Monetary Stabilization in a Structurally Unstable Financial Environment

Monetary Stabilization in a Structurally Unstable Financial Environment by Stefan Jungblut* University of Paderborn Abstract: This paper analyzes mo...
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Monetary Stabilization in a Structurally Unstable Financial Environment by

Stefan Jungblut* University of Paderborn

Abstract: This paper analyzes monetary stabilization in a structurally unstable economy. The economy has multiple stationary states, differing in credit market conditions and economic activity. Under certain conditions two monetary stationary states are stable and self—fulfilling deflationary crises can occur. The model implies that adjusting long— run monetary conditions is insufficient to coordinate the inflation expectations of agents. To invalidate deflationary expectations a monetary impulse must overshoot the saddle—path to the high activity stationary state and be complemented by a long—run inflation target. The target can credibly be set subject to maintaining long—run price stability. Keywords: Deflation, Financial Markets, Central Banking. JEL Classification: E31, E44, E58, O53.

*University of Paderborn, 33095 Paderborn, Germany. E-Mail: [email protected]

1 Introduction This article focuses on monetary stabilization policies for economies characterized by low inflation and financial instability. Stimulated by the series of adverse shocks to the world economy, questions about the conduct of monetary policy under conditions of low inflation have recently gained substantial interest. Over the past decade many central banks have been quite successful in reducing the average level and the volatility of inflation, and it is generally accepted that low and stable inflation is economically advantageous in several dimensions. However, the Japanese experience during the 90s brought to mind that low levels of inflation can also limit the scope of central banks to counteract declines in economic activity with conventional policy measures.1 Recent developments in the world’s financial markets have increased the fear that central banks of other major economies could become constrained by similar limitations.2 For many central banks, short term nominal interest rates are important operating targets in the conduct of monetary policy. But if inflation is low, these interest rates will be low as well, especially in times of sluggish economic activity. This coincidence can impose a problem on monetary policy because nominal interest rates cannot fall below zero. Once the zero lower bound is binding, a decrease in expected inflation — due to an adverse shock or a change in expectations — cannot be offset by an appropriate interest rate cut. The gap between the nominal rate and expected inflation will thus increase. However, this gap is equal to the expected real interest rate. The decrease in expected inflation therefore implies a higher expected real cost of borrowing which can further accelerate the initial contraction in economic activity and decline in prices. The literature on monetary stabilization of deflating economies is rapidly growing.3 The variety of strategies ranges from setting an inflation target or a price level target4 to monetary easing and depreciating the currency5 , or a specific combination of different measures.6 Despite their heterogeneity, however, most approaches are based on two important insights. The first is the outstanding importance of expectations. To be successful, any monetary policy to stop deflation must eventually 1

See e.g. Bayoumi/Collyns (2000), Cargill/Hutchison/Ito (2000), Kashyap (2002) or Kuttner/Posen (2001) for a detailed discussion of the developments in Japan over the 1990s. 2 Most notably the US and Germany. See IMF (2003). 3 See BOJ (2001) and Fuhrer/Sniderman (2002) for collections of recent research and Svensson (2003) for an overview and further references. 4 See Bernanke (2000), Krugman (1998), Posen (1998, 1999) for a discussion of an inflation target and Svensson (2001) for a price level target. 5 Benhabib/Schmitt—Grohé/Uribe (2002), Clouse et al. 2000, Goodfriend (2000), Meltzer (2001), and Orphanides/Wieland (2000) consider monetary easing. Depreciating the currency is considered in Bernanke (2000), McCallum (2000), and Meltzer (2001). 6 The so called Foolproof Way. See Svensson (2001, 2003).

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succeed in affecting the inflation expectations of agents.7 As long as agents expect a deflation to prevail, the expected real interest rate will remain high. The high real rate, however, is one of the principal reasons for sluggish demand and investment activity in a deflationary environment.8 The second insight concerns credibility. Policies which rely too heavily on promised future actions that are contradictory to maintaining price stability may suffer from a lack of credibility. However, finally only a credible policy can support a revision of the expectations of agents.9 Although the importance of expectations and credibility is widely accepted, their determinants in the context of monetary stabilization are still hard to understand. This article focuses one of these determinants in more detail: the stability of the financial sphere. Deflation and financial weakness often appear as related problems. The most outstanding example of this conjunction is the Great Depression of the 30s. Yet the decade of stagnation in Japan, too, was triggered by a collapse in financial markets which seriously undermined the health of the financial system. Throughout the 90s, ongoing difficulties of financial institutions further eroded the public’s confidence. Similarly, financial weakness was one the primary reasons why the US economy and especially Germany became exposed to deflation in the early 2000s. However, financial institutions are an essential part of the monetary transmission mechanism.10 In times of deflation this so—called credit channel is particularly important because the interest rate channel may be disrupted. Further, financial institutions are specialized in improving the allocation of capital. If the financial system is fragile, its capacity for channeling funds from savers to borrowers is limited and will possibly restrict investment and economic growth. The health of the financial system is therefore part of the information set used by private agents to form expectations about the future course of the economy and future prices. The major finding of this paper is that under certain conditions the mutual dependence of inflation expectations and financial instability can crucially affect the outcome of a monetary impulse; it therefore imposes an additional constraint on effective monetary strategies to counteract deflation. The analysis is based on a dynamic monetary general equilibrium model in the spirit of Diamond (1965) and Tirole (1985).11 The model is developed in section 2. Under conventional conditions monetary models deliver a unique, saddle—path 7 The analysis focuses on ’bad’ deflation, i.e. deflation caused by sluggish demand rather than by an increase in supply and productivity. 8 See Krugman (1998). 9 Policies that contradict the goal of price stability, like an increase in the long—run inflation target or a lasting increase of the monetary base, are therefore considered particularly difficult to implement. See e.g. Krugman (1998), Eggertsson (2003). 10 See e.g. Gertler (1988), Bernanke (1993), Kashyap/Stein (1993) or Bernanke/Gertler (1995) for an overview and further references. 11 See Azariadis/Chakraborty (1999) and Azariadis/Smith (1996) for a related analysis.

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stable inside money equilibrium, and crises cannot occur.12 To allow for crises, a banking sector is incorporated into the model. Empirical evidence suggests that the risk of financial market—related recessions is substantially higher for economies with bank oriented financial systems than for economies where investment is largely financed by equity issuance.13 In the model, banks are considered producers of costly information about the creditworthiness of borrowers whose investment projects are opaque. However, to establish a credit relationship banks have to incur a cost. The cost is supposed to increase less than proportional with the volume of the credit. Intermediation activities are therefore subject to increasing returns to scale and the banking sector is characterized by imperfect competition.14,15 The solution of the model is derived in section 3. Due to the non—convexity in intermediation activity, the model has two different monetary stationary states. Accordingly, two different stationary credit market equilibria exist. The steady states differ with respect to real activity, intermediation, and the number of active banks. The high activity steady state is always saddle—path stable. The stability of the low activity steady state, however, depends on economic fundamentals. If banks are relatively efficient, and investment projects have high returns, it will be unstable and the saddle—path to the high activity stationary state is the unique dynamic equilibrium for the economy. But if banks are relatively inefficient and investment projects have low returns both stationary states can be approached on an equilibrium path, and the financial system is structurally unstable. Section 4 discusses the dynamics of economies with a structurally unstable financial system. Due the multiplicity of equilibria, these economies are generally exposed to coordination failures and self—fulfilling crises. A crisis is precipitated by a loss of confidence in the continuation of a dynamic adjustment along the saddle— path associated with the high activity stationary state. The loss of confidence will increase the demand for liquidity and trigger a withdrawal of funds from the banking system. The increased demand for liquidity will lower the price level, deflate outstanding nominal debt, and decrease the volume of intermediated credit. This reaction will propagate the shock to the real sphere of the economy and initiate a self—fulfilling contraction in economic activity and prices. Section 5 analyzes the effectiveness of long— and short—run monetary policies in a structurally unstable financial environment. Due to the mutual dependence of inflation expectations and financial instability, the policy implications of the model 12

See Azariadis (1993) for an extensive discussion of this model class. See e.g. IMF (2002, ch.2) and IMF (2003, ch.2). 14 For models with increasing returns to scale in lending see e.g. Williamson (1986), Bernanke/Gertler (1989), and Azariadis/Chakraborty (1999). McAllister/McManus (1993) or Noulas et al. (1990) give empirical evidence of increasing returns to scale. 15 Molyneux et al. (1994) and deBandt/Davis (1999) give evidence of oligopolistic competition in banking. 13

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differ from those of a conventional monetary model in several important dimensions. In a conventional monetary model the long—run stationary equilibrium is unique. However, if an economy is structurally unstable, different stationary states will exist, even for identical long—run monetary conditions. Therefore, these conditions alone cannot be sufficient to coordinate the inflation expectations of agents. Moreover, according to the model an expansionary short—run monetary impulse will always temporarily delay a contraction in intermediation and real activity. But if the expansion is too low the implied sequence of prices remains consistent with an adjustment to the low activity stationary equilibrium, irrespectively of the long—run monetary conditions. This helps to explain why — in a financially unstable environment — a monetary impulse may simply fade out without having a lasting effect. The model suggests that to invalidate undesirable deflationary equilibrium paths a monetary impulse must overshoot the saddle—path to the high activity stationary state, i.e. it must exceed the increased demand for liquidity at the time of a confidence crisis.16 The analysis also suggests that the impulse has to be time—limited17 and combined with a long—run inflation target. The inflation target is essential to establish a unique saddle—path and thus indispensable for a successful strategy. However, given that the real long—run equilibrium of an economy is independent of the level of inflation, the target itself is irrelevant. Therefore, the monetary expansion can be credibly set subject to the goal of maintaining price stability over the long—run.

2 The Economy This chapter introduces the dynamic general equilibrium model to analyze monetary stabilization policies in a structurally unstable financial environment. The economy has five types of agents: private households, goods—producing firms, financial intermediaries (banks), a monetary authority, and a fiscal authority. Households sell labor services to firms and use their income to finance consumption expenditures. Banks intermediate funds from households to firms. Intermediation is costly and characterized by increasing returns to scale. Firms use capital and labor services to produce the single good of the economy. The monetary authority issues fiat money and the treasury issues government bonds. The equilibrium demand for money, deposits, bonds, labor, and capital is subject to the utility maximization of households, and the profit maximization of firms and intermediaries.

16 17

See also Rogoff (2002). See Svensson (2003).

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Households The economy is populated by an infinite sequence of overlapping generations of agents, indexed by time t = 0, 1, . . . Each private agent lives for two periods, youth and old age. The total number of agents in each generation is constant and normalized to one. All agents are identically endowed with one unit of labor in youth. There is no disutility of labor, and working time is inelastically supplied. Agents consume only when they are old.18 Savings can either be deposited with banks, invested in government bonds, or held as fiat money. Deposits and government bonds earn interest, while money is valued because it generates valuable transaction services.19 Each agent maximizes his utility. The utility of an agent born at time t is supposed to be a log linear function of time t + 1 consumption, ctt+1 , and real balances, mtt+1 : U(mtt+1 , ctt+1 ) = (1 − β) ln mtt+1 + β ln ctt+1 ,

0 < β < 1.

The utility maximization is subject to the agent’s budget constraints. Let wt be the wage rate, dtt deposits, btt government bonds, and mtt money balances, each in real terms per capita. By definition, mtt+1 ≡ mtt /π t+1 , where π t+1 denotes the inflation D B factor. Further, let It+1 and It+1 be the nominal interest factors on deposits and government bonds, respectively. Then, the budget constraints of the representative agent are dtt + btt + mtt ≤ wt ,

(1)

and £ D t ¤ B t dt + It+1 bt + mtt /π t+1 . ctt+1 ≤ It+1

A simultaneous equilibrium in the deposit and the bond market requires that the nominal interest rate, It+1 , is the same for both assets D B It+1 = It+1 = It+1 .

The utility maximizing demand for real balances is It+1 wt . (2) It+1 − 1 The money demand function has the usual properties. Money demand is increasing in income, wt , and decreasing in the nominal interest factor on deposits and bonds, mtt = (1 − β)

18

Since we are interested in the allocation rather than the level of savings, this assumption is sufficient to characterize the private agents’ behavior while it helps to keep the model simple. 19 See e.g. Sidrauski (1967).

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It . For the later analysis later it will be convenient to break down the nominal interest factor into the real factor, denoted Rt+1 , and expected inflation factor, π et+1 . It is straightforward to show that these factors are related as Rt+1 ≡ It+1 /πet+1 . Thus, the Fisher equation holds and the demand for real balances can be expressed as mtt = (1 − β)

Rt+1 wt . Rt+1 − 1/π et+1

(3)

To complete the description of the household sector, we assume the existence of an initial generation of old agents at time t = 0. The initial generation is endowed with K0 > 0 units of capital goods and M−1 > 0 nominal units of fiat money. The initial generation fully consumes the gross returns of her endowment sold in the competitive markets for capital and money. Firms The homogeneous good of the economy is produced by competitive firms. Firms maximize profits and are price takers in the product and input markets. Inputs in production are capital, Kt , and labor, Nt . Each firm has access to an identical production technology, F (Kt , Nt ). The production technology is identical for all firms, has constant returns to scale, and satisfies the Inada conditions. Without loss of generality the depreciation rate of the capital stock is set to one. Let kt ≡ Kt /Nt denote the capital to labor ratio, and f (kt ) ≡ F (kt , 1) the intensive production function. Profit maximization implies that the real wage rate, wt , and the cost of capital, ρt+1 , satisfy wt = f (kt ) − f 0 (kt )kt ≡ w(kt ), ρt+1 = f 0 (kt+1 ).

(4) (5)

Throughout, we will assume that firms cannot issue securities but have to finance their investments with loans, denoted lt . The nominal interest factor on loans is L L It+1 . Credit market equilibrium then implies ρt+1 = It+1 /πet+1 and kt+1 = lt . Banks Investment activities of firms are opaque for individual households, and monitoring activities are necessary to eliminate this informational asymmetry. Since monitoring is costly, direct lending to firms is dominated in returns by lending through financial intermediaries, termed banks. Banks specialize in intermediation and monitoring activities to avoid the costly duplication of information disclosure. At the end 6

of each period t ≥ 0 banks offer households to deposit their savings. The funds obtained are loaned out to firms for one period of time. At the end of the following period, banks use the principal and interest on loans to service their own liabilities. At each date, the number of potential banks is large. Each of them has free access to an identical intermediation technology which is linear in deposits. However, to operate the technology an active bank has to pay a fixed amount of qtj units of final goods. The underlying assumption is that after a loan is approved the bank has to incur a verification or auditing cost to overcome the asymmetric information with respect to the investment outcome. The auditing cost comprises expenses for accountants or credit—assessment agencies and has to be paid after the loan is settled.20 Since a bank can avoid the costly duplication of information disclosure with respect to a particular borrower, increasing returns to scale in lending exist.21 The transaction cost is due per contract. The number of contracts each bank approves, however, depends on the size of the bank, which is endogenous in the model. To account for this size effect it is assumed that in a world of homogeneous agents the number of loan contracts is proportionate to the market share of a particular bank. Therefore, let q denote a non—negative constant representing the cost of servicing the total market and Jt the number of active banks at time t. Then, the fixed cost each active bank has to pay is qtj = q/Jt . It is important to note that the definition of qtj is not essential for the basic mechanism that is driving the dynamic adjustment of the economy. The main results of the model will be preserved as long as (i) the aggregate cost function q = q(lt ) is strictly positive and continuous, (ii) the elasticity of q(lt ) with respect to lt is strictly less than the elasticity of f (kt ) with respect to kt , and (iii) the production function satisfies the Inada conditions.22 However, contrary to conventional models of market entry the definition of qtj does not imply a duplication of costs when additional banks enter the market. Therefore, the model is free of inefficiencies generated by excess entry. Due to the fixed cost, the average cost of lending is decreasing in the volume of loans. Thus, as proposed by Fama (1985) and consistently supported by empirical studies, intermediation activities have increasing returns to scale and the banking sector is imperfectly competitive.23 The number of active banks is determined as a subgame perfect Nash equilibrium of a two stage oligopoly entry game. In the first stage of the game all potential banks simultaneously decide whether to enter or to stay out the market. In the second stage active banks maximize profits under 20

See for example Bernanke and Gertler (1989) or Williamson (1987) for an approach where the costs of informational asymmetries reduce the amount of net lending instead of net returns. 21 See also Williamson (1986), Bernanke/Gertler (1989), and Azariadis/Chakraborty (1999). 22 See Appendix 1 for further details. 23 See McAllister/McManus (1993), and Noulas/Ray/Miller (1990) for empirical evidence of increasing returns to scale, and Molyneux/Lloyd-Williams/Thornton (1994) and de Bandt/Davis (1999) for evidence of oligopolistic competition in banking.

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Cournot competition. Subgame perfection requires that neither active nor inactive banks must want to change their entry decision at the second stage of the game. Thus, for each active bank expected profits must be zero. Since all banks are symmetric q j /ltj ≡ q/lt , and zero profits imply: L D lt − It+1 dt − π et+1 q. 0 = It+1 L L D Making use of the definitions Rt+1 = It+1 /πet+1 and Rt+1 = It+1 /πet+1 , this condition can equivalently be expressed as l − q/lt . Rt+1 = Rt+1

(6)

The zero profit condition thus determines the real interest rate spread as a decreasing function of lending activity. Note that kt+1 = lt , i.e. loans are converted into capital one for one. Therefore, information costs eventually reduce the profits of banks and appear as lost earnings for households. Since the intermediation technology exhibits increasing returns to scale, however, lending activities become increasingly profitable as the average loan size increases. We assume that each bank knows the aggregate demand function for loans and takes as given the deposit rate as well as the number and loan supply of its competitors. The first order condition for profit maximization of the Cournot game can then be expressed as a modified Lerner condition24 l Rt+1 − Rt+1 1 = , Rt+1 ηJt

(7)

where −η denotes the aggregate demand elasticity for loans and 1/Jt is the average market share of banks. Since the interest rate spread is a decreasing function of lt the equilibrium number of banks is increasing in lt . Thus, a contraction in lending activity will decrease the number of active banks and increase the interest rate spread. This reaction is consistent with empirical evidence for periods of declining economic activity and financial crisis.25 Monetary and Fiscal Authority Monetary policy is conducted through open market operations by a single monetary authority, the central bank. We assume that the central bank’s policy goal is to maintain long—term price stability. The long—term inflation factor targeted by the 24

According to the Lerner condition, the distortion of the monopolist’s price margin relative to its marginal cost, i.e. the ’Lerner index of monopoly power’, is equal to the (negative) price elasticity of demand, η. It turns out that in the oligopoly case this condition has to be modified to account for the number of producers, i.e. banks, Jt . 25 See e.g. Stock/Watson (1989, 1999) and Friedman/Kuttner (1989) for evidence of the interest rate spread as a leading indicator of economic activity, and Gertler/Hubbard/Kashyap (1991) and Mishkin (1991) for evidence of financial crises.

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central bank is denoted π ˜ . Let σ be the growth factor of nominal money balances, mt . By definition, real balances in two successive periods are related mt+1 =

σ πt+1

mt ,

where π t+1 ≡ pt+1 /pt . In a steady state mt+1 = mt . Therefore, a constant long— term inflation factor implies a constant long—term growth factor of money balances σ ˜=π ˜. In addition to the central bank, a fiscal authority exists. The fiscal authority’s only activity is to role over the government’s public debt; taxes and government consumption are zero. Nominal government bonds are denoted Bt . We assume B−1 > 0. The fiscal authority also receives the seignorage from money creation. To maintain the government’s budget constraint for all t ≥ 0, the nominal value of newly issued bonds must equal the gross interest on outstanding bonds minus the seignorage received from the central bank: B Bt+1 = It+1 Bt − [Mt+1 − Mt ] .

In real terms the governments budget constraint is given by £ B ¤ bt + mt /π t+1 . mt+1 + bt+1 = It+1

(8)

(9)

The operation target of the central bank is the ratio of government bonds to fiat money, denoted θt : θt =

Bt bt ≡ . Mt mt

θt can be adjusted through open market operations, i.e. the market exchange of fiat money Mt for nominal government bonds, Bt . A high (low) value of θt indicates that monetary policy is relatively tight (loose). It is assumed that the central bank conducts an open market operation at time at time t = 0 to adjust θt according to the long—term inflation target π ˜ . The equilibrium value of θ can be derived using eq. (9). Given the definition of θt , and θt = θ, this equation can be expressed as mt+1 =

B +1 1 θt It+1 mt . π t+1 θt + 1

(10)

The steady state value of θ thus is θ=

1π ˜−1 , π ˜R−1 9

(11)

where R ≡ I B /˜ π denotes the real long—term interest factor on government bonds. The change in nominal money supply associated with the inflation target can be derived from eq. (10) as B θIt+1 +1 Mt . θ+1 This difference equation describes the change in Mt that will result if the central bank sets θ0 equal to the ratio consistent with the long—run inflation target π ˜ and then adjusts the monetary base such that θ remains constant for all t ≥ 0.

Mt+1 =

3 General Equilibrium 3.1 Dynamic Equilibrium In equilibrium all markets clear with prices and quantities solving the households’ utility maximization problem, the profit maximization problem of firms and intermediaries, and the equilibrium conditions for the entry game. Since the number of agents in each generation is normalized to one, aggregate and per capita values for money and deposit demand are identical: mt = mtt and dt = dtt . Moreover, according to the aggregate budget constraint dt = wt − (1 + θ)mt .

Equilibrium in the market for capital, loans, and deposits implies kt+1 = lt = dt . The law of motion for the capital to labor ratio can thus be expressed as kt+1 = w(kt ) − (1 + θ)mt .

(12.a)

The law of motion for real money balances can be derived from the money demand function (2) and the money supply function (10). If the first is used to substitute for π t+1 in the latter, the money market equilibrium condition reads ¸ · 1−β (12.b) wt Rd (kt+1 ), mt+1 = mt − 1+θ for all t ≥ 0. Equations (12.a) and (12.b) form a two—dimensional dynamic system for the state variables kt and mt . Any sequence {kt , mt }∞ 0 satisfying these equations for initial values k0 ≥ 0, M−1 > 0, and the policy parameter θ, constitutes a dynamic equilibrium for the economy. 3.2 Stationary State In a stationary state the capital to labor ratio and real balances are constant: ˜ m). ˜ (kt , mt ) = (k, 10

Rlt+1 Rt+1 (kt+1)

ú(kt+1)

Ø(kt+1) 1/b

0

1

∼ max k kI k

∼ kII

k+

kt+1

Figure 1: Stationary Credit Market Equilibrium.

Following eq. (12.a), a stationary state for kt must satisfy the condition 1 [w(kt ) − kt ] . (13.a) kt+1 = kt ⇐⇒ mt = 1+θ To derive the steady state condition for mt we make use of equation (10). This equation implies mt+1 = mt ⇐⇒ Rt+1 − 1/π t+1 = (1 + θ)(Rt+1 − 1).

If the rhs of this expression is used to substitute for Rt+1 − 1/π t+1 in the money demand function (2), we obtain the following steady state condition 1 − β Rt+1 (13.b) w(kt ). 1 + θ Rt+1 − 1 To solve for the steady state, the long—run deposit and credit market equilibrium must be derived. The inverse of the steady state demand function for deposits can be determined using eq. (13.b), (13.a), and kt+1 = kt : mt+1 = mt ⇐⇒ mt =

w(kt+1 ) − kt+1 := φ(kt+1 ). (14) βw(kt+1 ) − kt+1 The deposit demand function φ(kt+1 ) is shown in Figure 1. It is straightforward to prove that the first and the second derivative of the φ function are positive. Further, let k+ be the unique solution of βw(kt+1 ) = kt+1 . Then, R(kt+1 ) =

lim φ(kt+1 ) = 1/β,

kt+1 →0

lim φ(kt+1 ) = ∞.

kt+1 →k+

11

Since in equilibrium lt = dt , the aggregate supply functions for deposits and loans coincide: R(kt+1 ) = f 0 (kt+1 ) − q/kt+1 = ψ(kt+1 ).

(15)

The limits of this function are lim ψ(kt+1 ) = 0,

k→k−

lim ψ(kt+1 ) = 0,

k→∞

where k− denotes the unique solution of f 0 (k)k = q. The ψ(kt+1 ) function has an interesting property which leads to the following proposition: Proposition 1 Suppose the cost function q is strictly positive and the production function satisfies the Inada conditions. Then, in a stationary state the deposit supply is a hump—shaped function of kt . Proof : See Appendix. The long—run credit market equilibria are shown in Fig. 1 at the intersection of the functions φ(kt+1 ) and ψ(kt+1 ). Due to the shape of the deposit/credit supply function, either none or two stationary credit market equilibria exist. One of the credit market equilibria, k˜I , is associated with a low level of lending activity and a high interest rate spread. The other equilibrium, k˜II , has the opposite characteristics. Figure 1 also shows that a stationary credit market equilibrium will only exist if the supply of deposits is sufficiently high to use the intermediation technology. This condition will be satisfied whenever the intermediation technology is sufficiently efficient (i.e. q is sufficiently low), as is assumed throughout.26 Once the credit market equilibria are determined, it is straightforward to use equation (13.a) to solve for the corresponding steady state value of real balances. The stationary state solutions for k˜ and m, ˜ as well as the qualitative dynamics for 27 the state variables are shown in Fig. 2. The graph labeled KK shows eq. (13.a), and the graph labeled MM shows the correspondence (13.b). Given the properties of f (k), the graph of (13.a) is straightforward to derive. The derivation of MM is more difficult. The shape of the MM locus follows from the fact that for any feasible state, kt , none or two different values of kt+1 are consistent with a credit market equilibrium (see eq. (15) and Fig. 1). Therefore, none or two different values for mt exist which solve the law of motion for kt+1 .28 26

If this condition were not satisfied, the stationary interest rate on deposits would exceed the critical level and the credit market would eventually collapse. See also Mankiw (1986). 27 See the Appendix for further details on the figure and the equations governing the dynamic adjustment. 28 See Appendix A.3 for further details.

12

∼I m

∼ II m

0

k

∼I k

∼II k

Figure 2: Stationary States.

Since production and income per capita are positively related to kt , the stationary ˜ I ) and high activity equilibria will be termed as low activity stationary state (k˜I , m stationary state (k˜II , m ˜ II ), respectively. In addition to their respective production and income levels, the stationary states also differ in terms of credit and money market conditions. In the high activity stationary state the volume of intermediated credit is high. According to eqs. (6) and (7), the high volume of intermediated credit is associated with a relatively low average cost of lending and high competition in banking, i.e. a low spread between the borrowing and lending rate and a high number of active banks. In the low activity stationary state, the opposite is true. Here, credit market activity as well as competition in banking are low while the spread between the borrowing and lending rate is high. Finally, if θt = θ eq. (11) implies a positive relation between the long—run inflation rate π ˜ and the real interest rate on deposits and bonds, R(k). Since R(k) will always be higher at k˜II , the high activity stationary state is associated with a higher steady state inflation rate as well as a higher nominal interest rate on bonds and deposits. As a consequence, the intermediate target θ set by the monetary authority must implicitly be conditioned on one of the two long—run equilibria in order to support a particular inflation target π ˜.

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4 Structural Instability, Dynamic Adjustment, and Deflation Throughout the rest of the paper we will call an economy structurally unstable if trajectories to different stationary states are simultaneously feasible as rational expectations equilibria. Due to the multiplicity of equilibrium paths, a structurally unstable economy is vulnerable to extrinsic uncertainty and subjective beliefs. Moreover, since different adjustment paths are associated with different market conditions and prices, a sudden revision of the expectations can abruptly change the allocation of resources. In a worst case, i.e. if the revision is sufficiently strong, the reallocation of resources may even precipitate a crisis. To prepare the later analysis of monetary stabilization this chapter will provide a summarizing analysis of the dynamic adjustment of a structurally unstable economy and further characterize the conditions under which structural instability can arise. 4.1 Dynamic Adjustment and Confidence Crisis The starting point of the analysis is the multiplicity of steady states in an economy with increasing returns to scale in financial intermediation. As can be seen from Fig. 1, in the model economy the high—activity stationary state is always saddle— path stable. Therefore, the saddle—path is always a feasible dynamic equilibrium. For the low activity stationary state different cases are possible. These cases are illustrated in Figs 3.a and 3.b. Unique Stable Stationary State If the low activity stationary state is unstable, as is shown in Fig. 3.a, the saddle— path to the high activity stationary state is the only feasible dynamic equilibrium for the economy. On any of the remaining time paths the economy will eventually diverge. This implies that except for the rare case where k0 = k˜I , the low activity equilibrium can never be approached on an equilibrium path. Due to the saddle—path property of the high activity stationary state, the dynamic adjustment of the economy is determinate and smooth. For any kt there always exists exactly one equilibrium value for real balances, mt . Consequently, the price level, the inflation rate and the nominal interest rate are uniquely determined for all t ≥ 0. Accordingly, private agents will be able to coordinate their expectations upon the unique dynamic equilibrium for any given initial states k0 and M0 . This property implies that sudden revisions of expectations cannot occur and thus are ruled out as a potential source of instability. If agents decided to reduce their deposits below the saddle—path level, the interest rate would have to rise. For the higher level of real money balances to be consistent with a port14

∼I m

∼ II m

0

k

∼I k

k0

∼II k

Figure 3.a: Uniqe Stable Stationary State.

folio equilibrium, the expected returns on money balances would have to rise as well. This, however, would require an even higher demand for money in the period ahead, and so on. Although the increased demand for money could be sustainable for several periods, the sequence can never be a rational expectations equilibrium, because the economy would eventually diverge. A similar argument applies if the demand for money and the real rate of return on deposits are relatively low while capital accumulation is relatively high. For the low level of real money balances to be consistent with a portfolio equilibrium, expected inflation must be high in relation to the saddle—path equilibrium. The low demand for money and the high rate of capital accumulation, however, imply that the economy would eventually diverge to a non—monetary equilibrium (0, k). Multiple Stable Stationary States If the low activity stationary state is stable, as illustrated in Fig. 3.b, structural instability applies. In this case, an infinite number of competing rational expectations equilibria exists.29 All paths except for one eventually converge to the low activity stationary state. The one exception is the saddle—path to the high activity stationary state. Since each feasible dynamic equilibrium is associated with a different sequence of prices the inflation rate and the demand for real balances are no longer uniquely determined [see eq. (2)]. The demand for real balances depends 29

For a thorough discussion of indeterminacy in real and monetary models see e.g. Benhabib/Farmer (1999).

15

∼I m

∼ mII

0

k

∼I k

k0

∼II k

Figure 3.b: Multiple Stable Stationary States.

on real income w(kt ) and the nominal interest factor It+1 ≡ π et+1 Rd (kt+1 ). While income is a function of the given state kt , the nominal interest rate factor is a function of expected inflation and the real return on deposits. Since the inflation rate is neither unique nor predetermined, a sudden revision of expectations cannot be ruled out. For example, if the economy is shocked due to the failure of a major financial institution, a loss of confidence may occur.30 If the agents then fail to coordinate their beliefs upon a continued adjustment along the saddle—path, expected inflation will decrease and the demand for money will increase [see eq. (2)]. On aggregate the individually rational response will lead to a decline in prices, a deflation of outstanding nominal debt, and a withdrawal of funds from the banking system. Banks will then be forced to recall their loans and this will propagate the shock to the real sphere of the economy. The contraction in prices and economic activity will last until the economy finally approaches the low activity stationary state. The convergence to a stationary state then validates the initial withdrawal of funds as a rational expectations equilibrium. 4.2 Structural Instability and Fundamental Conditions Although the focus of the paper is on the consequences rather than the preconditions of deflationary crises, it is still worth to cover briefly the stability conditions for the stationary states. Based on the Determinant and the Trace of the Jacobian matrix of the dynamic system (12.a) and (12.b) it is straightforward to formally confirm 30

See e.g. Friedman/Schwartz (1963) and Schwartz (1986)

16

the saddle—path property of the high activity stationary state. As already pointed out this property guarantees that the high activity stationary state can always be approached on an equilibrium path. The stability of the low activity stationary state, however, depends on the particular parameter values of the model. The inspection of the Jacobian matrix reveals that the efficiency of the intermediation ˜ are most important technology q and the marginal productivity of investments f 0 (k) ˜ is high, the low activity equilibrium will be a in this respect. If q is low and f 0 (k) ˜ is low source and instabilities cannot occur. Conversely, if q is high and/or f 0 (k) the low activity stationary state will be a sink. Thus, it is primarily economies with weak economic fundamentals in terms of banking efficiency and investment productivity that will be exposed to instabilities of their financial system.31

5 Monetary Stabilization According to the analysis in chapters 3 and 4, increasing returns to scale in financial intermediation can lead to multiple stationary states and indeterminate dynamic equilibria. From an economic perspective, indeterminacy is undesirable. If an infinite number of feasible competitive equilibria exist, all very close to each other, the beliefs of agents about the future course of the economy can unexpectedly change. If the reallocation of resources induced by the change in beliefs is strong, a crisis occurs. According to the model it is primarily economies with weak real fundamentals that will be exposed to confidence crises and deflation. However, monetary factors are also important. In the model, instabilities only occur because different price levels are simultaneously consistent with a dynamic equilibrium of the economy. This chapter therefore examines how monetary conditions will in general affect an economy’s exposure to crises, and how monetary policy can be used to support an escape from deflation, once it occurs. 5.1 Long—Run Super—Neutrality of Money Any policy aiming to reduce structural financial instability must eventually be able to affect the stability properties of the stationary states. With respect to monetary policy, in principle two different possibilities exist to achieve this goal. The first is to change the monetary policy regime, the second is to appropriately adjust the long—run monetary conditions. Since we suppose that the overall goal of the central 31

This model property is fairly consistent with the experience in Japan over the 1990s, and more recently in Europe — especially in Germany. Weak performance of the banking and intermediation industry combined with high level of non—performing loans and unfavorable investment conditions are blamed for the economies’ exposure to instability, insufficient credit supply, and their depressed real economic activity. See e.g. IMF (2003).

17

bank is to maintain a constant long—run rate of inflation, we will not consider a change of the monetary regime as a feasible choice. Moreover, the adjustment of long—run monetary conditions will affect the stability of the stationary states if and only if money is either non—neutral and/or non super—neutral. However, it is easy to prove that none of these preconditions are satisfied in the model. Since money is valued in real terms and prices are flexible, a once—and—for—all change in the steady state money supply will be completely offset by a once—and—for—all shift in the steady state price level. Thus, money is neutral. The super—neutrality of money is implied by the steady state conditions (13.a) and (13.b). If these equations are ˜ the factor 1/(1 + θ) is cancelled out. The stationary state values for solved for k, kt are therefore independent of the money market conditions, i.e. independent of the long—run inflation rate π ˜ and the long—run growth rate of nominal money, σ. Since the Jacobian matrix is a function of k˜ only, changing monetary conditions will not affect the stability properties of the stationary states.32 Therefore, a change of the long—run monetary conditions will not affect the structural instability of the economy. Even more important, if the stationary states values as well as their stability are independent of θ, both stationary states are equally feasible under the same monetary conditions. This implies that changing the long—run monetary conditions is insufficient to coordinate the inflation expectations of agents. Therefore, a change of these conditions will also be insufficient as a single policy tool to manage an escape from deflation. 5.2 Short—Run Monetary Stabilization The model suggests that in addition to setting particular long—run monetary conditions, effective stabilization requires a short—run coordination of the expectations of agents on a particular dynamic equilibrium. This dynamic equilibrium is the saddle—path to the high activity stationary state. To analyze short—run stabilization policies, tc will be used throughout to denote the beginning period of a confidence crisis. Suppose that up to tc the economy moves along the saddle—path. Thus, up to tc private agents expect the high activity stationary state to be the long—run equilibrium for the economy. Suppose further that at time tc a loss of confidence occurs and private agents suddenly fear that the economy could contract. Since any path to the low activity stationary state is associated with lower prices as compared to the saddle—path, the loss of confidence will induce an unexpected and sudden increase in the individual demands for money. The increased demand for money will lead to a decrease in deposit demand, and finally to a self—fulfilling decrease in intermediation activity, investment, and income (see Figs 4.a and 4.b below). 32

See the Appendix for the Jacobian matrix.

18

To appreciate the scope for short—run monetary stabilization policy it is important to note that indeterminacy not only creates an exposure to expectation driven crises. Indeterminacy also implies that money is non—neutral at the time of the confidence crisis, once the expectations of agents are formed. This important property is summarized in the following proposition: Proposition 2 Let eq. (10) be the money demand function of households, π etc +1 the expected inflation factor, and (9) the government’s budget constraint. Then, for constant expected inflation, a change in the nominal money supply will have a real effect. Proof: See Appendix. According to Proposition 2, a change in the supply of money at the time of a confidence crisis will affect the crisis’ real outcome. To evaluate this outcome one first has to derive the implied future values of the per capita capital stock, ktc +1 , and real money balances, mtc +1 . Let Mtc and Btc denote the time tc supply of nominal money and bonds before the intervention, and ∆Mtc and ∆Btc be the change in the supply of nominal money and government bonds due to the intervention. Then, in a money market equilibrium Mttc = Mtc + ∆Mtc ⇐⇒ mttc = mtc + ∆mtc . Money demand is given by eq. (3) for inflation expectations π ¯ etc +1 : mttc = (1 − β)

R(ktc +1 ) w(ktc ). R(ktc +1 ) − 1/¯ π et+1

(16)

The nominal value of outstanding public debt, Mt +Bt , is predetermined. Therefore, the government’s budget constraint requires ∆Mtc + ∆Btc = 0 ⇐⇒ ∆mtc = −∆btc . Further, let θ be the ratio of bonds to money that will prevail one period after the crisis, and would have prevailed in the absence of the monetary intervention. Then, the next period’s per capita capital stock is given by ktc +1 = w(kt ) − (1 + θ)(mttc − ∆mtc ).

(17.a)

Similarly, eq. (12.b) can be used to express the expected real value of the next period’s money balances as · ¸ (1 − β) t mtc +1 = (mtc − ∆mtc ) − w(ktc ) R(ktc +1 ). (17.b) 1+θ 19

t

tc ∆mt m mt c

c

0

k0

ktc

Figure 4.a: Short—Run Monetary Stabilization, π ¯ etc +1 remains valid.

Equations (17.a) and (17.b) provide a convenient representation of the economy’s expected dynamic response to a short—run monetary expansion. Once ∆mtc is known, one can use eq. (3), with inflation expectations given by π ¯ etc +1 , to calculate the total value of real balances mtc ≡ mttc − ∆mtc . A variant of Fig. 2 can then be used to qualitatively derive the implied dynamic response. This is done in Figs 4.a and 4.b. Figures 4.a and 4.b show that increasing the supply of money at the time of a confidence crisis will always counteract the withdrawal of funds from banks and thus support real stability. However, the figures also reveal that a stabilization of real economic activity does not necessarily imply the end of the confidence crisis. Since a crisis is driven by expectations, the demand for money balances will continue to be high, even after time tc , unless the agents revise their expectations about the future course of the economy. Therefore, the overall success of a monetary stabilization policy crucially depends on its ability to invalidate the agents’ expectations of deteriorating economic activity and declining prices. This requirement puts an additional restriction on ∆mtc , as is summarized in the following proposition. Proposition 3 Let mtc = mttc (¯ πetc +1 ) be a money market equilibrium for expectations π ¯ etc +1 . If the associated dynamic equilibrium is indeterminate, a small increase in money supply will not affect the validity of π ¯ et+1 as a rational expectation of the future inflation rate. Conversely, π ¯ etc +1 will always be invalidated if the increase in money demand due to the confidence crisis is overcompensated by an increase in nominal money supply. 20

t

∆mt

m tc

c

mt

0

c

k0

ktc

Figure 4.b: Short—Run Monetary Stabilization, π ¯ etc +1 invalidated.

Proof: Indeterminacy means that an infinite number of dynamic equilibria exist, all very close to each other. Therefore, if mtc = mttc (¯ π etc +1 ) is an equilibrium, t e π tc +1 ) will also be an equilibrium, if ∆mtc is small. On the mtc + ∆mtc = mtc (¯ contrary, eqs (17.a) and (17.b) imply that the equilibrium values ktc +1 and mtc +1 , will be located below the saddle—path in the k − m plane if ∆mtc overcompensates the initial increase in money demand. Since such combinations are inconsistent with a dynamic equilibrium, the increase of money supply will invalidate π ¯ etc +1 as a rational expectation of the future inflation rate. ¤ In Fig. 4.a the increase in money supply is relatively small. In particular, it is too small to invalidate π ¯ etc +1 as a rational expectation. The implied time path for the higher money supply and lower real value of money balances mtc = mttc − ∆mtc , is still associated with a feasible dynamic equilibrium. Therefore, the monetary intervention will delay the contraction in economic activity, but it will not end it. A different outcome is obtained if the additional supply of money is sufficiently high. This case is shown in Fig 4.b. Here, the implied values for kt+1 and mt+1 are on the lower right of the saddle path. Since the new money market equilibrium is no longer associated with a feasible dynamic equilibrium for the economy, the expectations of agents, implicit in their money demand mttc , are no longer rational. The intervention thus not only stabilizes economic activity, but also forces the private agents to revise their expectations of future inflation, π etc +1 . According to the analysis, a prompt and sufficiently high increase in money supply at the time of a confidence crisis will force private agents to revise their 21

expectations of deflation. If the central bank is willing to respond in this way whenever a crisis occurs the saddle path will be established as the only feasible rational expectations equilibrium for the economy. However, it is important to note that the central bank’s success in coordinating the expectations of private agents crucially depends on the existence of a clear—cut long—run inflation target. In the analysis it was assumed that the monetary expansion will be completely reversed at tc + 1. Since θtc +1 equals θ, the long run inflation target π ˜ (θ) as well as the saddle—path remain intact throughout the monetary intervention. This is clearly an important precondition for a successful coordination of expectations. If the central bank does not explicitly distinguish between short and long run changes in the money supply the coordination function of the intervention will be reduced or even invalidated. Finally, it is worth recalling that crises are only possible because a multiplicity of dynamic equilibria exists. This implies that a credible commitment by the central bank to aggressively counteract deflation can effectively preempt confidence crises even if the economy is structurally unstable.

6 Conclusion This paper uses a dynamic general equilibrium model to analyze monetary stabilization policies under conditions of low inflation and financial instability. The economy is characterized by increasing returns to scale in the financial intermediation sector. Due to this non—convexity the model economy has two monetary stationary states. One stationary state is a low activity equilibrium with a low number of active banks, low real economic activity, and a high spread between the borrowing and the lending rate. The other equilibrium is a conventional saddle—path long—run monetary equilibrium. Here, the number of active banks and real economic activity is comparatively high while the interest rate spread is relatively low. If economic fundamentals in terms of intermediation efficiency and returns on investments are weak, both stationary states can be approached on an equilibrium path. In this case the financial system is structurally unstable and the economy is exposed to instabilities and self—fulfilling crises. A crisis is precipitated by a loss of confidence in the future course of the economy and leads to an increase in the demand for liquidity and a withdrawal of funds from the banking system. The increased demand for liquidity will decrease the price level, deflate outstanding nominal debt, and initiate a self—fulfilling and accelerating contraction in intermediation and real activity. Although the structural instability is caused by weak real fundamentals, according to the model the central bank can effectively limit the economy’s exposure to crises and support an escape from a deflation, once it occurs. However, sev22

eral important qualifications apply. In a structurally unstable economy, different stationary states values are equally feasible under the same monetary conditions. Therefore, adjusting these conditions alone will be insufficient to coordinate the inflation expectations of agents. Accordingly, setting a long—run inflation target will be insufficient as a single policy tool to manage an escape from deflation. Effective stabilization additionally requires a coordination of the agents’ expectations on a particular dynamic equilibrium, the saddle—path to the high activity stationary state. A short—run expansion of the monetary base can be an appropriate measure to achieve this goal if two conditions are met. Firstly, the expansion has to be relatively strong and must be time—limited. Successful coordination requires an overcompensation of the demand for liquidity at times of crisis to invalidate the undesirable equilibrium paths. If the expansion is too low, the implied sequence of prices will remain consistent with an adjustment to the low activity stationary state, and the monetary impulse will eventually fade out without having a lasting effect. Secondly, the existence of a saddle—path is an essential precondition for effective coordination. Therefore, the short—run expansion of the monetary base has to be combined with an explicit long—run inflation target. However, the targeted long— run rate of inflation is not of primary importance for stabilization. It can therefore credibly be set subject to the goal of maintaining long—run price stability. Finally, the analysis suggests that a credible commitment of the central bank to aggressively counteract deflation can help to preempt confidence crises in a financially unstable economy.

23

References Ahearne, Alan et al. (2002), ’Preventing Deflation: Lessons from Japan’s Experience in the 1990s’, International Finance Discussion Paper, Board of Governors of the Federal Reserve System. Azariadis, C. (1993), ’Intertemporal Macroeconomics’, Oxford: Blackwell. Azariadis, C. and Chakraborty, S. (1999), ’Agency costs in dynamic economic models’, Economic Journal, 109, 222—41. Azariadis, C. and Smith, B.D. (1996), ’Private information, money and growth: indeterminacy, fluctuations, and the Mundell-Tobin effect’, Journal of Economic Growth, 1, 309—32. Bank of Japan (2001), ’The Role of Monetary Policy under Low Inflation: Deflationary Shocks and Policy Responses’, Monetary and Economic Studies, 19 S1, Bank of Japan. Bayoumi, T. (2000), ’The Morning After: Explaining the Slowdown in Japanese Growth’, in: T. Bayoumi/C. Collyns (eds.), Post—Bubble Blues: How Japan Responded to Asset Price Collapse, Washington: International Monetary Fund, 10-44. Bayoumi, T./C. Collyns (2000), Post—Bubble Blues: How Japan Responded to Asset Price Collapse, Washington: International Monetary Fund. Benhabib, J. and Farmer, R. (1999), ’Indeterminacy and Sunspots in Macroeconomics’, in Taylor, J. B. and Woodford, M. (eds.), Handbook of Macroeconomics, Vol. 1A, 387—448, Elsevier, Amsterdam. Benhabib, J./ S. Schmitt—Grohé/M. Uribe (2002), ’Avoiding Liquidity Traps’, Journal of Political Economy 110 (June), 535—63. Bernanke, B.S. (2000), ’Japanese Monetary Policy: A Case of Self—Induced Paralysis?’, in A. Posen/R. Mikitani (eds.), Japan’s Financial Crisis and Its Parallels to U.S. Experience, Washington: Institute for International Economics. Bernanke, B.S. and Gertler, M. (1989), ’Agency Cost, Net Worth and Business Fluctuations’, American Economic Review, 79, 14—31. Bernanke, B.S./ Mark Gertler (1995), ’Inside the Black Box: The Credit Channel of Monetary Policy Transmission’, Journal of Economic Perspectives 9(4), 27—8. Bernanke, B.S. (1993), Credit in the Macroeconomy, Federal Reserve Bank of New York, Quarterly Review. Cargill, T.F./M.M. Hutchison/T. Ito (1999), ’Inflation Targeting, Liquidity Traps, and the New Bank of Japan’, Paper Presented at the European Network on the Japanese Economy Conference, Oxford, UK, July 30-31. 24

Cargill, T.F./M.M. Hutchison/T. Ito (2000), ’Financial Policy and Central Banking in Japan’, Cambridge, Mass.: MIT Press. Clouse, J./D. Henderson/ A. Orphanides//D.H. Small/P.A. Tinsley (2003) ’Monetary Policy When the Nominal Short—Term Interest Rate is Zero’, Topics in Macroeconomics, 3 (1). Cooper, R./D. Corbae (1997), ’Financial Fragility and the Great Depression’, NBER Working Paper 6094, Cambridge, Mass.: National Bureau of Economic Research. Cooper, R./J. Ejarque (1995), ’Financial Intermediation and the Great Depression: A Multiple Equilibrium Interpretation’, NBER Working Paper 5130, Cambridge, Mass.: National Bureau of Economic Research. Davis, E.P. (1995), Debt, Financial Fragility, and Systemic Risk, Oxford: Claredon Press. deBandt, O./E.P. Davis (1999), ’A Cross—Country Comparison of Market Structures in European Banking’, European Central Bank Working Paper 7. Diamond, D./P. Dybvig (1983), ’Bank Runs, Deposit Insurance, and Liquidity’, Journal of Political Economy 91, 401—19. Eggertsson, G. (2003), ’How to Fight Deflation in a Liquidity Trap: Committing to Being Irresponsible’, IMF Working Paper 03/64. Fama, E.F. (1985), ’What’s Different About Banks’, Journal of Monetary Economics 15, 29—40. Fischer, I.M. (1933), ’The Debt Deflation Theory of Great Depressions’, Econometrica 1, 337—57. Friedman, B.M./K.N. Kuttner (1989), ’Money, Income, and Prices after the 1980s’, NBER Working Paper 2852, Cambridge, Mass.: National Bureau of Economic Research. Friedman, M./A.J. Schwartz (1963), A Monetary History of the United States 1867—1960, New York, NBER. Fuhrer, J.C./ M.S. Sniderman (2002), ’Monetary Policy in a Low—Inflation Environment’, Journal of Money, Credit, and Banking 32(4), 845—69. Gertler, M./R.G. Hubbard/A. Kashyap (1991), ’Interest Rate Spreads, Credit Constraints, and Investment Fluctuations: An Empirical Investigation’, in G. Hubbard (ed.), Financial Markets and Financial Crises, Chicago: University of Chicago Press, 11-31. Goodfriend, M. (2000), ’Overcoming the Zero Bound on Interest Rate Policy’, Journal of Money, Credit, and Banking 32 (4) 845-69. Goodfriend, M. (2001), ’Financial Stability, Deflation, and Monetary Policy’, Bank of Japan, Monetary and Economic Studies 19 S1, 143—76. IMF (2002), World Economic Outlook (WEO), April 2002, Washington: International Monetary Fund. 25

IMF (2003), World Economic Outlook (WEO), April 2003, Washington: International Monetary Fund. Kashyap, A.K. (2002), ’Sorting Out Japan’s Financial Crisis’, Federal Reserve Bank of Chicago Economic Perspectives 4Q/2002, 42—55. Kashyap, A.N./ J.C. Stein (1993), ’Monetary Policy and Bank Lending’, NBER Working Paper No. 4317, Cambridge, Mass.: National Bureau of Economic Research. Krugman, P.R. (1998), ’It’s Baaack: Japan’s Slump and the Return of the Liquidity Trap’, Brookings Papers on Economic Activity 2, 137—205. Kuttner, K.N./A.S. Posen (2001), ’The Great Recession: Lessons for Macroeconomic Policy from Japan’, Brookings Papers on Economic Activity 2001 (2), 93-185. Mankiw, N.G. (1986), ’The Allocation of Credit and Financial Collapse’, Quarterly Journal of Economics 101(3), 455—70. McAllister, P.H./D. McManus (1993), ’Resolving the Scale Efficiency Puzzle in Banking’, Journal of Banking and Finance 17 (2-3), 389—405. McCallum, B.T. (2000), ’Theoretical Analysis Regarding a Zero Lower Bound on Nominal Interest Rates’, Journal of Money, Credit, and Banking 32 (4), 870—904. McKinnon, R.J. (1999), ’Comments on ”Monetary Policy Under Zero Inflation” ’, Bank of Japan, Monetary and Economic Studies 17(3), 183—87. Meltzer, A.H. (1999), ’Comments: What More Can the Bank of Japan Do?’, Bank of Japan, Monetary and Economic Studies 17(3), 189—91. Meltzer, A.H. (2001), ’Monetary Transmission at Low Inflation: Some Clues From Japan’, Monetary and Economic Studies 19 S1, Bank of Japan, 13—34. Meredith, G. (1998), ’Monetary Policy: Summary of Staff Views’, in: B.B. Aghevli /T. Bayoumi/G. Meredith (eds.), Structural Change in Japan: Macroeconomic Impact and Policy Challenges, Washington: IMF, 105—8. Mikitani, R. (2000), ’The Nature of the Japanese Financial Crisis’, in R. Mikitani/ A.S. Posen (eds.), Japan’s Financial Crisis and Its Parallels to U.S. Experience, Washington: Institute for International Economics. Mishkin, F.S. (1991), ’Asymmetric Information and Financial Crises: A Historical Perspective’, in: G. Hubbard (ed.), Financial Markets and Financial Crisis, Chicago: University of Chicago Press, 69—108. Molyneux, P./D.M. Lloyd-Williams / J. Thornton (1994), ’Competition Conditions in European Banking’, Journal of Banking and Finance 18, 445— 459. Morsink, J./T. Bayoumi (2000), ’Monetary Policy Transmission in Japan’, in: T. Bayoumi/C. Collyns (eds.), Post—Bubble Blues: How Japan Responded to Asset Price Collapse, Washington: International Monetary Fund, 143—63. 26

Motonishi, T./H. Yoshikawa (1999), ’Causes of the Long Stagnation of Japan during the 1990s: Financial or Real?’, Journal of the Japanese and International Economies, 181—200. Noulas, A.G./S.C. Ray/S.M. Miller (1990), ’Returns to Scale and Input Substitution for Large U.S. Banks’, Journal of Money, Credit, and Banking 22 (1), 94—108. Ogawa, K./K. Suzuki (1998), ’Land Value and Corporate Investment: Evidence from Japanese Panel Data’, Journal of the Japanese and International Economies 12, 132—49. Okina, K. (1999a), ’Monetary Policy under Zero Inflation: A Response to Criticisms and Questions Regarding Monetary Policy’, Bank of Japan, Monetary and Economic Studies 17(3), 157—82. Okina, K. (1999b), ’Rejoinder to Comments made by Professors McKinnon and Meltzer.’, Bank of Japan, Monetary and Economic Studies 17(3), 192-97. Orphanides A./V. Wieland (2000), ’Efficient Monetary Policy Design near Price Stability’, Journal of the Japanese and International Economy 14 (Dec), 327— 65. Posen, A.S. (1998), ’Restoring Japan’s Economic Growth’, Washington, D.C.: Institute for International Economics. Posen, A.S. (1999), ’Nothing to fear, but the fear (of inflation) itself’, International Econ Policy Briefs, Washington, D.C.: Institute for International Economics. Rogoff, K. (2002), ’Revitalizing Japan: Risks and Opportunities. Commentary’, Nihon Keizai Shimbun (Nov). Schreft, S.L./ B. Smith (1998), ’The Effects of Open Market Operations in a Model of Intermediation and Growth’, Review of Economic Studies 65, 519—50. Schreft, S. L./B. Smith (1997), ’Money, Banking, and Capital Formation’, Journal of Economic Theory 73, 157—82. Schwartz, A.J. (1986), ’Real and Pseudo—financial Crisis’, in F. Capie/G.E. Wood (eds.), Financial Crisis and the World Banking System, London: McMillan, 1131. Sidrauski, M. (1967), ’Inflation and Economic Growth’, Journal of Political Economy 75, 796—810. Stock, J.H./Watson M.W. (1989), ’New Indexes of Coincident and Leading Economic Indicators’, in: O.J. Blanchard/S. Fischer (eds.), NBER Macroeconomics Annual 1989, Cambridge, Mass.: MIT Press, 351—94. Stock, J.H./Watson M.W. (1999), ’Business Cycle Fluctuations in US Macroeconomic Time Series’, J.B. Taylor/M. Woodford (eds.), Handbook of Macroeconomics, Vol. 1A, 3—64. Svensson, L.E.O. (2001), ’The Zero—Bound in an Open Economy: A Foolproof 27

Way of Escaping from a Liquidity Trap’, Monetary and Economic Studies 19 S1, Bank of Japan, 277—322. Svensson, L.E.O. (2003), ’Escaping from a Liquidity Trap and Deflation: The Foolproof Way and Others, Journal of Economic Perspectives 17 (4), 145—66. Williamson, S.D. (1986), ’Costly Monitoring, Financial Intermediation, and Equilibrium Credit Rationing’, Journal of Monetary Economics 18, 159—79. Williamson, S.D. (1987), ’Financial Intermediation, Business Failures and Real Business Cycles’, Journal of Political Economy 95, 1196—216. Woo, D. (1999), ’In Search of ”Capital Crunch”: Supply Factors Behind the Slowdown in Japan’, International Monetary Fund Working Paper 99/3.

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Appendix

A.1 Proof of Proposition 1 Proof: In a stationary credit market equilibrium kt = lt . Moreover, zero profits imply Rd (kt ) = f 0 (kt ) − q. Since the production function satisfies the Inada conditions limkt →0 f 0 (kt )kt = 0 and limkt →∞ f 0 (kt ) = 0. Thus, if q is strictly positive limkt →0 f (kt )kt − q = −q < 0. Therefore, there must be a capital intensity k− such that Rd (kt ) = 0 for kt ≤ k − . We also have limk→∞ Rd (kt ) = limk→∞ [f 0 (kt ) −q/kt ] = limk→∞ f 0 (kt ) = 0. To see that Rd (kt ) must be positive for some kt ∈ (k− , ∞) note that limkt →∞ f 0 (kt )kt − q = ∞. Thus, the net return on intermediation Rd (kt )kt must be positive for some k− < kt < ∞. This implies that the deposit rate Rd (kt ) is positive for some k− < kt < ∞ , too. ¤ A.2 Proof of Proposition 2 Proof: Let Z¯t ≡ Mt−1 + It Bt−1 denote the nominal value public debt outstanding at time t. Since Z¯t is predetermined, the real value of public debt satisfies (1+θt )mt = ¯ t . Therefore, kt+1 = w(kt ) − Z¯t /pt , and the equilibrium demand for money must Z/p always satisfy mtt = (1 − β)

R(w(kt ) − Z¯t /pt ) w(kt ). R(w(kt ) − Z¯t /pt ) − 1/π et+1

Thus, if π et+1 is constant the price level reaction of a change in nominal money supply can generally not be one for one. ¤

A.3 Derivation of the KK and MM Correspondence For further reference we define the following functions mt =

1 [w(kt ) − kt ] ≡ ψ KK (kt ), 1+θ

(KK)

mt =

1 − β R (w(kt ) − (1 + θ)mt ) w(kt ) ≡ ψ MM (kt , mt ) 1 + θ R (w(kt ) − (1 + θ)mt ) − 1

(MM)

to represent the equilibrium loci for kt and mt given by (13.a) and (13.b) [see also Fig. 2]. Their properties can be characterized as follows. Since the production function f (k) is well behaved, ψ KK (kt ) is a concave function. To derive the shape of 29

the MM — correspondence recall that any feasible interest factor Rt+1 is associated with two distinct values for kt+1 . Moreover, since the demand for money must be finite, any equilibrium interest factor will satisfy R (kt+1 ) − 1 > 0, with kt+1 = w(kt ) − (1 + θ)mt . Let (kmin , kmax ) = R−1 (1). Then, for any given kt the equilibrium demand for money will satisfy mmin < mt < mmax , t t where 1 [w(kt ) − kmax ] , 1+θ ¤ 1 £ ≡ w(kt ) − kmin . 1+θ

mmin ≡ t mmax t

max , and the Since money demand approaches infinity as mt approaches mmin t , mt equilibrium interest factor is a hump—shaped function of mt , either none or two equilibrium values for mt exist for a given state kt . Finally, note that kt → ∞ ⇒ max mmin → ∞. t , mt

A.4 Qualitative Dynamics of kt and mt The adjustment dynamics for the state variables kt and mt are described by eqs. (12.a) — (12.b). These equations imply kt+1 ≥ kt ⇐⇒ mt ≤

1 [w(kt ) − kt ], 1+θ

(A.2.a)

and mt+1 ≥ mt ⇐⇒ mt ≥

1 − β R (kt+1 ) w(kt ). 1 + θ R (kt+1 ) − 1

(A.2.b)

Inequality (A.2.a) is straightforward. Inequality (A.2.b) is more difficult to read. 1 [w(kt ) − kt+1 ], it can be expressed as Noting that mt = 1+θ mt −

1 − β R(kt+1 ) w(kt ) − kt+1 w(kt ) ≥ 0 ⇐⇒ R(kt+1 ) ≥ . 1 + θ R(kt+1 ) − 1 βw(kt ) − kt+1

Since βw(kt+1 ) − kt+1 > 0 we have

d w(kt ) − kt+1 (1 − β)w(kt ) = > 0. dkt+1 βw(kt ) − kt+1 |kt [βw(kt ) − kt+1 ]2 30

Ro

ots

D

II.1

Sink

e d ad

IS

Source

Co

mp l ex

I II II.2

l

1 B

0

T D=-1+T

-1

Figure 5: Determinant and Trace of the Jacobian Matrix.

Thus, the rhs of the inequality is monotonically increasing. Since R(kt+1 ) is a + − hump—shaped function, the inequality defines an interval kt+1 ∈ (kt+1 , kt+1 ) for which inequality holds. Therefore, we finally arrive at mt+1 ≥ mt ⇐⇒ k − ≤ kt+1 ≤ k+ ⇐⇒ mmax ≥ mt ≥ mmin t t ,

(A.3.b0 )

with 1 [w(kt ) − kmax ] , 1+θ ¤ 1 £ w(kt ) − kmin . mmax ≡ t 1+θ The qualitative dynamics implied by inequalities (A.2.a) and (A.2.b) are shown in Figure 2. mmin ≡ t

A.5 Local Stability of the Stationary States The Jacobi matrix of the dynamic system (12.a) and (12.b) evaluated at a steady state is · 0 ¸ w (k) £ −(1 + θ) ¤ J= , − 1−β Rd (k) + w(k)Rd0 (k) w0 (k) [R(k) + (1 − β)w(k)R0 (k)] 1+θ with Determinant

D = βRw0 (k), 31

and Trace dR(k) . dk Generally, the higher q, the lower the distance between the steady state values k˜I and k˜II . In the limit, both steady states collapse and the MM and KK loci have a tangency point (see Figs 1 and 2). At this point T = w0 (k) + R(k) + (1 − β)w(k)

dmt dmt = dkt |MM dkt |KK

⇐⇒ D = −1 + T.

The bifurcation point is labeled B in Figure .33 If k˜I and k˜II are distinct, the point (D(k˜II ), T (k˜II )) will always be on the lower right of the locus D − 1 + T = 0 and thus saddle—path stable, while (D(k˜I ), T (k˜I )) will be on the upper left. At the bifurcation point, D will be the lower, the lower ˜ Thus, the higher q and the lower R(k˜I ), the more likely that k˜I is a source. R(k).

33

See Azariadis (1993) for further details.

32