Abstract
In this paper a simple optimizing model is developed to analyze the implications of a banking crisis. Banks are incorporated by assuming that they intermediate funds between firms and households. It is shown that when depositors perceive the quality of deposits to have deteriorated, they switch from deposits to cash. Because of the higher cost of liquidity, consumption, M2 and the M2 multiplier decline, interest rates on deposits and loans increase and output contracts. The findings of the paper match the key stylized facts of banking crises.
I. Introduction
Banking crises have become prevalent both in developing and developed countries in recent years. Lindgren, Garcia, and Saal (1996), report that since 1980 almost three fourths of the member countries of the IMF have experienced significant problems in their banking sectors.
The causes of banking crises may range from an external shock to the banks or their private debtors- such as a deterioration in the terms of trade, a devaluation of the currency, or a crash in equity or property prices, etc. – or to self-fulfilling runs.2 But once they occur, their effects on the economy have been observed to be quite severe. Besides entailing a significant impact on economic activity, banking problems have often necessitated a large scale bailout of the banking sector and have been accompanied by weaker currency. Calvo and Reinhart (1999) show that the GDP growth rate averaged -3.2 percent during the banking crises episodes in their sample of 20 countries, the cost of bailing out the banking sector exceeded the historic mean by 15 percent of GDP during 1995-97 in East Asia, and by 8.3 in Latin American countries. In a similar vein, Kaminsky and Reinhart (1999) had earlier found that since the 1970s half the currency crises in their sample of 20 Asian, European and Latin American countries were preceded by banking crises.3
The theoretical literature on banking crisis until recently had mainly focused on closed economy models to explain bank runs. Important early contributions to this literature include Diamond and Dybvig (1983) and Gorton (1988). Due to the increased importance of capital flows and the effect of external disturbances on banking sectors throughout the world, the literature has recently been extended to include open economy models of bank runs. Contributions include Chang and Velasco (1998) and Goldfajn and Valdes (1997). However, while explaining the mechanics and the dynamics leading up to the bank run, none of these papers study the period after the banking crisis.
A number of papers, e.g., Gorton (1988), Lindgren, Garcia and Saal (1996), Calvo and Reinhart (1999) and Kaminsky and Reinhart (1999), have studied the period around the banking crises empirically and established several stylized facts pertaining to the aftermath period.4 In these papers the aftermath period has been shown to be accompanied by the following characterization of monetary and real variables: a withdrawal of deposits, a decline in the demand for money, an increase in the ratio of cash to deposits, a decline in the bank credit, an increase in the interest rates on credit and deposits, an increase in the M2 multiplier, and a decline in economic activity (these stylized facts have been summarized in Table 1).
Stylized Facts on Banking Crisis
The study covers 131 members countries of the IMF. However, a smaller sample of 34 countries has been used for the analysis of the effects of banking crisis.
Stylized Facts on Banking Crisis
| Sample | Episodes | Stylized Facts | |
|---|---|---|---|
| Gorton (1988) | United States, 1873-1914 | 7 panics in U.S. National Banking Era Panics | Cash to deposit ratio declined, deposits suffered losses, output declined. |
| Kaminsky and Reinhart (1999) | 20 countries, 1970-1997 | 26 episodes of banking crisis | M2 multiplier declines, deposits decline, domestic credit-to-GDP ratio increases, output smaller, lending-to-deposit interest rate increases. |
| Lindgren, Garcia and Saal(1996) | 34 countries, 1980-Spring 1996 1/ | 36 episodes | High interest rates and high interest rate spreads, financial disintermediation (credit crunch, lower growth, decline in deposit to GDP ratio), increase in the cash to deposit ratio, decrease in money multiplier, increased credit to the banks, substantial cost of restructuring, loss in international reserves and depreciated exchange rate. |
The study covers 131 members countries of the IMF. However, a smaller sample of 34 countries has been used for the analysis of the effects of banking crisis.
Stylized Facts on Banking Crisis
| Sample | Episodes | Stylized Facts | |
|---|---|---|---|
| Gorton (1988) | United States, 1873-1914 | 7 panics in U.S. National Banking Era Panics | Cash to deposit ratio declined, deposits suffered losses, output declined. |
| Kaminsky and Reinhart (1999) | 20 countries, 1970-1997 | 26 episodes of banking crisis | M2 multiplier declines, deposits decline, domestic credit-to-GDP ratio increases, output smaller, lending-to-deposit interest rate increases. |
| Lindgren, Garcia and Saal(1996) | 34 countries, 1980-Spring 1996 1/ | 36 episodes | High interest rates and high interest rate spreads, financial disintermediation (credit crunch, lower growth, decline in deposit to GDP ratio), increase in the cash to deposit ratio, decrease in money multiplier, increased credit to the banks, substantial cost of restructuring, loss in international reserves and depreciated exchange rate. |
The study covers 131 members countries of the IMF. However, a smaller sample of 34 countries has been used for the analysis of the effects of banking crisis.
The purpose of this paper is to present an analytical model that may be useful in understanding these implications of banking crises. In an important contribution Edwards and Vegh (1997) have embedded banks in an open economy perfect foresight framework and use the framework to explain how the banking sector affects the propagation of domestic and external
shocks. This paper differs from that of Edwards and Vegh in the following respects: first, it specifically analyzes the issue of a banking crisis, and for this purpose it explicitly incorporates the possibility of a banking crisis in the households’ maximization problem and derives the effects of banking crisis on the monetary aggregates and real variables and thereby assist understanding the above stylized facts. Among the modelling aspects, it allows the households to hold both deposits and cash to finance consumption, thus explaining the switch from deposits to cash and the effects on the monetary aggregates after a banking crisis.
The model uses a representative agent, perfect foresight model where households can use cash and deposits for liquidity; firms use bank credit to finance the import of an input which is used in the production of a final good. The banks are modeled as in Edwards and Vegh (1997), and are assumed to operate in a perfectly competitive environment and to intermediate funds between households and firms by accepting deposits from households and making loans to firms. Banking is assumed to be a costly activity, where the cost of intermediation depends on the total amount of loans and deposits. The cost function is assumed to be convex with complementarity in the production of deposits and loans. The results are also compared with costless banking in the paper.
The dynamics of the model are analyzed when banks are perceived to be unhealthy by depositors such that they believe that either the banks will restrict the withdrawal of deposits or will default on their deposits, since these are the common responses of the banks during crises, specially if deposit insurance is incomplete or nonexistent. In either case, by losing their liquidity or their value, the deposits deteriorate in quality.
First we analyze the case when depositors perceive the banks to be fragile only for a temporary period. Thus they believe that at a certain date in the future the deposits will regain their quality. Second, we discuss the case when health of the banking sector is perceived to have deteriorated permanently, a belief which may be revised later, e.g. after a restructuring of the banking sector. We find that when the quality of deposits deteriorates then the opportunity cost of holding deposits increases and consumers switch from deposits to cash; the demand for broad money and money multiplier decline.5 The decline in deposits causes a liquidity squeeze for the bank and there is financial disintermediation: the interest rate on credit increases, the demand for credit declines and output contracts. If the deterioration in the quality of deposits is perceived to be temporary then, due to the liquidity-in-advance constraint, the current effective price of consumption is higher and there is an intertemporal substitution of consumption. The net effect on the demand for cash and current account depends on the intertemporal elasticity of substitution, the degree of substitution between cash and deposits and the output effect of crisis. When the deterioration is perceived to be permanent, there is no intertemporal substitution of consumption and the current account always balances.
The paper proceeds as follows. The model is developed and the equilibrium conditions are derived in Section II. The implications of a banking crisis are analyzed in Section III and Section IV concludes.
II. Basic Model And Equilibrium Condition
A small open economy is considered which operates under a predetermined exchange rate and is inhabited by four types of representative agent: households, banks, firms and the government. One internationally traded final good is produced and consumed in the economy. This good is used as the numeraire and all the real variables are measured in terms of this good.
There is free movement of the good across countries and purchasing power parity holds. Thus, assuming that the foreign price of the good is constant, the rate of inflation of the domestic good, πt, equals the rate of depreciation of the nominal exchange rate, εt. The world real interest rate, r, is assumed to be constant. Perfect capital mobility implies that the interest rate parity condition holds, therefore the nominal interest rate equals the real international interest rate plus the expected rate of depreciation, i.e., it = r + εt. The households consume the final good and use cash and demand deposits denominated in domestic currency for liquidity. The production of the good requires an imported input. The firms produce the final good and finance the import bill through loans from the banks. The banks, operating in a perfectly competitive industry, accept deposits from the households and also borrow internationally. The government returns the proceeds from the inflation tax and interest income to households in each period.
A. The Household
The households maximize the present discounted value of lifetime utility which they derive from the consumption of the final good. The objective function of the representative household is given by:
The instantaneous utility function, u(.), is assumed to be increasing in c, twice continuously differentiable and strictly concave, ρ denotes the constant subjective discount rate, which is assumed to be equal to the world interest rate. The consumer is subject to a “liquidity in advance” constraint whereby he needs to hold liquid assets to make purchases.6 In the current formulation of this constraint he can hold cash and demand deposits denominated in domestic currency for liquidity services. The liquidity-in-advance constraint requires that consumption should not exceed the liquidity services provided by cash and deposits, i.e.,
where zt and dt denote the real balances of cash and demand deposits respectively; l(.) is a concave, homogeneous of degree 1, twice-continuously differentiable function; a subscript with l is used to denote the partial derivative of the function with respect to that argument. The consumer also holds an internationally traded bond,
The nominal yields on zt and dt equal zero and
adding and subtracting rzt + rdt in the R.H.S. of (equation (4)) we get
(Equation (5)) says that the rate of change in the wealth of the household consists of the return on wealth, a lump-sum transfer from the government, profits from the firms and banks, less consumption expenditure and the opportunity cost of holding deposits and cash. Integrating forward and imposing the no-Ponzi condition, the household’s lifetime budget constraint reduces to:
The household chooses the optimal time paths of ct, zt and dt to maximize (equation (1)) subject to equations (2) and (6), given the initial real wealth,
where λ is the time invariant Lagrange multiplier associated with constraint given by (equation (6)).7 (Equation (7)) has the interpretation that the marginal utility of consumption equals the marginal utility of wealth times the effective price of consumption. The effective price of consumption equals the market price of the good which is equal to unity, plus the marginal cost of producing the liquidity services required to purchase a unit of the consumption,
The effective price of consumption is higher, the higher the cost of liquidity. Thus Ρ increases in it and decreases in
where ϕ′ [.] < 0. By combining equations (2) and (10), the demand for cash can be written as a positive function of consumption and a negative function of the relative opportunity cost of cash and deposits; the demand for deposits can be written as a positive function of consumption and a positive function of the relative opportunity cost of holding cash and deposits.
An increase in the relative opportunity cost of holding cash induces the household to increase the ratio of deposits to cash. Since cash is more productive at the margin, the demand for deposits increases by more than the decline in the demand for cash, therefore the demand for money increases. Thus, we may write the demand for money, defined as the sum of cash and deposits, to be a positive function of the relative opportunity cost of cash and deposits and a positive function of consumption. More specifically the demand for cash, deposits and money may be expressed as below8:
where mt = zt + dt.
B. The Bank
The representative bank accepts deposits from households, holds cash reserves, lends to firms and invests in an internationally traded bond. The financial assets of the bank consist of international bonds,
Net assets evolve according to the following equation:
where
It is assumed, à la Edwards and Vegh (1997), that banking is a costly activity. The assumption of costly banking has previously also been made by Fischer (1983) and Calomiris (1999). Various types of costs that banks may have to incur include: evaluating creditors, managing deposits, renting buildings, maintaining ATMs, etc. Calomiris (1999) argues that banks invest in private information to allocate capital, which is reflected in the special quality of bank lending and in bank-firm relationships, e.g. they screen new customers and keep track of and control the behavior of existing customers. Since these activities are costly, banks are paid for their trouble in the form of higher fees and interest. In this paper the cost function is assumed to be linearly homogenous, strictly increasing and convex:10
Thus, the marginal cost of providing credit and accepting deposits is positive and increases with an increase in the stock of loans or deposits. The negative cross partial derivative between loans and deposits indicates that there is complementarity in the production of credit and deposits. Thus the marginal cost of granting credit increases for the bank if deposits decrease. This may reflect the fact that the fall in deposits lowers the available information on borrowers which makes it more costly to monitor loans (also see Fama (1985) for such an interpretation). It may also reflect the fact that when banks are flush with deposits they scrutinize the creditors less, rather than when deposits are relatively scarce.11 Similarly, the marginal cost of holding deposits increases for the bank if loans decrease or do not increase proportionately. To close the model it is assumed that the household and/or firm collects the operational cost from the bank as payments for the input services provided.12
By integrating forward and imposing the no-Ponzi condition, the present discounted value of the total distributed profits can be written as:
The bank chooses the time paths of lt and dt given the initial value of its assets, a0, and paths of r, it,
Equations (19) and (20) simultaneously determine the supply of loans and deposits by the bank for given
Interest Rates and Supply and Demand of Credit and Deposits
Citation: IMF Working Papers 2000, 096; 10.5089/9781451851908.001.A001
Interest Rates and Supply and Demand of Credit and Deposits
Citation: IMF Working Papers 2000, 096; 10.5089/9781451851908.001.A001
Interest Rates and Supply and Demand of Credit and Deposits
Citation: IMF Working Papers 2000, 096; 10.5089/9781451851908.001.A001
The intersection of respective demand and supply schedules determines the equilibrium interest rates on credit and deposits. Each bank takes these interest rates as given and determines its supply of credit and deposits, as shown in panels Β and D in the figure. A decline in deposits would make the supply of credit more costly and by shifting the supply curve to the left results in an increase in the interest rate on credit. Also notice that for the costless banking,
C. Firm
The firm produces the final good by using an imported input denoted by nt. The production function, f(nt), satisfies the usual concavity properties.14
It is assumed that the firm is subject to a loan in advance constraint, which says that it needs to hold bank credit to finance its import bill, given by (equation (22)),15
where pt denotes the terms of trade.
In principle, firms can borrow domestically or in the international capital market. Domestically, the firm borrows from a domestic bank. The international capital market offers two types of financial instruments: an international bond and a foreign bank credit line. The firm accumulates its wealth in international bond,
We assume that even if the firms have access to a foreign bank credit line, in practice (because of the lower cost) they rely exclusively on domestic banks for such credit needs. The assumption is consistent with the evidence which shows that the firms in developing countries predominantly depend on domestic banks for most of their credit needs.16 The assumption can further be justified by arguing that in equilibrium the firms and domestic banks may find it optimal to build relationships with each other, since the cost of building such relationships may be lower than with foreign creditors (e.g., because of the physical proximity). Moreover, since domestic agents hold deposits with the domestic banks, the latter may find it less costly to evaluate the credit worthiness of the firms and therefore may be able to offer cheaper credit.
Thus, the representative firm accumulates its wealth in the form of international bonds and uses the credit line from the domestic bank for liquidity purposes. The net financial wealth of the firm,
where
The firm chooses the optimal path of nt to maximize (equation (24)) given the initial stock of assets,
which says that at an optimum the firm equates the marginal product of imported input to the opportunity cost of buying the input which equals the market price at which the input is purchased plus the opportunity cost of using credit to finance it.
D. Government (Monetary Authority)
The government issues high powered money, Ht, which is held by households in the form of cash and by banks in the form of cash reserves, i.e.
and sets the path of the rate of devaluation and the minimum reserve requirement ratio. It makes credit available to the banks, holds international bonds,
Integrating forward and imposing the no-Ponzi condition, the lifetime budget constraint of the government can be written as:
where
Therefore change in b equals the change in H (minus government consumption if any) at time t, i.e.,
E. Equilibrium Conditions
The economy’s life-time resource constraint, obtained by combining equations (6), (18), (24) and (28), is given as:
where b0 denotes the economy’s initial bond holdings, which equals the sum of bonds held by all the agents in the economy. The above equation says that the present discounted value of consumption equals the present discounted value of the resources in the economy, the latter being equal to the stock of international bonds and the present discounted value of net output. We derive the equilibrium path of consumption assuming a log utility function, i.e. u (c) = log (c). The first order condition for consumption is:
Using equations (31) and (32), the equilibrium value of the Lagrange multiplier can be written as:
By substituting for λ into (equation (32)) we get the equilibrium consumption path as:
The first term on the right hand side of (equation (34)) can be interpreted as the average effective price of consumption over the interval [0, ∞); and the denominator in the second term as the current effective price of consumption. Thus, consumption is greater than the present discounted value of resources, if the current effective price is lower than the average effective price of consumption and vice versa. The equilibrium current account path can be derived by combining equations (5), (16), (23) and (27) and may be written as:
Current account thus equals the interest on foreign assets and output net of imported inputs and consumption.
III. Banking Crises
Banking crises have been defined in several alternative ways in the literature. A distinction is often made between a bank run and bank insolvency, but the latter also often results in a run on the bank. A widely accepted definition of bank panics is provided by Calomiris and Gorton (1991) whereby: a banking panic occurs when bank debt holders at all or many banks in the banking system suddenly demand that banks convert their debt claims into cash to such an extent that the banks suspend convertibility of their debt into cash. A bank, on the other hand, is said to be insolvent if its net worth is negative. Caprio and Klingebiel (1996) find that the financial insolvency in the banks is usually preceded by shocks such as a deterioration in the terms of trade, a crash in equity or property prices, etc.
The major explanations of banking crisis have been provided in Random Withdrawal Hypothesis (put forth by Diamond and Dybvig (1983)) and Asymmetric Information Hypothesis (by Gorton (1988)). According to the Random Withdrawal Hypothesis, panics can occur as a result of self-fulfilling beliefs. In the Asymmetric Information Hypothesis panics are most likely to occur when bad news follows a period of high loan demand and a prolonged expansion in economic activity, as bank leverage is high. The shock causes depositors to revise their perceived risk of deposits if they are uninformed about bank asset portfolio values.
The banks’ response to a run may be either to suspend or limit the withdrawal of their liabilities, which are predominantly deposits, or to liquidate its assets at a loss and return a proportionate amount to its creditors, who are mostly depositors. In either case the relative opportunity cost of holding the deposits increases for the consumer. In our model we introduce two parameters, μ and θ, to measure the impact of banking crisis on the liquidity and value of the deposits, respectively, μ denotes the liquidity parameter associated with deposits and θ denotes the rate of default on deposits.18
Since we are primarily interested in the aftermath of the banking crises, the source of the crisis is not important to the analysis. The depositors perceive, possibly after a shock, that either the liquidity or the asset quality of the bank is poor and therefore the bank would restrict the withdrawal of deposits or not redeem them at their par value. Some possible factors which may generate these kinds of beliefs include: a revelation about the poor asset or liquidity position of the bank which makes the depositors update their beliefs about the true health of the bank and the safety of their deposits; a sudden cessation of capital flows etc.19
Ignoring domestic credit, a withdrawal of deposits needs to be met through a reduction in bank credit and/or the cash reserves or an inflow of international credit, otherwise the bank will have to restrict the withdrawal of deposits. Thus, each depositor would be allowed to withdraw only a certain proportion of deposits, which would be determined by the available funds. Thus, assuming that the banks do not hold any excess reserves and that the international flows dry up at the same time (or precede) when there is a run on the banks, the following equation needs to hold at each point in time:20 (1 − γ) Δd = Δl or Δd = Δl/(1 − γ).
If, however, credit contracts by less than the amount required to reimburse the depositors (net of cash reserves), then the amount of deposits that can be withdrawn will be constrained to the available liquid funds. Thus, μ = Δl/(1 − γ)Δd, is the proportion of deposits that can be withdrawn by households. It is assumed that each depositor takes μ as given, i.e. he cannot affect μ unilaterally. In equilibrium μ will of course be determined by the total deposit withdrawal from the banks as compared to the liquidity that the banks can arrange from loans and other sources such as the international capital market, the monetary authorities etc. If the banks could arrange sufficient funds from the government or from the international financial market then they would not have to restrict liquidity. After incorporating μ, the liquidity in advance constraint can be written as:
where
If instead of restricting the withdrawal of deposits the bank decides to liquidate its assets at a loss, i.e. it engages in a fire sale of its assets in order to meet the demand for liquidity, and decides to pass on the losses to the depositors, then the net yield on deposits is reduced by the rate of default. Thus the net return on deposits becomes
Though default on deposits is admittedly a less frequently observed phenomenon in the real world, since deposits are usually federally insured, it remains relevant because often these guarantees are implicit and the rules of the game are ill defined. Moreover, default also becomes a possibility when the total amount of deposit guarantees falls short of the extent of insolvency; this situation is likely to arise when there is a system wide bank insolvency. Here we are assuming that the explicit deposit guarantee is not sufficient to rule out a default, for simplification we may assume the guarantee to be zero. After incorporating μ and θ in the maximization problem of the household, the first order conditions may be written as
From (equation (38)) an increase in θ or a decrease in μ, at given
Below we discuss the effects of a decrease in μ. Since an increase in θ is an analytically similar case, we do not discuss it separately. We first analyze the case when depositors perceive the decline in μ to be a temporary phenomenon, and they expect that at a certain date in the future μ will revert back to the higher level. For analytical interest we also discuss the case where banks are perceived by consumers to have become permanently weaker, though they may revise their beliefs later. We also discuss the implications of deterioration in the quality of deposits when banking is costless.
A. Temporary Decrease in the Liquidity Parameter of Deposits
Suppose that at time 0 the liquidity of deposits worsens such that μ decreases from μΗ to μL, and that depositors perceive that at time Τ in the future it will be brought back to μΗ,22 which may be assumed to be equal to one, and that εt = ε, θ = 0, pt = p and γt = γ for t ≥ 0. More formally,
where μL < μΗ. Initially, at time 0, there is steady state and consumption is equal to rb0 + f(n) − pn, therefore the current account is in balance. The following proposition summarizes the behavior of relevant variables following a temporary decrease in μ. Main results of this exercise are also summarized in Figure 2.
A Temporary Decrease in μ
Citation: IMF Working Papers 2000, 096; 10.5089/9781451851908.001.A001
A Temporary Decrease in μ
Citation: IMF Working Papers 2000, 096; 10.5089/9781451851908.001.A001
A Temporary Decrease in μ
Citation: IMF Working Papers 2000, 096; 10.5089/9781451851908.001.A001
Consider a perfect foresight equilibrium path along which θt = θ = 0, εt = ε, pt = p and γt = γ for all t є [0, ∞), if μt decreases temporarily at t = 0 then l/d increases, il and id increase, d and l decline,
We first show that when μ decreases temporarily at time 0,
Suppose that when μ decreases at time 0,
remains unchanged, i.e. From equations (19) and (20) this implies that are unchanged and combined with (equation (25)) it has the implication that l and thus d remain unchanged. From (equation (38)) the ratio of cash to deposits increases at given . If deposits remain unchanged then it implies that cash holdings and M2 increase; there is an intertemporal substitution of consumption, and consumption declines. This gives a contradiction with an increase in M2 and an increase in the share of cash in M2. Suppose that when μ decreases at time 0,
decreases, i.e. . From equations (19) and (20) this implies that increase and combined with (equation (25)) it has the implication that l increases, thus d increases proportionately more. From (equation (38)) the cash to deposit ratio increases, which implies that cash increases proportionately more than deposits, therefore M2 increases. However the current effective price of consumption is higher both because of a decline in μ and an increase in thus there is an intertemporal substitution of consumption and consumption declines. This gives a contradiction with an increase in M2 and an increase in the share of cash in M2.
Therefore when μ decreases at time 0,
If the increase in id more than offsets the decline in μ, then from (equation (38)) we get a decline in the ratio of cash to deposits. Also the effective price of consumption is now lower and therefore consumption increases. A decline in deposits combined with a decline in the ratio of cash to deposits implies that cash decreases proportionately more than the decline in deposits. Therefore demand for money declines which gives a contradiction with an increase in consumption.
Notice that because of a decline in l, output is smaller as well between period 0 and T. Since both output and consumption are smaller between 0 and T, the effect on the current account is ambiguous. The current account at time Τ will depend on the intertemporal elasticity of substitution, IES, and the output effect. If output does not contract much between period 0 and Τ and the IES is large, then the current account will become positive. The level of consumption at T, as compared to the period prior to the crisis, is also not clear and depends on the current account. If the intertemporal substitution effect and output effects are strong enough to yield a positive current account between period 0 and T, then the economy will accumulate foreign assets and consumption at time Τ will be higher than the pre-crisis level and vice versa. Panels D and F in Figure 2 exhibit these various possibilities.
The demand for cash is subject to two offsetting forces: a positive substitution effect, because of the higher cost of holding deposits, and a negative level effect, because of lower consumption. The net effect is ambiguous. The level effect would be stronger than the substitution effect if the IES is high and/or the intratemporal elasticity of substitution between cash and deposits is small.23 Notice that the demand for M2 is lower both because there is a switch to a more costly and therefore more productive source of liquidity, the substitution effect, and because of lower consumption. Because of the substitution effect, the decline in M2 is proportionately more than the decline in consumption, therefore M2 multiplier (defined as M2/consumption) is smaller.
Thus to summarize: a worsening of the liquidity of deposits increases the opportunity cost of holding deposits; and the effective price of consumption increases. Therefore households switch from deposits to cash and consumption and total money demand declines. A decline in deposits implies that the banks find it more costly to offer credit, therefore the interest rate on credit increases and output declines.
When banking is costless, (equation (8)) reduces to
Identical dynamics are obtained if instead of restricting the liquidity of deposits the bank defaults on them. Thus, suppose that at time 0, θ becomes positive and equals θH, and at time Τ it is brought back to 0 and that εt = ε, μ = 1, pt = p and γt = γ for t ≥ 0; the results are analytically similar to the previous case in which the liquidity of deposits worsens.
B. Permanent Decrease in the Liquidity Parameter of Deposits
Suppose that at time 0 the liquidity of deposits worsens such that μ decreases from μΗ to μL, and that εt = ε, θ = 0, pt = p and γt = γ for t ≥ 0. More formally,
When the depositors perceive the deposits to have deteriorated in quality permanently, the intertemporal substitution in consumption does not take place. Since deposits become more costly the switch from deposits to cash still takes place. Thus the deposits are withdrawn, which in turn causes id and il to rise and l and output to contract Consumption falls at time 0 from the pre-crisis level because of the negative output effect, but stays constant there after. The current account balances in each period. Because of the substitution and level effects, the demand for cash, as compared to the pre-crisis level, is not clear and M2 and the money multiplier are smaller compared to their pre-crisis levels.
Now suppose that depositors’ confidence in the banking system is revived at some time, let’s say T, possibly due to positive news, such that they revise their beliefs, and bring μt back to μΗ. Until time T, the dynamics remain the same as when the decline in μ was perceived to be a permanent change, but at time Τ the reverse dynamics are obtained: the depositors switch back into deposits, which brings interest rates down, increases credit and output; consumption, M2 and the M2 multiplier increase (the current account, however, balances from period Τ onwards as well). See Figure 3.
A Permanent Decrease in μ: Beliefs Revised at Time T
Citation: IMF Working Papers 2000, 096; 10.5089/9781451851908.001.A001
A Permanent Decrease in μ: Beliefs Revised at Time T
Citation: IMF Working Papers 2000, 096; 10.5089/9781451851908.001.A001
A Permanent Decrease in μ: Beliefs Revised at Time T
Citation: IMF Working Papers 2000, 096; 10.5089/9781451851908.001.A001
IV. Conclusion
This paper explains the stylized facts which show that banking crises are associated with: a withdrawal of deposits, a decline in the demand for money, an increase in the ratio of cash to deposits, a decline in bank credit, an increase in the interest rates on credit and deposits, a decrease in the M2 multiplier and lower economic activity. The paper shows that a banking crisis makes deposits less attractive relative to cash for a consumer who uses cash and deposits for liquidity purposes; thus, there is a switch from deposits into cash. The demand for consumption declines because of the higher opportunity cost of holding liquidity. Deposit withdrawal, in turn, results in a credit crunch and higher interest rates, and thereby a decline in economic activity.
Several extensions are possible within the framework developed in the paper. First, the model can be used to analyze the effects of financial liberalization. In the model, financial liberalization will result in a decline in the intermediation cost and more favorable interest rates on loans and deposits, and will encourage economic activity and generate a lending boom.
If, however, in a zeal to lend the surplus funds the banks’ scrutiny of potential debtors slackens, then it can eventually result in defaults and losses and culminate in banking distress and panic. Second, it is also possible to show in the existing framework another channel whereby banking and currency crises may be linked. This channel is different from the bailing out story, and works through a decline in the demand for money which accompanies the banking crisis. The weaker demand for money would increase the possibility of a currency crisis.
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This paper is based on Chapter 2 of my dissertation. I am grateful to Guillermo Calvo, Enrica Detragiache, Allan Drazen, Arvind Panagariya, Carmen Reinhart, Peter Wickham and the seminar participants at the Federal Reserve Bank of New York, Inter-American Development Bank, SEA Meetings (1997), SUNY-Buffalo, University of Maryland and the University of Oregon for many valuable suggestions and comments.
See Caprio and Klingebiel (1996) for the evidence on the sources of the banking crises for a sample of 69 countries.
Also see Reinhart, Gupta, and Kaminsky (1999).
In a forthcoming paper Demirgüc-Kunt, Detragiache and Gupta (1999) systematically study the aftermath of a large number of banking crises cases.
We assume that international funds dry up at the same time that deposits are withdrawn. If the banks could raise sufficient liquidity from other sources then they will not have to restrict the liquidity of their deposits or engage in a fire sale of the assets.
The assumption of a cash-in-advance or liquidity-in-advance constraint is quite standard in the literature, see, e.g., Calvo and Vegh (1990), Calvo and Vegh (1995), Edwards and Vegh (1997) etc. For an interpretation of the cash-in-advance constraint in continuous-time models see Feenstra (1985).
It is assumed that i and i − id are positive, hence the liquidity in advance constraint holds with equality at all times.
For further details see Calvo and Vegh (1990).
We assume that the deposits are offered in terms of domestic currency only. The model can also be extended to the case where banks offer deposits denominated in foreign currency as well.
A possible form of the cost function which satisfies these properties is
It would then also imply that if the banks can attract a large amount of deposits, there would be a credit boom and the quality of bank credit would deteriorate. However, since it is beyond the scope of the paper we do not analyze this phenomenon here.
We could have also assumed that government obtains the operational cost from the bank, as has been done by Edwards and Vegh (1997). If, instead, this expenditure is assumed to be a social waste then it would show up in the economy wide equilibrium condition and would imply that the cost for the economy increases when the total absolute amount of loans or deposits increases.
Due to the assumptions of perfect competition and constant returns to scale, the bank earns zero profit in equilibrium.
We could include labor as a factor of production as well. It would, however, not add much to the analysis.
To interpret the loan in advance constraint in continuous timing α can be interpreted as the length of time for which the firm must hold credit to finance its import bill; see Feenstra (1985).
For evidence see, Rojas-Suarez and Weisbord (1995), and Calomiris (1999).
We are assuming that the government balances the budget in each period. We could have also assumed that the government runs a fiscal deficit, but this would result in a depletion of reserves and culminate in a currency crisis. See Calvo (1995) for details on the mechanics of a balance of payments crisis in a cash-in-advance setup.
See Lindgren et al. (1996) for the instances of banking crises where the withdrawal of deposits has been constrained in practice.
Other shocks such as deterioration of the terms of trade or a productivity shock to the firm, may also trigger banking problems by increasing problem loans. These will, however, have some additional effects of their own; e.g., they will lowering the demand for credit by the firm, thus lower the interest rate offered on deposits, resulting in lower consumption and output. As we will see below, most of the real and monetary effects of banking crises will remain the same in such cases, but their magnitudes will differ.
Velasco (1987) assumes that because of uncertainty and the possibility of default, there may be a ceiling on the international borrowings.
In Gruben and Welch (1993) a similar parameter θ is defined as one minus the proportion of deposits returned to each depositor by an insolvent bank; the latter equals the ratio of the market value of assets to total deposits, which is less than one for an insolvent bank.
Either because the shock is temporary or because the bank will be restructured by the government at time T.
Empirically, in many papers the IES has been found to be less than 1. The estimates of IES found by Ostry and Reinhart (1992) fall in the range of 0.4 to 0.8.
