Bank panics, suspensions, and geography: some notes on the "contagion of fear" in banking.

Smith, Bruce D.

BANK PANICS, SUSPENSIONS, AND GEOGRAPHY: SOME NOTES ON THE "CONTAGION OF FEAR" IN BANKING

Recent attempts to understand bank panics tend to emphasize informational asymmetries or the possibilities of multiple equilibria. Such approaches stand in contrast to historical research that emphasizes legal factors influencing the organization of the banking system. This paper constructs a model of a banking system operating under regulations similar to those in effect under the National Banking System and in which information is complete. In all other respects the model resembles that of Diamond and Dybvig [1983]. The results indicate that, given the regulatory environment, it would have been surprising if suspensions of convertibility had not recurred periodically.

I. INTRODUCTION

Traditional explanations of panics under the National Banking System (1863-1913), offered both by scholars and contemporaries, stressed three factors. (1) Limitations on branching created incentives for the development and heavy use of correspondent banking relations. (2) Regulations favored holding interbank deposits with (a relatively small group of) New York banks. This concentrated the reserves of the banking system in one location, guaranteeing that heavy withdrawals of interbank balances from any source would affect New York banks, and through them, the entire banking system. (3) Legal restrictions prevented banks (especially those holding large interbank deposits) from adjusting interest rates in order to "protect" those deposits during periods of heavy withdrawal demand.(1)

This traditional explanation of the periodic recurrence of panics, which emphasizes the organization of the banking system, stands in marked contrast to more recent theories of panics, which tend to focus on various informational asymmetries between banks and depositors.(2) Most of the recent literature on panics follows Diamond and Dybvig [1983] in modelling banks as a mechanism for pooling liquidity risks faced by depositors. More specifically, potential depositors can invest in the same primary assets available to banks. However, primary assets are costly to liquidate, and depositors face random future liquidity needs at the time they make their investment decisions. In such a framework the role of banks is to create and issue liabilities more liquid than their assets. This activity provides insurance to depositors against random liquidity needs.

In Diamond and Dybvig's paper, exogenous shocks to agents' "liquidity preference" motivate withdrawal demand. Contracts between banks and depositors allow agents with liquidity needs to liquidate deposits at a lower cost than would be incurred in liquidating the primary asset. However, for each withdrawal due to inopportune liquidity needs, a bank must liquidate primary assets and bear these costs. Hence the provision of liquidity by banks is feasible only if withdrawal demand is restricted to those actually requiring liquidity.

In the model of Diamond and Dybvig,(3) panics can occur because the liquidity needs of individuals are private information. In particular, banks are assumed to be unable to observe whether any individual needs liquidity and hence cannot limit payments to individuals who actually need to withdraw funds. Banks are thus subject to "runs" as the result of self-fulfilling prophecies: if all depositors fear a run and they all seek to withdraw, it will not be feasible for the banking system to provide liquidity to all of them. Thus the banking system must either suspend payments or be rendered insolvent. Of course, a crucial component of this reasoning is that banks cannot distinguish "legitimate" from panic motivated withdrawals, and hence cannot ration funds on this basis.

This model of panics provides no role for the organization of the banking system. It therefore suggests that different countries (or different regulatory regimes within the same country) should have similar histories with respect to panics (so long as they had similar deposit insurance schemes, and similarly behaving lenders of last resort). However, this has been far from the case. For instance, while the U.S. had recurring panics from 1863-1933, Canada had none. A model of panics should be able to confront the different historical experiences of the U.S. and Canada. Given that Canada had unlimited branching, it might be reasonable to place some credence on the traditional explanation of panics given above.

A further feature of panics that needs examination is what Friedman and Schwartz [1963] term geographic "contagion." Many historical panics, such as those in 1893 and 1930-33, originated in distinct geographic locations and were transmitted to money center banks (and hence the remainder of the banking system) through correspondent banking relations. This suggests the importance of interbank relations in originating and transmitting systematic panics. Of course, an understanding of the role of correspondent banking relationships must involve some understanding of the total organizational and institutional structure of the banking system in place.

Relatedly, one feature of post-Civil War panics in the U.S. was that the most important component of withdrawal demand from New York (money center) banks was the demand for withdrawal of interbank deposits. In many instances withdrawals by interior banks seem to have had a large speculative component,(4) and interbank withdrawals were rationed in practice (even by banks meeting all non-bank withdrawal demand). Thus actual suspensions often treated bank and non-bank customers asymmetrically. This again indicates the necessity of understanding the nature of interbank relations. It also raises a further issue. As noted above, models following Diamond and Dybvig give rise to runs only if banks cannot limit withdrawals to agents with legitimate liquidity needs. Such models therefore require either that liquidity needs be unobservable, or that banks not be permitted to ration funds to depositors who are speculating on their solvency. However, in practice, banks have actively attempted to distinguish among depositors and to ration funds on this basis during panics. At times banks have restricted interbank withdrawals while meeting withdrawal demands by individual customers with demonstrable liquidity needs. To the extent that banks were able to accurately distinguish among depositors, this suggests the importance of explaining panics without appealing too heavily to the possession of private information by depositors.(5)

Finally, to return briefly to the theme of geographic contagion, Rolnick and Weber [1985] argue that the susceptibility of the banking system to this contagion was lower during the Free Banking period than it was to be later. If true, geographic contagion is more or less likely under different regulatory regimes, which again focuses attention on the organization of the banking system.

While there are many reasons to prefer the "traditional" explanation of panics, then, this explanation has yet to be formalized. I show here that such a formalization is easily accomplished by drawing on the insights of the Diamond-Dybvig analysis. In particular, the Diamond-Dybvig model provides an explicit framework for thinking about liquidity provision by banks, and about how this provision of liquidity makes banks vulnerable to heavy withdrawal demand. This paper takes a version of the Diamond-Dybvig model and adds several features meant to resemble legal restrictions imposed under the National Banking System. It then shows that these regulatory features, by themselves, tend to favor the development of correspondent banking relations and the concentration of reserves discussed above. Moreover, under legal restrictions limiting variability in interest rates on interbank deposits, the banking system will be prone to periodic suspensions whenever there are heavy withdrawals of interbank deposits. This formalizes the "traditional" explanation of panics and suspensions of convertibility. Finally, to emphasize that this can be done without appealing to private information, all information is assumed to be publicly available, and banks are free to utilize it except when legal restrictions prevent them from doing so. Thus this paper resembles earlier literature (e.g., Kareken and Wallace [1978]) in attributing banking instability to the consequences of regulation.

In the next section of the paper I review some of the historical features of the National Banking System and identify some particulars that a model of panics might want to address. Not surprisingly, given the "traditional" explanation of panics described above, I argue that it is important for the model to provide an incentive for the formation of interbank relations. Another important feature that the model should capture is that under the National Banking System deposits with designated "reserve agent" banks were counted as reserves, which favored concentration of interbank deposits. Finally, reserve agent banks argued that legal restrictions limited their ability to vary interest rates according to level of withdrawal demand, and hence prevented them from altering deposit rates enough to "protect" their deposits during panics. Since Diamond and Dybvig also rely on this same inability, I think it is useful to explore the implications of taking this seriously as a feature of the National Banking System. (This issue is discussed further in section II.)

With respect to the observations to be explained, section II shows that panic related withdrawal demands (on New York banks) came heavily from interior correspondent banks. And restrictions of payments by New York (and other money center) banks fell much more heavily on correspondent banks than non-bank depositors. Thus it is important to address the role of interbank relations in panics.

In addition, I argue that it is not necessary to have panics result from any unusual weaknesses of the banking system, or any "mistrust" of banks by depositors. Panics under the National Banking System typically did not involve unusual depositor losses or high bank failure rates. Finally, panics need not result from low levels of reserves or unusual monetary circumstances.

A model should also be able to confront the observed "geographic contagion" of panics, in which regionally localized banking problems are transmitted to New York (and because of concentration of reserves, the entire banking system) via correspondent banking relations. However, in doing so the model should be able to address why the banking system appears to be more susceptible to geographic contagion under some regulatory regimes than others. Relatedly, it should also be able to explain the different histories of countries operating under alternative regulatory regimes (say the U.S. and Canada).(6)

Section III develops a model that draws heavily on Diamond and Dybvig [1983] and Bhattacharya and Gale [1985], and incorporates some of the features listed above. As in Diamond and Dybvig, there is a set of identical (ex-ante) agents, who choose between investment in an illiquid primary asset and deposits in a bank. As in Bhattacharya and Gale, depositors and banks are assigned to specific locations and, after investment decisions are made, each location experiences a shock to the liquidity preference of its members. However, unlike Diamond and Dybvig or Bhattacharya and Gale, these shocks are publicly observable.

In keeping with the regulations under the National Banking System, each location has a bank that cannot branch. Thus correspondent banking relations are desirable as a means of pooling risk across locations. In order to capture the concentration of reserves in New York, it is assumed that regulations force interbank deposits to be held in one location, where the bank is designated as a "reserve agent."

In order to illustrate starkly the incentives for risk pooling across locations, the model is set up so that a desire for liquidity in any location implies that banks in that location will want to liquidate, and hence withdraw any interbank deposits. In addition, the number of locations experiencing these shocks to liquidity preference is itself random. Thus when a large number of locations desire liquidity, reserve agent banks will face heavy withdrawal demand. In keeping with the discussion above, reserve agents are not allowed to make payments to these liquidating banks state contingent. Hence, as in Diamond and Dybvig, if withdrawal demand is too high, the reserve agent will find it infeasible to provide liquidity to all correspondent banks needing it. The reserve agent must therefore either restrict payments to correspondents or be rendered insolvent. Thus panics (associated definitionally with suspensions by New York reserve agent banks) will occur whenever enough locations experience "difficulties." These difficulties are transmitted to reserve agents by correspondent banking relations and affect the banking system generally by necessitating suspension.

Finally, to illustrate how the regulatory regime affects the susceptibility of the banking system to panics, the behavior of the model when correspondent links are ruled out is considered. In some respects, this makes the model resemble a stylized version of the Free Banking System. As will be seen, this system is substantially more resistant to panics than was the National Banking System. Nevertheless, the model shows it to be a highly inefficient system, indicating that efficiency and "stability" of the banking system need not be at all related. This issue is explored somewhat further in the conclusion.

II. SOME HISTORICAL OBSERVATIONS

The National Banking System

This section undertakes a capsule description of the National Banking System circa 1873. The year 1873 is chosen since it contains the panic that was least complicated "because of the comparatively small number of state banks and trust companies" (Sprague [1910, 3]).

In 1873 national banks, and many state banks, were prohibited from branching. As a result, unit banks were the rule. These banks could be divided into three categories. Adopting contemporary terminology, "country banks," which constituted most of the banking system, were banks outside of designated "reserve" or "redemption cities." These banks were required to hold vault cash equal to 6 percent of deposit liabilities, and until 1874, 6 percent of their outstanding bank notes. Their remaining 9 percent required reserve could be held as deposits with approved "reserve agents" in reserve cities. In fact, in 1873, country banks held reserves exceeding one-third of deposits, with amounts due from reserve agents routinely exceeding cash [Sprague, pp. 11-12].

In the model below, country (or "interior") banks hold all of their "reserves" with reserve agents. This simplification does not violence to the observed behavior of country banks in times of difficulty. During the panic of 1873 (specifically, from September 12 to October 13) the deposits of country banks fell by $45,000,000. Meanwhile, these banks increased their cash reserves by $3,000,000, while reducing deposits with reserve agents by $26,000,000 [Sprague, p. 86]. This experience, which is typical of the actions of country banks in crises, suggests that these banks drew only on reserve agents at these times. In fact, cash reserves of country banks were "almost stationary" in normal periods [Sprague, p. 19], and generally rose during panics. Hence nothing is lost by abstracting from cash reserve holdings by country banks.

The remaining banks, located in fifteen designated redemption cities, fell into two groups. Those banks outside New York were required to hold a reserve of 25 percent, half of which could be deposited with New York banks. Until 1887 only New York was designated a "central reserve" city, giving the New York banks a unique position at the heart of the banking system. These banks motivate the "reserve agent" to be modelled below. In the model there is a single reserve agent. While not an accurate description of the banking system, it also does little violence to reality. First, although there were fifteen reserve cities, and in New York alone fifty national banks, seven New York banks held 70 percent--80 percent of all the bankers' deposits in the city [Sprague, p. 15]. Moreover, during the panic of 1873 all the national banks of New York "were converted, to all intents and purposes, into a central bank [which]...included virtually all the banking power of the city" [Sprague, p. 90]. Thus it is not unreasonable to develop a model with a single reserve agent.

In the model, the reserve agent holds only bankers' deposits, i.e., it has no individual depositors. Again this simplification does little violence to reality. The seven large New York reserve agents had liabilities to bankers three times as great as those to individuals.(7) As stated by Sprague [p. 18], it "seems clear that these banks ...were carrying on their operations almost wholly upon the unstable basis provided by the deposits of the out-of-town banks." Moreover, he notes "the movement of loans and reserves [of the New York banks] was in close correspondence with known movements of bankers' deposits" [Sprague, p. 22]. This is particularly true of call loans, which were an important component of the assets of the New York reserve agents. The volume of call loans "moved closely with the volume of bankers' balances in New York" (James [1978, 103]). Finally, during much of the period bankers' balances averaged nearly one-half of total loans for all national banks of New York. Thus, the events affecting reserve agents during panics (and more generally) involved interbank deposits in a crucial way. It is therefore reasonable to focus on bankers' balances and to abstract from the holding of individual deposits by reserve agents.

A last fact to be noted is the perceived lack of latitude of reserve agents to vary interest rates according to economic circumstances. According to the New York Clearinghouse report of 11 November 1873, "the associated banks of New York...are deprived by usury laws of the power, which is so effectively used by the principal banks in Europe, of protecting or augmenting their resources by adjusting the rate of interest to the necessities of the occasion."(8) This suggests the appropriateness of following Diamond and Dybvig in not permitting (reserve agent) banks to make interest payments contingent on withdrawal demand. Here, however, this should be viewed as a legal restriction.

The Panic of 1873

Prior to the panic of 1873 there were no significant changes in the monetary circumstances of the U.S., nor was there any unusual expansion of bank credit [Sprague, pp. 5-6]. Bank reserves were high by historical standards [Sprague, p. 10],(9) and the panic did not appear to be a response to the arrival of "bad news" about banks or the banking system. According to Sprague,

All of the failures which occurred during the crisis were...due to the "criminal mismanagement of their officers or to the neglect or violation of the National Bank Act on the part of their directors."

It would not be difficult to find many quite normal periods during which both the number of failures and the losses of creditors were far more considerable than in 1873. The solvency of the banks was at no time in question. The defects in the banking system which were disclosed were in its organization... Moreover, the banks were in what was for them a normal condition of strength at the time [p. 81].

Moreover, "few banks failed during the crisis or during the subsequent months and years of depression. And of the failures which did occur hardly any involved serious loss to the creditors" [Sprague, p. 2].(10) Thus the model should allow panics to arise without any unusual occurrences other than that real activity is depressed. Also, some banks should be liquidated during the panic, but should be liquidated with relatively little loss to depositors.

Second, the bulk of withdrawals during the panic were made by agents with readily observable characteristics. In particular, James [1978, 120] reports that variations in the loans and reserves of New York banks were accounted for mainly by reductions in bankers' deposits, with the decline in bankers' balances being "almost equivalent to the decline in reserves." Since country banks were augmenting their cash reserves, these types of withdrawals seem likely to have been speculative.(11) Moreover, such withdrawals were rationed. For instance, on September 24 the Chicago clearinghouse association voted to recommend suspension of currency payments to country banks. The Chicago banks that did so were ones with large deposits of country banks, while "other banks,...having to deal with only city depositors, have been paying all demands upon them." [Chicago Tribune, 25 September 1873, quoted in Sprague, p. 66]. Thus banks did take actions to restrict withdrawals with substantial speculative components. At the same time, banks attempted to meet withdrawal demands by agents with demonstrable liquidity needs. Sprague [p. 63-66] provides examples of efforts of banks to meet (observably) urgent withdrawal demands of local customers during suspensions. Noyes [1909, 195] goes further, and suggests (for 1893, which he argues was unusually severe) that "most of the banks cashed freely the checks of depositors where it was shown that the cash was needed for personal or business uses."(12) In short, it is consistent with observation to proceed as though banks were able to distinguish between "speculative" and other types of withdrawal demand, and that under appropriate circumstances, reserve agents were able to ration payments on bankers' deposits.(13)

Third, while the panic of 1873 appears to have originated in New York itself, the magnitude of the panic derived from the reserve agent roles of the seven New York banks. Sprague states:

Had all the New York banks been purely local institutions, with no responsibilities to the rest of the country, there can be little doubt that they would have been able to weather the storm without further difficulty. But the most considerable withdrawals of currency which they had to meet came from the out-of-town banks, and demands from that quarter showed no signs of diminishing [p. 51]. Suspension of cash payments occurred on September 24 in New York ,shortly thereafter becoming general throughout the U.S. This suggests the necessity of having a model in which panics occur because of the special position of reserve agents in the banking system. (The discussion of the panics of 1893 and 1930-33 will make this even more apparent.) In particular, it appears to be important to subject reserve agent banks to speculative withdrawal demand by other banks.

The Panic of 1893

As was the case in 1930-33, the panic of 1893 had a distinct geographic flavor to it. Again, as in 1873, the New York banks were in a (historically) strong position with respect to reserve holding: "they were far more amply provided with cash than has been customary in periods of active business either before or since" [Sprague, p. 153]. In fact, the reserve position of the banking system as a whole was "reasonably satisfactory" [Sprague, p. 161]. In addition, the period prior to the panic was one of general monetary expansion [Sprague, pp. 158-9], and the months of July and August saw large monetary increases [Sprague, p. 184]. Finally, "there is no evidence that depositors had become distrustful of the banks" [Sprague, p. 181]. Thus circumstances do not suggest that the panic was caused either by monetary factors, or by the kinds of factors stressed by Diamond and Dybvig or Chari and Jagannathan, for instance.

The sense in which the panic had a geographic aspect is as follows. The major banking development in the years before 1893 was the expansion of bankers' deposits with reserve agents. "During the two years after July, 1890, these deposits by interior banks in the city institutions had increased one-third; in New York, they had actually doubled... It was a 'run' of depositors on these Western banks which in 1893 precipitated the urgent demand for return of deposited reserves from Eastern institutions" (Noyes [1909, 190]).

In fact, at the end of May 1893 cash reserves of New York banks were high, and cash flows from interior banks were positive. But in the three weeks ending on June 17 the reserves of New York banks fell 18 percent, and their surplus reserves fell nearly 65 percent. "The withdrawal of money from New York was directly due to the failure and suspension of large numbers of banks, both state and national, and of private bankers in the West and South" [Sprague, p. 168]. The problems of these banks were attributable to adverse real events precipitating large numbers of mercantile failures: "These failures exceeded both in number and in the amount of liabilities those which had occurred in any other period of equal length in our history" [Sprague, p. 169].

While the outflow of cash had yet to create difficulties for New York banks, on June 15 mechanisms for issuing clearinghouse loan certificates were established. Thus New York banks were anticipating problems that might be caused by their reserve agents positions, even though "no bank in the city was in difficulty" [Sprague, p. 170].

By July 8, the total loss of reserves of the New York banks was $40 million.(14) Nonetheless, this "serious strain had been met boldly and successfully" [Sprague, p. 173]. However, "during the third week of July a second wave of distrust of the banks spread over the West and South" [Sprague, p. 175]. The outflows of funds from New York occasioned by these regional problems then led the New York banks to restrict cash payments. It is apparent, then, that this restriction was due to the reserve agent role of the New York banks. Further, suspension of payments in New York closely preceded nationwide suspension.

Two final points of note are as follows. First, "in 1873 suspension was one of the initial causes interrupting the normal course of business. In 1893 it was rather of the nature of a last straw adding to the burdens resting on the business community" [Sprague, p. 199]. Thus it is reasonable to view the problems of 1893 as occurring in the context of (rather than being the cause of) depressed business conditions.(15) Second, of the 158 national bank failures that occurred in 1893, 153 were in the South and West (Noyes [1909, 193]). Thus problems that caused bank liquidation were geographically confined to certain regions.

The Panic of 1907

Some aspects of this panic that are challenging for existing models are discussed by Smith [1984]. Hence it is sufficient to make a single point about the reserve agent role of New York banks. The (partial) suspension of cash payments in New York occurred on 16 October 1907. Shipments of cash by New York city clearing-house banks to other states in September 1907 were $23 million, and were $48 million in October. The analogous numbers for 1906 were $27 million and $30 million, respectively, while in 1908 the analogous numbers were $18 million and $13 million.(16) Thus, as previously, suspension by money center banks followed large demands for shipments of cash by interior banks. And, "although there were runs on some banks in scattered parts of the country due to local causes, loss of confidence was displayed less by the public than by country banks" (Friedman-Schwartz [1963, 160]).

The Panics of 1930-33

As in 1893, the sequence of panics from October 1930 to March 1933 had distinctly regional aspects. Moreover, the transmission mechanism for regional banking disturbances involved correspondent relations in an integral way. This section establishes these facts, and attempts to address the question: why was the experience of 1930-33 more severe than that of earlier panics? Following Friedman and Schwartz, the suggested answer is that money center banks were deterred from suspending payments by the presence of the Federal Reserve System. As suggested by the model of the following section, only such a suspension could prevent insolvency of money center banks under the banking system in place.(17)

A number of authors have noted that the first banking crises of the period (beginning in October-November 1930) had obvious regional origins: "a crop of bank failures, particularly in Missouri, Indiana, Illinois, Iowa, Arkansas, and North Carolina, led to widespread attempts to convert demand and time deposits into currency... A contagion of fear spread among depositors, starting from the agricultural areas... But such contagion knows no geographical limits" (Friedman and Schwartz [1963, 301]). In short, a panic with regional origins was transmitted to money center banks.(18) Wicker [1980] argues that the panic began with the failure of Caldwell and Company, the largest southern investment banking firm, and that this failure "led to the suspension within a two-week period of more than 120 banks in four states" (Wicker [1980, 576]). Moreover, Wicker argues that the failure of Caldwell and Company, and subsequent related failures, was not due to the depression, but rather was an exogenous shock (consistent with the modelling strategy employed below). Finally, Wicker's argument suggests that a single shock was responsible for the banking problems of an entire (four-state) region. This is again consistent with the model developed below in which all the agents in a given location are subject to the same disturbance.

Another aside relevant to the formulation of the model concerns two additional facts about the panic of 1930. First the panic produced "no discernible interest rate effects" (Wicker [1982, 47]). This allows the model to follow Diamond and Dybvig in viewing rates of return on investments as technologically determined. Such a formulation, while not consistent with all observations from historical panics, is also not inconsistent with all panic experiences. Second, the panic produced relatively minor expenditure effects (Wicker [1982, 440-441]). Thus it is not inappropriate to model the onset of a panic as a shock which bank failures do not necessarily feed back on. This strategy is adopted below.

The second crisis of the period at hand occurred in March 1931, and then sustained difficulties began with a "renewed series of bank failures...in the last quarter of 1932, mostly in the Midwest and Far West" (Friedman and Schwartz [1963, 324]). Runs in particular states occurred, leading to the declaration of state banking holidays in Nevada, Iowa, Louisiana, and Michigan by 14 February 1933. Thus, as previously, the onset of the panic had a regional nature. However, these regional difficulties were transmitted generally by correspondent banking relations, as described by Friedman and Schwartz:

While the holiday halted withdrawals in a given state, it increased pressure elsewhere, because the banks that had been given temporary relief withdrew funds from their correspondents in other states in order to strengthen their position... The main burden of the internal drain fell on New York city banks. Between February 1 and March 1, interior banks withdrew $760 million in balances they held with those banks (leaving $900 million) [p. 325-6].

Finally, rumors of devaluation led to a demand by interior banks for remittances in gold coin or gold certificates. "Mounting panic at New York city banks on these accounts were reinforced in the first few days of March by heavy withdrawals from savings banks and demand for currency by interior banks" [Friedman and Schwartz, p. 326]. Thus, as in earlier panics, withdrawals from New York by interior banks continued to play a crucial role.

A national bank holiday was proclaimed on March 6. The severity of banking problems in 1930-33 relative to earlier panics is summarized by Friedman and Schwartz [p. 329]: "in none of the earlier episodes, with the possible exception of the restriction (of payments) that began in 1839 and continued until 1842, was there any extensive series of bank failures after restriction occurred." The contrast with the aftermath of the banking holiday is clear.

Why were the consequence of the panics of 1930-33 so much more severe than those of earlier panics? Friedman and Schwartz argue that the existence of the Federal Reserve System prevented a suspension of cash payments:

We have already expressed the view that under the pre-Federal Reserve banking system, the final months of 1930 would probably have seen a restriction, of a kind that occurred in 1907, of convertibility of deposits into currency... Restriction would almost certainly have prevented the subsequent waves of bank failures that were destined to come in 1931, 1932, and 1933 [p. 311].

Moreover, they argue [p. 311] that "the existence of the Reserve System prevented concerted restriction." Thus the failure to suspend cash payments was responsible for the severity of the banking problems of 1930-33.(19)

The Free Banking Era (1837-1863)

Having emphasized issues related to the concentration of reserves and the geographic contagion of regional banking difficulties, I now consider briefly experiences during a period when reserves were less concentrated, and when the banking system seemed less susceptible to such contagion. While correspondent relations between interior and New York banks were important even during this period (see Myers [1931, ch. 6]), the ratio of bankers' deposits to individual deposits in New York was less than one-third of its 1872 level in 1846, and less than half its 1872 level in 1856 (Myers [1931, 119]). In fact, deposits of country banks in New York in 1857 comprised only about one quarter of total New York bank deposits (Myers [1931, 141]).(20)

As described by Rolnick and Weber [1983; 1984; 1985], regulations on state banks favored holding a considerable portion of bank reserves in the form of state bonds, which were placed on deposit with the auditor or treasurer of the chartering state. Since banks in a given state therefore often had similar portfolios, the banks in each state often also experienced very similar shocks to the value of their assets. Thus large numbers of banks in a given state might tend to experience difficulties simultaneously. As shown by Rolnick and Weber [1985], there were episodes when large numbers of state banks were forced to liquidate simultaneously. In later periods regional liquidations of such large magnitude were transmitted generally. However, Rolnick and Weber [1985] demonstrate that many such episodes under free banking were geographically confined, suggesting that contagion is not inherent to all possible organizations of the banking structure.(21)

Two points relevant to the formulation of the model in the next section might also be noted. First, because free banks within a given state often had similar portfolios, all of the customers of a given bank were affected by a similar set of disturbances. The model of the next section adopts, as a simplification, a specification in which all the depositors of any given (interior) bank experience the same shock. This makes the incentives for the formation of correspondent banking relations very obvious, without doing violence to reality in some important instances.

Second, while some states had very poor experiences under free banking, Rolnick and Weber [1985, 5] discuss some instances where there were large scale bank liquidations that involved very little loss to noteholders. The next section constructs a model where large scale liquidation can occur, while all liquidated regional banks meet their contractual obligations.

III. THE MODEL

The Model Without Correspondent Banking

The discussion above suggests that understanding the incentives for correspondent banking relations to form, and the limitations placed on such relations by legal restrictions, is important in understanding panics, and perhaps more so than informational frictions. This section develops a model closely related to those of Diamond and Dybvig [1983] and Bhattacharya and Gale [1985], but which incorporates some of the institutional features discussed in section II. It is demonstrated that periodic suspensions are natural in such a context to prevent general insolvency of the banking system. To emphasize that informational frictions are inessential to the argument, the model assumes complete information.

To begin, a version of the model with no correspondent banking relations is considered. This version of the model is meant to capture crudely certain features of the free banking period, and to illustrate the incentives for formation of correspondent banking. As will be obvious, with no correspondent links in place geographic contagion cannot occur, and the model is specified in such a way that (absent these links) liquidated banks always pay off their obligations "at par."

The model has three periods with time indexed by t = 0, 1, 2, and with the physical environment similar to that of Diamond and Dybvig.(22) In particular, all agents are endowed at t = 0 with one unit of a single good. One unit "invested" in a single "primary asset" at t = 0 pays off one unit if the investment is liquidated at t = 1, and R > 1 units if the investment is held until t = 2. This primary asset and bank deposits are the only investment opportunities.

In addition to the agents just described (depositors), banks are allowed to form. It is useful to think of banks and depositors as being assigned at t = 0 to distinct "locations," which then remain fixed. Thus agents are geographically immobile. There is assumed to be a continuum of locations, contained in some interval S the non-negative real line. Let s [Epsilon] S index locations. Each location has one bank, and some (identical across locations) number of depositors, which is arbitrary.

All banks and depositors are identical ex ante (i.e., as of t = 0), and depositors are identical to those described by Diamond and Dybvig. In particular, letting [c.sub.t] [is greater than or equal to] 0 denote the consumption of an arbitrary depositor at date t, depositors (as of t = 0) have utility functions , with is a random variable realized at time 1, and which takes the same value for all depositors in location s. For each s, [Phi](s) has the probability distribution (1) [Phi](s) = 0 with probability p

[Mathematical Expression Omitted]

[Phi](s) = 1 with probability 1-p. Thus, at this point, there is no aggregate uncertainty. Finally, the realization of [Phi](s) publicly observable.(23)

Banks behave as follows. Banks in location s take deposits (at most) from depositors in location s. Inter-location asset trade is precluded, as are interbank interactions.(24) Let [r.sub.t](s) denote payments by banks in location s to depositors who withdraw at date t; t = 1, 2. Then, since all depositors in location s are identical at t = 1, clearly

[Mathematical Expression Omitted]

In short, without correspondent banking there is no scope for these banks to pool the risks implicit in the model.

It should be clear that panics cannot occur here if banks in location s are permitted to suspend if [Phi](s) but there are withdrawal demands at t = 1.(25) Also, a fraction p of banks will be liquidated at t = 1, and will be liquidated "at par," i.e., they fulfill all contractual obligations. Thus this banking system is very safe. It is also very inefficient since the expected utility of depositors (as of t = 0) is pU(1) + (1 - p)U(R).(26)

A Model With a Reserve Agent and no Aggregate Uncertainty

Suppose the government now designates a single bank as a "reserve agent," which is the only bank allowed to hold interbank deposits. This bank, then, plays the role of the seven New York city reserve agents. The reserve agent, for simplicity, does not hold individual deposits.

As a consequence of the kinds of legal restrictions discussed in section I, the reserve agent is required to announce deposit contracts satisfying the "sequential service constraint" of Diamond and Dybvig. Thus the reserve agent announces, at t = 0, a pair ([r.sub.1], [r.sub.2]), where [r.sub.t] is the amount paid (per unit deposited) to a bank that withdraws from the reserve agent at t. The sequential service constraint prevents [r.sub.1] from being contingent on the volume of withdrawals at t = 1. The reserve agent, then, can make payments at t = 1 state contingent only by suspending cash payments. Regulators permit suspension only when a failure to suspend will result in insolvency of the reserve agent.(27)

Following Diamond and Dybvig, the reserve agent is a cooperative entity that maximizes the expected utility of regional bank depositors as of t = 0. (Alternatively, there could be some fixed finite number of reserve agents, each serving large numbers of "country banks," that compete for interbank deposits.) Then, at t = 0, all banks will, for risk sharing reasons familiar from Diamond and Dybvig, deposit all of their funds with the reserve agent. At t = 1 bank s will withdraw all its reserve agent deposits if [Phi](s) = 0, receiving [r.sub.1] per unit deposited. The proceeds are divided in a pro rata manner among the depositors of bank s. Hence per person consumption in location s is [r.sub.1] if [Phi](s) = 0, and is [r.sub.2] if [Phi](s) = 1 (and there is no "run").(28) Then ([r.sub.1], [r.sub.2]) is chosen to maximize pU([r.sub.1]) + (1 - p) U([r.sub.2]) subject to the resource balance condition (2) [r.sub.2] = R/(1-p) - R[p/(1 - p)][r.sub.1] and an incentive compatibility condition (3) [r.sub.2] [is greater than or equal to] [r.sub.1]. The incentive condition (3) has an interpretation different from that in Diamond and Dybvig. In their paper (3) must be satisfied since [Phi](s) is unobservable, and hence depositors must be given an incentive to truthfully reveal their realization of [Phi]. Here, [Phi](s) is observable. However, the reserve agent cannot ration withdrawals except via a (permitted) suspension of convertibility. Equation (3) requires that suspensions be necessary only in the event of a "run," or in other words, that banks with [Phi](s) = 1 find it optimal (in the absence of a run) not to withdraw their funds from the reserve agent at t = 1.

The solution to the problem of maximizing pU([r.sub.1]) + (1-p)U([r.sub.2]) subject to the resource balance condition (2), denoted , satisfies. Thus the values, satisfying and equation (2) solve the reserve agents's problem. Clearly satisfies.(29) Thus the introduction of a reserve agent improves the performance of the banking system, and in fact, supports a Pareto optimal allocation of resources.

[Mathematical Expression Omitted]

"Runs"

As mentioned above, if local banks are permitted to suspend convertibility under appropriate circumstances then local runs cannot occur. Runs on the reserve agent are a possibility, although these can be forestalled by appropriate suspensions as well. Runs on the reserve agent here are of exactly the Diamond-Dybvig variety, but have a somewhat different interpretation. In particular, runs occur only because the reserve agent is prevented (by regulation) from restricting time 1 withdrawals (except through suspensions), and hence are simply consequences of the "sequential service constraint."

To see that runs on the reserve agent can occur, suppose that local banks conjecture that a fraction f of all banks will withdraw at t = 1. If f satisfies (4) then each bank has an incentive to withdraw from the reserve agent at t = 1. Moreover, since , condition (4) is satisfied for f sufficiently near one. Thus if f = 1, a run which is a self-fulfilling prophecy occurs.

[Mathematical Expression Omitted]

As in Diamond and Dybvig, runs can be prevented if the reserve agent suspends whenever time 1 withdrawal demand is too large. In particular, if the reserve agent suspends whenever f (the fraction of country banks withdrawing at t = 1) exceeds p, then only banks with [Phi](s) = 0 will withdraw at t = 1, and runs do not occur. Notice that suspension does not involve a failure by any banks to make payments to individual depositors, but only involves a refusal by the reserve agent to make shipments to country banks.

Of course if the reserve agent suspends whenever f > p, runs will not occur and suspensions will never be observed. Thus this section should be viewed as leading expositionally to the introduction of aggregate uncertainty.

The Model With Aggregate Uncertainty

The model is now modified by adding aggregate uncertainty about the demand for withdrawals at t = 1. Following Diamond and Dybvig, p in equation (1) is now a random variable realized at t = 1. Realizations of p are common knowledge. The distribution of p will be denoted G(p), with associated (continuous) density function g(p). The function g(.) has support [Mathematical Expression Omitted] contained in [0,1]. It is assumed that [Mathematical Expression Omitted]. Other aspects of the environment are as described above.

Similarly, the behavior of banks and reserve agents, including the regulations under which they operate, are essentially the same as previously. To capture one feature of the National Banking System described in section II, the reserve agent announces an interest rate for first period withdrawals, [r.sub.1], that is not permitted to be contingent on the state p or on total withdrawals at t = 1. Let f denote the fraction of interbank deposits withdrawn at t = 1. Then the resource balance condition (2) is replaced by (5) [r.sub.2](p,f) = R/(1 - p) - R[f/(1 - p)][r.sub.1].

Finally, as a description of regulatory behavior, f = p unless banks (the reserve agent, and hence banks in general) suspend convertibility of deposits. Suspension is permitted if and only if a failure to suspend results in insolvency of the reserve agent at t = 1. Here insolvency involves an inability to pay all country banks who at t=1 withdraw [r.sub.1] per unit deposited. Insolvency occurs if payments at t = 1, f[r.sub.1], are such that [r.sub.2](p,f) < [r.sub.1], since then all country banks have an incentive to withdraw at time 1. Hence a suspension occurs whenever f [is greater than or equal to] [p.sup.*], where [p.sup.*] satisfies (6) Thus total withdrawals at t = 1 are given by f = min(p,[p.sup.*]), which should be viewed as a regulatory restriction. (It is verified below that the set of p values requiring a suspension is, in fact, an interval.) [p.sup.*] is a choice variable for the reserve agent at t = 0.

[Mathematical Expreession Omitted]

It remains to describe what transpires in the event of a suspension (p > [p.sup.*]) at t = 1. If the reserve agent suspends, then it makes payments of [r.sub.1] per unit deposited until the fraction of banks that have withdrawn equals [p.sup.*]. Any additional banks wishing to withdraw thereafter are unable to do so, so that the "sequential service constraint" remains in effect. Country banks that wish to withdraw at t = 1 are assigned an arbitrary position "in line" so that, conditional on p, the probability of a country bank making a desired withdrawal at t = 1 is min[([p.sup.*]/p), 1]. Since [Mathematical Expression Omitted] [by (7), (8), and f = min(p,[p.sub.*])] country banks that experience [Phi](s) = 1 make withdrawals from the reserve agent only at t = 2.

Reserve Agent Behavior

For given values of [r.sub.1] and [p.sup.*] [satisfying (6)], let [c.sub.t](p) denote the date t consumption of a representative depositor. Then (7) and (8.a) [c.sub.2](p) = R/(1-p) - R[p/(1-p)][r.sub.1]; p [is less than or equal to] [p.sup.*] (8.b) [c.sub.2](p) = R/(1-p) - R[[p.sup.*]/(1-p)][r.sub.1]; p [is greater than or equal to] [p.sup.*] Equation (7) is the sequential service constraint, with suspensions occurring whenever p > [p.sup.*], and (8) is the resource balance condition [using f = min (p,[p.sup.*])].(30) Finally, incentive compatibility requires that (9), of course, satisfies (9) with equality.) Equation (9) requires that country banks with [Phi](s) = 1 find it optimal not to withdraw at t = 1 if convertibility has not been suspended.

[Mathematical Expression Omitted]

As before, the reserve agent is a cooperative entity, which chooses [r.sub.1] and [p.sup.*] to solve the problem subject to equations (8) and (9). In addition, (10) R/(1-[p.sup.*]) - R[[p.sup.*]/(1 - [p.sup.*])][r.sub.1] [is greater than or equal to] [r.sub.1] with equality unless [p.sup.*] = p [bar], and subject to (11) (12) 1/[p.sup.*] [is greater than or equal to] [r.sub.1] [is greater than or equal to] 0. The solution to this problem gives equilibrium values of [r.sub.1] and [p.sup.*].

[Mathematical Expression Omitted]

Equilibrium Suspensions of Convertibility

If , partial suspensions of convertibility occur with positive probability (since). Thus suspensions occur whenever enough locations experience "bad" realizations ("local liquidations"), which is exactly the geographic transmission of disturbances. Moreover, suspensions can occur even if there are no demands for liquidity by depositors in the reserve agent's location. Thus, given the organization of the banking system, periodic suspensions are to be expected so long as.

[Mathematical Expression Omitted]

It is therefore of interest to provide conditions implying that. One (although by no means the only) set of sufficient conditions for this is now stated. PROPOSITION: The solution to the problem (P) sets [r.sub.1] > 1. In addition, if and (13), then REMARKS: The assumption that cU [double prime](c)/U [prime](c) < - 1 implies U [prime](1) > RU [prime](R). This, in turn, implies that (13) will hold if p [bar] is sufficiently close to one.

[Mathematical Expression Omitted]

The proof of the proposition is straightforward but tedious, and is therefore omitted here. A complete proof appears in Smith [1987], which is available from the author on request. Notice that (recalling the remark) the proposition asserts that periodic suspensions will be observed if p can assume a large enough range of values. The probability of a suspension at any date is, of course, 1-G([p.sup.*]).(32)

IV. CONCLUSIONS

Traditional explanations of bank panics, such as those offered by Sprague [1910], Hepburn [1915], and Myers [1931; 1970] emphasize the role of the organization of the banking system in allowing panics to occur. The analysis in the previous section shows that existing models of bank liquidity provision that follow Diamond and Dybvig [1983] can easily be modified to incorporate organizational features of the banking system. When these are introduced, such models can readily explain observed panics without relying on informational asymmetries or multiple equilibria. This fact is important not just because it demonstrates that traditional explanations of panics can be formalized. It also raises the possibility, which is important from a policy perspective, that a reorganization of the banking system is a cheaper way of reducing the possibility of bank panics than are deposit insurance schemes (with their attendant adverse incentives for bank lending behavior). A formalization of this intuition must be left as a topic for future research, however.

In addition, the analysis offers some warnings against equating "safety" of the banking system with "efficiency" of the banking system. This point was illustrated specifically in the context of free banking, but is of course more general. For instance, a common policy prescription for increasing the stability of the banking system into the 1930s was the prohibition (or limitation) of interest payments on deposits, and especially on interbank deposits. According to Hepburn [1915, 318]," all the Comptrollers of the Currency down to and including Knox recommended the prohibition of interest upon deposits by reserve banks." As is easily verified, if restrictions on deposit rates are interpreted as ceilings on the value of [r.sub.1], effective interest rate ceilings will reduce the probability of suspension. Thus the model suggests that this action would have rendered the banking system less prone to suspension. Of course such an action also would have reduced the (ex ante) expected utility of depositors, so that again safer banking systems need not be the same thing as more efficient banking systems.

In addition to formalizing the traditional explanations of panics described above, the model also confirms some arguments about the differences between the panics of 1930-33 and earlier panics. As an example, Friedman and Schwartz [1963] argue that the presence of the Federal Reserve System in 1930-33 prevented (early) suspension by the New York banks, which made the panic of 1933 much more severe than earlier panics. To the extent that the first part of their argument is correct, the model confirms their conclusion. If the reserve agent chooses [r.sub.1] and [p.sup.*] to solve the problem (P) in section III, and then is inhibited from suspending ex post if p > [p.sup.*], the result is that [r.sub.2](p,f) < [r.sub.1] will hold. There will be consequent general demand for withdrawals from the reserve agent, which will be left insolvent.

Finally, the analysis suggests some questions that must be left as topics for future investigation. First, it has been common to argue that the Canadian banking system avoided the recurrent panics observed in the U.S. because Canadian banks were able to branch freely. (Such an argument appears in Myers [1931; 1970].) Interestingly, deposit interest rates paid by Canadian banks tended to display very little variation over long periods. An interesting question is whether unlimited branching alone (without significantly state contingent deposit rates) can account for the superior stability of Canadian banks. A second question, also raised by the differing experiences of Canada and the United States, concerns the relative costs and benefits (taking into account the possibility of panics) of having large banks with a national system of branches that are imperfectly competitive versus having small banks that behave competitively. A natural topic for investigation would be to derive conditions under which the superior stability properties of the former system would outweigh the costs of its associated distortions.

(1)Examples of literature offering this kind of explanation of panics include Sprague [1910] and Myers [1931; 1970]. Hepburn [1915, 314] describes this argument without either endorsing or disputing it. (2)Examples of such theories include those of Bental, Eckstein, and Peled [1985], Chari and Jagannathan [1984], Gorton [1985], Jacklin [1983], Smith [1984], and Waldo [1985]. (3)And in the related models of Chari and Jagannathan [1984], Bental, Eckstein and Peled [1985], and Jacklin [1983]. (4)"Speculative" withdrawal demand is defined here and throughout as withdrawal demand that occurs (only) because those seeking to withdraw are speculating about the ability of a particular bank (or the banking system) to maintain payments. (5)It should be mentioned that some models (e.g., Gorton [1985]) emphasize private information by banks about their own asset position in explaining panics and suspensions. However, as Rolnick banks [1987] demonstrates, such a position would be difficult to defend as a practical matter, since rates of interest on passbook accounts conveyed substantial information about the riskiness of bank portfolios. (6)An explanation for the differences between Canadian and U.S. banking history that is not considered here (suggested to me by Tom Courchene) is that Canadian banks were able to issue notes freely, and to use them in meeting withdrawal demand. This argument, while different from that considered here, would suggest that the susceptibility of a banking system to panics depends heavily on legal specifications regarding how depositors can demand payment. Interestingly, in Canada (with unlimited branching) the number of branch offices closed during 1930-33, as a percentage of total offices, was roughly equal to the percentage of U.S. banks that failed during the same period. This suggests a similar stimulus, but a very different response in the two economies. For an argument that the difference was due to the kinds of branching restrictions discussed in the text, see White [1984]. (7)This figure is from Sprague [1910]. As pointed out to me by David Laidler, Sprague's calculations deduct clearing-house exchanges from individual deposits. (8)Quoted by Sprague [1910, p. 97]. Incidentally, it is common in more modern studies to question the practical significance of usury laws and to suggest that their provisions were easily evaded. However, the conclusion of the clearing-house report is consistent with the fact that the rate of interest on interbank deposits paid by New York banks "remained remarkably stable at 2 percent per annum..." over the entire 1888-1907 period (James [1978, 263]). James [p. 265] reiterates this point: "in spite of substantial general downward pressure on interest rates in the 1890s, the rate on bankers' balances remained virtually fixed at 2 percent with some short-lived deviations." James attributes this to "competition," but does not state why competition would imply constant rates on interbank deposits in the face of significant movements in other rates. In fact, it appears that these interest rates were not used to "protect or augment" the resources of New York banks according to circumstances. Whether this is for the reason cited in the text or not would seem to require a careful study of the determination of interest rates on bankers' balances. I am aware of no such study, and such a study is clearly beyond the scope of this paper. However, since models following Diamond and Dybvig generally assume that interest rates could not be made sufficiently state contingent, it seems useful to explore the implications of taking the claim in the clearinghouse report seriously. (9)The ratio of cash holdings to individual deposits for national banks as a whole was higher in 1873 than in all but three subsequent years before 1910 (National Monetary Commission [1910, Table 12]). (It should be noted, however, that these figures do not include the holding of national bank notes by these banks.) It is true that this ratio was lower in 1873 than it had been in previous years, but even so Sprague argues that "the cash foundation of the credit structure had not been seriously weakened" [1910, 10]. Also, it might be noted that the seven largest New York reserve agents had a somewhat weaker reserve position than did the other New York national banks. How important this fact might have been is hard to know, since the New York Clearinghouse members pooled their reserves during the panic. (10)See also Gorton [1986], who concludes that depositors generally did not experience any unusual losses during the panics that occurred under the National Banking System. (11)In particular, in the face of declining deposits, the cash reserves of country banks rose by $3,000,000, which constituted an 8 percent increase. It might be argued that these banks increased their cash reserves in anticipation of further runs, so that this behavior was precautionary rather than "speculative." Two comments are in order. First, the cash reserves of country banks rose, and did not decline again until the end of the panic. If country bank behavior was precautionary, apparently these banks systematically over-predicted withdrawal demand (in other panics as well). Second, in view of the detailed information on the status of the various regional banks available in Sprague, it seems likely that reserve agent banks could have gathered considerable information on which of their correspondents were likely to be run. Whether they favored such correspondents is not discussed in any literature that I am familiar with, but again the possibility of rationing speculative withdrawal demand is raised.

An interesting discussion of some of these issues in the context of the panic of 1907 appears in Laughlin [1912, 55-6]. (12)According to Friedman and Schwartz [1963, 163], the panic of 1893 was more severe than that of 1907, of which they argue "payroll difficulties apparently were less conspicuous than in 1893, for banks generally supplied their customers' requirements for this purpose in one way or another." This is despite the fact that New York banks suspended again to prevent a drain of reserves to interior banks [Friedman-Schwartz, p. 160]. (13)An alternative strategy, suggested to me by Edward Prescott, would be to have banks observe depositor characteristics at some cost. A costly state verification model of bank panics (with banks doing the verification) would be an interesting topic for future research. (14)Parenthetically, Sprague states that country banks increased their cash reserves during May and June, just as they did in the panic of 1873 [1910, 173]. This serves to emphasize that, during panics, country banks drew only on their deposits with reserve agents. This is further validation of the abstraction from the holding of reserves by country banks in the model below. (15)This is not to say that the panic did not accentuate these conditions. See Sprague [1910, 200], for a discussion of some of its consequences. (16)These figures are from Statistics for the United States, 1867-1909, Table 18. (17)Parenthetically, state banks continued to hold reserves in the form of deposits with New York, as they had under the National Banking System (Kent [1963, 48]). Other aspects of the panics of 1930-33 that mirror earlier panics are discussed by Friedman and Schwartz [1963, 167, 311]. (18)Friedman and Schwartz [1963, 311] argue that New York banks began to be affected almost immediately. They suggest, for instance, that the Bank of the United States might have been able to reopen (as the Knickerbocker Trust did in 1908) had the New York banks suspended payments in 1930. (19)While suspensions could have occurred as they did earlier, Friedman and Schwartz [1963, 311] offer some arguments as to why incentives to suspend were attenuated by the presence of the Federal Reserve System. (20)While several factors are important in explaining why relations with New York banks were generally less important during this period, regulations concerning how reserves could be held likely played a significant part. While some states allowed interbank balances in New York to count as reserves by the 1850s (James [1978, 97]), regulations about how interbank balances could be counted against reserve requirements were less favorable to the concentration of reserves in New York than they were to be under the National Banking System. That regulations allowing deposits in New York to count as reserves were important in concentrating bankers' balances there is supported by Myers's [1931, 109] discussion of Vermont banks in the 1850s. This again emphasizes the importance of institutional features of the banking system. (21)Two comments are in order. First, the episodes examined by Rolnick and Weber [1985] involved shocks affecting the value of bank assets, whereas in the model below, shocks affect the liquidity preference of depositors. However, as will be clear, shocks to liquidity preference affect the value of bank portfolios in a way that would seem to capture the general phenomenon discussed by Rolnick and Weber. Also, it would be easy to allow both for liquidity preference shocks and shocks to bank portfolios in the model, although this would not alter the basic point.

Second, while there was a systemic panic in 1857, this was not the result of geographic contagion of the type discussed in the panics of 1893 or 1930-33. The panic originated in New York (Myers [1931, 142]), although interestingly, "the drawing down of country balances marked the beginning of the strain" (Myers [1931, 143]). (22)It would be straightforward to embed the model in an overlapping generations setting. This would allow the arrangements described to be repeated over time, with suspensions occurring periodically. Since such an extension is fairly trivial, for ease of exposition only a "one-shot" version of the model is considered. (23)The assumption that all depositors in location s experience the same shock merits some comment. While inessential to the analysis, this assumption permits all liquidated banks (in this section) to pay off obligations "at par." It is also the simplest way of illustrating the incentives for the formation of interbank relations. Of course it is possible to relax this assumption at the cost of some complication. One way of relaxing this assumption would be to make the model more closely resemble that of Bhattacharya and Gale [1985]. (24)Interbank relations are, of course, ruled out only for the purposes of this section. Interlocation asset trading (that does not occur through banks) is ruled out for two reasons. First, as is the case in Diamond and Dybvig and related literature, the role for banks hinges on the absence of share markets in which claims to capital in process can be traded. (On this point see Jacklin [1983]). Second, a natural question about real world arrangements would be: if legal restrictions inhibited banks from creating optimal risk sharing arrangements, why weren't other financial markets used to accomplish this objective? A natural answer is that legal restrictions inhibited the formation of nationally integrated asset markets in general (Davis [1965, 381-3]). Thus the assumption in the text is a natural one. (25)In practice, suspensions and subsequent resumptions were common by interior banks in periods of stringency. Thus this does not appear to be an overly strong assumption. (26)Thus depositors are indifferent between deposits and direct investment in the primary asset. This indifference could be remedied by having direct investments by individuals be subject to some risk of theft, for example. It will also disappear when correspondent relations are allowed. (27)Legally banks could suspend only by ceasing discounting operations under normal circumstances. During panics suspensions were sometimes sanctioned by some states, and were "tolerated in the rest" (Friedman-Schwartz [1963, 161]). Of course banks did not cease operations during these episodes (other than the bank holiday of 1933). For a discussion of official encouragement of suspension by states in the panic of 1907, see Andrew [1908]. (28)It goes without saying that this "contract" between local banks and depositors in optimal, given the behavior of the reserve agent. In particular, the only other feasible contracts between local banks and depositors either induce depositors with [Phi](s) = 1 to withdraw at t = 1, or randomize payments among depositors. No contracts with these features can be optimal (29)This result and both follow from the assumption that cU [double prime](c)/U [prime] (c) < -1, as in Diamond and Dybvig. (30)In other words, the bank in location s pays its depositors [r.sub.1] at t = 1 if if [Phi](s) = 0 and if it receives funds from the reserve agent. The latter event occurs with probability min[[p.sup.*]/p, 1]. If [Phi](s) = 1, the bank in locations withraws from the reserve at t = 2, and pays depositors [r.sub.2](p,f). Again giveen the actions of the reserve agent, this is an optimal contract between local banks and depositors for the reasons stated in footnote 28. (31)The fact that [r.sub.1] > 1 implies that [c.sub.2](p) is decreasing in p. Hence if (9) holds with equality for [p.sup.*] it is violated for all p > [p.sup.*]. Thus suspension of convertibility is required for all p > [p.sup.*]. This validates the assertion above that suspensions must occur whenever f [Epsilon] [[p.sup.*], p [bar]]. (32)A natural modelling question would involve analyzing the consequences of introducing deposit insurance or a "lender of last resort" into this economy. This exercise is not undertaken here, since the focus of this paper is on understanding historical panics. During the episodes discussed in section II there was, of course, no (federal) government deposit insurance scheme in effect. There was a lender of last resort during 1930-33, but the failure of the Federal Reserve System to function effectively in this regard is well known.

[Mathematical Expression Omitted]

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BRUCE D. SMITH, Cornell University and Rochester Center for Economic Research. In writing this paper I have benefitted from duscissions with, and the assistance of, Charles Calomiris, Edward Prescott, Richard Sylla, and Warren Weber. I would especially like to thank William Kostak for conversations that more or less directly led to the writing of the paper. Also, I would like to thank Sudipto Bhattacharya, Phillip Dybvig, Scott Freeman, David Laidler, Arthur Rolnick, Richard Sweeney, Eugene White, and two anonymous referees for their detailed comments on earlier draft. In addition, I have benefitted from the comments of seminar participants at the Bank of Canada, the Federal Reserve Bank of Minneapolis, the University of California at Santa Barbara, the University of Western Ontario, and the University of Wisconsin, as well as participants in sessions at the American Finance Association meetings and the conference "Approaches to the Business Cycle" held at McGill University. Finally, this paper was done in part while I was a visitor at the Federal Reserve Bank of Minneapolis, which is thanked for its support. I alone am responsible for the contents, however.