A Framework for the Analysis of Financial Reforms and the Cost of official Safety Nets
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

This paper builds a multiperiod, general equilibrium framework for analyzing the macroeconomic effects of financial reforms in developing countries and the costs of maintaining official safety nets under the financial system during such reforms. While a financial liberalization yields efficiency gains, adverse macroeconomic effects can arise if the creditworthiness of the nonfinancial sector is weak. In this situation, financial liberalization may also increase the authorities’ expected deposit insurance funding obligations even with strong prudential supervision. Moreover, given the distortions in a repressed financial system, an increase in the required bank capital-asset ratio may increase the funding obligations associated with deposit insurance, particularly when the debt-servicing capacity of nonfinancial firms is low.

Abstract

This paper builds a multiperiod, general equilibrium framework for analyzing the macroeconomic effects of financial reforms in developing countries and the costs of maintaining official safety nets under the financial system during such reforms. While a financial liberalization yields efficiency gains, adverse macroeconomic effects can arise if the creditworthiness of the nonfinancial sector is weak. In this situation, financial liberalization may also increase the authorities’ expected deposit insurance funding obligations even with strong prudential supervision. Moreover, given the distortions in a repressed financial system, an increase in the required bank capital-asset ratio may increase the funding obligations associated with deposit insurance, particularly when the debt-servicing capacity of nonfinancial firms is low.

I. Introduction

Many Fund-supported adjustment programs for developing countries have included structural reforms aimed at strengthening the financial system. Countries often start such reforms with extensive financial restrictions, including interest rate ceilings for both deposits and loans, limitations on competition and entry into the financial sector, high required reserve ratios, and various credit allocation rules. Usually, these countries also have weak systems for prudential supervision of the financial sector. As a result, the financial reforms have often initially focused on removing or raising ceiling interest rates, reducing required reserve ratios, permitting freer entry into the financial system, and strengthening prudential supervision.

As noted by Diaz-Alejandro (1985), however, a number of reform efforts have ended in periods of financial instability that required extensive restructuring of both the corporate and financial sectors and created large public sector funding obligations as the authorities provided emergency lending to enterprises and financial institutions. These experiences have raised the issues of what factors contribute to financial instability 1/ and whether a financial reform is likely to expose the authorities to new credit risks through the operation of any official safety net underpinning the domestic financial system.

In general, these official safety nets have been designed to prevent financial disturbances from creating disruptions in either the payments system or the intermediation of credit that would have large spillover effects on the real economy. The provision of short-term emergency liquidity assistance by the central bank, some form of private or official deposit insurance, and direct short- or medium-term emergency assistance for large troubled financial institutions have often been key elements in such safety nets. While such provisions have helped contain the effects of financial crises, they have also exposed the authorities to credit risks through lending to troubled financial institutions, either directly or through the central bank’s discount window, and through the fulfillment of insurance obligations to depositors.

In developing a framework for analyzing the effects of financial reforms on the cost of official safety nets, it is important to recognize that the desire to maintain a stable financial system and to limit the authorities’ exposure to the credit risks associated with official safety nets has been a primary motivation for policies specifying minimum capital adequacy standards, systems of prudential supervision, limits to risk-taking by institutions and individuals, restrictions on competition and activities and, in some countries, ceilings on interest rates. 1/ Such limitations on activities, portfolio choices, and interest rates have been perceived as a means of promoting stability by creating financial institutions with strong market and capital positions, limiting speculative behavior, and restricting competition. These considerations suggest that a useful direction for developing a better understanding of why financial reforms sometimes lead to instability and impose large costs on official safety nets is to construct an analytic framework with microeconomic foundations that focus explicitly on how depositors, borrowers, and financial intermediaries are likely to respond to the relaxation or elimination of various types of financial restrictions. 2/

This paper presents an optimizing model that focuses explicitly on the conditions under which firms and financial intermediaries become bankrupt, on how the incidence of failure is affected by various financial reforms, and on the size of the funding obligations the government incurs in a system with an official safety net containing explicit or implicit deposit insurance. A multiperiod general equilibrium framework is developed that includes three types of optimizing agents: households, firms, and banks. The linkages between financial reforms and the authorities’ funding obligations reflect the fact that, since firms face uncertain production shocks, there is the possibility that they will default on their debt-service obligations to the banks. To reduce the likelihood of defaults, banks will spend resources to monitor the firms’ investment plans and production outcomes. Under some contingencies, however, the number of firms that default may leave a bank unable to service its deposit payment obligations, in which case the authorities will incur funding obligations through the deposit insurance system.

One key determinant of the economy’s response to a financial liberalization is the extent to which banks ration credit to firms. The amount of credit that banks make available to firms may be rationed in our model for two reasons. In the first place, the presence of official constraints on financial activities may leave banks unable to attract sufficient deposits to satisfy fully the prevailing demands for credit. This type of situation is often referred to as “disequilibrium credit rationing;” both suppliers and rationed demanders (of deposits and/or credit) have incentives to bid up interest rates, but official restrictions prevent interest rates from rising to market-clearing levels. In addition, the amount of credit that banks find it optimal to extend to firms may be a backward bending function of the loan interest rate, since an increase in the loan rate may increase the probability that the borrower will default and, beyond some point, may reduce the banks’ expected rate of return. This represents a form of “equilibrium credit rationing.” 1/

A large part of the paper is devoted to developing the analytic framework we require (Section II) and to describing its long-run properties through comparative “steady-state” analysis (Section III). We also devote specific attention to the size of the funding obligations the government can expect to incur when it provides deposit insurance (Section IV). Further analysis of short-run dynamics, perhaps including simulation experiments, has been left for subsequent papers.

Although the analysis undertaken in this paper does not focus on the short-run consequences of financial reforms, the comparative static responses of macroeconomic variables suggest a number of important policy conclusions. Whatever the system of prudential supervision, it is clear that the responses of macroeconomic variables to financial liberalization measures depend critically on the perceived creditworthiness of the nonfinancial sector. If banks regard firms as highly risky, the elevation or removal of ceilings on loan interest rates, for example, may actually reduce the scale of financial intermediation and the level of economic activity. Accordingly, one important policy implication is that any financial difficulties or creditworthiness problems of the nonfinancial sector should be addressed at an early stage: otherwise, financial reforms may well be contractionary.

A second conclusion pertains to systems in which the authorities provide implicit or explicit deposit insurance. In such systems, financial liberalization may increase the expected funding obligations of the government, especially when the creditworthiness of the nonfinancial sector is low. This is likely to be true even if the authorities put in place a strong system of prudential supervision.

A third conclusion is that, given the distortions that are likely to exist in a repressed financial system, an increase in the required capital-asset ratios of banks may have the perverse effect of increasing the expected funding obligations associated with deposit insurance, especially when the nonfinancial firms have weak financial positions. This effect reflects the fact that the presence of deposit insurance may encourage banks to lend fully against whatever capital they have in place.

In general, our analysis indicates that, even with good prudential supervision and enhanced capital adequacy requirements, countries undertaking or contemplating financial reform confront a tradeoff between financial efficiency and the risk of larger safety net funding obligations. While a financial reform can increase efficiency, it may also burden the authorities with greater risks via the official safety net. The authorities can improve on this tradeoff, however, by acting at an early stage in the reform process to strengthen the financial positions of nonfinancial firms and the prudential supervision system.

II. A Model of Financial Repression

In this section we characterize the optimizing behavior of each of the three types of private economic agents: firms, households, and banks. The authorities influence behavior through the restrictions they impose on the domestic financial system and through their control over the rate of expansion of high powered money, which banks must hold to fulfill their reserve requirements. The restrictions imposed on the financial system in our model are those that are most typically encountered in financially repressed systems in developing countries: namely, ceilings on loan and deposit interest rates, a required reserve ratio, and a minimum capital-asset ratio.

1. Firms

The production sector of the economy is composed of competitive firms, each of which is operated by an entrepreneur who maximizes the expected discounted utility of his planned consumption over time. For simplicity, assume that each entrepreneur (denoted by j) is risk neutral, and that his utility during period t (Uj,t) is linearly related to the level of his consumption (Cj,t). Thus:

(1)Uj,t=γjFCj,t

with rjF representing the marginal utility of consumption.

Each entrepreneur owns a firm and produces output (Yj) of a single homogenous good, using capital (Kj) and labor (Lj). A production lag implies that output available for sale in period t is produced using capital and labor employed in the previous period. Output produced by each firm is subject to a random shock or productivity factor (λj). While all entrepreneurs are assumed to know the distribution of shocks, they do not know the actual value of the shocks that will impinge upon their output during the current and future periods. Specifically,

(2)Yj,t=λj,tfj,t(Kj,t1,Lj,t1)

with fj,t exhibiting decreasing returns to scale 1/ and λj,t being uniformly distributed between 0 and 1 for all firms. 2/

The rationale for borrowing in our model is to finance production, and given our traditional neoclassical production function with no material inputs, it is convenient to assume that labor must be paid at the beginning of each production period. 3/ The funds that entrepreneurs borrow from banks to finance their wage bills during period t (Bj,t) are obtained at the ceiling interest rate Rj,t and are repaid at the beginning of the next period when the firm sells its output. 4/ The entrepreneur has the constraint that:

(3)Bj,t=WtLj,t

where Wt is the wage rate in period t. In addition, the entrepreneur knows that, when interest rate ceilings are binding, the amount of credit that will be made available to him will be rationed by any bank he approaches. Thus:

(4)Bj,tB¯j,t

where B¯j,t is the maximum amount of credit that banks will supply to firm j. 1/ As will be shown, B¯j,t is determined by the bank’s credit rationing decision, which is influenced by interest rate ceilings and other prevailing financial policies.

In addition to placing demands for labor and credit, entrepreneurs formulate plans for consumption (Cj,t) and investment (Kj,t - Kj,t-1). For simplicity, it is assumed that capital does not depreciate over time, but that once purchased it cannot be resold, either because it is bolted into place or because it is otherwise transformed into plant and equipment that can only be used productively by the specific firm to which it belongs. The firm’s budget constraint can be written as

(5)Cj,t+Kj,tKj,t-1=Yj,t(1+Rt1)Wt1PtLj,t1

where Pt is the price of goods in period t and it is understood that Cj,t and Kj,t-kj,t-1 must each be non-negative. 2/

In formulating his plans, the entrepreneur recognizes that some production shocks will leave the firm unable to service its debt obligations out of the proceeds from the sale of its output. Let λj,t+1* denote the scale of the shock or productivity factor for which the market value of the firm’s entire output is just sufficient to meet its debt obligations. Thus:

(6)λj,t+1*=(1+Rt)(Bj,t/Pt+1)fj,t+1

When the firm experiences a productivity factor less than λj,t+1*, the firm is considered to be in “default” and the entrepreneur “dies”--that is, his current and future consumption levels are zero. 1/

The entrepreneur’s optimal choice of consumption, capital, and labor in this uncertain environment corresponds to the plan that maximizes the value function (indirect utility function) defined by:

(7)Vj(.t)=maxEt[Uj,t+βjFVj(.t+1)]+Φj[B¯j,tPt+1WtLj,tPt+1]

subject to the budget constraint given in (5), the production function given in (2), and the utility function described in (1), where Vj(0) = 0 and the argument of the value function is given by:

(8)Vj(.t)=Vj(Cj,t+Kj,t)

In equation (7), βjF is the firm’s discount factor (0 < βjF < 1), E is the expectations operator, Φj reflects the shadow price of relaxing the credit rationing constraint given in (4), and the working capital requirement described by (3) has been used to substitute for Bj,t.

As shown in Appendix II, the first order conditions for a maximum imply that the expected marginal product of capital, conditional on the firm’s survival, must equal the reciprocal of the entrepreneur’s marginal rate of time preference:

(9)1βjF=λj,t+1*1[1+λj,t+1fj,t+1Kj,t]dλj,t+1

When the credit rationing constraint is binding, the entrepreneur’s constrained demand for labor is simply Lj,t=B¯j,t/Wt. Equation (9) then implies that the entrepreneur’s demand for capital can be written as a negative function of both the expected real wage (Wt/Pt+1) and the loan rate (1+Rt) and, under normal conditions, a positive function of the real stock of credit made available to the firm. Thus:

(10)Kj,t=Kj,t(WtPt+1(),1+Rt(),B¯j,tPt+1(+))forB¯j,tbinding

where (+) or (-) above a variable indicates the sign of the partial derivative of Kj,t with respect to that variable. If the credit rationing constraint was not binding, the entrepreneur’s behavior would be described by his notional demands for both capital and labor, which normally are negatively related to both the expected real wage and the loan rate.

(11)Kj,t=Kj,t[WtPt+1(),1+Rt()]forB¯j,tnotbinding
(12)Lj,t=Lj,t[WtPt+1(),1+Rt()]forB¯j,tnotbinding

2. Banks

Banks facilitate the savings and investment process by providing entrepreneurs with working capital and by providing the savings instrument (deposits) that allows households to transfer consumption over time. Loans and deposits constitute the only financial instruments in our economy; workers do not acquire equity claims on the firms’ capital and firms do not issue debt securities. These simplifying assumptions seem in line with the observed limited development of markets for equities and securities in most financially-repressed developing countries.

The owners of banks must make decisions regarding the optimal scales of their intermediation activities during the current period as well as intertemporal consumption decisions. 1/ At the beginning of period t, the owner of bank i inherits an equity position, Si,t-1, a stock of loans to firms made at the beginning of the previous period, Σj=1nBi,j,t1, and a stock of deposits accepted at the beginning of the previous period, Di,t-1. It is assumed that the authorities require that a fraction k of all deposits must be held in the form of noninterest-bearing reserves at the central bank. Since the owners of the banks are assumed to be risk neutral, they will not hold any excess reserves (see Appendix III). The balance sheet constraint for period t-1 is thus

(13)Σj=1nBi,j,t1=(1k)Di,t1+Si,t1.

At the beginning of period t, firms will use their proceeds from selling output to service the debts incurred during period t-1 (as well as to fund their consumption and investment purchases). 2/ From those firms that have sufficient output to meet their full debt payments and thus avoid default, the bank will receive interest income and loan repayments equal (in real terms) to ΣjϵN1(1+Rt1)(Bi,j,t1/Pt), where N1 is the set of firms that do not default. For those firms that default (i.e., for which λj,t<λj,t*), the bank receives the output of the firms ΣjϵN2[λj,tfj,t], where N2 is the set of firms that default.

In making loans to entrepreneurs, the banks engage in both ex ante evaluation and ex post monitoring of their borrowers. When a bank receives a loan application from an entrepreneur, it evaluates the firm’s production and investment plans so as to determine its vulnerability to potential production shocks. It is assumed that this requires an expenditure of resources, through which ex ante evaluation the bank essentially acquires full information about the firm. The bank is thus able to use equation (6) to calculate the range of shocks that would lead the entrepreneur to default on his debt-servicing obligations, but it does not know ex ante the actual shock that will occur for the firm during the period. In addition, when an entrepreneur reports at the end of the period that he cannot meet his debt-service obligations, the bank engages in ex post monitoring to ensure that it is being provided with accurate information. Such ex post monitoring, however, is unnecessary for those firms that meet their entire debt-servicing obligations. 1/ The sum of the evaluation and monitoring costs that bank i incurs can be represented, in real terms, as:

(14)Mi=m0+m1Σj=1nBi,j,t1Pt+m2n2

where n is the total number of loans and n2 is the number of firms that default (i.e., the number of firms in the set N2). The first two terms on the right side of (14) represent the fixed and proportionate costs of ex ante evaluation. The third term represents the cost associated with ex post monitoring. 2/

Banks must fully service their deposit obligations in each period. During period t, this involves payment of interest and repayment of principal totalling (1+rt-1)(Di,t-1/Pt), where rt-1 is the interest rate on the deposits. 3/ To meet part of these payments, bank i can make use of its reserve holdings (kDi,t-1/Pt). The remainder must come from loan payments received from firms. Any profits from the bank’s operations are used by the owner to purchase consumption goods (Ci,t) and to add to his real equity (Si,t/Pt) in the bank. Equity funds can be lent out to firms, which provides the bank’s owner with an incentive to accumulate such funds, especially if his ability to attract deposits is limited by a ceiling on deposit interest rates.

The net profit or loss position that bank i experiences at the beginning of period t (Πi,t) reflects both the financial decisions taken during period t-1 and the values of production shocks realized in period t. This net position can be written as:

(15)Πi,t=ΣjϵN1(1+Rt1)[Bi,j,t1Pt]+ΣjϵN2[λj,tfj,t]m0m1Σj=1nBi,j,t1Ptm2n2(1+rt1k)(Di,t1/Pt)

For simplicity, it is assumed that the owner’s utility during period t is linearly related to the level of his consumption:

(16)Ui,t=γiICi,t

The choices that the owner must make in period t, subject to various constraints, are his current level of consumption (Ci,t), his equity in the bank (Si,t), the amount of deposits to raise (Di,t), and the amount of lending that he will make to each of the firms (Bi,j,t). The owner’s consumption level and equity holdings must be non-negative and are thus jointly constrained by: 1/

(17)Ci,t+Si,tPt=max[0,Πi,t]

The financial variables he must choose are subject to his balance sheet constraint (condition 13) and a regulatory requirement that his equity exceed some minimum proportion s of his loans:

(18)Si,tsΣj=1nBi,j,t

Moreover, in the presence of financial market restrictions, the bank knows that the amount of deposits it can raise will sometimes be limited to a ceiling level D¯i,t, such that

(19)Di,tD¯i,t

In general, the ceiling level of deposits that the bank can raise from households will depend on the levels of the parameters that the government controls, including in particular the ceiling interest rate on deposits. 1/

Ex ante, the profit or loss that bank i expects in period t+1 (EtΠi,t+1) can be described as:

(20)EtΠi,t+1=Σj=1n(1+Rt)λj,t+1*1Bi,j,tPt+1dλj,t+1+Σj=1n0λj,t+1*[λj,t+1fj,t+1]dλj,t+1(1+rtk)Di,tPt+1m0m1Σj=1nBi,j,tPt+1m2Σj=1nλj,t+1*

where Σj=1nλj,t+1* represents the expected number of defaults. This expected profit or loss position reflects both the choices that the bank makes in period t and the probability distributions of the production shocks that will be experienced by the firms to which the bank lends. The first two terms on the right hand side of equation (20) represent the expected revenues from lending. These terms reflect full repayment from any firm j that experiences a shock in the range λj,t+1* to 1 and partial repayment (equal to λj,t+1 fj,t+1) where shocks are in the range 0 to λj,t+1*. The third term represents principal and interest payments that must be made to depositors, minus the bank’s required reserve holdings (which are available to repay deposits). The final three terms are the expected costs of evaluation and monitoring.

For purposes of this paper we restrict attention to the case in which households’ deposits with banks are insured by the government, but in a manner that limits any moral hazard problem for banks. Accordingly, it is assumed that the authorities supervise each bank and impose a “prudent man rule” which effectively forces the bank’s owner to maximize the present discounted value of a utility function that gives equal weight to his private consumption and any losses that his activities might force the government to absorb through the deposit insurance system. More precisely, the “prudent man rule” completely internalizes the negative externalities by equating the marginal disutility of government losses to the marginal utility of the bank owner’s private gains: 1/

(21)U¯i,t={γiICi,twhenΠi,t>0γiIΠi,twhenΠi,t0

This rule is therefore equivalent to establishing an appropriate risk-based pricing scheme for deposit insurance.

The owner’s optimal consumption, equity, and financial intermediation decisions under the “prudent-man” supervisory system are those that maximize the value function (indirect utility function) defined by:

(22)Vi(.t)=maxEt(U¯i,t+βiIVi(.t+1))ΦiS(sΣj=1nBi,j,tPt+1Si,tPt+1)+ΦiD(D¯i,tPt+1Σj=1nBi,j,t(1k)Pt+1+Si,t(1k)Pt+1)

where the argument of the value function is given by:

(23)Vi(.t)=Vi(Πi,t)

and Vi(0)=0. The terms ΦiS and ΦiD are Lagrangian multipliers associated with the minimum equity requirement (18) and the upper bound on deposits (19). 1/

The bank monitors each firm’s investment and output plans when a loan application is received, and it is assumed that the bank’s owner maximizes his value function with full information about the ex ante decisions that firms will make under different conditions. We restrict attention in this paper to the analysis of financially repressed economies in which the existence of interest rate ceilings and other constraints leads to disequilibrium credit rationing; this is the case in which constraint (4) is binding and the behavior of firm j is characterized by (3), (4), and (10). The level of credit that firm j receives in period t is in this case one of the choice variables of bank i (B¯j,t=Bi,j,t). 2/ The bank, in maximizing its value function, essentially uses the information summarized by (3) and (10) to evaluate how the choice of its decision variables will influence its expected profits (as described by equation (20)). For the case of disequilibrium credit rationing, it is convenient to characterize the bank’s behavior in terms of its choices for the Bi,j,t/Pt+1 and Si,t/Pt+1. The implied level of deposits that the bank must raise is then described by (13), 1/ and the implied level of the owner’s consumption is described by (17).

It should be emphasized that, even though each firm deals with only one bank, and even though the bank through its ex ante evaluation activities obtains full Information about the ex ante behavior of firms, the financial market environment reflects competitive conditions. 2/ Banks offer the standard type of loan contracts found in competitive markets, rather than seeking to extract all the profits that borrowers can earn. Indeed, in choosing the levels of its loans and deposits, the individual bank takes as given the ceiling interest rates on loans and deposits. 3/

The first-order conditions for bank’s optimal level of real lending to each firm j (Bi,j,t/Pt+1) and real equity position (Si,tPt+1) can be written as

(24)0=Vi(.t)(Bi,j,tPt+1)=βiIEt{Vi(.t+1)(Bi,j,tPt+1)} -ΦiD1-K -sΦiS
(25)0=Vi(.t)(Si,tPt+1)=γiI(1+ρt+1)+βiIEt{Vi(.t+1)(Si,tPt+1)}+ΦiD(1K) +ΦiS

where 1+ρt+1 = Pt+1/Pt denotes the expected rate of inflation and letting z denote either choice variable: 4/ 5/

(26)Et{Vi(.t+1)Z}=Et{Vi(.t+1)(.t+1)(.t+1)Z}=γiIEt{Πi,t+1Z}

As shown in Appendix III, these conditions imply: 1/

(27)0=γiIβiI{(1λj,t+1*)(1+Rt)+λj,t+1*22fj,t+1Lj,tPt+1Wt+λj,t+1*22fj,t+1Kj,tKj,t(Bj,t/Pt+1)1+rtk1km1m2λj,t+1*(Bj,t/Pt+1)}sΦiSΦiD1K

and

(28)0=γiIβiI(1+rt-k)(1-k)+ΦiS +ΦiD1-k -γiI(1+ρt+1).

Equations (27) and (28) can be explored under different combinations of the constraints that may be binding on the bank. When the structure of official constraints leads to both a binding ceiling on deposit availability (ΦiD>0) and creates an incentive to hold only the minimum level of equity (ΦiS>0), 1/ then the total amount of lending by the bank will be constrained as:

(29)ΣjBi,j,tPt+1 =(1k)(1S)D¯i,tPt+1forΦiD>0,ΦiS>0.

In this situation, the amount of lending to each individual firm will differ from the notional amount that the bank would lend (at the prevailing ceiling loan interest rate) if it could obtain all the deposits it wished at the prevailing deposit interest rate. The actual lending to each firm will be such that the shadow price of an additional dollar of lending to any firm will be equalized across the portfolio.

Disequilibrium credit rationing can also emerge when the bank faces a binding ceiling on deposit availability (ΦiD>0) but nevertheless has an incentive to expand its equity position beyond the required minimum level (ΦiS=0). Equation (27) indicates that the bank will increase its lending to firm j until the discounted marginal revenue from lending an additional dollar just matches the marginal cost (in terms of the consumption foregone to raise an additional dollar of equity). An extra dollar of lending increases the expected revenue of the bank since it allows the credit constrained firm to expand its output by employing more labor. Moreover, as shown in the previous section, a larger amount of credit would also induce the owners of firms to increase the firm’s capital stock and thereby its output. Since the production shock for firm j is uniformly distributed between 0 and 1, 1λj,t+1* represents the ex ante probability that the bank will be fully repaid on its loan; the associated expected marginal revenue would be (1λj,t+1*)(1+Rt). If the firm defaults, however, the bank would obtain whatever output is produced. The second and third terms inside the brackets in equation (27) represent the effect of additional lending on the expected value of the output that would be available if the firm defaults. 2/ An additional real dollar of lending also affects expected monitoring costs both immediately (the m1 term), and by altering the probability of default by λj,t+1*/(Bj,t/Pt+1). It is easily shown by differentiating (6) that λj,t+1*/(Bj,t/Pt+1)>0 for the “normal case” in which the total elasticity of output with respect to real credit availability is less than one. 1/

Equation (27) implies that, when banks hold more equity than the required minimum level, the constrained supply of loans to each firm is a function of the loan interest rate, the real wage, the monitoring cost parameters, and the expected rate of inflation: 2/

(30)Bj,tPt+1=Bj,tPt+1(1+Rt(?),WtPt+1(),m1(),m2(),ρt+1())forΦiD>0,ΦiS =0.

The signs of the partial derivatives are derived in Appendix III.

In this situation, default risk implies that the bank’s supply of credit to each particular firm is likely to be a backward bending function of the loan rate. At any given loan rate, the slope depends on whether the revenue associated with a larger loan (at a higher interest rate) would be offset (in an expected value sense) by a higher probability that the entrepreneur would default (which would imply a loss of revenue and higher ex post monitoring costs). At a sufficiently high loan rate, the bank would not be willing to lend additional funds to an entrepreneur, and might even reduce the amount of lending relative to the desired level of constrained lending at a lower interest rate--i.e., the constrained supply of loans becomes backward bending. 3/ Notice that, since entrepreneurs may differ in the scales of their investment and production plans (for example, due to different marginal utilities of consumption), the amounts that a bank is willing to lend to different entrepreneurs at a given interest rate also will differ.

Although the partial derivative of Bj,t/Pt+1 with respect to Wt/Pt+1 is ambiguous, under reasonable assumptions, particularly when the probability of default (λj,t+1*) is relatively small, a higher real wage will reduce the bank’s desired amount of lending. Higher monitoring costs will also reduce the bank’s desired amount of lending. A higher real wage effectively increases the probability that the firm will default on its debt-service obligations, whereas higher monitoring costs imply lower net returns from lending.

A higher expected rate of inflation will also reduce the attractiveness of additional lending to any firm, essentially by increasing the amount of nominal equity that will be needed to fund a loan. Since the bank focuses on providing a loan whose real value (Bi,j,t/Pt+1) is measured in terms of the price level in period t+1, a higher expected rate of inflation means that the bank will have to accumulate a greater stock of equity at time t. Since this implies a lower level of consumption in period t, there is an incentive to reduce real lending as expected inflation rises.

3. Households

Households supply labor services to firms, hold deposits with banks, and attempt to maximize the expected discounted value of the utility of their consumption over time. The representative household’s utility during period t (Uh,t) is taken as a positive function of the level of its consumption (Ch,t) a negative function of the labor services (Lh,t) it supplies, and a positive function of the real value of its deposit holdings. 1/ Thus:

(31)Uh,t=Uh,t(Ch,t,Lh,t,Dh,t/Pt+1)
withUh,tCh,t>0,Uh,tLh,t<0,Uh,t(Dh,t/Pt+1)>0
2Uh,tCh,t2<0,2Uh,tLh,t2<0,2Uh,t(Dh,tPt+1)2<0,2Uh,tCh,tLh,t=0
2Uh,tCh,t(Dh,t/Pt+1)=0,2Uh,tLh,t(Dh,t/Pt+1)=0

The household’s budget constraint implies that its consumption plus whatever additions it makes to its deposit holdings during period t must equal the sum of the interest it earned on its deposits during period t-1 and its wage income.

(32)Ch,t+Dh,tPtDh,t1Pt =rt1Dh,t1Pt + WtPtLt

The household’s optimal consumption, labor supply, and saving decisions are those that maximize the value function

(33)Vh(.t) =maxEt{Uh,t(Ch,t,Lh,t,Dh,tPt+1)+βhHVh(.t+1)}

where:

(34)Vh(.t) =Vh(Ch,t+Dh,tPtWtLh,tPt) =Vh((1+rt1)Dh,t1Pt)

The first order conditions for a maximum are:

(35)Vh(.t)Lh,t=0=Uh,tCh,tWtPt +Uh,tLh,t
(36)Vh(.t)(Dh,tPt+1)=0=(1+ρt+1)Uh,tCh,t+βhH(1+rt)Uh,t+1Ch,t+1+Uh,t(Dh,t/Pt+1)

As shown in Appendix IV, these conditions imply that the household’s steady state real deposit holdings will be a positive function of both the deposit interest rate and the real wage, and a negative function of the expected rate of inflation. Moreover, its steady state demand for consumption goods will be a positive function of the real wage. The effects of changes in the deposit interest rate and the expected rate of inflation on steady state consumption are ambiguous, however, when there is a binding ceiling on the deposit interest rate. Similarly, the desired supply of labor services will normally be a positive function of the real wage but, under a binding deposit rate ceiling, could be either a positive or negative function of the deposit interest rate and the expected rate of inflation. Thus,

(37)Dh,tPt+1=Dh,tPt+1((rt(+),WtPt(+),ρt+1())
(38)Ch,t=Ch,t(rt(?),WtPt(+),ρt+1(?))
(39)Lh,t=Lh,t(rt(?),WtPt(+),ρt+1(?))

If the deposit rate exceeds the expected rate of inflation, Ch,t will depend positively on rt and negatively on ρt+1, as the income effect will outweigh the substitution effect, while Lh,t will depend negatively on rt and positively on ρt+1.

III. Steady State Solutions

Financial regulations and creditworthiness considerations will be key determinants of the long-run behavior of a financially repressed economy. Since our analysis focuses on an economy where the authorities establish ceiling loan and deposit interest rates that are below market clearing levels, entrepreneurs, bank owners, and households will not all simultaneously achieve their desired spending and portfolio plans. In particular, firms that are credit rationed will be unable to employ the level of labor that they would find profitable to use at the prevailing real wage and loan interest rate. As a result, the level of employment and output will be constrained by credit availability. In addition, banks will be unable to ‘obtain all the deposits that they would like to have at the prevailing ceiling deposit interest rate and the stock of real deposits will reflect the households’ desired holdings of deposits.

1. Steady state relationships

Since the economy is subject to stochastic production shocks, the realized period-to-period outcomes for the economy will not converge to a steady state, but meaningful steady state solutions do exist for ex ante expectations of these outcomes and hence for the ex ante plans of economic agents. This section analyzes the long-run properties of our model in terms of the ex-ante plans formulated by the entrepreneurs, bank owners and households.

The economy’s long-run behavior can be described in terms of four relationships (where all variables for period t+1 are specified in terms of their expected values at time t):

(40)Lt=ΣhLh,tH(rt,Wt/Pt,ρt+1)ΣjLj,tF(1+Rt,WtPt+1)
(41)(a)BtPt+1 =ΣiΣjbi,j,t(1+Rt,WtPt+1,m1,m2,ρt+1)=ΣhWtPt+1Lh,tH(rt,Wt/Pt,ρt+1)
(b)BtPt+1=Σh(1K)(1S)Dh,tHPt+1(rt,Wt/Pt,ρt+1)=ΣhWtPt+1Lh,tH(rt,Wt/Pt,ρt+1)
(42)  (a)ΣiSitPt+1=Σh(1K)Dh,tHPt+1(rt,Wt/Pt,ρt+1)=ΣiΣjbi,j,t(1+Rt,WtPt+1,m1,m2,ρt+1)
(b)ΣiSi,tPt+1 =SΣh(1K)(1S)Dh,tHPt+1(rt,Wt/Pt,ρt+1)
(43)DtPt=ΣhDh,tHPt(rt,Wt/Pt,ρt+1)=Ht/kPt

Equation (40) represents the relationship between the sum of the firms’ unconstrained ex-ante demands (when they are not credit rationed) for labor and the sum of the households’ desired supplies of labor. If the firms could obtain all the credit they desired at the prevailing interest rate, then ΣjLj,tF defines the amount of labor they would hire (given the existing real wage). However, when the banks credit ration the firms, firm j can hire only Lj,t=B¯j,t/Wt (equations (3) and (4)) where Bj,t is the credit made available to it. The real wage will therefore adjust until the sum of the firms’ credit-constrained demands for labor equals the households’ desired supply of labor services ΣhLh,tH.

Ex ante credit market equilibrium is achieved when the ex ante supply of bank credit is sufficient to support the anticipated real wage bill. However, as indicated by equations (41a) and (41b), this equilibrium could be achieved either when the banks’ owners hold only the minimum officially required level of equity or when they hold more than the minimum required level of equity. Given the banks’ cost structures and the ceiling deposit interest rate, there will be a range of low ceiling loan rates for which the bank owners will find it profitable to operate with only the minimum required level of equity (see Appendix V). In this situation, the banks’ supply of credit will equal Σ(1K)(1S)Dh,tH, where k is the required reserve ratio and s is the minimum required ratio of bank equity to total lending. For the level of lending to support the real wage bill, equation (41b) must hold. There will also be a middle range of ceiling loan interest rates, however, for which bank owners will find it profitable to fund their lending activities by holding more than the minimum required level of equity. 1/ As a result, the banks will achieve their desired level of lending to each firm (equation (41a)) 2/ by substituting equity for deposits as a source of funding. For an ex ante credit market equilibrium, the sum of the banks’ desired lending to firms must equal the economy’s wage bill.

The level of equity in the banking industry is given in equations (42a) and (42b), Equation (42b) describes the level of equity when the banks hold only the minimum required level of equity; whereas equation (42a) indicates the level of equity when the banks hold more than the minimum required level of equity.

Equation (43) describes the conditions for ex ante money market equilibrium. Since households do not hold currency and banks do not hold excess reserves, the supply of deposits equals Ht/K, where Ht is the stock of base money. The household’s real holdings of deposits are given by

ΣhDh,tHPt.

Since we assume that the authorities, in issuing money to finance government spending, keep the stock of base money growing at a constant exogenous rate (which must equal the expected rate of inflation, ρ), the price level (Pt) will adjust to ensure that equation (43) is satisfied at each point in time.

The role that financial repression and creditworthiness considerations play in determining the economy’s steady state position can be illustrated using Figure 1 (see Appendix V for derivations). In the northeast (NE) quadrant, curve 1 represents the combinations of the loan rate (1+Rt) and real wage (Wt/Pt+1) that would set the sum of the firms’ unconstrained (not credit-rationed) demands for labor equal to the sum of the households’ desired supplies of labor. This curve has a negative slope since a higher real wage, which would reduce the firms’ demand for labor (and increase the households’ supply), would have to be offset by a lower loan rate, which would increase the firms’ demand for labor. Any point to the left of curve 1 represents a situation where the firms’ unconstrained demand for labor exceeds the households’ desired supply of labor.

Curve 2 in the NE quadrant represents the combinations of the loan rate and real wage that would lead banks--when firms are credit rationed--to provide a real supply of credit that equals the real wage bill. This curve has two segments: AB is relevant over the range of R in which banks would be induced to hold only the minimum required level of equity, and BC is relevant over the range in which banks would hold more than the minimum required level of equity. 2/

As shown in Appendix V, the banks’ owners will hold the minimum required level of equity whenever the loan rate is between R** and R* (equation (41b) holds). 1/ For loan rates below R** the banks’ owners would not find it profitable to utilize all of the deposits the households would make available and the ceiling deposit rate would no longer be a binding constraint. 2/ Between R** and R*, the banks’ owners would find it profitable to use all deposits made available by the households but would hold only the minimum amount of equity. 3/ In this situation, there is only one level of the real wage (W¯p) that would ensure that the real supply of bank credit (Σh(1k)(1s)Dh,tHPt+1) equals the real wage bill Σh(WtPt+1)Lh,tH. 4/

In the range BC of curve 2, the banks’ owners would find it profitable both to use all deposits made available to them by the household sector and to hold more equity than the minimum level required by the authorities. This segment of curve 2 is positively sloped at relatively low values of R, since a higher real wage implies a large wage bill which the banks will fund only if the loan rate rises. 5/ In this range, the banks will see a higher expected profit from an addition dollar of lending since the firms will have relatively low debt servicing obligations (due to both a low loan interest rate and a small stock of loans). However, as the loan interest rate rises and the stock of loans held by firms expands, the probability that the firms will default on their debt servicing obligations will begin to rise; and, eventually, the banks’ owners will see the expected return from lending an additional dollar, even at a higher interest rate, turn negative.

Curve 3 in the northwest (NW) quadrant of Figure 1 indicates the amount of real credit that banks would extend at different loan interest rates. The curve has two segments: one where the banks hold only the minimum required level of equity (DE) and another where they hold more than the minimum required level of equity (EF). As already discussed in the case of curve 2, there is only one real wage (W¯/P) at which the stock of real credit [Σh(1k)(1s)DhHPt+1] will equal the real wage bill when the banks’ owners hold only the minimum required level of equity. Given the values of (W¯/P), k, s, ρt+1, and rt, the real supply of credit will therefore be fixed until the loan rate rises to a level high enough to induce the banks’ owners to hold more than the minimum required level of equity. Thus, just as in the case of curve 2, curve 3 has a vertical segment (DE) in the range of loan rates between R** and R*. 1/

Segment EF of curve 3 describes the supply of real credit at different loan interest rates when the banks’ owners find it profitable to hold more than the minimum required level of equity. However, when banks have more than the minimum required level of equity, it has already been noted that increases in the loan interest rate (R) will change the real desired supply of bank credit and thereby the real wage bill that can be funded. As a result, the real wage would also change. Since curve 3 portrays the banks’ desired real supply of lending solely as a function of the loan interest rate, the relationship between Rt and Wt/Pt+1 implicit in curve 2 must be used to describe the Wt/Pt+1 that would prevail at each value of Rt. This relationship can be substituted into the banks’ desired supply of loans (ΣiΣjbi,j,t) in order to obtain a relationship between the supply of bank credit, Rt, and the other policy variables and cost parameters (see Appendix V). The real supply of credit initially will rise with a higher loan interest rate, since the expected profit on an additional dollar of lending will be positive when interest rates are relatively low and the firms have limited debt servicing obligation. As the loan interest rate rises, however, a point will eventually be reached where the expected profit on additional lending turns negative when firms face relatively large debt service obligations. As a result, the supply of bank credit will eventually be backward bending as loan interest rates rise.

Curve 4 in the southeast (SE) quadrant of Figure 1 portrays the level of deposits that would be provided by the household sector (net of required reserves (Σh(1K)Dh,tH/Pt+1)) to the banks at each level of the real wage (Wt/Pt+1). As noted in (37) and Appendix IV, the households’ desired real holdings of deposits is a positive function of the real wage.

2. Financial policies and intermediation costs

The relationships in Figure 1 can be used to illustrate the macroeconomic effects of changes in financial policies and the costs of intermediation. If the authorities establish a ceiling loan rate of R^, for example, then the banks’ owners would find it profitable to supply a level of real credit equal to OG. Such a level of lending would support a real wage bill that would be consistent with the real wage (W/P)1. Given the ceiling deposit interest rate and the expected rate of inflation, the supply of real deposits from the household sector, net of required reserves, would be equal to OM (=GI). This implies that the banks would hold equity equal to IJ, which would exceed the required amount GH. At this level of lending, the firms would have an excess demand for credit, which is indicated by the fact that, at R1, a real wage equal to ON would be needed before the firms’ excess demand for labor would be eliminated.

Since R1 lies in the range where the banks’ owners would see an expected profit from lending an additional dollar at a higher interest rate, increases in the ceiling loan rate would result in a larger stock of credit, reflecting the willingness of the banks’ owners to expand their holdings of equity. The resulting increase in the supply of credit would allow firms to hire more labor which would in turn lead to the real wage being bid up. As the real wage rose, the households would expand their real holdings of deposits. However, if the ceiling loan rate was in the range where the bank owners would see a negative return on an additional dollar of lending even at a higher interest rate (such as R2), 1/ then raising the loan interest rate would result in a lower stock of credit, a lower real wage, and a smaller real stock of deposits.

This result has important policy implications. Although financial reforms that involve raising the ceilings on loan interest rates are likely to be expansionary when firms’ debt-servicing positions are relatively strong, a higher ceiling loan interest can be contractionary if the debt-servicing position of the firms is relatively weak (e.g., there is a high probability that they will default on their debt-service obligations). This indicates the importance of dealing with the debt-servicing difficulties of firms at an early stage in any adjustment program that incorporates sharp increases in nominal and real interest rates in an economy with a repressed financial system.

As examples of the macroeconomic consequences of changes in the banks’ cost structure, Figures 2 and 3 illustrate the effects of an increase in the banks monitoring costs and a higher required reserve ratio, respectively. With higher monitoring costs, the minimum loan rate at which the banks’ owners would find it profitable to fully utilize the deposits made available by households and hold either the minimum required level of equity (R**) or more than the minimum level of equity (R*) would have to rise (Figure 2). 1/ The new minimum loan interest rates would now be R’* and R’*. However, the scale of the banks’ lending in the range between R’** and R’* would be the same as in the range between R** and R*. As discussed in Appendix V, this reflects the fact that, when banks hold only the minimum required level of equity (as in the ranges R’** to R’* or R** to R*), the real supply of credit (Σh(1k)(1s)Dh,tHPt+1) is independent of the banks’ monitoring costs (equation (41b)).

However, in the range where the banks hold more equity than the minimum required level (between R’* and R*’), the amount of credit the banks would extend at any given loan interest rate will be smaller when monitoring costs increase. With higher monitoring costs, the banks’ owners would attempt to ensure that they obtain a higher expected return on any loan. At a given loan interest rate, a higher expected return can be achieved only by restricting the amount of credit extended to a firm, which would lower the probability that the firm would default on its debt-servicing obligations. As a result, curves 2 and 3 both shift in toward the origin.

At the given ceiling loan interest rate (R1), higher operating costs will lead the banks to reduce the real supply of credit from OG to OG’. This would reduce the firms’ ability to hire labor which would result in a decline in the real wage (from (W/P)1 to (W/P)2). With a lower real wage, households would also reduce their real holdings of deposits (deposits net of required reserves would fall from OM to OM’). Thus, reduced financial efficiency can depress the economy’s real wage and the stocks of real credit and deposits.

A higher required reserve ratio would also result in a contraction of the stocks of real credit and real deposits, as well as a fall in the real wage (Figure 3). With a higher required reserve ratio, the banks’ effective cost of using deposits would rise, since a small proportion of each dollar of deposits could be used to fund lending activities. As a result of these costs, the minimum loan interest rate (R**) at which the banks’ owners would find it profitable to fully utilize all deposits supplied by the households at the ceiling deposit interest rate and hold just the minimum amount of equity must rise (to R’**). However, the loan interest rate (R*) at which the banks’ owners would find it profitable to use all available deposits and hold more than the minimum required equity would not be changed (see Appendix V). This reflects the fact that at R* bank equity rather than deposits are the marginal source of bank funds, and the marginal cost that is relevant for lending decisions is the implicit cost of foregone consumption associated with adding an extra dollar of equity. This also means that, over the range where banks’ owners hold more equity than the required minimum (between R* and R*), the supplies of bank credit would have the same slope (see Appendix V).

A higher required reserve ratio would also reduce the amount of credit that the banks would supply when they hold only the minimum required level of bank equity, which equals Σh(1k)(1s)Dh,tHPt+1. The smaller amount of credit can naturally support only a smaller real wage bill (Σh(WtPt+1)Lh,tH).

In terms of Figure 3, the value of (W¯/P) that results in an equality between the real supply of credit and the real wage bill must fall from (W¯/P)0 to (W¯/P)1. A higher required reserve ratio thus shifts curve 2 in toward the origin from ABC to A’B’C’, and curve 3 shifts from DEF to D’E’F’. In addition, the curve in the SE quadrant relating the real wage (Wt/Pt+1) to the amount of net deposits received by the banking system shifts up (to reflect a higher k).

At a given ceiling loan interest rate (such as R1), a higher k would thus reduce the real supply of bank credit from OG to OG’. Since firms would have less credit, they would be able to hire less labor, and the real wage would fall from (W/P)0 to (W/P)1. The stock of real deposits net of required reserves would also fall from OM to OM’. Although not explicitly examined in Figure 3, a higher k would produce even sharper declines in the stock of real credit and the real wage if the ceiling loan interest rate was in the range where the supply of bank credit was backward bending.

IV. Financial Reform, Prudential Supervision, and the Cost of Official Safety Nets

During the past two decades, many developing countries have liberalized their financial systems in order to improve financial sector efficiency, to increase financial savings, and to achieve a more efficient mix of investments. These liberalizations often involved the removal or elevation of ceiling interest rates, reductions in required reserve ratios and freer entry into the financial system. As noted earlier, however, a number of these reform efforts ended in periods of financial instability that required extensive restructuring of both the corporate and financial sectors and often created large public sector funding obligations as the authorities provided emergency lending to a broad range of enterprises and financial institutions.

This experience has raised the issue of whether a financial reform is likely to expose authorities to new credit risks through the operations of any official safety net underpinning the domestic financial system. Since the authorities in most developing countries have implemented either explicit deposit insurance arrangements or have historically intervened to prevent widespread losses for depositors, there is often the perception that depositors, especially small depositors, will be fully protected in the case of an institutional failure. This can naturally make depositors indifferent regarding the lending activities of the financial institutions. Since depositors are the primary source of funding for banks in developing countries, this eliminates an important source of market discipline on the banks’ managers and owners and places a correspondingly greater burden on the bank supervisors to monitor for fraud and mismanagement.

The potential funding obligations of the authorities that are associated with maintaining an official safety net can be linked to the scale of deposits in financial institutions and the probability that some of these institutions will fail. In general, it is difficult to characterize the probability that a financial institution will fail, especially if the authorities are considering a long time horizon. However, the analysis that we have developed in this paper can be used to formulate an explicit measure of the probability at the beginning of the period that a bank will default on its deposit payment obligations at the end of the period. Moreover, this formulation will allow us to gauge the effects of changes in financial policies during a reform period on the probability of institutional failure.

1. Deposit insurance obligations and the probability of institutional failure

Our analysis assumes that the authorities guarantee the repayment of both the principal and the interest payments that households are to receive on their deposits. 1/ For bank i, the authorities maximum potential deposit insurance payments (measured in terms of period t+1’s price level) is (1+rt-k)Di,t/Pt+1, since the authorities can use the banks required reserves (kDi,t) to help meet their deposit insurance obligations. Note that this upper bound will be realized only if the authorities cannot recover any of the bank’s earnings when the bank fails. 2/

A bank will fail if the revenues it receives on the loans that it made at the beginning of the previous period are less than the sum of the payments it owes to depositors. 3/ In Section II, it was assumed that a bank’s end of period revenues equal the sum of the interest and principal repayments of loans made by borrowers that do not default plus the entire value of the output (less ex post monitoring costs) of all the firms that do default on their loan obligations. In this section, our objective is to characterize the ex ante expected value of the authorities’ deposit insurance payments (EDP), and to analyze how financial reforms influence the expected size of these safety net obligations. Accordingly, to make the analysis tractable, we will employ four simplifying assumptions: First, we will consider the case where the banks get full repayment from borrowers that do not default and nothing from firms that do default. 4/ Second, we will continue to assume that the bank supervisory authorities impose a prudent man standard on the bank’s owners. As noted earlier, this implies that the bank’s owners will incorporate the potential losses arising from bad loans (including those that would be sufficient to force the bank into bankruptcy) into their decisions (in the form of negative utility for the owners) regarding the optimal scale and direction of their lending activities. Third, all banks will be taken as holding only the minimum required level of equity. Finally, we will assume that each bank lends to a set of n identical borrowers. 5/

In this situation, let Zi,j,t be the real revenues that will be received by bank i as a result of a loan made to firm j in period t:

(44)Zi,j,t={(1+Rt)Bi,j,t/Pt+1withprobability1λj,t+1*0withprobabilityλj,t+1*

The net profits of bank i in period t is thus:

(45)Πi,t=ΣjnZi,j,t -(1+rt -k)Di,tPt+1

If Πi,t < 0, the bank defaults. When all borrowers are identical, the minimum number of borrowers (ns) that must successfully service their debt obligations to ensure that Πi,t ≥ 0 can be defined as the solution to

(46)Πi,t=ns(1+Rt)Bi,j,tPt+1(1+rtk)Di,tPt+1=0

where Bi,j,tPt+1=1n(1K)(1S)Di,tPt+1 1/

This implies that

(47)ns =(1+rtk)(1s)(1+Rt)(1k) n

Since the probability that any given firm will service its debt insurance is given by 1λj,t+1* and is independent of what happens to the other firms, the expected deposit insurance payments (EDP) faced by the authorities at the beginning of the period is given by

(48)EDPt=Συ=0nsb(υ;n,(1λj,t+1*))[(1+rtk)Di,tPt+1υ(1+Rt)Bi,j,tPt+1]

where

(49)b(υ;n,(1λj,t+1*))=(nυ)(1λj,t+1*)υ(λj,t+1*)nυ

is the Binomial probability that exactly υ(<ns) loans will be repaid and the bank will default. As already noted, the first term inside the square bracket represents the authorities’ maximum deposit insurance payment obligation; whereas the second term inside the bracket represents the amount of loan repayments that the authorities collect when the bank enters bankruptcy. Since b(υ;n,1λ*)) can be approximated by a Poisson distribution, 1/ we can write equation (48) as

(50)EDPt=(1+rtk)Di,tPt+1Συ=0nsδυeδυ!(1+Rt)Bi,j,tPt+1Συ=0nsδυeδυ!υ

Equation (50) indicates the importance of closure rules in determining the extent of the authorities’ potential losses from the deposit insurance system. For example, if the bank’s owner can use the revenues from the successful loan repayments to finance consumption expenditures prior to a declaration of bankruptcy, the first terra on the right hand side of equation (50) represents the authorities’ anticipated loss. The second term represents the expected recovery of loan repayments receipts if the authorities can prevent the bank’s owner from using these resources to fund his consumption. By combining

equations (47), (50), and Bi,j,tPt+1=1n(1k)(1s)Di,tPt+1, we can write

(51)EDPt=(1+rtk)Di,tPt+1Συ=0nsδυeδυ!(1υns)

where δ=n(1λj,t+1*)

To examine the conditions under which a financial reform can increase the authorities’ potential funding obligations, we must consider how the expression in equation (51) responds to a change in financial policies. In particular, we will be concerned with the effects of increases in the ceiling interest rates on loans (R) and deposits (r), a reduction in the required reserve ratio (k), and an increase in the minimum equity ratio (s). If X represents the financial policy instrument being changed, then equation (51) implies

(52)EDPtX=EDPt(1+rtk)(1+rtk)X+EDPt(Di,t/Pt+1)(Di,t/Pt+1)X+(1+rtk)Di,tPt+1Συ=0ns(1υns)(υδ1)δυeδυ!δX+(1+rtk)Di,tPt+1Συ=0nsδυeδυ!(ns)2υnsX

with υδ -1<0sinceδ=n(1λj,t+1*)>nsυ. 1/ Since δX=nλj,t+1*/X, we can write equation (52) as:

(53)EDPtX=EDPt(1+rtk)(1+rtk)X+EDPt(Dit/Pt+1)(Di,t/Pt+1)X(1+rtk)Di,tPt+1Συ=0ns(1υns)(υδ1)δυeδυ!nλj,t+1*X+(1+rtk)Di,tPt+1Συ=0nsδυeδυ!(ns)2nsX

For the case in which banks hold only the minimum required level of equity, then (53) can be further simplified by noting that in the steady state Di,tPj+1,λj,t+1*, and ns can be expressed as functions of Rt, rt, s, and k. In particular, holdings of the real deposits will be positively related to rt and s, a negative function of k, and an ambiguous function of the expected rate of inflation (ρt+1). 1/

(54)Di,tPt+1=Di,tPt+1(rt(+),s(+),k(),ρt+1(?))

The critical number of loan repayments (ns) is a negative function of Rt and s and a positive function of rt and k. 2/

(55)ns =ns(1+Rt(),rt(+),k(+),s())

and the probability (λj,t+1*) that the firms will default on their debt-service payments can be shown to be positively related to Rt and rt but negatively related to k. 3/

(56)λj,t+1*=λj,t+1*(1+Rt(+),rt(+),k(),s(+))

These relationships imply that changes in the ceiling loan and deposit interest rates would not have symmetric effects on the authorities’ expected deposit insurance payments (EDPt). If the ceiling deposit interest rate was increased in isolation, for example, the authorities’ EDPt would increase. A higher deposit interest rate would directly increase both the interest payments on each deposit and the stock of deposits that banks would be able to attract from the household sector. Even with an unchanged probability of bankruptcy, this would increase the payments the authorities would expect to make under the deposit insurance system. However, the probability of a bank failure would also increase for two reasons: (1) the minimum number of successful loan repayments (ns) needed to ensure that a bank could service its deposit obligations would rise; and (2) since the larger stock of deposits would allow the bank to extend more loans to firms, the probability that the firms would default on their debt-service payments would also increase.

In contrast, a higher ceiling loan interest rate would have an ambiguous effect on the authorities’ EDPt. When banks hold only the minimum required level of equity, it was shown in Section III that a change in the loan rate would not lead to a change in the ex ante steady state levels of either the real stock of credit or the real wage. Thus, the real stock of deposits and the banks’ deposit interest payments would remain unchanged (as long as the ceiling deposit interest rate remained unchanged). However, the probability of a bank defaulting on its deposit payments could either rise or fall. On the one hand, a higher loan rate reduces the minimum number of loan repayments (ns) that are needed to enable a bank to successfully service its deposit obligations. On the other hand, a higher loan rate increases the probability that the bank’s borrowers will default on their debt-service obligations. In this situation, the initial debt-servicing levels of the firms (and thereby their probabilities of default) will play a crucial role in determining whether the authorities’ EDP increases. In particular, the larger the firms’ initial debt-servicing obligations, the more likely it will be that an increase in the loan rate will increase the authorities’ EDP. This indicates the importance of dealing with any debt-servicing difficulties of nonfinancial firms at an early stage, or (preferably) prior to undertaking a financial reform.

It has often been argued that increasing the minimum required level of equity in the banks (enhanced “capital” adequacy) is one means of reducing the authorities’ EDP during a financial reform by creating a larger “buffer” between the deposit insurance system and a bank failure. 1/ In our analysis, it is indeed true that a higher minimum equity ratio (s) for the banks reduces the number of successful loan repayments that would be needed in order for a bank to avoid defaulting on its deposit payment obligations. However, when banks hold only the minimum level of equity, a higher s means that the banks in a repressed financial system would ultimately extend a larger stock of loans.

Why is this the case? With a ceiling deposit interest rate, the shadow price (or extra expected profit) of an additional dollar of deposits exceeds the deposit interest rate, and the banker has an incentive to use all the deposits he can obtain. However, the bank can stay in business and have access to those deposits only if it meets the minimum capital adequacy standards. When the bank’s owner decides to hold only the minimum required level of bank equity, we have noted that this corresponds to the situation where the expected profit that can be made from creating an extra dollar of equity (which is the rate at which consumption can be transferred from t to t+1) is less than the owner’s internal rate of discount. Holding equity (rather than relying exclusively on deposits) thus imposes an intertemporal cost on the bank’s owner. In this situation, a higher capital adequacy requirement represents a higher operating cost for the banker. However, the banker can minimize the cost of a higher capital adequacy requirement by using his new equity to fund additional loans. The interest earnings on this additional lending provides at least a partial offset to the intertemporal costs imposed by the higher capital adequacy requirement.

Such additional lending would lead firms to attempt to hire additional labor, which would be forthcoming only at a higher real wage. A higher real wage would in turn increase EDP both directly, by increasing the stock of deposits in the banking system, and indirectly, by increasing the probability that firms will default on their debt-service payments and thereby the probability that the banks will default. Once again, a key issue is the scale of the firm’s initial debt-servicing obligations and the probability that they will default on those obligations. 1/ The higher the initial probability that the firms will default on their debt-service obligations, the more likely it will be that a higher s will not reduce the authorities’ expected deposit insurance payments.

Finally, many financial reforms have encompassed a lowering of required reserve ratios. A decline in k can reduce the authorities’ EDP by reducing the minimum number of successful loan repayments (ns) that are needed if the bank is to avoid defaulting on its deposit payments. However, a lower k will also allow banks to extend more loans to firms, which will drive up both the real wage (and thereby the level of bank deposits) and the probability that the firms will default on their debt-service obligations.

These results suggest that a financial reform encompassing increases in ceiling interest rates and the lowering of required reserve ratios can potentially increase the authorities’ expected deposit insurance payments even if the reform is accompanied by higher minimum equity requirements for banks and strong prudential supervision. In particular, an increase in the authorities’ EDP is most likely when the firms’ debt-servicing positions are relatively weak (as reflected in a high probability that they will default on their debt-service obligations). This implies that, if the authorities do not want to face a large EDP, a financial reform should be preceded by steps to deal with any debt-service difficulties in the nonfinancial sector.

V. Conclusions

This paper has focused on developing a framework for the analysis of the macroeconomic effects of financial reform and the effects of such reforms on the cost of maintaining an official safety net. The analysis considered a multiperiod general equilibrium model of an economy with a repressed financial system which emphasized the interdependence between production shocks, firm creditworthiness, credit rationing, bank failures, and the cost of maintaining an official deposit insurance system. It was argued that any financial difficulties of nonfinancial firms should be addressed at an early stage, or a financial reform could have a contractionary effect on output. In systems with either explicit or implicit deposit insurance, a financial reform may increase the authorities’ potential funding obligations even if the authorities put in place strong prudential supervision and enhanced capital adequacy standards. Indeed, the authorities may be able to attain the efficiency gains associated with a financial reform only if they are willing to accept the risk of greater funding obligations in the deposit insurance system. However, this tradeoff between financial efficiency and funding risk can be improved by strengthening the financial position of nonfinancial firms and the system of prudential supervision at an early stage in the reform process.

APPENDIX I Notation

General subscripts and superscripts

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Real quantities and related variables

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Financial quantities and related variables

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Prices, wages, and interest rates

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Policy variables

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Preferences and shadow prices

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Other notation

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APPENDIX II The Firm

This Appendix derives conditions (9)-(12) in the text, which describe the behavior of the firm. The first order conditions for the firm’s optimal utilization of capital and labor are derived by differentiating the firm’s objective function, as described by equation (7), to obtain:

(II.1)Vj(.t)Kj,t=γjF+βjFλj,t+1*1Vj(.t+1)(.t+1)(.t+1)Kj,tdλj,t+1βjFVj(.t+1|λj,t+1=λj,t+1*)λj,t+1*Kj,t
(II.2)Vj(.t)Lj,t=βjFλj,t+1*1Vj(.t+1)(.t+1)(.t+1)Lj,tdλj,t+1βjFVj(.t+1|λj,t+1=λj,t+1*)λj,t+1*Lj,tΦjWtPt+1

Note that:

(II.3)Vj(.t+1|λj,t+1=λj,t+1*)=Vj(0)=0
(II.4)Vj(.t+1)(.t+1)=γjF(the Benveniste-Scheinkman condition, asdisscussed by Sargent(1987), pp. 21-22).
(II.5)(.t+1)Kj,t=1+λj,t+1fj,t+1Kj,t

and

(II.6)(.t+1)Lj,t=λj,t+1fj,t+1Lj,t(1+Rt)WtPt+1

Hence,

(II.7)Vj(.t)Kj,t=γjF+γjFβjFλj,t+1*1(1+λj,t+1fj,t+1Kj,t)dλj,t+1

and

(II.8)Vj(.t)Lj,t=γjFβjFλj,t+1*1((1+Rt)WtPt+1+λj,t+1fj,t+1Lj,t)dλj,t+1ΦjWtPt+1

Equation (9) follows immediately from (II.7) when Vj(.t)Kj,t = 0.

Now consider the case in which the credit-rationing constraint is not binding, so that Φj = 0 in (II.8). To characterize the optimal joint choices of Kj,t and Lj,t in terms of variables exogenous to the firm (namely, 1+Rt and Wt/Pt+1), consider the system of identities

(II.9)VKKdKj,t+VKLdLj,t=VKRd(1+Rt)VKWd(WtPt+1)
(II.10)VLKdKj,t+VLLdLj,t=VLRd(1+Rt)VLWd(WtPt+1)

where the Vk. and VL. terms--for. = K,L,R,W--denote the partial derivatives of Vj(.t)Kj,tandVj(.t)Lj,t with respect to Kj,t, Lj,t, 1+Rt and WtPt+1.

From the conditions for a maximum we know that

VKK<0,VLL< 0,andΔ=|VKKVLKVKLVLL|> 0.

Accordingly, to establish (11) and (12) from the system (II.9) and (II.10), we need to examine the signs of VKL, VKR, VKW, VLR, and VLW.

By differentiating (II.7) and using (6), it can be seen, to begin with, that:

(II.11)VKR =γjFβjF[1+λj,t+1*fj,t+1Kj,t]λj,t+1*(1+Rt)<0

since

(II.12)λj,t+1*(1+Rt)=WtPt+1Lj,tfj,t+1>0

and

(II.13)VKW =γjFβjF(1+λj,t+1*fj,t+1Kj,t)λj,t+1*(Wt/Pt+1)<0

since

(II.14)λj,t+1*(Wt/Pt+1)=(1+Rt)Lj,tfj,t+1>0.

Similarly, by differentiating (II.8), it can be seen that:

(II.15)VLR=γjFβjFWtPt+1[1λj,t+1*(Lj,tλj,t+1*λj,t+1*Lj,t)]

and

(II.16)VLW=γjFβjF(1+Rj)[1λj,t+1**(Lj,tλj,t+1*λj,t+1Lj,t)]

where

(II.17)λj,t+1*Lj,t=1fj,t+1[(1+Rt)WtPt+1λj,t+1*fj,t+1Lj,t]

This implies VLR < 0 and VLW < 0 whenever Lj,t*λj,t+1*λj,t+1*Lj,t<1λj,t+1*, which will presumably hold for sufficiently small λj,t+1*. Finally, by differentiating (II.7), it can be seen that:

(II.18)VKL=γjFβjF[1(λj,t+1*)222fj,t+1Kj,tLj,t(1+λj,t+1*fj,t+1Kj,t)λj,t+1*Lj,t]

So VKL = VLK > 0 whenever

(II.19)Lj,tλj,t+1*λj,t+1*Lj,t<1λj,t+1*λj,t+1*[(1+λj,t+1*)Lj,t2fj,t+1Kj,tLj,t2(1+λj,t+1*fj,t+1Kj,t)]

which will presumably hold for sufficiently small λj,t+1*.

Conditions (11) and (12) describe the “normal case” for which the probability of default (λj,t+1*) is sufficiently small to make both VLR and VLW negative and VKL positive. For this case, application of Cramer’s Rule to the system (II.9) and (II.10) indicates that the optimal levels of Kj,t and Lj,t have unambiguously negative partial derivatives with respect to both (1+Rt) and Wt/Pt+1.

Next consider the case in which the credit rationing constraint is binding, so that Lj,t is defined by (3) with Bj,t=B¯j,t. To derive (10) we examine the signs of the second derivatives in the identity:

(II.20)VKKdk=VKRd(1+Rt)VKWd(WtPt+1)VKB¯d(B¯j,tPt+1)

where VKB¯=2Vj(.t)Kj,t(B¯j,t/Pt+1). We again differentiate (II. 7) using both equation (6) and

(II.21)dLj,t=Pt+1Wtd(B¯j,tPt+1)(Pt+1Wt)2B¯j,tPt+1d(WtPt+1)

The terms VKK and VKR are unchanged from the previous case. Moreover:

(II.22)VKW=γjFβjFλj,t+1*1[λj,t+12fj,t+1Kj,tLj,tB¯j,tPt+1(Pt+1Wt)2]dλj,t+1βjFγjF[1+λj,t+1*fj,t+1Kj,t]λj,t+1*(WtPt+1)<0

since

(II.23)λj,t+1*(WtPt+1)=λj,t+1*fj,t+1fj,t+1Lj,tB¯j,tPt+1(Pt+1Wt)2>0

By contrast

(II.24)VKB¯=γjFβjFλj,t+1*1λj,t+12fj,t+1Kj,tLj,t(Pt+1Wt)dλj,t+1βjFγjF[1+λj,t+1*fj,t+1Kj,t]λj,t+1*(B¯j,t/Pt+1)

is ambiguous in sign, with

(II.25)λj,t+1*(B¯j,tPt+1)=(1+Rt)fj,t+1λj,t+1*fj,t+1fj,t+1Lj,t(Pt+1Wt)

Equation (10), which follows immediately from equation (II.20) and the signs we have established for the second derivations, describes the “normal” case in which VKB¯>0. It is straightforward to show that this is the case for which the probability of default (λj,t+1*) is sufficiently small to satisfy equation (II.19). As indicated by equation (II.24), this amounts to the case in which the rise in the marginal “value” of capital associated with an increase in the amount of labor the firm can employ (the first term on the right hand side of equation (II.24)) outweighs the decrease in the marginal value of capital associated with a higher probability of default (the second term on the right hand side of equation (II.24)).

APPENDIX III The Bank

This Appendix derives conditions (27)-(30) in the text, which describe the behavior of the bank. It also establishes that it is not optimal for the risk-neutral bank to hold excess reserves.

The first order conditions for the bank’s optimal lending, equity and excess reserve levels are derived by differentiating the value function described by equation (22) in the text. To establish that it is optimal not to hold any excess reserves, note that, with nominal excess reserve holdings denoted by Xi,t, the bank’s balance sheet constraint would be altered from (13) to

(III.1)Σj=1nBi,j,t+Xi,t=(1K)Di,t+Si,t

and the value function would be modified by subtracting Xi,t(1K)Pt+1 from the bracketed expression that multiplies ΦiD in equation (22). Accordingly, using (26), (20), and (III.1), we would have

(III.2)Vi(.t)[Xi,tPi,t+1]=βiIγiI(1+rtk1k)ΦiD1k

This derivative is negative since ΦiD is positive when D¯i,t is binding and zero otherwise. This implies that Xi,t = 0 is always optimal.

To obtain the derivatives of the value function with respect to the choice variables Bj,t/Pt+1 and Si,t/Pt+1 (recalling that Bj,t = Bi,j,t), we can use conditions (24)-(26) and (20). By differentiating equation (20) with respect to the choice variables, after using (13) to substitute out Di,t, it can be seen from (24)-(26) that

(III.3)Vi(.t)[Bj,tPt+1]=βiIγiI{(1λj,t+1*)(1+Rt)+(λj,t+1*)22fj,t+1Lj,tPt+1Wt+(λj,t+1*)22fj,t+1Kj,tKj,t(Bj,t/Pt+1)1rt+k1km1m2λj,t+1*(Bj,t/Pt+1)} -ΦiD1k -ΦiSs
(III.4)Vi(.t)[Si,tPt+1]=γiI(1+ρt+1) +βiIγiI(1+rtk1k)+ΦiD1k +ΦiS

Accordingly, conditions (27) and (28) follow immediately at an optimum point where both of these derivatives vanish.

For the case in which the bank’s operations are constrained by both the ceiling on deposits and the minimum capital requirement, it is straightforward to show that (29) follows from (13). For the case in which the deposit ceiling is binding (ΦiD>0) but the minimum capital requirement is not binding (ΦiS=0), we can substitute (28) into (III. 3) to obtain

(III.5)Vi(.t)[Bj,tPt+1]=βiIγiI{(1λj,t+1*)(1+Rt)+(λj,t+1*)22fj,t+1Lj,tPt+1Wt+(λj,t+1*)22fj,t+1Kj,tKj,t(Bj,t/Pt+1)m1m2λj,t+1*(Bj,t/Pt+1)}γiI(1+ρt+1)

Letting V--for · = B, R, W, m1, m2, ρ--respectively denote the partial derivatives of Vi(.t)(Bj,t/Pt+1) with respect to Bj,t/Pt+1, 1+Rt, Wt/Pt+1 m1, m2, and 1+ρt+1, we can characterize the optimal choice of Bj,t/Pt+1 by considering the identity

(III.6)VBBd(Bj,t/Pt+1)=VBRd(1+Rt)+VBWd(Wt/Pt+1)+VBm1dm1+VBm2dm2+VBρd(1+ρt+1)

From the second-order conditions for a maximum, we know VBB<0. The signs of VBR, VBW, VBm, VBm1, and VBρ2 can be established by differentiating (III.5) and using the information that VBB<0. In general, it is straightforward to show that VBm1 and VBρ are negative, and that VBm2 is also negative whenever the elasticity of the optimizing firm’s output with respect to credit is less than unity. This establishes (30).

Under the assumptions:

(III.7)(1+Rt)Kj,t(B1,t/Pt+1) =(Wt/Pt+1)Kj,t(Bj,t/Pt+1)=0

it can be shown that

(III.8)VBW=βiIγiI{[1+Rt+m2(Bj,t/Pt+1)]λj,t+1*(Wt/Pt+1)(1ϵfB)(ϵfKϵKBϵfL)1+Rt2(Wt/Pt+1)ϵfL}
(III.9)VBR=βiIγiI{1m2fj,t+1(1ϵfB)(1ϵfR)λj,t+1*[1+(1ϵfB)(1ϵfB)]}

where ϵf. and ϵK.--for = B, K, L, R--represent the elasticities of fj,t+1 and Kj,t with respect to Bj,t/Pt+1, Kj,t, Lj,t, and 1+Rt. Note that for small λjt+1*, VBW < 0, and (for m2/fj,t+1 also small) VBR < 0. Note also that ϵfK > 0, ϵfL > 0, ϵfR < 0 (from (10)), and under normal conditions ϵKB > 0 (from (10)). Accordingly, when there are decreasing returns to the scale of credit (i.e., when ϵfB < 1), it can be seen from (III.8) that VBW < 0 will hold in general if ϵfL > ϵfK ϵKB. Moreover, it can be seen from (III.9) that VBR > 0 will hold for λj,t+1*>[1m2fj,t+1(1ϵfB)(1ϵfR)]/[1+(1ϵfB)(1ϵfR)].

APPENDIX IV The Household

This appendix derives conditions (35)-(39) in the text, which describe the behavior of the household. The first order conditions for the household’s supply of labor and real deposit holdings are derived by differentiating the household’s objective function, as described by condition (33) in the text, to obtain the general form

(IV.1)Vh(.t)Zt =Uh,tZt +Uh,tCh,tCh,tZt +βhHEt{Vh(.t+1)(.t+1)(.t+1)Zt}

where Zt represents the relevant choice variable for period t (i.e., Lh,t or Dh,t/Pt+1). Note from (34) that Ch,tLh,t=WtPt andCh,t(Dh,t/Pt+1)=(1+ρt+1); also note from updating (34) that (.t+1)Lh,t=0and(.t+1)(Dh,t/Pt+1)=1+rt.

Finally note, as the Benveniste-Scheinkman condition, that Vh(.t+1)(.t+1) =Uh,t+1Ch,t+1. 1/ Thus, it is readily seen that (35) and (36) must hold at an optimum.

Consider next the system of steady-state equations obtained by totally differentiating the first order conditions (equations (35) and (36)) and the budget constraint (equation (34)) under the steady-state conditions Ch,t =Ch.t+1andDh,t1Pt =Dh,tPt+1. This system of equations can be written as:

(IV.2)WtPtUCCdCh,t +ULLdLh,t = -UCd(Wt/Pt)
(IV.3)[βhH(1+rt)(1+ρt+1)]UCCdCh,t+UDDd(Dh,t/Pt+1)=βhHUCdrt+UCdρt+1
(IV.4)dCh,t+(ρt+1rt)d(Dh,t/Pt+1)WtPtdLh,t=Lh,td(Wt/Pt)+ (Dh,t/Pt+1)drt(Dh,t/Pt+1)dρt+1

where UC =Uh,tCh,t,UCC =2Uh,tC2h,t,UDD =2Uh,t(Dh,t/Pt+1)2,

ULL =2Uh,tL2h,t, and all second-order cross derivatives vanish (recall assumption (31)). The left-hand side of this system has the matrix form

[(Wt/Pt)UCC0ULL[βhH(1+rt)(1+ρt+1)]UCCUDD01(rtρt+1)(Wt/Pt)][dCh,td(Dh,t/Pt+1)dLh,t]

and the determinant of the square matrix is

(IV.5)Δ=(Wt/Pt)2UCCUDD(rtρt+1)[βhH(1+rt)(1+ρt+1)UCCULLUDDULL

Notice that, by differentiating (35) and (36) subject to (34) and the steady-state conditions,

(IV.6)2Vh(.t)Lh,t2=ULL
(IV.7)2Vh(.t)Lh,t(Dh,t/Pt+1)=WtPtUCCCh,t(Dh,t/Pt+1) =(rtρt+1)WtPtUCC
(IV.8)2Vh(.t)(Dh,t/Pt+1)2=[βhH(1+rt)(1+ρt+1)](rtρt+1)UCC+UDD

The second order condition for a maximum is:

(IV.9)2Vh(.t)Lh,t22Vh(.t)(Dh,t/Pt+1)2(2Vh(.t)Lh,t(Dh,t/Pt+1))2>0

Accordingly, from (IV.6)-(IV.9)

(IV.10)UDDULL<(rtρt+1)[βhH(1+rt)(1+ρt+1)]UCCULL(rtρt+1)2(WtPt)2(UCC)2

Thus, by combining (IV. 5) and (IV. 10), it can be seen that

(IV.11)Δ<(WtPt)2UCCUDD -(rtρt+1)2(WtPt)2(UCC)2<0

By applying Cramer’s Law, the system (IV.2)-(IV.4) can be solved to yield:

(IV.12)dCh,t=1Δ{(WtPtUCUDDLh,tULLUDD)d[WtPt]+[βhH(rtρt+1)UCULL(Dt/Pt+1)ULLUDD]drt[(rtρt+1)UCULL(Dt/Pt+1)ULLUDD]dρt+1 }
(IV.13)d(Dh,tPt+1)=1Δ{[βhH(1+rt)(1ρt+1)][Lh,tULLWtPtUCC]UCCd[WtPt]+[βhH(WtPt)2UCUCC+[βhH(1+rt)(1+ρt+1)]Dh,tPt+1ULLUCC+βhHUCULL]drt[(WtPt)2UCUCC+[βhH(1+rt)(1+ρt+1)]Dh,tPt+1ULLUCC+UCULL]dρt+1}
(IV.14)dLh,t=1Δ{[WtLh,tPtUCCUDD+{(rtρt+1)[βhH(1+rt)(1+ρt+1)]UCC+UDD}UC]d[WtPt]+[WtPtDh,tPt+1UCCUDDβhHWtPt(rtρt+1)UCUCC]drt[WtPtDh,tPt+1UCCUDDWtPt(rtρt+1)UCUCC]dρt+1}

Note also, from (36), that

(IV.15)[βhH(1+rt)(1+ρt+1)]< 0

since Uh,tCh,t>0andUh,t(Dh,t/ρt+1)>0.

Accordingly, it can be seen that, in general:

Ch,t(Wt/Pt)>0,Dh,t(Wt/Pt)>0,Dh,trt>0,andDh,tρt+1<0. It can also be seen from (IV.14) that Lh,t(Wt/Pt)>0 whenever rt-ρt+1 < 0 and UcWtLh,tPtUcc>0, or since 2Vh(.t)(Dh,t/Pt+1)2<0 must hold as a second order condition (recall (IV.8)), whenever rt - ρt+1 > 0 and UDD is negligible. This explains the “unambiguous” signs shown in (37) - (39). Note further that, when the expected real interest rate (rt-ρt+1) is positive: Ch,trt>0andCh,tρt+1<0 (i.e., the income effect on consumption dominates the substitution effect), Lh,trt<0,andLh,tρt+1>0.

APPENDIX V Steady State Solutions

As noted in the text, equations (40)-(43) describe a financially repressed economy’s long-run position. Using these relationships, this appendix first derives the slopes of the curves in Figure 1 and then considers the effects on the economy of alternative financial policies.

1. Slopes of curves in Figure 1

Curve 1 in the northeast quadrant of Figure 1 represents the combinations of (1+Rt) and Wt/Pt+1 under which condition (40) holds as an equality. The slope of curve 1 equals 1/

(V.1)d(1+Rt)d(Wt/Pt+1)=ΣhLh,tH(Wt/Pt)(1+ρt+1)ΣjLj,tF(Wt/Pt+1)ΣjLj,tF(1+Rt)

In curve 2, the segment AB, corresponding to condition (41b), represents the situation when

(V.2)Σh(1k)(1s)Dh,tHPt(rt,(Wt/Pt+1)(1+ρt+1),1+ρt+1)=Σh(WtPt+1)(1+ρt+1)Lh,tH(rt,(WtPt+1)(1+ρt+1),1+ρt+1)

where WtPt+1(1+ρt+1) has been substituted for Wt/Pt. Since rt, ρt+1, k and s are given in the steady state by the authorities monetary and financial policies, there is only one value of Wt/Pt+1 (W¯/P) that satisfies (V.2). Changes in (W¯/P) will be related to the other variables by

(V.3)Σh[(1k)(1s)(Dh,tH/Pt)(Wt/Pt)(WtPt+1)()(1+ρt+1)Lh,tH(Wt/Pt)Lh,tH(1+ρt+1)]d(W¯P)=Σh[(WtPt+1)(1+ρt+1)Lh,tHrt(1k)(1s)()(Dh,tH/Pt)rt]drt+Σh[(1k)(1s)(Dh,tH/Pt)ρt+1(1k)(1s)(Dh,tH/Pt)(Wt/Pt)(?)(WtPt+1)+(WtPt+1)(1+ρt+1)Lh,tH(1+ρt+1)+(WtPt+1)2(1+ρt+1)Lh,tH(Wt/Pt)]dρt+1+ΣhDhH/Pt(1s)(+)dkΣh(1k)(1s)2(Dh,tH/Pt)()ds

where the signs reflect the assumptions that the households’ labor supply is more sensitive to changes in the real wage than their demand for deposits, and that the demand for deposits is more sensitive to changes in r than the supply of labor. Under these assumptions, W¯P is an increasing function of rt and s and a decreasing function of k.

The segment BC of curve 2, corresponding to condition (41a) represents the situation where the banks hold more than the minimum required level of equity and

(V.4)ΣjΣjBi,j,tPt+1=ΣiΣjbi,j,t(1+Rt,WtPt+1,m1,m2,1+ρt+1)=Σh(WtPt+1)Lh,tH(rt,Wt/Pt,1+ρt+1)

This implies that

(V.5)0=ΣjΣjbi,j,t(1+Rt)(?)d(1+Rt)+[ΣiΣjbi,j,t(WtPt+1)ΣhLh,tH()ΣhWtPt+1Lh,tH(Wt/Pt)(1+ρt+1)]d(WtPt+1)+ΣiΣjbi,j,t,m1dm1()+ΣiΣjbi,j,t,m2dm2()Σh(WtPt+1)Lh,tHrt(?)drt[Σh(WtPt+1)Lh,tH(1+ρt+1)+Σh(WtPt+1)2(?)Lh,tH(Wt/Pt)ΣiΣjbi,j,t(1+ρt+1)]dρt+1

The slope of curve (2) along segments BC therefore equals

(V.6)d(1+Rt)d(WtPt+1)|(2)=[ΣiΣjbi,j,t(Wt/Pt+1)ΣhLh,tHΣh(WtPt+1)Lh,tH(Wt/Pt+1)(1+ρt+1)]ΣiΣjbi,j,t(1+Rt)><0asbi,j,t(1+Rt)><0

Curve 3 (in the northwest quadrant of Figure 1) also has two segments: DE and EF. As discussed in the main text, the segment DE is defined only in the range of loan interest rates between R** and R*, which corresponds to the range in which ΦiD and ΦiS are both greater than zero. Using the banks’ first order conditions (equations (27) and (28)) this implies that

(V.7)sγiI[(1rtk)βiI(1k)(1+ρt+1)]<γiIβiI{(1λj,t+1*)(1+Rt)+λj,t+1*22fj,t+1Lj,t(Pt+1/Wt)+λj,t+1*22fj,t+1Kj,tKj,t(Bi,j,t/Pt+1)(1rt<