Table 1, moving from the average radio penetration rate in

1930 (22%) to no radios would have reduced the decline in deposits by .13 (-.57*.22) log points. With

an average decline in deposits of .59 log points, eliminating the radio would have not eliminated

banking failures, but it would have substantially ameliorated the decline in deposits by a little over

1/5. This of course is the average effect and it is interesting to consider the distributional effects.

So for each county, I calculate the predicted change in deposits if the county had had no radios

∆ logDepNRi = ∆ logDepi − αRadioi

I report in Table 3 the distribution of the decline in deposits ∆ logDepi and ∆ logDepNRi . What

the results show is that approximately counties making up 5% of the total population would have

been spared any declines in deposits if the radio had been invented sometime after the Depression.

Again this counterfactual shows that radio was not at the heart of the bank runs. I do not think

that would have been a reasonable outcome in any case, but it still shows that the radio did play

a key role in deepening the panics.

2.4 Effects For Different Sub-periods

The masterwork of Friedman and Schwartz (1971) argued that the collapse in the banking sector

during the first half of the Great Depression really came from 4 separate banking “panics” in Fall

1930, Spring 1931, Fall 1931, and Winter 1933. FS believed that all of these panics were liquidity

driven rather than related to insolvency and that they were national in scope. The debate since

then has turned around these two central claims. Wicker (1996), while supporting the idea that

the panics were all illiquidity driven, argued that only the panic in Fall 1931 and Winter 1933 were

truly national in scope. Work by Calomiris and Mason (1997) has argued that fundamentals played

a key role in all of the panics. I attempt to examine whether the radio had similar effects across

these different subperiods.

Table 4 reports these results. Unfortunately, because the data are annual, it is impossible to

separate them into 4 panic periods. Instead I lump all of 1930 and 1931 as the first panic and 1933

as the second panic. The first column shows the results for the first period and the second for the

see.

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second panic period. What is quite striking is that the effect of the radio is only for the “first”

panic period with basically a null result for the latter period. A skeptical interpretation of this

result would simply be that as we move further away from 1930, the radio penetration rate from

that year becomes a worse and worse predictor of radio penetration for the year in question. This

leads to a classical error in variables setting where estimates are biased towards 0 as observed in the

results. What gives me pause in this interpretation is the fact that many of the other coefficients

for the controls, which are also from 1930 and presumably affected by attenuation bias, also change.

For example, the agricultural effects actually flip signs. This leads me to believe that the different

results for the two subperiods reflect something about the character of the panics.

2.5 Longer Run Effects

I focus on the 1930 to 1933 period for the simple reason that this is where the vast majority of the

decline in deposits during the Depression is concentrated. Banking panics, more or less, stopped in

March 1933 with FDR’s bank holiday and the “stress tests” imposed by the legislation authorizing

the FDIC. However, the FDIC data run through 1936. So I now consider the “longer run” effects

of the radio through the end of the sample. In Table 5, I show the results for long-run outcomes.

In columns 1 and 2, I examine the effect on the total decline in deposits between 1930 and 1936.

The first column does not trim tails while the second trims the 1% tails. What is evident is that

the effect of radios through 1936 is slightly attenuated but is still strongly negative. Columns 3

and 4 restate this result in a different way by rebasing the initial level of deposits to that in 1933.

Columns 3 and 4 show the results here for the no tail trimming and 1% trimming cases. Now th

effects of banks is approximately nil. Again this should not be surprising given we know the total

effect for 1930 to 1936 is very close to the effect for the 1930 to 1933 period.

The question then is how should we interpret these results. Of course, like the previous results

on different subperiods, it is possible to explain them as the result of attenuation bias. For now,

take them at face value. What they suggest in this case is that whatever the basic source of bank

failures illiquidity or insolvency, reducing information flows during crisis periods can have relatively

long lasting impacts. The logic for why this might be valuable in the case where illiquidity is the

main source of failures is quite obvious. The problem is not the bank but the people coordinating

their actions. Making that more difficult to do through limiting what people know about other

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people’s actions will be beneficial. The question is why should this matter in the case of insolvency.

If a bank is truly insolvent, then limiting what people know about it or what other people are doing

should only delay the inevitable. This might lead to smaller declines in deposits now, but eventually

the information will be revealed and declines in deposits should then increase. This pay back effect

is simply not present in the data. The absence of this phenomenon is suggestive of the elasticity of

the meaning of the word “insolvency” during times of crisis. The other explanation relevant to this

setting is the fact that counties with low levels of radio penetration in effect “bought time” for the

forced recapitalization of many banks under the emergency banking act of 1933. Unfortunately,

taken together, all of this discussion suggests that comparing short versus long term effects will not

be helpful in disentangling the relative importance of illiqudiity versus insolvency.

2.6 Effects across Areas with Different Urbanization Rates

Here I consider how the effects of radio differ depending on the characteristics of the county.

I consider in Table 6 whether the effects of radio were larger or smaller in more or less urban

counties. Columns 1 and 2 show the results for no tail trimming and the 1% tails trimmed. What

the results for both dependent variables show is that the effect of the radio was increasing in the

share of the population living in urban areas. In fact, the baseline effect for rural counties is a very

sizable negative estimate. If the hypothesis was that the radio effectively served to bring news to

areas previously under-served by newspapers, then one would have supposed that this was strongest

in rural areas. This, in turn, would suggest that the effects of the radio for bank runs should be

largest in rural areas. Apparently, this is not the case. Instead the fact that urban areas are more

sensitive to the effects of the radio suggests that what matters is whether people can actually use

the information to coordinate their actions. This may simply not have been the case in rural areas

where transportation was difficult.

2.7 Robustness Checks

Here I consider some robustness checks. Column 1 in Table 7, instead of using robust (or effectively

county-clustered) standard errors, reports the standard errors for state clustered errors. While

some statistical significance is lost, the radio variables still remain significant at conventional levels.

Column 2 runs a weighted regression where I weight counties by the amount of deposits in the county

13

in 1930. The coefficient is very little changed in terms of magnitude or statistical significance. The

third column uses 1929 as a base instead of 1930. Again there are strong effects though mitigated

relative to the baseline specification in terms of magnitude and statistical significance. I conclude

that these three modifications make minor differences to the baseline effects.

The most interesting robustness check is in Column 4 where I control for trends in some of the

economic control variables between 1920 and 1930. Many authors writing about the Depression

argue that it was in some form a “payback” for what happened in the 1920s. FS emphasize the

role of run up in the value of farm land and its effects on bank failure rates. This was in response

to the shocks of the beginning and the end of World War I.15 So while it is important to control for

the current state of a local economy as I do in the baseline regressions, it may also be important

to control for how a particular county got to that level in 1930 over the course of the 1920s. The

econometric worry is that these trends would simultaneously predict banking outcomes during the

Depression and levels of radio penetration at the start of the Depression. Following FS, I focus on

agricultural variables and include trends in the per capita value of crops and farm buildings.16 Even

after controlling for these trends, I still find a very large effect of radios though slightly smaller

than in the baseline specification.

Turning to the trends themselves, both agricultural trends matter, statistically and economi-

cally. Somewhat strangely, they matter in opposite ways. Large run ups in the value of crops during

the 1920s predicts larger declines in deposits while large run ups in the value of farms during this

same period predicts smaller declines in deposits. Without direct evidence on farm mortgage debt,

it is difficult to offer a definitive explanation. One possible story is as follows. In counties that

experience large increases in the value of crops, this leads farmers to leverage up to reap the value

of these high prices. This, however, results in greater banking stress between1930 and 1933 when

agricultural prices collapse. Conversely, when the value of farm buildings increase sharply in a given

county, this, all else equal, tends to reduce the leverage ratio of farmers in that county. This, then,

15In a similar vein, Field (1992) argues that the depressed construction sector was an important reason for theduration of the Depression. He further more goes on to suggest that the slow recovery was due to “uncontrolled”land development in the 1920s which led to, for example, subdivisions were created with little forward thinking. Thisled to a major overhang as subdivisions had to be replotted and zoning regulations changed. Finally, others such asOlney (1990, 1999) emphasize the role of “financial innovation” in the 1920s that gave consumers for the first timethe opportunity to buy durable goods on credit. All of these authors in one way or another point to the role ofoutcomes in the 1920s for explaining outcomes in the 1930s.

16I would have liked to include a trend in unemployment as well, but that data does not appear to exist for 1920.

14

leads to lower levels of bank distress during the banking crisis of the Depression. It is interesting

to note that these somewhat strange results are not driven by a multi-collinearity problem between

these two variables. In fact, the correlation between the change in the value of crops and the change

in the value of farm buildings is a rather minor 0.087.

The final robustness checks are reported in Table 8. Here I redo the baseline regression but

instead use the log change in the number of banks rather than the log change in deposits as

the dependent variable. As noted above, there are reasons to think that this is messier outcome

variable. Reassuringly, signs of the effect of the radio are unchanged while the magnitude of the

effect in a statistical sense is somewhat reduced. That being said, unconditionally, I retain statistical

significance and using the percentile variable for radio also results in a statistically significant effect.

3 Model: Angeletos and Werning (2004)

The question then becomes how do we interpret these results. Does this provide evidence that

many of the bank failures could have been avoided by limiting the flow of information? Would a

policy of that sort be socially beneficial? To do this, I turn to the model of Angeletos and Werning

(2006)17 to allow for heterogeneously informed groups of agents. There is a continuum of agents

where each agent i can choose between two actions, either attack (“run”), ai = 1 or not, ai = 0.

The payoff from not attacking is normalized to 0 and the payoff from attacking is 1− c if the bank

suspends payments and −c otherwise, where c ∈ (0, 1) is the cost of attacking. The status quo

is abandoned if A > θ where A =∫ 10 aidi is the total number of people that attack and θ is the

exogenous fundamental representing the strength of the status quo. The payoff for agent i is then

U(ai, A, θ) = ai(1A>θ − c)

where 1A>θ is an indicator for a regime change.18

The key feature of this setup is the existence of strategic complementarities in the sense that

the payoff to an agent i attacking is increasing in the average action A. From this, going back to

Diamond and Dybvig (1983), when θ is common knowledge, then there exists a range θ > θ > θ

17This in turn was an extension of Morris and Shin (2005, 2002).18I will return to this later in discussing the utility specification, but this setup though more general mirrors that

in Goldstein and Pauzner (2005) who explicitly study bank runs in this global games setting.

15

where both A = 1 and A = 0 are equilibria.19 Following Morris-Shin, rather than assume common

knowledge of θ, information is assumed to be imperfect, asymmetric, and private. At the beginning

of the game, θ is drawn from an improper uniform prior over the real line. All agents then receive

a private signal xi = θ + σxξi where ξi is a standard normal that is independent across agents. In

the original Morris-Shin approach, agents also received a noisy exogenous public signal regarding

the fundamental. Here the term exogenous refers to the information content of the public signal,

which is taken to be determined outside of the model. Part of the goal of the Morris-Shin paper

was to show that in certain cases, increasing the quality of the public signal could decrease welfare.

I depart from that exogenous information structure and follow Angeletos and Werning (2006)

who consider public signals with endogenous amounts of information. Angeletos and Werning

(2006) initially study the case where agents infer information from prices20 In particular, following

Dasgupta (2007), AW and I assume that the signal on A is given by

y = Φ−1(A) + σεε

This setup of observing a transformation of A preserves the linearity of the signal structure without

changing the basic idea of model. As Angeletos and Werning (2006) point out, taken literally this

clashes with the simultaneous move structure of the game, but they show in an extension that it

can be rationalized as the limit of a particular sequential move game discussed in the working paper

version (Angeletos and Werning, 2004). In this extension, which I will consider more extensively

below, only a subset of agents will observe that signal about the average action. The better informed

agents, those possessing the radio in my case, are allowed to condition their behavior on the signal

regarding the average action of those who moved first.21

Turning to the results, I first show that simply thinking about the radio as improving the exoge-

nous component of the quality of public information for everyone cannot rationalize my empirical

19Note that this range combined with some assumption about the distribution of the fundamental θ gives a way tocalculate something like the probability that a run could occur, but the model does not require a bank run to occurin this region.

20Other work such as Amador and Weill (2010) has considered situations where agents attempt to infer informationabout the state of the economy from endogenous objects such as prices.

21A richer setup would incorporate the fact that presumably those who move later, in the case of a run, wouldexperience lower payoffs as a result of an assumption of sequential filling of demands for deposits. This, then, wouldintroduce a tradeoff where those that own the radio could either decide to run to the bank early on the basis of aprivate signal or wait for the public signal on the radio at the expense of potentially being late to arrive at the bankthough more certain of what is occurring.

16

findings. Rather the effect of increasing the quality of the public signal is to increase the probabil-

ity of a run only in the case when fundamentals are good. Whatever can be said about the major

source of the bank runs during the Depression, there is little debate that the fundamentals of the

banking sector were not exceedingly strong. With this in mind, I consider the effects of changing

the number of agents that receive the public signal. This model formulation more closely matches

my regression specification though not perfectly since the probability of a run is not exactly the

same as the size of the decline in deposits, which is my measure.

3.1 The Simultaneous Move Game

This section closely follows AW in deriving the equilibrium outcome. First, equilibrium is defined

as

a(x, y) ∈ argmax E[U(a,A(θ, y), θ)|I]

A(θ, y) = E[a(x, y)|θ, y]

y = Φ−1(A) + σεε

where I denotes the information set of a given agent. For this case, it includes both the private

signal x and the public signal y. AW look for a monotone equilibrium meaning agent i attacks if

and only if xi < x∗(y). Then the status quo is abandoned if θ ≤ θ∗(y) where θ∗(y) is an object to

be determined in equilibrium.

To find the equilibrium, AW proceed in three steps: (1) link the signal regarding A to a public

signal on θ, (2) solve the model assuming a particular exogenous public information structure and

(3) sub in for the link between the informativeness of public and private signal. So in a monotone

equilibrium, the size of the attack will be given by

A(θ, y) = Pr(x < x∗(y)|θ) = Φ(√αx(x∗(y)− θ))

i.e. the fraction of agents who receive a private signal less than x∗(y) given a realized (though

unobserved to the agent) value of θ and the public signal y. Now substituting this expression into

17

the expression for the public signal,

x∗(y)− σxy = θ − σxσεε

where, by definition,√αx = 1

σx. It will be useful to define for later Z(y) = x∗(y) − σxy. This

expression defines a correspondence between the function of public signal Z(y) and z = θ − σxσεε,

an exogenous public signal on the fundamental itself. Also, keep in mind for later that this defines

a negative relationship between θ and z. Note that

σz = σεσx ⇒ αz = αεαx

This shows that the implied quality of the public signal on θ, αz = 1σ2z, is increasing in the quality

of both the private signal αx and the exogenous component of the public signal αε. We will return

to the question of the uniqueness of this correspondence later. For now, assume that observing the

public signal for y, and, hence, Z(y) is equivalent to observing the public signal on θ, z.

Under the assumption of monotone strategies, x∗(y) will solve an indifference relationship where

the expected value of attacking is equal to the cost.

Pr(θ ≤ θ∗(y)|x∗(y), y) = c

The expected value of attacking is equal to probability that the status quo is abandoned, which

happens when θ ≤ θ∗(y). At the threshold x∗(y), then the expected benefits will be equal to the

costs c. In turn, θ∗(y) is defined as the solution to A(θ, y) = θ, which is the level of the fundamental

θ where given a particular public signal y, the attack is just successful.

The expression for the public signal can be rewritten as

θ = Z(y) + σxσεε

Hence, the posterior for θ given x and Z(y) will be normal with mean αxαx+αz

x + αzαx+αz

Z(y) with

18

precision αx + αz.22 Hence,

Pr(θ ≤ θ∗(y)|x, y) = Φ

(√αx + αz

(θ∗(y)− αx

αx + αzx− αz

αx + αzZ(y)

))

So the indifference relationship reads

Φ

(√αx + αz

(θ∗(y)− αx

αx + αzx∗(y)− αz

αx + αzZ(y)

))= c

Now using the definition of θ∗(y), they find

A(θ∗(y), y) = θ∗(y)⇒ Φ (√αx (x∗(y)− θ∗(y))) = θ∗(y)

This can be solved for x∗(y) to find

x∗(y) = θ∗(y) +1√αx

Φ−1 (θ∗(y))

Now subbing this expression into the indifference relationship as well as the definition of Z(y), it

follows that

θ∗(y) = Φ

(√αx

αx + αzΦ−1(1− c) +

αzαz + αx

y

)Given this value for θ∗(y), it follows that

x∗(y) = Φ

(√αx

αx + αzΦ−1(1− c) +

αzαz + αx

y

)+

√1

αx + αzΦ−1(1− c) +

1√αx

αzαz + αx

y

We have used the following fact −Φ−1(c) = Φ−1(1−c). Summing up, given a value of y, it is trivial

to compute the threshold cutoff x∗(y) from the previous expression and in turn to calculate, θ∗(y).

For any value of θ, it is then easy to calculate the size of the attack A(θ, y). Then given the attack

size A(θ, y), it is possible to calculate the probability of a run as a function of θ by integrating out

the random variable y.

22Remember that AW has assumed that the prior for θ is the improper uniform on the real line. So the posteriorsimply equals the likelihood.

19

3.1.1 Non-Fundamental Volatility

Now, this model introduces non-fundamental volatility driven by variation in the public signal

unrelated to the fundamental. The information structure dictates how agents will respond to

noise shocks, ε. AW define non-fundamental volatility in the region of determinacy as ∂θ∂ε where

θ(ε) = θ∗(y(ε)). Now recall that

y = Φ−1(A) + σεε

Parallel to AW, it is easy to check that

∂θ

∂ε=σzσxφ(

Φ−1(θ))

= σεφ(

Φ−1(θ))

It follows that θ satisfies a single crossing property23 with respect to σε. Note that in this setting,

sensitivity (in the SCP sense) to non-fundamental shocks does not depend on the informativeness of

the private shock since θ∗ is independent of σx. Furthermore, for a given value of θ, the sensitivity

is increasing with the quality of exogenous component of the public signal σx.

3.1.2 The Probability of a Run and the Role of the Radio

I can also calculate the probability of a run conditional on a public signal y as

Pr(θ ≤ θ∗(y)|y)

where, as before, θ|y is distributed normal with mean Z(y) and standard deviation 1/√αεαx.

Hence,

Pr(θ ≤ θ∗(y)|y) = Φ(√αεαx(θ∗(y)− Z(y)))

Now it is straightforward to check that

sign

(∂Pr(θ ≤ θ∗(y)|y)

∂αε

)= sign

[1

2

√αεαx

(θ∗(y)− Z(y)) +√αεαx

(∂θ∗

∂αε− ∂Z

∂αε

)]

The behavior of this derivative can be summarized as follows.

23To be more specific, let ε0 be the unique value for which ∂θ∂σε

= 0, then for any ε1, ε2 such that ε1 < ε0 < ε2, then∂|θ(ε2)−θ(ε1)|

∂σε< 0.

20

Proposition 1. In the region of determinacy, if y is large enough, then ∂Pr(θ≤θ∗(y)|y)∂αε

≥ 0.

Proof. See appendix.

This result provides one rationale for interpreting the empirical results. The radio increased

the quality of the public signal and during the Depression when y was high, the radio exacerbated

the problem of bank runs. This echoes the intuition in Dang et al. (2012) where public information

is most dangerous when the situation is most dire. The logic for this is the asymmetry in payoffs.

When an agent knows that many people are already running, this greatly increases the incentive

to run as well. The same incentive does not hold when few people are running, and the strength of

this incentive is increasing in the quality of the public signal, αε. While rationalizing the empirical

results, this approach does not exactly fit with the cross-sectional regressions where I really look for

the effects of changing the number of people who own the radio. To do this, I turn to a sequential

form of the game.

3.2 The Sequential Move Game

AW show how their simultaneous move model can be rationalized as the limit of a particular

sequential move game. Here I study the game when µ < 1. In this game, a fraction µ of agents

move first based on their private signal. Then the remaining fraction of agents 1 − µ observes

besides their private signal, a public signal y on the aggregate action A1 of the early movers.

y = Φ−1(A1) + σεε

This specification brings the model closer to the cross-sectional regressions I have run. So now

early agents can only condition their actions on their private information. As before, an attack is

successful if and only if µA1 + (1− µ)A2 ≥ θ.

I look for a monotone equilibrium like before in the sense that an uninformed agent attacks if

and only if xi < x∗1 and an informed agent attacks xi < x∗2(y). With this in place, as before, I can

first calculate

A1(θ) = Φ(√αx(x∗1 − θ))

21

As before, an observation on y is equivalent to observing z, where

z ≡ x∗1 −1√αxy = θ − σxσεε

which is a public signal on θ with precision αz = αεαx. The aggregate attack of late agents is then

A2(θ, y) = Φ(√αx(x∗2(y)− θ)) and the overall attack is A(θ, y) = µA1(θ) + (1− µ)A2(θ, y).

Parallel to before,

θ∗(y) = µΦ(√αx(x∗1 − θ∗(y))) + (1− µ)Φ(

√αx(x∗2(y)− θ∗(y))) (1)

The threshold for late agents will be similar to the simultaneous move game.

Φ

(√αz + αz

(αx

αx + αzx∗2(y) +

αzαx + αz

Z(y)− θ∗(y)

))= 1− c (2)

At the same time, early agents face a slightly more difficult problem. They have to use their private

signal to not only forecast the fundamental but also to forecast the public signal received by the late

agents.

Now for the early movers, the threshold x∗1 solves Pr(θ ≤ θ∗(y)|x∗1) = c where y is a random

variable with a distribution conditional on x. Now since z and y have the same informational

content when the mapping between the two is unique. We can instead consider integrating out z

with respect to its conditional distribution to find

∫Φ(√αx(x∗1 − θ∗(z))︸︷︷︸

Pr(θ≤θ∗(z)|x∗1,z)

√α1φ(

√α1(x

∗1 − z))︸︷︷︸

Pr(z|x)

dz = 1− c (3)

where α1 = αxαε1+αε

. To reemphasize, we are using the fact that z is distributed normally with mean

θ and standard deviation σxσε.

Following the same notational simplification as above, I will not write the dependence on z

instead of y. Then an equilibrium will be a joint solution for {θ∗(z), x∗1, x∗2(z)} to Equations 1, 2,

3. The system of equations can be reduced by noting that x∗2(z) can easily be computed given

22

x∗1, θ∗(z). From Equation 1,

x∗2(z) = θ∗(z) +1√αx

Φ−1(θ∗(z) +

µ

1− µ(θ∗(z)− Φ(

√αx(x∗1 − θ∗(z)))

)

Then x∗2 can be subbed out in the expression for θ∗(z) to obtain

Γ(θ∗(z), x∗1) = g(z) (4)

where

Γ(θ, x1) = − αz√αxθ + Φ−1

(θ +

µ

1− µ(θ − Φ(

√αx(x1 − θ)))

)and g(z) =

√1 + αz

αxΦ−1(1 − c) − αz√

αxz. So the equilibrium can be reduced to computing the

solution to Equations 4 and 3. An important property of Γ is that it will satisfy a SCP property

with respect to µ. In particular, note that when θ = Φ(√αx(x1 − θ)), then Γ is independent of µ.

Call this value θ.24 Furthermore, if µH > µL, then for θ > θ, Γ(θ, µH) > Γ(θ, µL).

Another important property is that θ∗(·;µ, x1) : R→ (θL(µ), θH(µ)) ⊆ [0, 1] where

θL(µ) +µ

1− µ(θL(µ)− Φ(

√αx(x1 − θL(µ)) = 0

and

θH(µ) +µ

1− µ(θH(µ)− Φ(

√αx(x1 − θH(µ)) = 1

It is easy to check that ∂θL

∂µ > 0, ∂θH

∂µ < 0 and θL(0) = 0, θH(0) = 1.

3.2.1 The Role of µ in the Sequential Move Game

First, let us calculate probability of a run in this setting as

Pr(θ ≤ θ∗(y)|y) = Φ(√αεαx(µΦ(

√αx(x∗1 − θ∗(z))) + (1− µ)Φ(

√αx(x∗2(z)− θ∗(z)))− z)

where I have chosen to write the probability on the RHS in terms of z rather than y. Like before,

from SCP, it is easy to check that like before,

24This is a strengthening of the usual SCP since this θ holds for all µ and not just pairs of µ.

23

Proposition 2. If y is large, then ∂Pr(θ≤θ∗(y)|y)∂µ < 0.

This result is actually even more straightforward than the previous one for the simultaneous

move game since µ does not enter probability directly but only through θ∗(y). This is unlike the

quality of the public signal which not only effects the cutoff but also the distribution of the public

signal. The intuition for this result is not particularly deep. It simply says that when the signal on

θ is bad (y is large), then if more people hear that signal, then there will be a greater chance of a

bank run.

What is more interesting is that even if the comparative statics are correct, the quantitative

magnitude of large changes in µ seems rather minor. Consider Figure 4, which shows the effect of

changing µ from .02 to .98. As is quite transparent, moving from very few people (µ high) having

the radio to almost ubiquitous radio ownership (µ low) has very small effects on the probability

on the order of a few percentage points in either direction. This does not seem promising as a

quantitative explanation for the empirical results. This issue is not essentially related to the choice

of the other parameters c, αx, αε.

The (rough) reason for this comes from the SCP property of Γ with respect to µ. Consider

taking a first order Taylor approximation to θ∗ in terms of z about z such that θ∗(z) = θ.25 Then

∂θ∗

∂z is implicitly defined as

− αz√αx

∂θ∗

∂z+

1

φ(θ)

(∂θ∗

∂z+

µ

1− µ

[∂θ∗

∂z+ φ(√αx(x1 − θ))

√αx∂θ∗

∂z

])= − αz√

αx

which implies that

∂θ∗

∂z=

1

1−√αx

(1−µ)αzφ(θ)(1 + µ

√αxφ(

√αx(x1 − θ))

≡ γ(µ)

Now consider

∫(Φ(√αx(x1 − θ(z;µH , x1))− Φ(

√αx(x1 − θ(z;µL, x1)))

√α1φ(

√α1(x1 − z))dz

Then taking a first order Taylor approximation to Φ(√αx(x1 − θ(z;µ, x1)) about z, we have two

25This z is implicitly defined as g(z) = − αz√αxθ + Φ−1(θ) where I have defined the value for θ above.

24

parts to consider. First,

∫z∈(zL(µH),zH(µH))

1√αxφ(

√αx(θ − x1)

(γ(µH)− γ(µL))(z − z)φ(√α1(x1 − z))dz

and, second,

∫z /∈(zL(µH),zH(µH))

(Φ(√αx(x1 − θ(z;µH , x1))− Φ(

√αx(x1 − θ(z;µL, x1)))

√α1φ(

√α1(x1 − z))dz

where zH(µH) solves θ∗(zH , µL) = θH(µH) and zL(µH) solves θ∗(zL, µL) = θL(µH). The first

integral is then equal to 0 when z = x1 and zH(µH) − z = z − zL(µH). Roughly speaking in this

region, because of the SCP, the differences between θ∗(z;µH) and θ∗(z;µL) cancel out. For the

second integral, note that the difference between Φ(√αx(x1−θ(z;µH , x1))−Φ(

√αx(x1−θ(z;µL, x1))

can always be bounded by 1. So that the second integral can be bounded by the probability that

z /∈ (zL(µH), zH(µH)). These are tail events so with the thin tails assumption of the normal,

this probability will be quite small. Taken altogether, this implies that the integral defining x∗1

is basically unrelated to µ since it only matters through the dependence of θ∗ on µ. Then given

this, the effect of changes in µ on the probability of a run will be negligible since, in effect, we can

redefine the fundamental by subtracting off the fixed size of the attack of the early movers.

3.3 A Side Note on the Welfare Implications of the Radio

I have demonstrated conditions under which more radios increases the probability of a bank run.

The question is whether this decreases social welfare. In this setting, there are, of course, the

possibility of “efficient” bank runs in the case when θ is very small in the sense that from a social

perspective the benefits to suspending deposits outweigh the (direct) costs to attacking c. At the

same time, the possibility of “inefficient” runs driven by noise shocks are also possible and more

likely in the case when many people here the common public signal.

This is tradeoff between inefficient and efficient bank run is at the heart of why public infor-

mation may be bad in MS. Intuitively, the condition in that slightly different setting states that if

the public is already well informed through their private signal, then additional public information

is deleterious as agents will tend to disregard their better private information in order to make

25

sure they coordinate their actions with other agents. This increases non-fundamental volatility i.e.

volatility driven by noise in the public signal on θ. In the language of econometrics, increasing the

informativeness of the public signal increases the accuracy of the “estimator,” the aggregate action

of the population, while also decreasing the precision of this action, more volatility. Depending on

how these desiderata are weighted, increases in precision may not compensate for losses in accuracy.

So how should public information be evaluated from a social perspective in this case? As AW

point out, this depends crucially on how u(0, A, θ) is defined. For their positive results, it was

sufficient to normalize it to 0. What is important for the complementarities in actions was that

U(1, A, θ) − U(0, A, θ) was increasing in A. This is trivial satisfied since U(1, A, θ) is (weakly)

increasing in A and U(0, A, θ) is independent of A. Yet in this setup, we know that the welfare

effects cannot be large because changes in µ have trivial effects on the probability of a run. STill

this remains an important question for future more quantitatively successful versions of the model.

4 Conclusion

As noted by Holmstrom (2012). there are many instances in the history of economic crises where

opacity has been intentionally increased. During the Scandinavian banking crisis of 1991 and

1992, toxic assets were placed in bigger capitalized banks thereby obscuring the overall quality

of individual banks. Gorton (1985) discusses how clearinghouses before the existence of Federal

Reserve often united banks in times of crisis as a way to obscure the quality of individual banks.

This paper has highlighted one innovation that served to free up the flow of information: the radio.

My results suggest that this freer flow of information did not help stabilize the banking system but

rather exacerbated the panics of the Great Depression.

The results are quite striking with a 10 percentage point increase in radio penetration rates

leading to an approximately 5 percentage point greater decline in deposits. Putting it in a different

perspective, eliminating the radio would have mitigated the fall in deposits by 1/5 of the total

decline between 1930 and 1933. I then build a model that stresses the effects on the behavior of the

part of the population that does not have access to this public information. In equilibrium, this

group of agents become even more sensitive to “fundamentals” than the informed agents. Not only

do they try to infer the fundamental from their private signal but they also try to infer the public

26

signal and how the informed agents will respond to it. This is more so the case when fundamentals

are bad.

In terms of future research, a useful extension would be to more carefully trace out the infor-

mational flows between counties. So far the work has not specified very carefully how the radio

matters. I hinted at one possibility where the radio broadcasts information on bank failures in

neighboring counties, and this is what leads people to run. With higher frequency data, it would

be possible to trace out these panics in real time. Still these geographic links could be explored by

examining how the spatial correlation varies with the degree of radio penetration. This analysis

would extend that of Calomiris and Mason (2003b) who also looked at effects of state failure rates

on individual banks.26

A second avenue for future research would exploit the fact that radio is such a strong predictor

of banking outcomes. This suggests that it would provide an excellent instrument for estimating the

relationship between economic outcomes and bank failures during this time period. The difficulty

is always in identifying which direction causality flows. Cole and Ohanian (2004) report that there

is no correlation at the state-level between number of bank failures and subsequent changes in

income. However, subsequent work by Calomiris and Mason (2003a) using instrumental variables

found large negative effects of bank failures.27 The question with that paper is the validity of

using lagged values of banking variables for instruments. A county-level analysis of the relationship

between economic activity and banking outcomes with the use of radio penetration rates as an

instrument would potentially provide a more convincing result on the relationship between the

two.

Information flows are seemingly at the heart of financial decisions and even more so in times of

crisis. Identifying this link has proven difficult with so much information all around us. The slower

times of the not so distant past provide a rich set of discrete jumps in communication technology,

and those jumps provide a useful lens through which to study this most central question in finance.

26In some preliminary regressions, I find that state-level bank failure rates are strong predictors of county-levelfailure rates, but that the correlation with state-level rates is no greater in counties with higher radio penetrationrates. This may simply be due to the fact that the state is not a particularly good “reference group” for a particularcounty.

27Ziebarth (2013) considers a particular natural experiment and, too, finds large negative effects.

27

5 Appendix: Omitted Proofs from the Text

5.1 Indeterminacy in the Simultaneous Move Game

Whether or not there exist multiple equilibria depends on whether the mapping between y and z

is one to one. As AW show, this question is equivalent to studying the mapping F (y) = z where

F (y) = Φ

(αz

αz + αxy + q

)+

1√αx

(− αxαx + αz

y + q

)

with q =√

αxαx+αz

Φ−1(1 − c). This comes from substituting out for x∗ in terms of θ∗. It is clear

that F (y) is continuous in y and F (y)→ −∞ as y →∞ and F (y)→∞ as y → −∞. Hence, there

must exist a solution and, therefore, an equilibrium. Differentiating the function, AW show that

sign(F ′(y)) = −sign

(1− αz√

αxφ

(αz

αx + αzy − q

))

Now the maximum value that φ can take on is√

2π. So if αz√αx≤√

2π, then F is strictly decreasing

and, hence, the solution of F (y) = z is unique. If this condition fails, then there exists an interval

(z, z) where there are multiple solutions and, therefore, multiple equilibria depending on the selec-

tion rule. It is important to emphasize that the size of the attack will still be uniquely defined. It

is only in terms of what agents infer from the signal about the fundamental that is undetermined.

5.2 Proof for the sign of ∂Pr(θ≤θ∗(y)|y)∂αε

First, it is easy to check that

∂Z

∂αε=∂x∗

∂αε=∂θ∗

∂αε+∂Φ−1(θ∗(y))

∂αε

and

θ∗(y)− Z(y) =y√αx− 1√αx

Φ−1(θ∗(y))

So it remains to check the sign of

1

2αε[y − Φ−1(θ∗(y))]−

√αxαε

∂Φ−1(θ∗(y))

∂αε

28

Note two more facts

y − Φ−1(θ∗(y)) =1

1 + αεy −

√1

1 + αεΦ−1(1− c)

and

∂Φ−1(θ∗(y))

∂αε=

1

2√αε + 1

Φ−1(1− c) +1

(1 + αε)2y

Putting everything together,

1

2

√1

αε

(1

1 + αεy −

√1

1 + αεΦ−1(1− c)

)−√αεαx

[1

2√

1 + αεΦ−1(1− c) +

1

(1 + αε)2

]

Then collecting like terms, I have

−1

2Φ−1(1− c)

[1

2

√1

αε(1 + αε)+

√αεαx

1 + αε

]+ y

[1

2√αε(1 + αε)

−√αεαx

(1 + αε)2

]

It is easy to see that if c ≥ .5, then the constant terms is weakly larger than 0 since Φ−1(1−c) ≤ 0.

Now consider the term multiplying y, the bound on αε, αx for determinacy implies that

−√αεαx ≥

1√αε2π

Hence,

1

2√αε(1 + αε)

−√αεαx

(1 + αε)2≥ 0⇔ αε ≥

2√2π− 1

But 2√2π− 1 < 0 and αε > 0 by definition. Since that term is positive, for y large enough, the

second term will be greater than the first term in absolute value. The result is established.

29

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32

Figure 1: Histogram of fraction of households that own a radio within a county.

33

Figure 2: Kernel density of log change in deposits between 1930 and 1933 within a county.

34

Figure 3: Kernel density of log change in number of banks operating between 1930 and 1933 withina county.

35

Figure 4: Effects of changing µ on the probability of a bank run as a function of z. For both lines,c = .2, αX = .2, αε = .2.

36

(1) (2) (3) (4) (5) (6)Log Change in Deposits from 1930 to 1933

% Radio -0.523∗∗∗ -0.486∗∗∗ -0.509∗∗∗ -0.815∗∗∗ -2.495∗∗∗

(0.184) (0.163) (0.170) (0.0659) (0.963)Radio Percentile -0.252∗∗∗

(0.0951)

% Woodland -0.242 -0.317 -0.314 -0.132(0.266) (0.212) (0.234) (0.249)

Crop value -0.0243 -0.0193 -0.0242 -0.0539∗∗ -0.0226(0.0172) (0.0140) (0.0155) (0.0221) (0.0170)

Farm value 0.0320 0.0163 0.0260 0.137∗∗ 0.0131(0.0241) (0.0213) (0.0227) (0.0548) (0.0246)

Unemployment -3.168∗ -4.655∗∗∗ -3.753∗∗ -3.144 -3.424∗

(1.897) (1.662) (1.751) (1.972) (1.848)

Retail Wage -0.113 -0.0671 -0.124 0.102 -0.0789(0.0989) (0.0810) (0.0925) (0.150) (0.0903)

Rural dummy -0.0495 -0.0412 -0.0430 0.000907 -0.0592∗

(0.0332) (0.0285) (0.0308) (0.0404) (0.0317)

Population -0.00973 -0.0120 -0.0173 -0.0257 -0.00744(0.0215) (0.0192) (0.0202) (0.0234) (0.0211)

Population density 0.0355∗ 0.0257 0.0331∗ 0.114∗∗∗ 0.0156(0.0211) (0.0182) (0.0191) (0.0425) (0.0206)

% urban 0.141 0.183∗∗ 0.159∗∗ 0.329∗∗∗ 0.142∗

(0.0863) (0.0751) (0.0790) (0.127) (0.0841)

% black 0.119 0.00730 0.0474 -0.0118 0.137(0.114) (0.0778) (0.0885) (0.132) (0.105)

Observations 2613 2558 2586 2807 2610 2798R2 0.193 0.231 0.219 0.051 0.161 0.188Trim 0 1% 2 % 0 0 0

Standard errors in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Table 1: Effect of radio on log change in deposits between 1930 and 1933. Standard errors arerobust and all regressions include state and Federal Reserve district fixed effects. Farm variablesand radio penetration rate are from the 1930 Census of Population while the retail wage variableis from the 1930 Census of Retail. Variables are logged where appropriate.

37

(1)% Radio

Conductivity 0.00219∗∗∗

(0.000236)

% Woodland -0.301∗∗∗

(0.0261)

Crop Value -0.0227∗∗∗

(0.00246)

Farm Value 0.0638∗∗∗

(0.00379)

Unemployment 0.128(0.251)

Wage 0.112∗∗∗

(0.0116)

Rural dummy 0.0276∗∗∗

(0.00372)

Population -0.00854∗∗∗

(0.00306)

Population density 0.0414∗∗∗

(0.00279)

% urban 0.129∗∗∗

(0.0119)

% black -0.0578∗∗∗

(0.00762)

Observations 2820R2 0.897


Table 2: First stage of Stromberg IV regressions with share of woodlands and ground conductivity.Standard errors are robust and state fixed effects are included in this regression. Farm variables andradio penetration rate are from the 1930 Census of Population while the manufacturing variable isfrom the 1929 Census of Manufactures.

38

∆ logDepi ∆ logDepNRi1% -2.36 -2.245% -1.54 -1.4010% -1.22 -1.1225% -0.81 -0.7050% -0.48 -0.3875% -0.27 -0.1790% -0.11 -0.0295% 0.01 0.0899% 0.49 0.52

Table 3: Distribution of actual declines in deposits versus decline net of effects of the radio.

39

(1) (2)Log change in deposits for “FS 1” Log change in deposits for “FS 2”

% Radio -0.323∗∗∗ -0.0338(0.105) (0.133)

share woodland -0.174 -0.0172(0.177) (0.172)

Crop value -0.0580∗∗∗ 0.0598∗∗∗

(0.0121) (0.0124)

Farm value 0.0439∗∗∗ -0.0464∗∗∗

(0.0141) (0.0172)

Unemployment -2.339∗∗ 0.665(0.995) (1.359)

Retail Wage -0.223∗∗∗ 0.0410(0.0496) (0.0613)

Rural dummy -0.00978 -0.00925(0.0208) (0.0248)

Population -0.0280∗∗ 0.00502(0.0125) (0.0158)

Population density 0.0266∗∗ -0.0149(0.0125) (0.0144)

% urban 0.0913∗ 0.0171(0.0486) (0.0647)

% black -0.0296 0.115(0.0653) (0.0844)

Observations 2690 2612R2 0.101 0.196


Table 4: Comparing the effects during the “first” and “second” banking crises. Standard errorsare robust and all regressions include state fixed effects. Farm variables and radio penetration rateare from the 1930 Census of Population while the retail wage variable is from the 1930 Census ofRetail.

40

(1) (2) (3) (4)Log change in deposits between...

1930 and 1936 1933 and 1936

% Radio -0.522∗∗∗ -0.359∗∗∗ 0.0443 0.0882(0.154) (0.135) (0.129) (0.109)

% woodland -0.216 -0.100 0.0190 0.120(0.274) (0.178) (0.224) (0.130)

Crop value 0.00745 0.0182 0.0330∗∗ 0.0340∗∗∗

(0.0161) (0.0136) (0.0135) (0.0114)

Farm value -0.00883 -0.0264 -0.0476∗∗∗ -0.0433∗∗∗

(0.0212) (0.0181) (0.0173) (0.0155)

Unemployment -4.257∗∗∗ -3.815∗∗∗ -0.774 0.459(1.600) (1.369) (1.281) (1.116)

Retail Wage 0.0307 -0.00455 0.0758 0.157∗∗∗

(0.0911) (0.0622) (0.0669) (0.0517)

Rural dummy -0.000697 0.00403 0.0465∗∗ 0.0516∗∗∗

(0.0273) (0.0225) (0.0223) (0.0186)

Population 0.0263 0.0290∗ 0.0192 0.0293∗∗

(0.0196) (0.0163) (0.0165) (0.0129)

Population density 0.0113 -0.00465 -0.0198 -0.0239∗

(0.0186) (0.0160) (0.0155) (0.0127)

% urban 0.158∗∗ 0.186∗∗∗ 0.0211 -0.0268(0.0685) (0.0583) (0.0603) (0.0498)

% black 0.197∗∗ 0.170∗∗ 0.120 0.147∗∗∗

(0.0991) (0.0688) (0.0781) (0.0524)

Observations 2644 2593 2595 2544R2 0.225 0.268 0.192 0.236


Table 5: Long-run effects. Standard errors are robust and all regressions include state and FederalReserve district fixed effects. Farm variables and radio penetration rate are from the 1930 Censusof Population while the retail wage variable is from the 1930 Census of Retail.

41

(1) (2)Log change in deposits between 1930 and 1933

% Radio -0.698∗∗∗ -0.683∗∗∗

(0.196) (0.188)

Interact - % Urban and % Radio 0.854∗∗∗ 0.608∗∗

(0.309) (0.296)

% Woodland -0.280 -0.236(0.267) (0.262)

Crop value -0.0255 -0.0271(0.0175) (0.0171)

Farm value 0.0416∗ 0.0362(0.0248) (0.0241)

Unemployment -2.706 -3.082∗

(1.894) (1.867)

Retail Wage -0.104 -0.0895(0.0985) (0.0984)

Rural dummy -0.0777∗∗ -0.0883∗∗∗

(0.0345) (0.0334)

Population -0.0129 -0.0200(0.0216) (0.0210)

Population density 0.0303 0.0360∗

(0.0212) (0.0206)

% urban -0.116 -0.0728(0.131) (0.127)

% black 0.116 0.0835(0.114) (0.114)

Observations 2613 2559R2 0.195 0.190


Table 6: Effect across fraction of urbanized population. Standard errors are robust and all regres-sions include state and Federal Reserve district fixed effects. Farm variables and radio penetrationrate are from the 1930 Census of Population while the retail wage variable is from the 1930 Censusof Retail.

42

(1) (2) (3) (4)Log Change in Deposits

% Radio -0.523∗∗ -0.437∗ -0.351∗ -0.393∗∗

(0.231) (0.263) (0.185) (0.187)% woodland -0.242 0.339 -0.143 -0.409

(0.336) (0.357) (0.280) (0.275)

Crop value -0.0243 -0.00213 -0.0456∗∗∗ 0.0323(0.0174) (0.0341) (0.0174) (0.0203)

Farm value 0.0320 0.0270 0.0416∗ -0.0421(0.0242) (0.0357) (0.0247) (0.0296)

Unemployment -3.168∗ -7.040∗∗ -4.572∗∗ -3.979∗∗

(1.887) (3.277) (2.017) (1.934)

Retail Wage -0.113 -0.534∗∗∗ -0.206∗∗ -0.0903(0.0791) (0.186) (0.0932) (0.101)

Rural dummy -0.0495 -0.117∗∗∗ -0.0356 -0.0418(0.0342) (0.0427) (0.0334) (0.0335)

Population -0.00973 0.0469∗∗ -0.000762 -0.0118(0.0227) (0.0210) (0.0225) (0.0217)

Population dense 0.0355 0.0603∗∗∗ 0.0175 0.0215(0.0298) (0.0203) (0.0213) (0.0221)

% urban 0.141 0.200 0.294∗∗∗ 0.156∗

(0.0939) (0.125) (0.0889) (0.0866)

Change in Crop Value from 1920 to 1930 -0.0910∗∗∗

(0.0260)

Change in Farm Value from 1920 to 1930 0.0906∗∗∗

(0.0319)

Observations 2613 2613 2615 2595R2 0.193 0.431 0.214 0.198Note State-level clustered SEs Deposit Weighted Start 1929 Include pre-trends


Table 7: Some robustness checks. Specification 1 clusters standard errors at the state-level, therest are robust. The second weights observations by amount of deposits in 1930. Specification 3considers the change starting in 1929. Finally, specification 4 includes trends from 1920 to 1930 incrop values, and farm building values. The regressions include the controls from before with thoseestimates not reported for the sake of clarity.

43

(1) (2) (3) (4) (5) (6) (7)Log Change Banks between 1930 and 1933

% Radio -0.130 -0.124 -0.115 -0.673∗∗∗ -1.724∗∗

(0.138) (0.127) (0.121) (0.0504) (0.737)

Radio Percentile -0.138∗

(0.0742)

% Woodland -0.0868 -0.0986 -0.150 -0.0425 -0.522∗∗ -0.130(0.167) (0.157) (0.142) (0.154) (0.261) (0.168)

Crop value -0.0309∗∗∗ -0.0332∗∗∗ -0.0343∗∗∗ -0.0294∗∗∗ -0.0539∗∗∗ -0.0332∗∗∗

(0.0109) (0.0103) (0.00991) (0.0105) (0.0156) (0.0110)

Farm value -0.00532 -0.00967 -0.00261 -0.0171 0.0784∗ 0.00343(0.0174) (0.0159) (0.0153) (0.0151) (0.0419) (0.0182)

Unemployment -3.072∗∗ -3.156∗∗∗ -3.613∗∗∗ -3.174∗∗∗ -3.018∗∗ -2.946∗∗

(1.287) (1.211) (1.174) (1.228) (1.367) (1.293)

Retail wage 0.0226 0.0203 0.0406 -0.00455 0.196∗∗ 0.0391(0.0581) (0.0547) (0.0515) (0.0531) (0.0989) (0.0584)

Rural dummy -0.00622 -0.0306 -0.0230 -0.0285 0.0347 -0.00532(0.0248) (0.0215) (0.0201) (0.0221) (0.0311) (0.0247)

Population -0.0483∗∗∗ -0.0541∗∗∗ -0.0681∗∗∗ -0.0576∗∗∗ -0.0608∗∗∗ -0.0495∗∗∗

(0.0164) (0.0155) (0.0146) (0.0155) (0.0179) (0.0164)

Population density -0.0169 -0.0117 0.00137 -0.0113 0.0456 -0.0122(0.0153) (0.0142) (0.0134) (0.0134) (0.0320) (0.0153)

% urban 0.0396 -0.00697 0.00949 -0.0217 0.193∗∗ 0.0524(0.0635) (0.0563) (0.0531) (0.0556) (0.0982) (0.0640)

% black 0.0410 0.0112 0.0372 0.0345 -0.0639 0.0264(0.0677) (0.0630) (0.0575) (0.0654) (0.0836) (0.0682)

Observations 2618 2564 2507 2591 2812 2615 2618R2 0.230 0.227 0.235 0.221 0.062 0.193 0.231


Table 8: Effect of radio on log change in number of banks. Standard errors are robust and allregressions include state fixed effects. Farm variables and radio penetration rate are from the 1930Census of Population while the manufacturing variable is from the 1929 Census of Manufactures.Variables are logged where appropriate.

44

Documents

The Radio and Bank Runs in the Great Depression