Inflation and risky investment in an economy with asymmetric information and monopolistic loans markets

NIVEDITA MUKHERJI Oakland University Rochester, Michigan

Inflation and Risky Investment in an Economy with Asymmetric Information and Monopolistic Loans Markets* In the context of an economy in which investment projects are funded by monopolistic lenders, money is found to affect both the qualitaes of investment projects funded and the total quantity of capital used in the projects. The effects of changes in outside money's rate of return on investment in risky projects are analyzed under both public and private information of borrowers" types. When types are publicly observable, a decrease in money's return increases investment in the risky projects validating the Tobin-Mundell effect. With private information, however, the Tobin effect is not valid in all cases. In addition, simulation results show that, in many cases, money changes qualities and quantities of investments in opposite directions. As a result, it is not obvious that an economy's monetary policy should solely attempt to increase total investment. Moreover, credit rationing, a mechanism often used for self-selection in these types of models, is also found to influence the results significantly.

1. Introduction

That financial market imperfections pose problems for economic development is well recognized. These markets affect economic development primarily by influencing an economy's capital accumulation path. Monetary economists since Tobin (1965) have examined the role money can play in accelerating this capital accumulation process. The objective of this paper is to study the impact of money on capital in the context of an economy in which financial markets are not well developed and information regarding different types of investment projects is imperfect. The money-growth literature that Tobin's paper initiated has focused on a single type of investment opportunity. This explains the literature's concentration on the quantity of capital or total investment to draw conclusions regarding economic growth. This paper shows that, in the study of money's effect on investment, it may not be sufficient to exclusively concen*Financial support from Oakland University is gratefully acknowledged.

Journal of Macroeconomics, Winter 1998, Vol. 20, No. 1, pp. 107-132 Copyright © 1998 by Louisiana State University Press 0164-0704/98/$1.50

107

Nivedita Mukherji trate on the quantity of investment in the economy when qualities of investment opportunities vary. Although this extension of the hterature is natural because investment opportunities are rarely identical and information regarding them is rarely perfect, it has remained relatively unexplored. The framework used to address this issue is one in which owners of investment projects have access to one of two types of projects---high risk and low risk. These projects are, however, funded by a different group of agents in the economy, called lenders, who act as monopolists in spatially separated loans markets. (Petersen and Rajan 1995 show that small borrowers actually benefit when lenders are monopolistic rather than competitive). The objective here is to study the impact of informational asymmetries between such monopolistic lenders and borrowers on the money-capital relationship) To isolate the impact of informational asymmetry, a benchmark case is studied in which lenders have perfect information of the projects they finance. Informational asymmetry is subsequently introduced by assuming that the quality of a project is privately observable by only the owner of the project. The nature of the relationship between money and investment is found to be quite complex in such an economy. The complexity is primarily due to the complexity of the incentive compatible contracts offered by lenders. It is shown that with imperfect information, an increase in money's return not only changes the quantity of investment in the economy but has a significant impact on the qualities of the investment projects that are financed. In some eases, the overall quality of the projects funded worsens with dedines in total investment, while in others, the overall quality actually improves when money's return rises. When such improvements in quality accompany declines in quantity, the relationship between quantity of capital and output becomes complicated. This impact of money on the qualities of projects has been largely ignored by the money-growth literature, which has predominantly focused on the eonditions under which money influences the stock of capital. This emphasis on whether or not money has any impact on capital is due to the contrasting results obtained by Tobin (1965) and Sidrauski (1967a, 1967b). While Tobin argues in his (1965) paper that infation increases the stock of capital per person in the steady state, Sidrauski (1967a, 1967b) show that, if savings functions are derived from individual maximization problems in infinite horizon models, money is superneutral. As Orphanides and Solow (1990) argue in their survey paper, the subsequent literature studying the money-growth issue has concentrated on the conditions under which the 1Bencivenga-Smith(1992) also studyfiscaland monetarypoliciesin "financiallyrepressed" economies. 108

Inflation and Risky Investment Tobin and Sidranski results hold. For example, Drazen (1981), Gale (1983) among others, have shown that, in finite horizon models, money influences capital accumulation even when savings functions are derived from individual optimization problems. In these models, individual heterogeneity is argued to be the source of the non-superneutrality results. The importance of individual heterogeneity in the validity of the Tobin effect can be also found in Weft (1986) and Whitesell (1988). The validity of the Tobin effect has been studied in the context of many other frameworks. See for example Stockman (1981), Romer (1986), Danthine, Donaldson and Smith (1987). If anything, this literature has successfully proven that it is possible for changes in money's return to influence an economy's capital accumulation path. If this non-superneutrality is accepted, the next logical question is, Does money affect all types of investment opportunities symmetrically? What happens if information regarding the types of investment projects is not symmetrically held? Azariadis and Smith (1991, 1993) and Bencivenga and Smith (1993) have studied the consequences of adverse selection problems for capital accumulation and have found that the relationship between capital accumulation and growth is much more complex when such informational problems are considered. Capital market imperfections also lie at the heart of recent developments in the literature on intermediation (for example, Diamond 1984 and Williamson 1986) and the literature studying the relationship between intermediation and growth (see for example Greenwood and Jovanovic 1990 and Bencivenga and Smith 1991). In the chain of links between money, capital, and growth, papers like Bencivenga and Smith study the role of information asymmetry in the link between capital and growth. This paper examines the role of informational asymmetry in the link between money and capital. It remains for future research to develop models that consider the entire chain that links money and growth when information imperfections exist in capital markets. The rest of the paper is organized as follows. Section 2 describes the economy. Section 3 solves the lender's problem under public and private information, then it solves a benchmark case and shows that when information is public, the Tobin effect is valid for both types of projects. The conclusions of this section are found to differ from those of its first subsection, in which information regarding some factors is private and incomplete. Section 4 concludes the paper.

2. Description of the Economy The economy consists of N spatially separated regions in each of which n + i young individuals are born each period. These individuals have twoperiod lives and their generations overlap. In each region, of the n + 1 109

Nivedita Mukherji young agents born each period, one agent is called a lender and the rest are called borrowers (or entrepreneurs). Agents cannot travel to other regions in the first period of their lives and both lenders and borrowers receive utility from old age consumption only. Each of the entrepreneurs owns a risky investment project. A fraction 8 of the projects succeed with probability Pis and such projects are called high-risk while the rest succeed with probability pL and are called low-risk. Depending on the risk of the project owned, an entrepreneur is classified as high risk or low risk. It is assumed that PL > pH and the outcome of any project is public knowledge. Although the entrepreneurs own these projects, they cannot operate them unless they have access to a capital good. The good that is used to produce capital goods is available only to the lenders of the economy. It is then imperative for entrepreneurs to obtain this good from lenders before production begins. Entrepreneurs are risk neutral and supply their services inelastically if their projects are funded. If an entrepreneur is unsuccessful in obtaining the good, he liquidates his project and enjoys utility 0 in the second period. Unlike entrepreneurs, each lender receives as endowment, in the first period of his life, co units of the good that is necessary to operate the investment projects owned by entrepreneurs. Like entrepreneurs, lenders also derive utility from second period consumption only. This poses a problem for lenders because the good is perishable and no storage facilities exist, forcing them to find alternative ways for saving the value of their endowments. There exist two such opportunities in this economy; lenders can finance the investment projects available to entrepreneurs or hold flat money. When used in an investment project, the endowment good is easily converted into a capital good that depreciates completely after one use. The investment projects use this capital good to produce a consumption good identical to the endowment good. In addition to converting the endowment good to capital, lenders can also hold fiat money which is introduced by way of government transfers to the old each period. Young lenders receive money by selling their endowment to the current old. Unlike the investment opportunity, money is risk-less. For the investment projects to be funded, the return from the projects must be greater than the return from money. This however does not drive money out of the economy because lenders are risk averse.2 If a lender decides to invest a portion of his endowment in a risky project, he offers a loan contract to all entrepreneurs in his region. (Recall that each lender has monopoly status regionally.) After reviewing the contract the entrepreneurs submit their loan applications. From the pool of 2Without risk aversionthere will be no demand for moneyin this economy. 110

Inflation and Risky Investment applications the lender randomly selects one. To ensure that an equilibrium exists it is assumed that the lottery is played only once. Further, to eliminate diversification of loans, it is assumed that the resources of a lender can finance the project of, at most, one entrepreneur. In this model then, if a borrower-lender pair in one region agrees on the terms of the loan contract offered by the lender, the project is financed and both parties share the proceeds in the following period. If no agreement is reached or if the lender refuses the loan, even if the terms of the contract are mutually agreeable, the lender sells his entire endowment for money and the borrower liquidates his project. The first two parts of section 3 derive the contracts offered by the lenders of this economy. A contract offered by a lender to an entrepreneur of type i (i = L, H) is a 3-tuple {x~,bi, r~}, where x~ is the probability with which a lender offers a loan, b, is the quantity of the loan offered, and r~ is the return to the lender per unit lent or the loan rate. Since lenders operate like monopolists in the loans market a the contract maximizes the utility of the lender given the reservation utilities of the borrowers. A lender's utility is a function of the returns from the investment project he finances and the money he holds. An investment project with b units of capital yields Rb P~

(1)

with probability pi(i = L, H), 0 otherwise. For the projects to be financed, the expected return from a unit of capital (R) must exceed the return from a unit of money (p). I f P t is the price at time t,

D=

Pt-1

is the gross rate of return on money or the inverse of the gross inflation rate. By assumption, p is determined in some initial period and fixed thereafter. Ifbi is the quantity of loan (which is converted to the same quantity of capital by the entrepreneur) and ml is the real value of the quantity of money held, the expected utility of a lender matched with a type i borrower (i = L, H) is given by aAcompetitivelenderwouldtake the loan rate as a market determinedrate. Loansmarkets are oftenimperfectlycompetitive,especiallyin economieswithunder-developedfinancialmarkets. Thispaper studiesthe moneyoutputrelationshipin sucheconomies.However,the framework is applicableto competitiveloansmarketsalso. 111

Nivedita Mukherji

E

t,[n~[p~ ln(r,b~ + pm~ + h,) + (1 - p,)ln(pm,

z=L,H

+ h3] + (1 - n~)ln(pc0 + h2)].

(2)

In the above equation, h~ and h2 are the real values of the monetary transfers reeeived when the real quantities of money held are mi and co respectively, and ti equals 8 for i = H and 1 - 8 for i = L. The term multiplying 7h in the utility function indicates the expected utility when a loan is offered. 4 Since the project yields no return when it fails, the lender receives nothing if he finances a project that ultimately fails. The last term in (2) gives the lender's utility if he rejects the loan application and converts his entire endowment into money. A contract offered to an entrepreneur is acceptable only if it guarantees an expected utility of at least U. (Recall, (? is the utility received by an entrepreneur if he liquidates his project.) This leads to the following individual rationality or participation constraint pi

-

r~b~ >- (J.

(3)

In addition, a lender also faces the simple budget constraint co = bi + ms.

(4)

3. Solution of the Lender's Problem Before discussing the problem under private information, the model is analyzed when information regarding types of entrepreneurs is publicly available.

Public Information If a lender knows the true type of an entrepreneur who applies for a loan, the lender determines the loan quantity and loan rate by maximizing his expeeted utility, given by (2), subject to the par~cipation constraint (3), his budget constraint (4), standard constraints on the probabilities, and usual 4As mentioned earlier, the terms of the contract specify a probability n~ with which a loan will be granted. Even if r¢, < 1 is derived from the optimal contract, a lender will have the incentive to always offer a loan when an entrepreneur submits a loan application. This is because the higher expected return from the project implies that the expected utility from the diversified portfolio is greater than the utility from holding money only. To avoid such potential time inconsistency problems it is assumed that a mechanism exists that enforces the terms of the contract.

112

Inflation and Risky Investment non-negativity constraints. We assume that outside money transfers are proportional to initial money holdings for each category of lenders, that is, h~ = ms - 9m~, and he = c0 - pc0. Being a very small part of the market, each lender takes these transfers as exogenously determined constants (recall that although the lenders act as monopolists locally, there are many lenders in the entire economy). As a result, they do not take into consideration the impact of their individual actions on these transfers. Using the steady state money market equilibrium condition: m = pm + h, the following result is obtained from the lender's optimization problem. Result 1. 1. A lender invests a portion of his endowment in the risky project with probability 1. 2. The quantity of loan and the loan rate are respectively given by b~ = p~(R -

O)c0 + ( t -

p~)oC;.

p~(R - P) + (1 - p , ) R p

(5)

'

Rb z -

-

pib~

(6)

The first part of the result is intuitive. The lenders prefer to finance these projects because the expected return from them exceeds the return on money, by assumption. Since they know the types of the borrowers perfectly, they design contracts that are agreeable to both parties. Thus, when all information is symmetrically shared, lenders are always better offby approving the loan applications. Nonetheless, portfolios of lenders include money also because of risk aversion. It is noteworthy that the contract forces the borrower to his reservation utility level. This is because of two reasons: 1) the lender acts as a monopolist 5 2) the borrower inelastieally supplies his services as long as his expected return is at least as high as his reservation value. Since the primary objective of this paper is to an~yze how investments in the risky projects change as money's return changes, the solution for bi from Equation (5) is differentiated with respect to p. 3b____ 2 = oo

p,(1 - p~)R(Ro3 - (Y) [p,(R (1 -

p,)(~,

p) + (1 - p,)Rp] ~ _

r2) + ( ~ -

Pi -(R

-

O) -

(1 R p - -

p~)

b,)

(7)

P, 3A lender in a competitive market would take tile net return to borrowers as a market determined variable, which may or may not equal the reservation utility level.

113

Nivedita Mukherji The numerator is clearly positive and the denominator is negative because R > p must be satisfied for the loan to be offered. This derivative shows that investment in the risky project is inversely related to money's return, validating the Tobin effect.6 The effect of a change in money's return on the loan rate is also negative from (6). A decrease in money's return then increases investment in the risky projects by making these projects relatively more attractive, as predicted by the Tobin-Mundell effect. The following proposition summarizes these effects. PROPOSITION 1. Investment in a risky project and the corresponding loan rate decrease as outside money's rate of return increases, validating the Tobin-Mundell effect.

Private Information Informational asymmetry is introduced into this economy by assuming that the type of the investment project owned by an entrepreneur is the entrepreneur's private information; a lender cannot directly observe the type of the entrepreneur who applies for a loan. As a result, the contract offered by a lender must incorporate the possibility that an entrepreneur may misreport his type. To see this, assume that the contract under public information is offered. The analysis under public information proved that when information is symmetrically held, the contract forces the entrepreneurs to their reservation utilities. The loan rates and quantities then are such that Rb~ - p~r~ = U. Since PH < PL, RbL - pHrL > U providing the high risk entrepreneurs the incentive to misreport their types. For similar reasons, a low risk entrepreneur will not find it attractive to choose the contract offered to high risk agents. To eliminate this incentive to misreport types, an optimal contract must consider the following self selection conditions: 7

n.p.[~p;-r.b.]+(1-

=.)CY>_~ . [ ~ : -

r~bL] + (1 - ~L)tY;

(s)

"ELPL[~L -- rLbL] q- (1-- ~L)U >- 7tt~pL[~LH rHbH]+ (1--1tH)U.

(9)

6Here the portion of endowmentthat is used in the investmentprojects is called capital. Since there is a one-to-onerelationshipbetween capital and loans, the concept of the Tobin effectis extendedto the relationshipbetweenmoneyand loans. 7The effectsof adverse selectionon the directionof the Tobin effect are analyzedwhen a separating contract is offered (note that the single crossingproperty of indifferencecurves holds). Althoughother typesof equilibriamaybe theoreticallypossible,they are ignoredin this paper.

114

Inflation and Risky Investment

The first constraint ensures that the terms of the contract are such that a high-risk entrepreneur's expected utility is greater if he chooses the contract for high-risk agents than if he chooses the one for low-risk agents. Equation (9) provides a similar constraint for the low-risk agents. The lender's problem under private information incorporates these additional constraints to the problem solved in the public information section. The lender's problem is then maximize 8~H[PH ln(rnbH + pmH + hH) + (1 -- PH) ln(pmn + hH)]

+ 5(1 -- nil)ln(p¢O + h2) + (1 - 8)nL[PL ln(rcbL + PmL + hL) + (1 -- PL)ln(pmL + hL)] + (1 -- 5)(1 -- rCL)ln(pco + h2) subject to O) = b u - mH, 0) = b L - m L ,

Pn

pL

rubn >- U,

~L

)

rLbc >- (/,

the incentive compatibility constraints (8) and (9), 1 ~ g/_/,

1-----gL,

and standard non-negativity constraints. Typically the incentive compatibility constraint for the low risk agents does not bind. It is, however, possible that the contract to high risk agents, who have an incentive to misreport, is made so attractive that the low risk agents may want to mimic the high risk. These types of solutions are ruled out in the ensuing analysis by restricting analysis to the cases in which the constraint (9) does not bind. The following two propositions follow from the lender's problem described above. PROPOSITION 2. The loan contracts offered to entrepreneurs are such that 1) the expected utility received by a low risk entrepreneur equals the reser115

Nivedita Mukherji ration utility level U; 2) the expected utility of a high risk entrepreneur is greater than his reservation utility. Typically informational asymmetry makes good quality agents worse off but leaves the utility levels of poor quality agents unchanged. This discrepancy in utility levels is necessary to achieve self selection. Proposition 3, however, states that the utilities of low risk agents are unchanged while those of high risk agents rise under private information. The reason for this apparent reversal of the results in this ease is as follows. In this economy the two types of agents have identical reservation utilities and as the previous seetion showed, lenders force borrowers to their reservation utilities under perfect information. Self selection in that ease cannot be achieved by lowering the utility level of a low risk borrower any further. As a result, the contract leaves the expected utility of the low risk agent unchanged but improves the utility of the high risk agent. PROPOSITION 3. i) The probability of receiving a loan is 1 for a type H entrepreneur but is either strictly less than I or equal to I for a type L entrepreneur, ii) The quantity of loans to low risk agents under private information is less than the quantity that equates the marginal utilities from investing and holding money for the lender. This proposition follows directly from the first-order conditions derived from the lender's problem 8 and shows that, with private information, some of the low risk entrepreneurs may be credit rationed. 9 The high risk entrepreneurs, however, always get their loans approved. This possibility of denying loans to low risk agents is also present to make the contract to these agents less appealing to high risk agents. Although the low risk agents may receive a loan with probability 1, part ii) of the proposition shows that they receive a quantity of loan that is less than the one that equates a lender's marginal utilities from holding the alternative assets. As a result, there always exists some quantity rationing in addition to the probable rationing by number of loan approvals with private information. Whether the probability of loan approval is less than or equal to one, the first-order conditions and Proposition 3 yield the following expressions for the loan rates: aDetafls are available from the author. 9Smce only one of the n borrowers in each region is funded by the only lender of that region, the other n - 1 borrowers are always credit rationed. The term rationing is not used to characterize this phenomenon. Rather, the term is used when no entrepreneur in a region receives loans making the total number of projects financed less than the number of lenders in the economy.

116

Inflation and Risky Investment

( R - p)m~

Rb L

rc -

(lO)

pH)pbz-i'

rH = (1 -

-

(11)

pLbL

The final solutions for loan quantities and loan rates depend on whether credit is rationed or not. The ease of no rationing by number of loans, that is nL = 1, is examined first. No Rationing by Number of Loans This section an~yzes the solutions when rcn = gL of b n and bc are derived from the following equations:

=

1. The solutions

R e 0 - [ R + p;(R_ p~/)pj(P)] c0 - bt~) = RbL - pHrzbc ;

(R - P)

(12)

1](c0 - b~) _ [6(pc -- p,)R][ k ~ -2 6)-~L ]L(R -

(rLb L _+ mc)m L

p)mc -

(1 -

]

pL)prcbLJ"

(13)

Equation (12) is derived from the binding incentive compatibility constraint, (8), and Equation (13) is derived by equating the value of the Lagrange multiplier associated with this binding constraint obtained from lending to high risk and low risk agents. Although it is clear from these that closedform solutions are obtainable, they are quite complex functions of the parameters. To gain some insights into the solutions, simulations were performed. The following tables summarize some of the results. 1° The results obtained from the simulations performed may be broadly categorized into two types, examples of which are given in Tables 1 and 2. Although a very large number of possible combinations of parameter values are possible, the simulations did not provide any set of combinations that yielded results that qualitatively differed significantly from those summarized below. This table shows that as the value of p (money's return) increases • Investments in both high risk (bn) and low risk (be) projects decrease. • The ratio of investment in high risk to low risk projects increases steadily. l°Mathematicawas usedto conductthe simulations. 117

Nivedita Mukhe~i TABLE 1. R = 0.85, U =

0,5

w = 1, PH = 0.1, PL

P 0.01 0.06 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 0.51 0.56 0.61 0.66 0.71

= 0.2, =

0.2

bH

bL

bJbL

0.956417 0.774068 0.635369 0.526318 0.438326 0.365831 0.30507 0.253409 0.208947 0.170277 0.136338 0.106312 0.0795593 0.0555734 0.0339464

0.955723 0.770419 0.629439 0.518583 0.429131 0.355432 0.293663 0.241147 0.195949 0.156643 0.122146 0.0916292 0.0644413 0,0400669 0,0180916

1.00073 1.00474 1.00942 1.01492 1.02143 1.02926 1.03884 1.05085 1.06633 1.08704 1.11618 1.16024 1.2346 1.38701 1.87636

TABLE 2. R = 0.65, (3 = 0, 5 = 0.2, w = 4, PH = 0.3, PL = 0 . 5

p 0.01 0.06 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 0.51 0.56

118

bH

bL

bH/bL

3.94403 3.66449 3.38399 3.10057 2.81227 2.51718 2.21332 1.89868 1.57114 1.2285 0.868373 0.488219

3.95528 3.72297 3.47532 3.21103 2.92865 2.62663 2.30321 1.95647 1.58428 1.1843 0.753907 0,290229

0.997156 0.984291 0.973721 0.965601 0.960262 0.958331 0.960972 0.970461 0.991707 1.03732 1.15183 1.68218

Inflation and Risky Investment

bH

b L Figure 1.

Since b H and bL both fall as p increases the Tobin effect is validated in this range of parameter values. Tests for possible reversals of the effect failed in all reasonable ranges of parameter values. Figure 1 explains why the Tobin effect cannot be invalidated in this situation. Observe that this graph captures the relationship between bH and bL, as derived from Equations (12) and (13). It is easy to show that the relationship between the two variables is positive and linear in Equation (12), as represented by line (1) in Figure 1, while it is negative and concave in Equation (13), as represented by curve (2) in Figure 1. Since the intersection of the two functions determines the solutions for the high and low risk loan quantities, the impact of an increase in money's return on these quantities is studied by analyzing how the functions shift as the return increases. Keeping the loan quantity bL constant, differentiation OfbH in Equations (12) and (13) with respect to 9 and evaluating bH and bE at the initial solution values show that curve (2) shifts more than line (1). This is indicated by the broken curves in Figure 1. As long as both (1) and (2) in Figure 1 shift down and (2) shifts more than (1), the equilibrium quantifies of both bH and bE will fall as money's return increases. The intuitions behind the shifts just described are as follows. It is expected that, as money's return increases, individuals will find money to be relatively more attractive and increase its quantity in their portfolios. Figure 1 shows that in the presence of information asymmetry in the 119

Nivedita Mukherji loans market, the same reaction to an increase in money's return is observed when lenders always hold diversified portfolios, and such a change does not violate incentive compatibility. To see this, note that, as money's return increases, if, for example, b c is kept constant and bn decreases because of the standard portfolio adjustments, incentive compatibility will be violated unless other factors change. Notice that an increase in money's return reduces the loan rate rn for each unit lent. This fall in r n reduces the incentive for high risk agents to misreport their types. It is this lower loan rate that allows the lender to reduce the loan quantity to high risk agents without violating incentive compatibility. The simulation results obtained from Table 1 also indicate that investments in low risk projects fall at faster rates than investments in high risk projects. As a result, as p increases, not only is the total quantity of investment lower, the mix of projects financed by lenders changes in favor of high risk projects, decreasing the overall quality of the projects that are financed. In contrast to the results obtained from Table 1, Table 2 shows that, for a certain range of values for p, the ratio of high risk to low risk investment deereases as p increases. Nonetheless, investments in both types of projects fall as the return on money increases, as suggested by the Tobin effect. For this set of parameter values then, a range of values for money's return is found for which the mix of projects being financed by lenders shifts in favor of good quality projects while investments in all types of projects fall as money's return rises. Except for the values of the probabilities, the parameter sets considered in Tables 1 and 3 are identical. Unlike Table 1, where an increase in the ratio of investment in high risk to low risk projects accompanied increases in money's return, Table 3 shows that for almost the entire range of values for the return on money, the ratio bH/bL decreased as p increased. This type of sensitivity of the ratio to changes in the success probabilities was also found in other ranges of values for the other parameters. Tables 1, 2, and 3 show that the proportion of investment in high risk to low risk projects may increase or decrease with an increase in money's return. To understand what factors determine how this ratio changes as money's return changes, first rearrange the incentive compatibility constraint to get

b__g_H= bL

R 1 -

+

(1

R + Pn(R(1

-

PH)P b c

-

p)

pu)o

The derivative of this ratio with respect to p is 120

Inflation and Risky Investment TABLE 3. R = 0.85, U = 0,~ = 0.2, w = 1, pn = 0.7, pL = 0.8 p 0.01 0.06 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 0.51 0.56 0.61 0.66 0.71 0.76 0.81

RI-~-~R -

-

bu

bE

bJbL

0.99622 0.976388 0.954848 0.931369 0.905672 0.87742 0.846203 0.811519 0.772737 0.729061 0.679462 0.622587 0.556604 0.478963 0.385957 0.271915 0.127514

0.997394 0.983573 0.968272 0.951243 0.932173 0.910672 0.886245 0.85825 0.825845 0.787899 0.74286 0.688541 0.621754 0.537678 0.428663 0.281845 0.0739134

0.998823 0.992695 0.986136 0.979108 0.971571 0.963486 0.954819 0.945551 0.935693 0.925324 0.914657 0.904212 0.895215 0.890798 0.900373 0.964767 1.72518

~-_

R

~

R R +

abL

; -

-

This derivative gives some of the parameters that impact the change in the ratio of high to low risk investments as money's return changes. The first term of the expression is always negative while the second is positive (recall that (ObH)/(Op) < 0). The derivative is positive or negative depending on the parameters and the magnitude of bL and ObL/Op. The parameters that most significantly contribute to a negative value of the derivative, indicating that a rise in money's return decreases the ratio of high to low risk projects, are the probabilities PH and PL. In particular, the derivative becomes more negative as the probabilities get closer. This is because the closer is PH to PL, the lower is the incentive for high risk agents to mimic the low risk which results in a higher quantity of loans offered to both types of agents. Recall 121

Nivedita Mukherji that the utilities of high risk agents are increased above their reservation level to induce truthful behavior. As the incentive to lie decreases, the loan offered to these agents is reduced since they no longer need as much incentive to reveal their true type. Consequently, lenders offering loans to high risk agents have greater flexibility in adjusting their portfolios to changes in money's return. This explains the relatively rapid fall of b~/to an increase in p that results in a fall of the ratio bH/bL. Other than the probabilities the parameters that appear in the derivative above are co, R, p. An increase in the endowment received by lenders, co, has no impact on either the ratio bjbL or its derivative. Any change in endowment has only pure wealth effects. The relationship between the ratio and the returns p and R is more interesting. Simulations show that, as the difference between p and R diminishes, the derivative of the ratio of loan quantities increases. Although the ratio often falls at low values of p as p increases, it tends to increase at values very close to R. The reason for this increase in the ratio is somewhat similar to the situation where the probabilities get closer. When the return on money and the return on successful projects get closer, the ineentive to offer loans decreases (recall investment is risky while money is not). As the loan quantity is reduced, the utilities of high risk agents decrease. To induce them to truthfully reveal their types, the lender loses some of the flexibility with which he can rearrange his portfolio to changes in money's return. Consequently we observe that relative to b L, bu decreases at a slower rate. From all ranges of parameter values that were considered for the simulation exercises, the following conclusions can be derived: An inverse relationship exists between investment and the rate of return on money. Changes in the ratio of bad to good quality projects accompany changes in money's rate of return. The ratio tends to shift in favor of good quality projects as the success probabilities of the two projects get closer and the difference in the rates of return of money and investment increases. These conclusions show that, in addition to the changes in investment in the two types of projects, a change in money's return alters the overall risk of the projects financed by lenders. As Table 3 shows, although total investment falls as p increases, total risk of all projects financed also decreases. This may render the new equilibrium more desirable to lenders. These tables show that, when separating contracts are offered to borrowers under private information, lenders can no longer simply increase investment when money's return falls; any change in the portfolio implies changes in the terms of the contracts offered to the borrowers. The changes have to be such that the

122

Inflation and Risky Investment contracts continue to be incentive compatible. Since these types of interactions between the various types of investment opportunities do not arise under public information, the relationship between money and investment is much more straightforward in such models.

Rationing by Number of Loans Proposition 3 states that a fraction of the low risk agents may be denied loans due to asymmetric information. This section analyzes the solutions when such rationing occurs. The solutions for btt and bL are obtained from the following equations: (1 - ~) rub. + m.

(PL - Pu) (RbL -

[PL ln(rLbL + mE) (1)

PL

(14)

+ (1 - PL) ln(mL) -- In(c0)] ;

rubH + m , -- (PL -- pH)R LrLbZ + mE PL

mE

A"

These equations are derived by equating the Lagrange multiplier associated with the incentive compatibility constraint obtained from the first orderconditions related to =c, bE, and bu. Equation (15) is the same as Equation (13) discussed above. Equation (14) is due to the positive probability of denying loans to low risk borrowers. It shows that by denying loans with a positive probability, an additional distortion is introduced to the one discussed in Proposition 3 (ii). This distortion arises because lenders, in their efforts to coerce high risk agents to reveal their types, deny loans to low risk agents with a positive probability and hold only money in their portfolios even though the expected return of such portfolios is exceeded by those of a diversified portfolio. Figure 2 graphs the relationships between bu and bE in Equations (14) and (15). To analyze how a change in p will affect the solutions for bn and bE, note that if bL is kept constant,

R-

p

if

]db~_ + 1

do

R(co-bu) (1 -

<0,

from Equation (14) and 123

Nivedita Mukherji b

H

2

,

:2'

bL Figure 2.

R - p

[/i

+ 1] dbn

do

R(m - b . )

(1 -- pH)p z

(8(pL -- pn)R~ (robe + mL)mc --\ (1 -- ~)Pc J [(R - P)--~c-- il Z -~c)prcbc]2(me + (1 - pL)rcbc) < O, from Equation (15). Clearly the change in bn is larger in Equation (15) than in Equation (14) implying that the graph of Equation (15), represented by (1) in Figure 2, shifts more than the graph of Equation (14), represented by (2) in Figure 2. The leftward shift of both curves (depicted by broken curves) is due to the negative signs of dbn/dp obtained above. It is clear from the figure that since both curves shift to the left, bL falls as p increases. The change in bn is, however, ambiguous and depends on the magnitudes of the shifts of the two curves. Consequently, it is possible that bn increases as p increases, violating the standard Tobin effect. Such a case is shown in Figure 2. To understand why such a reversal is possible, note that, when loans 124

Inflation and Risky Investment

to low risk agents are denied with a positive probability, lenders offering loans to high risk agents do not have to make the contract as attractive as the one without the threat of loan denial. These lenders then benefit from the sacrifice of the lenders denying loans. When money's return increases and loans to low risk agents are decreased, these low risk lenders actually benefit, as they hold more of the asset that introduces no distortions. This change, however, tends to increase the probability of loan approval. As this probability rises, lenders offering loans to high risk agents are adversely affected because it makes the low risk contract relatively more appealing. This forces lenders to make their offer to high risk agents more attractive so that they reveal their types. This effect on the loan quantity to high risk agents may dominate the standard portfolio adjustment effect that a change in money's return initiates. In that event, loans to high risk agents may actually increase as money's return increases, violating the Tobin effect. Since such a reversal occurs as the shift of curve (1) becomes larger, it follows from the derivative dbH/d 9 obtained from Equation (15) that some of the parameters that will tend to make this outcome more likely are: high e0, 5, high R, and a smaller difference between the returns R and P. Due to the logarithmic nature of Equation (14), closed-form solutions for the endogenous variables cannot be obtained. However, numerical solutions with very high degrees of precision can be generated by Newton's method. 11 These results corroborate the findings from the graphical analysis. Results of the simulations performed are given in Table 4. The results obtained from this example are summarized as follows: • Investments in high risk projects increase with money's return indicating a reversal of the Tobin effect. • Investments in low risk projects decrease when money's return rises as suggested by the Tobin effect. • The probability of loan approval increases for low risk agents (recall the probability of loan approval for high risk agents is always 1). • The expected quantity of loans to low risk agents (rczbc) increases with money's return. • The ratio of loans to high risk and expected loans to low risk agents falls with money's return. These results are quite striking and indicate that, for the set of parameter values chosen, it is better for both low risk and high risk investments if money's return increases. Note that the probability of loan approval, 7rz, nTo find a solution to an equation of the formf(x) = 0 the method uses an initial valueand the formula:x. = x._ 1 - f ( x . _ i)/f '(x~_ 1) to sequentiallyfind the fixedpoint. 125

Nivedita Mukherji TABLE 4. R = 2 , 0 = 0,~ = 0.4, w = 1, pH = 0.2, pL = 0.7

p 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51

bH

bE

~L

0.450436 0.463648 0.47548 0.486126 0.495742 0.504454 0.512368 0.519569 0.526132 0.532116 0.537576

0.718742 0.705122 0.691149 0.676843 0.662226 0.647326 0.632172 0.616799 0.601242 0.58554 0.569733

0.358466 0.419797 0.47823 0.534454 0.589048 0.642506 0.695255 0.747665 0.800067 0.852757 0.906003

7rLbL

bH/~LbL

0.257644 0.296008 0.330528 0.361741 0.390083 0.415911 0.43952 0.461159 0.481034 0.499324 0.51618

1.74829 1.56633 1.43855 1.34385 1.27086 1.21289 1.16574 1.12666 1.09375 1.06567 1.04145

easily follows from the incentive compatibility constraint (8) are determined:

RbH - pHrUbH -- ~d UL = (PL -- pH)rLbL

once

bL

and bn

(16)

The rise in the probability of loan approval when bn rises and b L falls is obvious from this equation. In addition to these positive effects on quantities, the ratios bn/nLbL show that the mix of high risk and low risk projects changes in favor of the low risk projects. This again implies that the overall risk of the projects sponsored by lenders falls as money's return increases. As mentioned earlier, it is also possible for bu to fall as p increases. Such a case is shown in Table 5. This table clearly shows that, as money's return increases, • investments in both low risk and high risk projects decrease. • even though the probability of loan approval rises for low risk projects, the expected quantities of investment in low risk projects fall, as column 5 shows. • the ratio of investment in high risk to expected investment in low risk projects decreases. These results show that investments in both types of projects clearly fall as 126

Inflation and Risky Investment TABLE 5. R = 1.5, (7 = 0,5 = 0.2, w = 1, pn = 0.1, pL = 0.9

P 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51

bH

bL

EL

7~LbL

bH/TCLbL

0.566321 0.563972 0.561617 0.559264 0.556918 0.554587 0.552275 0.549988 0.54773 0.545506 0.54332

0.919116 0.915744 0.912267 0.908678 0.904974 0.901148 0.897194 0.893106 0.888877 0.884501 0.879969

0.588643 0.590813 0.592934 0.59503 0.597121 0.599227 0.601369 0.603564 0.605832 0.608191 0.610659

0.541031 0.541033 0.540914 0.540691 0.540379 0.539992 0.539544 0.539047 0.538511 0.537945 0.537361

1.04674 1.0424 1.03827 1.03435 1.03061 1.02703 1.0236 1.0203 1.01712 1.01405 1.01109

p rises, validating the Tobin effect. Unlike the case studied in Table 4, the rise in rcL is not substantial enough to offset the fall in bE. Consequently, the incentive compatibility constraint is relaxed a s ~LbLfalls and lenders offering loans to high risk agents can adjust their loans more appropriately as money's return rises. Nevertheless, the ratio of investment in the two types of projects clearly shifts in favor of the low risk projects. This again helps reduce the overall risk of the projects being financed by all lenders. It has been mentioned that one of the factors that affects the relationship between p and the loan quantities is the difference between the returns R and p. Table 6 shows that as this difference falls, bH first increases and then decreases. This is because of the rise in p reducing the need to hold assets that introduce distortions. As p gets closer and closer to R, the economy moves closer and closer to its distortion-free state and the Tobin effect begins to hold. These tables show that the money-investment relationship is further complicated when rationing by number of loan approvals is considered. The monetary authority in this environment must consider the effects of its actions on both the acceptance probability and the quantity of loans per borrower. When the acceptance probabilities are appropriately adjusted, the average quantity of loans to the low risk agents often rises with money's return reversing the Tobin effect. In numerous ranges of parameter values, investment in high risk projects increased when money's return increased. In particular, portfolio adjustments to changes in money's return must be such that the incentive compatibility constraint continues to hold. 127

Nivedita Mukhe~i TABLE 6. R = 2,/I

= 0,~

= 0.4, w = 2, pH = 0.1, p c =

p

bn

bE

rtc

0.21 0.26 0.31 0.36 0.41 0.46 0.51 0.56 0.61

0.800616 0.895882 0.926991 0.935775 0.936322 0.934348 0.932056 0.929855 0.927377

1.85524 1.79716 1.72751 1.64435 1.54583 1.43086 1.30013 1.15691 1.00664

0.143318 0.308662 0.398269 0.463186 0.52281 0.587975 0.666937 0.767539 0.89871

rcLbL 0.26589 0.554717 0.688013 0.761639 0.808177 0.841311 0.867107 0.887974 0.904674

0.8

bH/~cbL 3.01108 1.61503 1.34735 1.22863 1.15856 1.11059 1.0749 1.04716 1.0251

The exact directions of the changes are found to be dependent on the parameterization.

4. S u m m a r y

and Conclusion

This paper finds many new results regarding the relationship between money and investment when adverse selection problems are introduced. The numerical simulations have demonstrated that the impact of changes in money's return on investment depends on many factors. The wide range of possibilities shows that the nature of the relationship is much more complex than what one infers from the monetary growth literature. The results indicate that much caution is necessary in implementing policies aimed at changing investment in the economy. The major conclusions of this work are as follows: • A change in money's return changes total investment in the economy. Although the Tobin effect holds in many eases, reversals of the effect are also possible. • Changes in money's return ehange the ratio of the number of low risk to high risk projects that are sponsored by the lenders. When all loans are approved, the ratio often shifts toward high risk projects when money's return improves. When a fraction of the loans is rejected to ensure selfselection, the ratio of the two types of loans is more often found to move toward the low risk projects, as money becomes more attractive. • Changes in money's return may affect different types of projects differently. For example, investment in good quality (low risk) projects may 128

Inflation and Risky Investment decrease but investment in poor quality (high risk) projects may increase when money's return rises. • If lenders deny some loans with a positive probability, changes in money's return also change the probability of loan approval. In some eases, as money's return rises, total investment in low risk projects increases even when the quantity of loan received by a low risk borrower decreases. This is possible because an increase in the probability of receiving a loan outweighs the reduction in the quantity received by each. • Money affects investment differently depending on whether credit is rationed or not. These results, derived under private information, are more complex than those derived under public information because of incentive eompatibifity considerations. Lenders can no longer merely increase investment when money's return falls; any change in the portfolio implies changes in the terms of the contracts offered to the borrowers. The changes have to be such that the borrowers continue to self select. When the number of loans are not rationed, total investment always falls as money's return rises. However, the impact on the overall quality of investment in the economy is less obvious. It is this impact on quality that makes it difficult to conclude that an economy is better off with more capital. These effects are further complicated when rationing by number of loan approvals is considered. The monetary authority in this environment must consider the effects of its actions on both the acceptance probability and the quantity of loans per borrower. The paper finds that when the acceptance probabilities are appropriately adjusted, the average quantity of loans to the low risk agents often rises with money's return, thereby reversing the Tobin effect. In several ranges of parameter values, investment in high risk projects increased when money's return increased. The paper finds that as the loans to low risk agents fall and the probability of loan approval rises, the low risk contract may become more attractive to high risk agents. To deter these agents from misreporting their types, lenders may be forced to increase loans to these agents as money's return rises. As mentioned in the introduction, this paper has analyzed how changes in money's return affect capital when different investment opportunities exist and information is imperfect. It remains for future research to analyze the Tobin effect in the presence of such asymmetric information when capital accumulation over time is possible. In the current paper, the economic environment is repeated exactly each period, and the total output of each period is completely consumed by the current old. The endowments of the current young lenders which are used in the investment projects play the role of capital. As a result, this paper only studies the effect of money on 129

Nivedita Mukherji how lenders choose to divide their total endowment into money and capital. Nonetheless, we find that money affects capital in very important ways in this framework. The complexities that we find in this simpler model will carry over to a more complete model of money and capital, and money will affect not only current capital but future capital as well. Thus it will affect the entire capital accumulation process and affect the economy's long-run growth path. It is safe to conjecture that, if a change in money's return increases the quantity of capital and improves the overall quality of capital in the current model, such changes in a more complete model of economic growth will have growth enhancing effects. The contribution of the paper lies in demonstrating that money affects both the quantity and quality of capital used. It is left for future research to investigate exactly how these changes influence the economy's growth path. These results show that when adverse selection problems exist in capital markets, many unusual changes occur when money's return changes. Bencivenga-Smith (1993) also demonstrated that unusual changes occur when government policies change in economies with adverse selection problems. Demonstrating that, when economies experience adverse selection problems, government policies affect economic variables differently, these papers suggest that there remains ample scope for further research. For example, the relationship between money and investment can be studied in the context of models with competitive lenders, risk neutral lenders with alternative reasons for money demand, or financial intermediaries. Since the qualities of investments vary widely in any economy and information regarding them is rarely perfect, this remains a fruitful topic for further investigation. Received. November 1995 Final version: January 1997

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Inflation and Risky Investment tries: The Optimal Degree of Financial Repression." Oxford Economic

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Economic Studies 58 (April 1991): 195-209. Diamond, Douglas. "Financial Intermediation and Delegated Monitoring." Review of Economic Studies 51 (1984): 393-414. Danthine, Jean-Pierre, John B. Donaldson, and Lance Smith. "On the Superneutrality of Money in a Stochastic Dynamic Macroeconomic Model." Journal of Monetary Economics 20 (December 1987): 475-99. Drazen, Allan. "Inflation and Capital Accumulation under a Finite Horizon." Journal of Monetary Economics 8 (1981): 247-60• Gale, Douglas. Money in Equilibrium. New York: Cambridge University Press, 1983. Greenwood, Jeremy, and Boyan Jovanovic. "Financial Development, Growth, and the Distribution of Income." Journal of Political Economy 98 (October 1990): 1076-1107. Orphanides, Athanosios, and Robert Solow. "Money, Inflation and Growth." In Handbook of Monetary Economics Vol. I, edited by Benjamin M. Friedman and Frank H. Hahn, 223-61. Amsterdam: Elsevier Science B. V., 1990. Petersen, Mitchell A., and Raghuram G. Rajan. "The Effect of Credit Market Competition on Lending Relationships." Quarterly Journal of Economics 110 (May 1995): 407-43. Romer, David. "A Simple General Equilibrium Version of the Baumol-Tobin Model." Quarterly Journal of Economics 101 (November 1986): 663-85. Sidrauski, Miguel. "Inflation and Economic Growth." Journal of Political Economy 75 (December 1967a): 796-810. • "Rational Choice and Patterns of Growth in a Monetary Economy." American Economic Review 77 (July/August 1967b): 575-85. Stockman, Alan. "Anticipated Inflation and the Capital Stock in a Cash-inadvance Economy." Journal of Monetary Economics 8 (1981): 387-93. Tobin, James. "Money and Economic Growth." Econometrica 33 (1965): 671-84. Well, Phillip. "Monetary Policy and Budget Deficits with Overlapping Families of Infinitely-Lived Agents." Harvard University, 1986. Mimeo. Williamson, Stephen. "Costly Monitoring, Financial Intermediation, and Equilibrium Credit Rationing." Journal of Monetary Economics 18 (September 1986): 159-79. Whitesell, William. "Age Heterogeneity and the Tobin Effect with Infinite Horizons." Finance and Economics Discussion Series, Federal Reserve Board, 1988.

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Nivedita Mukherji

Appendix Notation N = n = 5= pi(i = L, H) = = R = bi = =

r~ = P=

P~ = m

=

h = = = L =

co

tc

132

n u m b e r of islands or regions in the economy. n u m b e r of borrowers (entrepreneurs) in each region. fraction of successful projects. probability of success of type i project. reservation utility of entrepreneurs. expected return from a unit of capital. quantity of capital (loan) used in project of type i. probability of receiving a loan by the owner of a type i project. loan rate for project of type i. gross return on money. price level at time t. real value of money demand. quantity of monetary transfer. quantity of endowment received by each lender. ~ , t u = 1 -- 5. Lagrange multiplier.