Working Paper Series 

Sources of Historical Banking Panics: 

A Markov Switching Approach 

Kathleen M. McDill, 

Kevin P. Sheehan 

Working Paper 2006–01 

FEDERAL DEPOSIT INSURANCE CORPORATION 
Sources of Historical Banking Panics: A 

Markov Switching Approach 

Kathleen M. McDill 

Senior Financial Economist 

Federal Deposit Insurance Corporation 

Division of Insurance and Research 

550 17th Street, NW 

Washington, DC 20420 

 Phone: 202-898-3705 

E-mail: kmcdill@fdic.gov 

Kevin P. Sheehan 

Vice President 

State Street Corporation 

Enterprise Risk Management 

225 Franklin Street 

Boston, MA 02110 

Phone: 617-664-0658 

E-mail: ksheehan@statestreet.com 

November 2006 

Working Paper No. 2006-01 

The views expressed in this working paper are those of the authors and not necessarily 

those of the Federal Deposit Insurance Corporation or State Street Corporation. 
Abstract 

Around the turn of the previous century banking panics in the U.S. happened fairly 

frequently. Before the creation of the Federal Reserve, major financial crises occurred in 

the United States in 1873, 1884, 1890, 1893, and 1907. Using a Markov-switching 

model (MSM) and weekly data between 1890 and 1909, we examine periods of panic and 

periods of relative calm and objectively date the onset and conclusion of the banking 

panics. The MSM also has imbedded within it a mechanism that allows us to examine 

the economic circumstances that might have precipitated a banking panic. This feature 

allows us to compare empirically several different hypotheses about what triggers a 

banking panic. 

2 
The underlying causes of banking panics are still very much up for debate. 

Widespread banking panics or even runs on a single bank are a rarity in the modern 

financial environment of the United States. The extent to which the modern financial 

environment (with regulation, deposit insurance, and a flexible money supply) is the 

cause of this stability, the aspects that are required for stability, and the question of 

whether the additional costs and agency problems are worth the additional stability are 

still hotly contested by academics and regulators. The primary goal of this paper is to 

examine the triggers of banking panics and compare competing hypotheses about the 

underlying causes of banking panics in the National Banking Era (1863–1913). 

Although banking panics are now rare in the United States, they were 

considerably more common around the turn of the previous century. During the National 

Banking era (before the creation of the Federal Reserve System), major banking panics 

occurred in the United States in 1873, 1884, 1890, 1893, and 1907. 

There is an ongoing controversy in the literature about the causes of these banking 

panics. The participants generally fall into two camps: those who see these panics as 

essentially a problem of illiquidity and those who base their explanations on insolvency. 

The earliest papers that looked at these crises were written by those who were 

alive at the time of the panics, and were largely descriptive in nature. Most 

contemporaries of the banking panics saw these panics as liquidity-driven events 

associated with an unusual spike in domestic demand for cash or international demand 

for gold. These changes in the demand for money were met with a “perverse elasticity,” 

as money left the banking system and there was essentially no ability to change the 

monetary base. These theories of banking panics as largely based on illiquidity led to the 

foundation of the Federal Reserve System. 

3 
A more recent set of papers and models view banking panics fundamentally as a 

function of bank insolvency. These papers argue that changes in the business cycle (or 

some other signal of a change in expected return) induced depositors to update their 

expectations of the banks’ abilities to repay them, and these revised expectations led 

depositors to withdraw their funds from all banks because of asymmetric information 

about which particular banks were holding questionable assets. 

Each theoretical approach has found backing in econometric studies. Empirical 

papers have generally used the dates of panics from studies produced for the National 

Monetary Commission—such studies, for example, as Sprague (1910) and Kemmerer 

(1910). However, these authors, and thus the subsequent authors that refer to them, differ 

on the events that constituted banking panics and on the dates that represent the 

beginnings and ends of the panics. These differences in what is considered a panic and in 

the relevant dates may partly explain the differences in conclusions. In addition, the 

econometric papers often use data that are in monthly or quarterly frequencies, and such 

data would be likely to emphasize the differences in the behavior of variables during 

panics rather than catching what is associated with the onset of a panic—that is, the 

trigger. 

To overcome these problems of dating panics and observing the triggers of 

panics, we are proposing a new approach to both dating the panics and examining the 

variables that are associated with going into (and out of) a banking panic. The Markov 

Switching Model uses the data themselves to determine the starting and ending points of 

banking panics. The Markov Switching Model also has the advantage that it is possible 

to parameterize the probability of transitioning into (and out of) a banking panic and to 

see what variables have actually been associated with triggering banking panics. 

4 
We use the Markov Switching Model method and weekly interest-rate data from 

the callable loan market to identify panic periods. The dates we find for panics are 

consistent with, but not exactly the same as, those from the more subjective dating 

methods used by other authors. The high frequency of our data allows us a great deal of 

precision in our dates for panic periods. In addition, we are able to use the estimation of 

the probabilities of transitioning into and out of a panic period to test a variety of 

potential triggers for banking panics. We derive the list of potential triggers from both 

sides of the illiquidity vs. insolvency debate mentioned above. We find the greatest 

amount of support for the traditional view of banking panics as driven by liquidity issues. 

Literature 

There are a number of theoretical models of what might cause a financial panic. 

With banks holding a fractional reserve, a loss of confidence in the banks’ ability to repay 

deposits can cause a run on deposits. A number of theoretical models have been put 

forward suggesting what might cause such a loss in confidence. 

As noted above, the basic views fall into two camps: an illiquidity-driven panic 

vs. an insolvency-driven panic. The first group focuses on the nature of banks with longterm assets and short-term liabilities, à la Diamond and Dybvig (1983). This perspective 

on banks is that banks are held together by the common self-fulfilling expectation that 

deposits will be repaid. If something changes the expectations of repayment, then 

depositors run the fractional reserve bank or banking system, which is also a selffulfilling equilibrium (see also Chari and Jagannathan, 1988). Other work, such as 

Bhattacharya and Gale (1987), has focused on what kinds of triggers or signals might 

cause expectations to change and thus cause a run on a bank. 

Kemmerer (1910), who was contemporaneous with the National Banking Era, 

notes that crises were more likely to occur during periods when the liquidity of the 

5 
fractional reserve system was already under strain, usually during the planting and 

harvesting seasons, when non-money-center banks withdrew their deposits. Miron 

(1986) documents the view that crises were much more common in the autumn, when 

demands for currency were high because of agricultural activity. Interest rates and 

reserve ratios also showed a clear pattern associated with the agricultural seasons. 

Eichengreen (1984) formalizes this observation with a model of checking and currency 

deposits, with the feature that money flowed to low-check-use areas of the country during 

the periods of the year when demand for money was highest in order to move crops. 

Thus the money supply fell when the demand for money was highest, exhibiting a 

“perverse elasticity.” 

During the National Banking Era (1863–1913), although banking panics were 

common in the United States, Canada and Great Britain did not have systemwide bank 

panics. By comparing the experience of the Canadian and U.S. banking systems in the 

late nineteenth and early twentieth centuries, both Williamson (1989) and Bordo, Redish, 

and Rockoff (1996) suggest that the branch banking system of Canada was more 

diversified and better able to weather adverse economic shocks. In the same vein, Chari 

(1989) extends the Diamond and Dybvig (1983) model to include community risk, where 

the proportion of impatient people varies by community. For a banking system without 

branching, the community risk is also the banks’ risk, and overcoming this risk requires 

interbank lending and verifiable reserves. However, Champ, Smith, and Williamson 

(1996) point out that in contrast to the U.S. system, where large withdrawals of gold and 

other base money were required to satisfy an increased currency demand during harvest 

seasons, Canadian banks also had more flexibility to issue additional banknotes when 

currency demand was high, and thus were not forced to contract in order to satisfy an 

increased demand for currency. 

6 
Jevons (1884) blames banking panics on unexpected events in conjunction with 

seasonal liquidity problems, which combine to undermine the depositors’ confidence in 

the system and leads to runs and the cascade of events. Sprague (1910), Freidman and 

Schwartz (1963), and Tallman and Moen (1998) emphasize an international component 

to banking panics, including gold outflows or increases in the Bank of England discount 

rate. Inability to offset the fall in bank reserves by increasing the money supply 

exacerbated the contractions and set off crises. Sprague (1910) and Dewald (1972) focus 

on the response of the New York money-center banks when faced with unusually high 

demands for cash given their inflexible and conservative reserve ratios of 25 percent 

minimum set by the clearinghouse association. They hold that it was this inflexibility 

that led to the crises. 

The strand of literature that focuses on insolvency as leading to panics generally 

concentrates on when in the business cycle the panics occur (Gorton, 1988; Calomiris and 

Gorton, 1991; Kindleberger, 1978). These authors note that crises tend to occur near the 

peak of a business cycle, and suggest that changes in the expected profitability of firms 

lead to either a contraction in lending or a banking/financial crisis or both. In the model 

by Calomiris and Gorton (1991), the source of panics is based on information asymmetry 

in the bank-depositor relationship. As the economy heads into recession, depositors 

notice that business profits are declining and may expect banks that lent heavily to 

troubled businesses to fail. To avoid potential losses, depositors withdraw their funds if 

they expect their bank to fail. However, depositors cannot easily observe the true 

liquidation value of bank assets because bank loans are not traded in secondary markets. 

With asset values uncertain, depositors cannot differentiate good banks from bad banks; 

as a result, depositors then run all banks since they are uncertain about the likelihood that 

their own bank(s) will fail. The bank panic forces a suspension of convertibility so that 

7 
 

the solvency of individual banks can be assessed. The clearinghouse has a pivotal role in 

establishing the credibility of the workout of insolvent banks. According to these 

models, the likelihood of a panic should increase as the macroeconomy is moving into a 

recession. 

A common feature of empirical papers on banking panics in this period is that 

they use information on panics derived from papers produced for the National Monetary 

Commission or another subjective dating system.1

 Sprague (1910) mentions panics that 

occurred in 1873, 1884, 1890, 1893, and 1907. Kemmerer (1910) finds 21 minor panics 

or “panicky periods” between 1876 and 1908.2 The subjective system of enumerating 

these panics leads to discrepancies about whether something actually constitutes a crisis 

and about the dating for the onsets and conclusions of these panics. It may be that some 

of the variation in the results found by the empirical studies can be traced back to the 

underlying uncertainty about the panics themselves. 

In a study that represents a springboard for our investigation, Donaldson (1992) 

performs an empirical investigation of these historical panics and finds that “panics are 

‘special events,’ in the sense that panic and non-panic data are generated by different 

economic systems.”3

 If the data were indeed generated by different economic systems, 

one way to examine these historical crises would be by using a Markov Switching Model. 

A switching model assumes a data-generating process that changes across time, and such 

a model would allow for differences in the process by which interest rates were 

determined during panic and non-panic periods. By differentiating between these datagenerating processes, we have an objective marker for the beginning of the panic and its 

1

 The empirical papers include Canova (1994), Donaldson (1992), Miron (1986), and Calomiris and Gorton 

(1991). 

2

 These were documented in what Kemmerer (p. 223) describes as “a rather hasty perusal of the Chronicle 

for the years 1876 to 1908.” 

3

 Donaldson (1992), 277–78. 

8 
 

 

end. This objective marker will improve our ability to distinguish the true triggers of 

episodes of panic. 

We use a switching model to examine short-term interest rates in this historical 

period. Regime-switching models have been used to examine interest rates in the modern 

era. Much of the work on interest rates being driven by changes in parameters over time 

is based on Hamilton (1989), who models discrete shifts in the underlying parameters 

driving short-term interest rates. Gray (1996) develops a generalized regime-switching 

model to examine short-term interest rates, which includes Markov switching of states as 

well as conditional heteroskedasticity component to the variance in the states. Ang and 

Bekaert (2002) look at the econometric performance of the regime-switching models in 

general for interest rates in a number of countries. 

Background 

The banking system in the National Banking Era was structured with a tiered 

reserve system. National banks in central reserve cities were required to hold a 25 

percent reserve on deposits in gold, coin, or cash in vault.4 National banks not in reserve 

cities were required to hold a 15 percent reserve, of which 60 percent could be held as 

deposits in reserve city or central reserve city banks. Reserve city banks could also hold 

a proportion of their reserves as deposits in the central reserve city banks. In addition to 

being reserves for the non-reserve-city banks, these deposits, or bankers’ balances, paid 

interest and facilitated the clearing of transactions. The banks in reserve cities or central 

reserve cities were commercial banks and not connected to a governmental body. The 

4

 New York, Chicago, St. Louis, Boston, Baltimore, Cincinnati, New Orleans, Philadelphia, and Providence 

were listed as redemption cities by the 1863 National Bank Act. The list of redemptions cities was 

modified by the 1864 revision of the National Bank Act. In 1887 an amendment to the law gave cities of 

50,000 or greater the ability to become reserve cities, and cities of 200,000 or more the ability to become 

central reserve cities. This is when St. Louis and Chicago were added to New York City as central reserve 

cities. 

9 
 

 

 

reserve requirements of the reserve city banks meant that some of what were “reserves” 

from the non-reserve city (sometimes referred to as “country”) banks could be loaned out 

in turn by the reserve city banks.5 

Banks in the reserve cities organized themselves into clearinghouse associations 

to facilitate the clearing of interbank transactions. The clearinghouse cleared transactions 

between banks, but it was also an organization of member banks, where mutual trust was 

an important part of the clearing process. Thus, clearinghouses had both the ability and 

the incentive to monitor the activities of member banks and could exact penalties from 

imprudent banks. In times of crisis the clearinghouse could elect to clear transactions on 

the basis of clearinghouse loan certificates, which were the mutual obligation of all the 

clearinghouse members.6 

Because of its position as the center of international commerce in the United 

States, New York was the most important of the central reserve cities, and New York 

City banks held by far the largest proportion of the reserves of correspondent country 

banks. 

Many of the bankers’ balances held by the New York clearinghouse banks were 

loaned to participants in the stock market on the callable loan market.7 Call loans could 

be demanded the same day and were basically overnight loans. The call loan interest rate 

reflected a competitive price on new loans, and the rate of interest for call loans that were 

renewed, or rolled over, was tied to the average interest rate for new loans that day. The 

loans were collateralized by the stock that was purchased, and a margin of 20 percent was 

required. Because of the nature of call loans—they were collateralized with stock, were 

short term, and were callable on demand—these loans were perceived as a very liquid 

5

 Moen and Tallman (2003). 

6

 Calomiris and Gorton (1991), Cannon (1910). 

7

 Moen and Tallman (2003). 

10 
 

and safe investment by New York clearinghouse banks.8 Banks optimized their 

portfolios across different types of investments, and the most liquid were considered to be 

call loans. As Myers (1931) puts it, “Banks invested in commercial paper, which usually 

bore a higher rate of interest than call loans, all the funds which they dared to tie up for a 

considerable length of time. Into the call loan market they put only those funds which 

they were holding against momentary withdrawal.”9 Thus the funds in the call market 

were there to some extent because they could be liquidated immediately if a bank felt the 

need. This characteristic gave the call market a very close tie to the reserve position of 

the banks. 

Under normal circumstances call market loans carried a lower interest rate than 

commercial paper, and banks would optimize their portfolios between the longer- and 

shorter-term loans on the basis of credit quality and opportunity cost.10 The generally 

lower interest rate on call market loans highlights the fact that these loans were 

considered safer than commercial paper. However, although the call market was a good 

place to lend money that a bank might need to liquidate quickly for an idiosyncratic risk, 

it proved to be unstable when there was a broad-based need to liquidate these loans. 

When a large number of the New York reserve banks were facing a need to liquidate their 

call loans, such as during a banking panic when several banks would face large 

withdrawal demands simultaneously, interest rates in the call loan market would become 

very high and unstable. It is these systemic events in the call market, and the spikes in 

call market interest rates that went with them, that we are examining as an indicator of a 

banking panic. 

8

 Myers (1931). 

9

 Ibid., 135. 

10 Ibid. 

11 
We use the call market interest rate in the Markov Switching Model framework to 

detect banking panics. The call market interest rate is a competitive interest rate in a 

market that has many participants on both sides of the transactions and in which liquidity 

is tightly linked to the reserve positions of the New York banks. In addition, the interest 

rate is available at very high frequency: weekly. For all these reasons, the call market 

interest rate is an excellent indicator variable for seeing when depositor withdrawals were 

widespread and substantial enough to cause serious liquidity problems for banks. 

Empirical Approach and Data 

The Markov Switching Model is designed to pick out changes in the generating 

mechanism of a variable. The model assumes more than one type of distribution, or 

generating mechanism, and an imperfect ability to observe when the switch between 

generating mechanisms occurs. The pattern in the call loan market interest rates of 

periods of stability with low interest rates and periods of instability with high interest 

rates is the type of pattern that might be best explained by shifts in the underlying 

behavior generating the observed variable. If these shifts in behavior were associated 

with banking panics, then the empirical observation would align well with the theoretical 

explanation that the changes in interest rates came from a broad-based withdrawal of 

liquidity by constrained banks. 

The model that we are using in this paper characterizes the interest rates from the 

call market as coming from two different generating mechanisms or states, which we 

have labeled as a panic or a non-panic state. The model estimates a probability of being 

in a panic or non-panic state on the basis of the information inherent in the data, giving us 

an objective approach to dating the panic periods. Our estimation method allows us to 

resolve differences in the categorization and the timing of panic periods. Other 

12 
estimation techniques are often very dependent on the timing of an event, which can be 

fairly subjective and can sometimes substantially affect the results. 

In addition, the Markov Switching Model assumes that shifting between panic and 

non-panic states is defined by transition probabilities. By estimating the probabilities of 

transitioning between the two states, we are able to compare differing hypotheses about 

the sources of these panics empirically. We can observe if a particular variable is 

associated with an increase in the probability of the start of a panic. For example, one 

can parameterize this transition probability with measures of macroeconomic activity, 

and the significance of these variables would support the asymmetric information theory 

of bank panics. Alternative theories can be tested in an identical manner and can also be 

compared with one another. 

The Data 

Panics are sometimes short events lasting in some cases only a few weeks or even 

days. Therefore, we based our analysis on the highest-frequency data available—weekly 

observations. The data series that we were able to obtain in a weekly frequency are 

shown in table 1, with their means and standard deviations. Our data set includes weekly 

observations from 1890 through 1909 on the call market interest rate, net flows of cash 

from New York City banks to the interior, excess reserves, discount rate of the Bank of 

England, the exchange rate of the dollar to the British pound, net gold imports, broad 

stock index changes, and commercial failures. These data allow us to compare directly a 

number of possible panic triggers mentioned in the literature. 

13 
 

 

 

 

Table 1: 

Summary Statistics 

Variable Variable Name Obs. Mean 

(Std Dev) 

Interest Rates 

Call Loan Interest 3.65

Rate Callrate 1043 (3.62) 

Difference in Call –0.0005

Loan Interest Rate difclrt 1042 (2.924) 

Liquidity 

Net Movement of 1.40

Deposits netmvmt 1043 (3.93)

 20.84 Excess Reserves exres 1043 (20.11) 

International 

Bank of England 3.30

Discount Rate BoE_disc 1042 (1.03) 

Change in BoE 0.0014

Discount Rate ch_disc 1041 (0.240) 

4.87 $/£ Exchange Rate Exch_lb 986 (0.02) 

0.0000 Change in $/£ ch_Exch 985 (0.006) 

388,887 Net Gold Flows goldflow 1043 (2,818,040) 

Business Cycle 

Percent Change in 0.077 pctchsv 1043 Stock Value (2.066) 

222.3 Commercial Failures commfail 990 (63.9) 

Change in 0.057 ch_fail 989 Commercial Failures (34.403) 

The indicator variable used by the Markov Switching Model to delineate banking 

panics is the Difference in Call Loan Interest Rate (difclrt). The Call Loan Interest Rate 

averaged 3.65 between 1890 and 1909, with a sizable standard deviation. This pattern of 

alternating periods of low interest rates and high interest rates can be seen in figure 1 and 

represents the heart of our use of a regime-switching model. For testing competing 

hypotheses about the triggers of panics, in some of the cases we used the change in 

variables rather than the level, that is, Change in Bank of England Discount Rate 

14 
(ch_disc), Change in $/£ Exchange Rate (ch_Exch), Percent Change in Stock Value 

(pctchsv), and Change in Commercial Failures (ch_fail). We used the variables Net 

Movement of Deposits (netmvmt) and Excess Reserves (exres) in levels, expressed in 

millions of dollars. The data series in table 1 comes from Kemmerer (1910), 

supplemented by various issues of the Commercial and Financial Chronicle. 

The Model 

The Markov Switching Model assumes the existence of two (or more) states and 

assumes, as well, that the state is not perfectly observable. The pattern of observed 

realizations of the time series variable is driven by switches between the underlying 

distributions, or states. These switches between the states evolve in first-order Markov 

process. 

In our specific version of the more generalized model, there are two states: a 

normal state and a panic state. The state variable is St = 0, 1, where zero indicates a 

normal state and one indicates a panic. In each period there is a probability that the state 

will transition into the other state. The transition probability of changing from a normal 

state into a panic would be Pr(St = 1| St-1 = 0, xt), and the probability of staying in the 

normal state would be Pr(St = 0| St-1 = 0, xt) = (1-Pr(St = 1| St-1 = 0, xt)), where xt is a set of 

variables that affect the probability of transitioning between states. If 

Pr(St = 0| St-1 = 0, xt) rises, the probability of switching into a panic state declines. It is 

this transition probability that we parameterize in order to test which variables had an 

effect on the probability of a crisis occurring. Similarly, there is a probability of staying 

in the panic state, so that we are also able to examine which factors may influence the 

ending of a crisis. 

15 
Figure 2 plots the first differences of weekly observations of the average interest 

rate charged on call loans at the NYSE for the period 1890–1909. Periods of calm are 

characterized by relatively stable interest rates, whereas the likely panic periods are 

characterized by extremely volatile interest rates. The variable that is being acted on by 

the state variable is the change in the call market interest rate, Δr ≡ r − r . The t t t−1 

realization of this variable is a function of a state-dependent mean and variance. 

Δ r ≡ μ + h z (1) t it it t 

for St = i. Here, for a given state, μit and hit define the conditional mean and conditional 

variance, respectively, and zt is an independent and identically distributed random 

variable with mean zero and unit variance. The conditional mean and conditional 

variance are specified to capture two well-known empirical attributes of short-term 

interest rates. First, any model of short-term interest rates must capture the important 

characteristic that the short rate is mean reverting. The simplest and most common way 

of modeling mean reversion is to let the change in the short rate depend linearly on the 

level of last period’s short rate. For each state, the functional form of the conditional 

mean incorporates mean reversion in this way and is specified by 

μ = a + a r 1. (2) it 0i 1i t−

In addition to mean reversion, the unconditional distribution of changes in the 

short rate is known to be leptokurtic—that is, “fat tailed.” Engle (1982) shows that a 

possible cause of the leptokurtosis in the unconditional distribution is conditional 

heteroskedasticity. Two ways of modeling this conditional heteroskedasticity are 

common in the literature. One can either use the ARCH/GARCH models of Engle 

(1982) and Bollerslev (1986) or simply specify the conditional variance of changes in the 

short rate as a function of the level of the short rate. We choose the latter approach and 

specify the conditional variance process of each regime as 

16 
h = exp(b + b r ) (3) it 0i 1i t−1 

A comparison of figure 1 (the level of call market interest rates) with figure 2 (the change 

in call market interest rates) provides justification for this specification: as the interest 

rates increased, the volatility also escalated. 

The states are not directly observed, so for every observation there is an estimated 

probability of being in a given state. The Markov Switching Model also calculates the 

transition probabilities and the distributions within the two states. The “Results” section 

below describes the pattern of the estimated probability of being in normal or panic state 

as it evolves over time and describes the relationship between the possible panic trigger 

variables and the time-varying transition probabilities. More detail about the process by 

which the Markov Switching Model estimates these parameters is given in the appendix. 

Results 

The Markov Switching Model assumes that the data are derived from more than 

one generating mechanism or distribution. However, although some previous research 

such as Donaldson (1992) find results that suggest that changes in the generating 

mechanism, others such as Calomiris and Gorton (1991) find that the major variables 

moved in a way that was consistent across panic and non-panic periods. Using the test 

from Garcia (1998), we tested call market interest rates to see if they were more 

consistent with having been generated by one distribution or with having been generated 

by two; we rejected the one-state null at above the 99 percent confidence level. 

We use the weekly call market data within the Markov Switching Model setting, 

first to determine the beginning and ending points of panic periods and then to 

parameterize the transition probabilities to shed light on triggering events. The first step, 

that of examining the dating of the panic periods, uses constant transition probabilities. 

We show that the model does a very credible job of identifying financial panics that 

17 
occurred during the time period under consideration. Once the panics have been 

identified, their causes will be determined when we reestimate the model by 

parameterizing the transition probabilities. 

Constant Transition Probability Model 

The first step was to estimate the model with constant transition probabilities so 

that we could focus on the process of finding the best structure for the underlying call 

market interest-rate data and dating panics and the switches in the data into and out of the 

panic state. 

Table 2 is broken into parameters for the normal and panic states. The stub 

indicates the parameters for the distributions of the normal and panic states. The names 

of the independent variables are found in column 1, and the remaining columns provide 

the estimation results for the different regime-switching models. These columns contain 

the coefficients for the conditional mean and conditional variances of the panic and 

normal periods and the probability of staying in a given state. In table 2 the probability 

of switching states is a constant. In the subsection “Time-Varying Transition 

Probabilities” below, we will examine the effect other variables may have on increasing 

or decreasing the probability of entering or leaving a panic state. 

The models each identify a low and a high interest-rate state. The columns 

represent different models with regard to the estimation of variance for each of the two 

states. Column 2 has constant variances within each state. Column 3 has conditional 

heteroskedasticity in the variance of the (high interest-rate) panic state but not of the (low 

interest-rate) normal state. Column 4 has conditional heteroskedasticity in the normal 

state but not in the panic state. And the rightmost column calculates a model with 

conditional heteroskedasticity in both states. When the log likelihood ratio test is used, 

18 
the rightmost column with the conditional heteroskedasticity for both variances has the 

best fit. 

Most of the observations fell into the normal, or non-panic, state, which had a low 

interest rate, averaging 2.9 percent, and a low variance. The negative sign on 

Callrate_lag, the level of last period’s short rate, confirms that interest rates in this state 

are mean reverting. In other words, interest rates in this regime will tend to revert to the 

low rate of 2.9 percent. For the panic periods the average interest rate is 9.2 percent, and 

again the negative sign of the coefficient indicates that in the panic state as well, the 

interest rates tend to be mean reverting. 

We estimated volatility by specifying the variance as an exponential function. 

That is, we rewrote equation (5) as h = exp(b + b r − ). For both the panic and normal it 0i 1i t 1 

states, the coefficient for the interest rate, CallRate_lag, is positive; therefore, in both the 

panic and normal states the variance increases with interest rate. For the normal state, if 

the interest rate were near its average of 2.9 percent, the variance would be about 0.16 

percentage points. In the panic state, again if the interest rate were near its average of 9.2 

percent, the variance would be 44.5 percentage points. 

We estimated the transition probability parameters by specifying the transition 

probabilities as a standard normal distribution function. The probability of staying in the 

normal (non-panic) state, Pr(St = 0 | St −1 = 0) , in the next period is 1.56 on the standard 

normal distribution, or a 94.1 percent probability in the full conditional heteroskedasticity 

model in the rightmost column. Thus, the probability of shifting into a financial crisis is 

about 6 percent, and this probability does not change across the entire sample period for 

these models. Similarly, the probability of shifting out of a financial panic is about 44 

percent, and this probability is also constant across the entire sample period. 

19 
 

 

 

 

 

 

 

 

Table 2: 

Constant Transition Probabilities 

Conditional Conditional Conditional No Conditional Independent Heteroskedasticity Heteroskedasticity Heteroskedasticity Heteroskedasticity Variables in Panic Periods in Normal Periods in Both 

Normal 

Conditional Constant 0.173 *** 0.151 *** 0.091 *** 0.096 *** 

Mean (0.035) (0.033) (0.026) (0.026) 

Callrate_lag -0.084 *** -0.082 *** -0.042 *** -0.047 *** 

(0.014) (0.013) (0.014) (0.014) 

Variance Constant -1.944 *** -2.266 *** -4.124 *** -4.172 *** 

(0.081) (0.094) (0.143) (0.140) 

Callrate_lag 0.792 *** 0.790 *** 

(0.041) (0.041) 

Transition p0 1.488 *** 1.452 *** 1.606 *** 1.562 *** 

Probability (0.080) (0.088) (0.084) (0.085) 

(probability) 93.2% 92.7% 94.6% 94.1% 

Panic 

Conditional Constant 4.054 *** 1.791 ** 5.487 *** 4.668 *** 

Mean (0.569) (0.716) (0.988) (1.128) 

Callrate_lag -0.536 *** -0.178 -0.565 *** -0.467 *** 

(0.059) (0.142) (0.082) (0.168) 

Variance Constant 3.334 *** 1.587 *** 3.896 *** 3.140 *** 

(0.105) (0.337) (0.150) (0.292) 

Callrate_lag 0.196 *** 0.071 ** 

(0.046) (0.030) 

Transition Constant 0.688 *** 0.891 *** 0.139 0.154 

Probability (0.122) (0.125) (0.171) (0.169) 

(probability) 75.4% 81.3% 55.5% 56.1% 

Value of Objective 

Function = -1301.67 -1277.79 -1106.49 -1099.44 

Note: Standard errors are in parentheses. 

* Indicates significance at the 10% level. 

** Indicates significance at the 5% level. 

*** Indicates significance at the 1% level. 

The model identifies a low interest-rate state and a high interest-rate state. Since 

these states are not directly observable, the model estimates a probability for each 

observation of being in the high or low interest-rate state. Specifically, we use the 

smoothed probabilities to identify the panic periods because these probabilities use all the 

20 
 

 

 

 

 

 

 

 

 

 

information across the sample. In our sample period, 1890–1909, we found five 

substantial panics and three minor panics. Figures 3 through 9 show the probability of 

panic for each of the years for which we found a panic period. In most cases the 

probability of being in a panic is near zero except for a few observations in the panic 

state, where the probability is close to one. We summarize these findings in table 3, 

where we compare our dates with those of six other sources. 

Table 3 

Financial Panics 1890–1909 

Year McDill and 

Sheehan Kemmerer Sprague Canova Donaldson Miron 

Calomiris 

and 

Gorton 

1890

1893

1896 

1899

 Major: Aug. 16 

 Major: Mar. 4 

 Jun. 10 

Minor: Oct. 31 

 Minor: Dec. 16 

Major:

 Nov. 10 

Major: May 5 

(or Feb 20) 

Minor: 

December 

Major: Late 

December 

Major: 

Nov.10 

Major: 

Feb. 26 

Major

Major

 Major 

 Major 

 Major 

Major 

Major 

Major 

Major: 

November 

Major: 

JuneAugust 

Minor: 

October 

1901 Major: May 9 Major Major 

1903 Major: March Major Major 

1905 Major: Nov. 4 Minor: April 

1906

1907 

 Major: Dec. 8 

Minor: Mar. 16 

Major: Oct. 26 

Minor: 

December 

Major: March 

and October 

Major:

 Oct. 21 Major Major Major Major: October 

Note: The dates for McDill/Sheehan are the beginning of the week in which the panic occurred. Minor panics from 

Kemmerer (1910, pp. 222–23) were derived from a list of “panicky periods.” 

Specifically, besides the present paper, the table refers to three other empirical 

studies of historical financial panics—Canova (1994), Donaldson (1992), and Miron 

(1986)—as well as the two sources that those three studies generally used as the basis of 

their dating for the panics: Kemmerer (1910) and Sprague (1910). In addition we 

included in table 3 the banking panic dates of Calomiris and Gorton (1991), who set their 

21 
own criteria for the definition of a banking panic. They defined banking panics as 

episodes of widespread suspension of convertibility by banks, episodes when 

clearinghouse loan certificates were issued, and episodes where the clearinghouses 

perceived a need to forestall suspensions. In each of the empirical studies, the dates of 

the financial panics are assumed, and analysis of this time period involves dummy 

variables for the dates of these crises. Notice that Donaldson (1992), based on Sprague 

(1910), assumes fewer major panics than either Canova (1994) or Miron (1986), both of 

whom looked to Kemmerer (1910) for panic dates. 

In general the Markov Switching Model approach closely matches the panics 

found by other authors, while allowing the data to speak for themselves about the dating 

of the crisis periods. 

Time-Varying Transition Probabilities 

At this point we investigate the possible triggers for moving into (and out of) a 

panic state. One of the earliest explanations (Kemmerer, 1910), which found favor later 

in the work of Miron (1986) and Eichengreen (1984), is that of seasonal movements in 

deposits from the reserve banks to the interior country banks because of seasonal demand 

for cash needed for planting, harvesting, and moving crops to market. We look at the 

variable netmvmt, which is the net movement of deposits from the country banks to the 

reserve center banks for the week. 

A related possibility is that the depositors were carefully watching the levels of 

excess reserves, exres, and running the banks if the reserves threatened to get so low that 

banks might have trouble repaying deposits. This possibility is very much within the 

realm of Chari and Jagannathan (1988), Chari (1989), and Williamson (1989). 

22 
We also examine the effect of gold flows in order to examine the possibility that 

domestic panics were a result of foreign inflows/outflows. In addition, we test changes in 

the Bank of England discount rate and changes in the exchange rate with the British 

pound. We include these variables in order to examine the effect of international triggers 

as suggested by Sprague (1910), Friedman and Schwartz (1963), and Tallman and Moen 

(1998). 

We also investigate the change in the stock market week to week, in case the 

spikes in call market interest rates are the result of sharp declines in stock market values. 

If the tightening of the call market interest rate is a function of declines in the values of 

the collateral, then the falls in the stock market should lead the rises in the call market 

interest rates. If the direction of causation runs from banks withdrawing liquidity in order 

to satisfy depositor demands, then the call market interest rates pattern should lead the 

stock market changes. In addition, stock market values are forward looking about 

expected business activity, and this quality should give us some ability to examine the 

expected-recession hypothesis of Gorton (1988) and Calomiris and Gorton (1991). 

Commercial failures should also give us a sense of the business climate at the time the 

panics began. 

The net movement of deposits appears to have a strong effect on the probability of 

going into a panic state. The positive sign on the coefficient for netmvmt in column 2 of 

table 4 indicates that the greater the inflow of deposits to the money-center banks, the 

higher the probability of staying in the non-panic, or normal, state. Conversely, as 

deposits drain from the money-center banks, the probability of a panic increases. 

23 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4: 

Liquidity Variables 

Net Deposit 

Independent Net Deposit Excess Movement & Ex. 

Variables Movement Reserves Reserves 

Normal 

Conditional Constant 0.124 *** 0.159 *** 0.163 ***

Mean (0.024) (0.025) (0.025) 

Callrate_lag -0.085 *** -0.091 *** -0.093 *** 

(0.012) (0.013) (0.013) 

Conditional Constant -4.159 *** -4.043 *** -4.002 *** 

Variance (0.119) (0.130) (0.125) 

Callrate_lag 0.671 *** 0.682 *** 0.665 *** 

(0.028) (0.039) (0.037) 

Transition Constant 1.01 *** -0.077 0.065 

Probability (0.088) (0.204) (0.205) 

Netmvmt 0.123 *** 0.152 *** 

(0.02) (0.035) 

Exres 0.103 *** 0.089 *** 

(0.017) (0.017) 

Panic 

Conditional 

Mean 

Constant 

Callrate_lag 

-0.284 

(0.192) 

0.541 *** 

-0.261 

(1.089) 

0.671 ** 

-0.498 

(0.955) 

0.737 *** 

(0.102) (0.306) (0.271) 

Conditional 

Variance 

Constant 

Callrate_lag 

-3.929 

(0.311) 

1.393 

*** 

*** 

1.409 

(0.432) 

0.282 

*** 

*** 

1.283 

(0.435) 

0.303 

*** 

*** 

(0.081) (0.064) (0.066) 

Transition 

Probability 

Constant 

Netmvmt 

-0.767 

(0.192) 

-0.098 

*** 

** 

-0.271 

(0.364) 

-0.544 

(0.184) 

-0.023 

*** 

exres 

(0.038) 

-0.039 

(7.964) 

-0.054 

(0.039) (18.758) 

Value of Objective Function = 

Note: Standard errors are in parentheses. 

* Indicates significance at the 10% level. 

** Indicates significance at the 5% level. 

*** Indicates significance at the 1% level. 

-1024.1 -1046.5 -1034.4 

Excess reserves, exres, which are the amount of reserves in the money-center 

banks minus the amount of reserves that the money-center banks were required to hold, 

24 
 

 

also seem to have a significant effect on the probability of a panic occurring. Again 

higher levels of reserves protected against the onset of a panic, while depleted reserves 

increased the probability of a crisis occurring. 

In the rightmost column of table 4 we also consider the possibility that net 

movements and excess reserves might be measuring the same thing. We found that when 

they were run together, both were significant. This result indicates that both flows from 

the money-center banks and the level of reserves that banks held, contributed to the 

probability of entering a panic period. 

In table 5 we show the results for the inclusion of international variables. 

Specifically, we looked at the possible effects that changes in the Bank of England 

discount rate, changes in the U.S. dollar–British pound exchange rate, and the net outflow 

of gold had on the probability of transitioning into or out of a crisis. Column 2 has the 

results for the changes in the Bank of England discount rate, but these changes did not 

have a significant effect. Similarly, the changes in the dollar/pound exchange rate did not 

appear to have a triggering effect. Freidman and Schwartz (1963) and Tallman and Moen 

(1998) discuss the effect of gold flows on the money supply in this period, but the weekly 

outflows of gold (column 4) do not appear to have had an effect in triggering panics.11 

11 The result for the panic period, however, seems to indicate that inflows of gold are associated with 

increasing the probability of staying in a panic state. A caveat to this result is that weekly net gold flows 

were a highly unstable series, and the optimization routine had difficulties finding a stable result with this 

variable. In later versions of the paper we will continue refining the use of this variable. 

25 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5: 

International Variables 

Change in Change in Independent Net Gold BoE $/£ Variables Flow Discount Rate exchange rate 

Normal 

Conditional Constant 0.004 0.046 ** -0.038 *** 

Mean (0.033) (0.023) (0.003) 

Callrate_lag 0.017 -0.046 ** 0.061 *** 

(0.020) (0.018) (0.007) 

Conditional Constant -4.785 *** -8.062 *** -3.890 *** 

Variance (0.139) (0.204) (0.002) 

Callrate_lag 1.293 *** 2.358 *** 1.087 *** 

(0.034) (0.073) (0.011) 

Transition Constant 1.706 *** 0.992 *** 3.003 *** 

Probability (0.096) (0.102) (0.000) 

ch_BoE 0.532 

(0.374) 

ch_exch 1.145 

(23.278) 

Goldflow 0.000 

(0.000) 

Panic 

Conditional Constant 4.061 *** 0.598 *** 4.840 *** 

Mean (0.109) (0.104) (0.003) 

Callrate_lag -0.896 *** -0.137 *** -0.392 *** 

(0.011) (0.029) (0.018) 

Conditional Constant 2.161 *** -1.622 *** 3.509 *** 

Variance (0.611) (0.139) (0.000) 

Callrate_lag -0.833 *** 0.360 *** -1.676 *** 

(0.143) (0.023) (0.000) 

Transition Constant 0.555 *** 1.161 *** 0.972 *** 

Probability (0.152) (0.096) (0.000) 

ch_BoE -0.646 

(0.627) 

ch_exch 0.060 

(14.117) 

Goldflow 0.001 *** 

(0.000) 

Value of Objective 

Function = -1435.73 -1010.98 -1529.36 

Note: Standard errors are in parentheses. 

* Indicates significance at the 10% level. 

** Indicates significance at the 5% level. 

*** Indicates significance at the 1% level. 

26 
 

 

 

 

 

 

 

 

 

 

 

 

 

In table 6, we consider the variables most consistent with the insolvency-based 

banking panic. The changes in the value of the stock market (pctchsv), week to week, did 

not appear to affect the likelihood of a panic beginning. The coefficient does have a 

positive sign, the direction one would expect, but is not significant. This fact indicates 

that financial panics did not tend to spread from the stock market to the banking sector, 

and the declines in the stock market associated with banking panics might have spread 

from the banking sector to the stock market via substantial reductions in liquidity. Given 

the forward-looking nature of the stock market, we did not find evidence to support the 

assertion that stockholders were anticipating an economic downturn in advance of the 

start of a banking panic. 

Commercial failures also did not appear to lead financial panics. When we used 

the change in commercial failures (ch_fail) to measure commercial health, an increase in 

failures had the expected sign but was not a significant predictor of an impending switch 

into a panic state. 

Table 6: 

Business Cycle Variables 

Independent Stock Market Change in 

Variables Change Commercial Failures 

Normal 

Conditional Constant 0.045 ** 0.094 *** 

Mean (0.022) (0.026) 

Callrate_lag -0.044 ** -0.048 *** 

(0.018) (0.014) 

Conditional Constant -8.044 *** -4.224 *** 

Variance (0.200) (0.144) 

Callrate_lag 2.356 *** 0.8 *** 

(0.073) (0.043) 

Transition Constant 1.009 *** 1.526 *** 

Probability (0.103) (0.088) 

Pctchsv -0.035 

(0.048) 

ch_commfail -0.003 

(0.002) 

27 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 6 (cont.): 

Time-Varying Transition Probabilities 

Panic 

Conditional Constant 0.582 *** 4.582 ***

Mean (0.098) (1.129) 

Callrate_lag -0.134 *** -0.461 *** 

(0.027) (0.172) 

Conditional Constant -1.693 *** 3.111 *** 

Variance (0.134) (0.298) 

Callrate_lag 0.366 *** 0.072 ** 

(0.023) (0.031) 

Transition Constant 1.184 *** 0.103 

Probability (0.101) (0.185) 

pctchsv 0.073 

(0.048) 

ch_commfail -0.005 

(0.005) 

Value of Objective Function = -1040.8 -1074.2 

Note: Standard errors are in parentheses. 

* Indicates significance at the 10% level. 

** Indicates significance at the 5% level. 

*** Indicates significance at the 1% level. 

The variables that were most significant in explaining the triggers of panics were 

the net movement of funds from the money-center banks to the country banks, and the 

level of excess reserves. Those two variables were complementary, and each enhanced 

the effect of the other. As excess reserves fell and deposits flowed out of the reserve 

banks, the probability of entering a crisis increased. These findings suggest that panics 

were a function of the declines in deposits and reserves, and they lend support to the 

theories of Kemmerer (1910), Eichengreen (1984), Chari and Jagannathan (1988), and 

others who are mentioned above. 

Also interesting to note were those variables that did not have an effect on the 

probability of entering a crisis: the stock market, business failures, changes in the Bank of 

England discount rate, and changes in the exchange rate. The lack of significance of the 

stock market variable is particularly interesting because it indicates that the transmission 

of these panics might have gone from the banking sector to the stock market. Also the 

stock market is forward looking, so any expectation of impending recession should have 

28 
shown up there first. Taken together, the lack of significance of both the business 

failures variable and the stock market variable in affecting the chances of moving into a 

panic state would tend to suggest that movements into a financial panic were not based 

on an expectation of an economic downturn and lowered business profits, as Calomiris 

and Gorton (1991) suggest. 

The international factors did not appear to play a strong role in triggering panics. 

Changes in the Bank of England discount rate and flows of gold out of the United States 

did not appear to have the strong effect on triggering these panics that Sprague (1910) 

and Tallman and Moen (1998) suggest. 

Conclusion 

First of all, the Markov Switching Model using the interest rate from the callable 

loan market does a very good job of picking out the periods of panic from the normal 

periods in the National Banking Era. The dates that the model finds are similar to the 

dates of banking panics found by other authors, but the model uses an objective 

mechanism derived from the data themselves. Our use of weekly data gives more 

precision to the dates for the onset and conclusion of panics and allows us to examine the 

possible triggers of panic periods more accurately. 

In studying the onsets of these panic periods, we have found that the net 

movement of deposits away from the money-center banks and low levels of excess 

reserves greatly increased the probability of financial panics between 1890 and 1909. 

This finding lends support to the theories of the contemporaries of these banking panics, 

such as Kemmerer (1910), as well as to the more recent work by Miron (1986), 

Eichengreen (1984), and Chari and Jagannathan (1988). 

29 
Equally important in many ways are the variables that were not significantly 

related to the onset of panics, such as changes in stock market values. The lack of 

significance for stock market changes suggests that falls in the stock market did not set 

off banking panics; rather, if stocks fell while banks were more troubled, the causality 

may well have run in the other direction—through a loss of liquidity in the call market. 

Also, we did not find support for the cause of bank panics hypothesized by Calomiris and 

Gorton (1991) and others; the theory that bank panics stem from a general change in 

sentiment in the economy about the prospects of business profits. Stocks are a forwardlooking measure of economic activity, and neither stocks nor the variable measuring 

business failures was a significant predictor of an impending banking panic. 

30 
 

Appendix 

The state variable, St, takes on a value of one if a panic period occurs, and it 

equals zero if such an event does not occur. This variable identifies the state of the 

economy, and these states are assumed to be path dependent and to evolve according to a 

first-order Markov process. The likelihood of moving between states is measured by 

transition probabilities, and according to the first-order Markov structure, these 

probabilities depend only on the state the process is in at t – 1. Information on states 

earlier than t −1 is not relevant to the transition probability; however, these probabilities 

may be influenced by a number of other factors in the model, where the transition 

probabilities are allowed to vary over time. 

The model assumes random movement between states, and the transition 

probabilities define the likelihood of shifting between states. The transition 

probability Pr(S =1| S = 0, x ) defines the likelihood of shifting into the panic state. t t−1 t 

The probability of staying in the same state is the same as 1 minus the probability of 

transitioning into a panic state, or 1– Pr(St = 1| St-1 = 0, xt), where xt represents variables 

that affect the probability of transition. Thus a decline in Pr(St = 0| St-1 = 0, xt) increases 

the likelihood of shifting into a financial panic. It is possible to incorporate transition 

probabilities that change over time and may be influenced by other factors. By 

identifying the factors that influence the transition probability Pr(St = 0| St-1 = 0, xt), we 

can determine the causes or triggers of these financial panics. For example, one might 

establish that Pr(S = 0 | S = 0, x ) is positively related to some measures of t t−1 t 

macroeconomic activity. In this case, the significance of these variables would confirm 

that the likelihood of a panic increased as the macroeconomy was moving into a 

recession. 

31 
 

One of the objectives of this paper is to determine the causes of historical 

financial crises by identifying variables that influence the transition probability 

Pr(S = 0 | S = 0, x ). Moreover, since Pr(S = 0 | S =1, x ) =1− Pr(S =1| S =1, x ) t t−1 t t t−1 t t t−1 t 

determines the likelihood of shifting out of a crisis, we also examine factors contributing 

to ending a crisis. We will perform this part of the analysis by identifying variables that 

influence the transition probability Pr(S =1| St 1 =1, x ). Of course, since t − t 

Pr(S =1| S =1, x ) defines the likelihood of remaining in a panic from one period to the t t−1 t 

next, parameterizing this probability also provides an opportunity to identify factors that 

might have prolonged a crisis. 

The observed variable is change in the call market interest rate, that is, 

Δr ≡ r − r . Using St, an observation from a given state can be expressed as t t t−1 

Δr ≡ μ[θ (S ),Φ ] + h[θ (S ),Φ ] z (A.1) t μ t t−1 h t t−1 t 

where θ μ andθ h are vectors of unknown parameters, Φt−1 is the agent’s information set at 

time t −1, and zt is again an independent and identically distributed random variable with 

mean zero and unit variance. 

For notational convenience, equation (A.1) is rewritten as 

Δrt ≡ μit + hit zt (A.2) 

for St = i. Here, for a given state St, the terms μit and hit define the conditional mean and 

conditional variance, respectively. 

Interest rates tend to be mean reverting. In order to have the flexibility to capture 

mean reversion if it should be the case in our specification, our model allows the change 

in the short rate to depend linearly on the level of last period’s short rate. The functional 

form of the conditional mean is specified by 

μit = a0i + a1irt−1. (A.3) 

32 
 

 

Another common trait of interest rates is to be leptokurtic. In order to control for 

the possibility of conditional variance, we specified the variance process as 

 ). h = exp(b + b r (A.4) it 0i 1i t−1 

Interest rates appear to be higher and more volatile during panic periods, and we 

model these differences in the level and volatility of interest rates by specifying a unique 

data-generating process for each regime. In equation (A.1), the variable St identifies the 

regime, and the conditional mean and conditional variance are then defined as functions 

of this state variable. Assuming normality for each regime, the conditional distribution 

of Δrt is the mixture of N(μ0t , h0t ) for regime 0 and N μ1t h1t ( , ) for regime 1. More 

formally, the conditional distribution of Δrt is written as 

⎧ N (μ 0t , hot ) with probability p0t 

Δrt | Φt −1 ~ ⎨ N(μ , h ) with probability p1t (A.5) ⎩ 1t 1t 

where p = Pr(S = 0 | Φ ) is the ex ante probability of regime 0 and 0t t t−1 

p = −1 Pr(S = 0| Φ ) is the ex ante probability of regime 1. 1t t t−1 

The model characterizes interest rates as realizations from either a panic or a nonpanic state. However, the states are not perfectly observable, and the assumption of a 

mixed distribution accounts for the uncertainty surrounding the unobserved states. The 

density function for a given interest rate regime can be written as 

1 − (Δrt − μ it )

2 

f (Δr | S ) ≡ i,Φ ≡ exp{ }. (A.6) t t t−1 2πhit 2hit 

The joint density-distribution function of Δrt and St can be expressed as 

1 − (Δrt − μit )

2 

p(Δr , S ≡ i | Φ ) ≡ p exp{ }. (A.7) t t t−1 it 2πhit 2hit 

Using this expression, we can write the density function for the mixed distribution as 

33 
 1 − (Δr − μ )

2 1 − (Δr − μ )2 

t 0t t 1t f (Δr | Φ ) ≡ p exp{ } + p exp{ }. (A.8) t t−1 0t 1t

2πh 2h0t 2πh 2h 0 1t t 1t 

For a given state, the density function in equation (A.6) represents a measure of 

the probability of observing a sample value. The density function in equation (A.8) is the 

weighted average of the different state density-functions, where the weights are the 

probabilities of the states. By weighting the state density functions in this way, the mixed 

distribution allows for the possibility that an observation could be associated with either 

state. Such a specification is appropriate, given the uncertainty surrounding the states. 

Since the states are not perfectly observable, one could never know with certainty that an 

observation was associated with a particular state. For example, although a very high 

interest rate would most likely be associated with the volatile interest-rate state, such a 

realization could always represent a tail event from the other state. 

As the states are unobservable, one needs to refer to a state by a probability 

measure. The ex ante probabilities from equation (A.5) correspond to the state 

probabilities. These probabilities are determined on the basis of the information that is 

available before the realization of Δrt . An ex post probability improves on this inference 

by using information about the time t observation of the dependent variable. By Bayes’ 

Rule, equations (A.7) and (A.8) can be used to determine the ex post probability as 

Pr(S ≡ k | Φ ) ≡ Pr(S ≡ k | Φ , Δr ) t t t t−1 t 

p(Δr , S = k |Φ ) (A.9) t t t−1 ≡ f (Δr | Φ ) t t−1 

The ex ante probabilities can be interpreted as the likelihood that the time 

t observation of the dependent variable is associated with a given interest-rate 

distribution. These probabilities depend in part on the regime in place in the prior period. 

The ex ante probability would equal the transition probability if the prior state were 

known with certainty. For example, Pr(S t = 0| Φt−1 ) = Pr(S t t = 0| S −1 = 0, x t ) if one knew

34 
with certainty that the prior period was a time of relatively stable interest rates. In this 

case, this state probability would be determined by the likelihood of remaining in St = 0 

from one period to the next, Pr(S = 0 | S = 0, x ). t t−1 t 

Unfortunately, the state cannot be observed with certainty. Consequently, one 

must account for the possibility that the process could have been in either state in the 

prior period. To account for this uncertainty, one determines the ex ante probability by 

weighting the transition probabilities by probability measures of the prior state. An 

expression for the ex ante probability of a non-crisis state can be written as 

1 

Pr(St = 0 | Φt−1) = ∑Pr(St−1 i | t−1) Pr(St = 0 | St−1 = i, x = Φ t). (A.10) 

i=0 

Equation (A.10) defines the ex ante probability as the sum of two terms, where each term 

is the product of an ex post probability and a transition probability. Similarly, an 

expression for the ex ante probability of a crisis state can be written as 

1 

Pr(St 1| t−1) = ∑Pr(St−1 i | t−1) Pr(St =1| St−1 = i, x = Φ = Φ t). (A.11) 

i=0 

The model specifies two states, where each state is characterized by a unique 

interest-rate distribution. However, since the states cannot be observed with certainty, 

the sample values are viewed as realizations from a mixture of the two interest-rate 

distributions. Equations (A.10) and (A.11) define the ex ante probabilities as weighted 

averages of the transition probabilities. After substituting the expressions for the ex ante 

probabilities into the density function in equation (A.8), one observes that the parameters 

of the mixed distribution necessarily include the parameters of the transition probabilities. 

Thus, estimates for these (and all other) parameters can be obtained by the use of 

observations from the mixed distribution. In other words, inferences about the unknown 

parameters use actual observations of short-term interest rates. 

35 
 

However, this estimation requires additional specification of the transition 

probabilities. Using an algorithm developed by Hamilton (1989), we obtain parameter 

estimates by means of maximum-likelihood estimation. The transition probabilities are 

further clarified as 

Pr(St = 0 | St−1 = 0, xt ) = p(xt ; β p ) 

Pr(St =1| St−1 = 0, xt ) =1− p(xt ; β p )

 (A.12) Pr(St =1| St−1 =1, xt ) = q(xt ; β q ) 

Pr(St = 0 | St−1 =1, xt ) =1− q(xt ; β q ) 

where p and q are specified as cumulative normal distribution functions. Maximumlikelihood estimation involves choosing parameters that maximize the value of a 

likelihood function. In equation (A.12), the functional form of p and q maps the 

variables xt into the open interval (0,1) and thereby guarantees a well-defined likelihood 

function. 

36 
References 

Ang, Andrew, and Geert Bekaert. 2002. Regime Switches in Interest Rates. Journal of 

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38 
 

60 

Figure 1 

Call Market Interest Rate 

Interest Rate 

50 

40 

30 

20 

10 

0 

1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1904 1905 1906 1907 1908 1909 

Call Market Interest Rate 

Figure 2 

Change in Call Market Interest Rate 

40 

30 

20 

10 

0 

-10 

-20 

-30 

1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1904 1905 1906 1907 1908 1909 

Change in Call Market Interest Rate 

39 
Probability Probability 

Figure 3 

1890 

Smoothed Probability of Panic State 

100% 

80% 

60% 

40% 

20% 

0% 

Jan Feb Mar Apr Ma Jun Jul Aug Sep Oct Nov Dec 

smoothed probabilities 

Figure 4 

1893 

Smoothed Probability of Panic State 

100% 

80% 

60% 

40% 

20% 

0% 

Jan Feb Mar Apr Ma Jun Jul Aug Sep Oct Nov De 

smoothed probabilities 

40 
Figure 5 

1896 

Smoothed Probability of Panic State 

100% 

80% 

60% 

40% 

20% 

0% 

Jan Feb Mar Apr Ma Jun Jul Aug Sep Oct Nov Dec 

smoothed probabilities 

Figure 6 

1899 

Smoothed Probability of Panic State 

100% 

80% 

60% 

40% 

20% 

0% 

smoothed probabilities 

Jan Feb Mar Apr Ma Jun Jul Aug Sep Oct Nov De 

Probability Probability 

41 
Figure 7 

1905 

Smoothed Probability of Panic State 

100% 

Probability Probability 

80% 

60% 

40% 

20% 

0% 

Jan Feb Mar Apr Ma Jun Jul Aug Sep Oct Nov De 

smoothed probabilities 

Figure 8 

1906 

Smoothed Probability of Panic State 

100% 

80% 

60% 

40% 

20% 

0% 

Jan Feb Mar Apr Ma Jun Jul Aug Sep Oct Nov De 

smoothed probabilities 

42 
Probability 

Jan Feb Mar Apr Ma Jun Jul Aug Sep Oct Nov Dec 

Figure 9 

1907 

Smoothed Probability of Panic State 

100% 

80% 

60% 

40% 

20% 

0% 

smoothed probabilities 

43