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1 This explanation has been artic -ulated in a number of recentpapers. See, for example,Azariadis and Smith (forthcom-ing), Boyd and Smith (forth -coming), and Schreft andSmith (forthcoming and1994).

FE D E R A L RE S E RV E BA N K O F ST. LO U I S

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Inflation, Financial Markets, and Capital FormationSangmok Choi, Bruce D.Smith, and John H. Boyd

A consensus among economists seemsto be that high rates of inflationcause “problems,” not just for some

individuals, but for aggregate economicperformance. There is much less agree-ment about what these problems are andhow they arise. We propose to explainhow inflation adversely affects an economyby arguing that high inflation rates tend toexacerbate a number of financial marketfrictions. In doing so, inflation interfereswith the provision of investment capital,as well as its allocation.1 Such interferenceis then detrimental to long-run capital for-mation and to real activity. Moreover, highenough rates of inflation are typically ac-companied by highly variable inflation andby variability in rates of return to savingon all kinds of financial instruments. Weargue that, by exacerbating various finan-cial market frictions, high enough rates ofinflation force investors’ returns to displaythis kind of variability. It seems difficultthen to prevent the resulting variability inreturns from being transmitted into realactivity.

Unfortunately, for our understandingof these phenomena, the effects of perma-nent increases in the inflation rate forlong-run activity seem to be quite compli-cated and to depend strongly on the initiallevel of the inflation rate. For example,Bullard and Keating (forthcoming) findthat a permanent, policy-induced increase

in the rate of inflation raises the long-runlevel of real activity for economies whoseinitial rate of inflation is relatively low. Foreconomies experiencing moderate initialrates of inflation, the same kind of changein inflation seems to have no significanteffect on long-run real activity. However,for economies whose initial inflation ratesare fairly high, further increases in infla-tion significantly reduce the long-run levelof output. Any successful theory of howinflation affects real activity must accountfor these nonmonotonicities.

Along the same lines, Bruno and Easterly (1995) demonstrate that a num-ber of economies have experienced sus-tained inflations of 20 percent to 30 per-cent without suffering any apparentlymajor adverse consequences. However,once the rate of inflation exceeds somecritical level (which Bruno and Easterlyestimate to be about 40 percent), signifi-cant declines occur in the level of real ac-tivity. This seems consistent with the re-sults of Bullard and Keating.

Evidence is also accumulating that in-flation adversely affects the allocative func-tion of capital markets, depressing the levelof activity in those markets and reducinginvestors’ rates of return. Again, however,these effects seem highly nonlinear. In across-sectional analysis, for example, Boyd,Levine, and Smith (1995) divide countriesinto quartiles according to their averagerates of inflation. The lowest inflationquartile has the highest level of financialmarket activity, and the highest inflationquartile has the lowest level of financialmarket activity. However, the two middlequartiles display only very minor differ-ences. Thus for the financial system, as forreal activity, there seem to be threshold ef-fects associated with the inflation rate.

Moreover, as we will show, high ratesof inflation tend to depress the real returnsequity-holders receive and to increasetheir variability. In Korea and Taiwan,there were fairly pronounced jumps in the

Sangmok Choi is an economist at the Korean Ministry of Finance. Bruce D. Smith is a professor of economics at the University of Texas, Austin.John H. Boyd is a professor of finance at the University of Minnesota and is with the Federal Reserve Bank of Minneapolis. The authors thankSatyajit Chatterjee; Pamela Labadie; and the participants of seminars at the University of Texas, the Federal Reserve Bank of Dallas, and theWorld Bank for helpful comments on an earlier draft of this article. The views expressed herein are those of the authors and not necessarilythose of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

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rate of inflation in 1988 and 1989, respec-tively. In each country, before those dates,inflation’s effects on rates of return to eq-uity, rate of return volatility, and transac-tions volume appear to be insignificant.After the dates in question, these effectsare generally highly significant. Thus itseems possible that—to adversely affectthe financial system—inflation must be“high enough.”

Why does inflation affect financialmarkets and real activity this way? Weproduce a theoretical model in which—consistent with the evidence—higher in-flation reduces the rate of return receivedby savers in all financial markets. By itselfthis effect might be enough to reduce sav-ings and hence the availability of invest-ment capital. However, we do not believethat this explanation by itself is very plau-sible, for two reasons. First, to explain thenonmonotonicities we have noted, the sav-ings function would have to bend back-ward. Little or no empirical evidence ex-ists to support this notion. Second, almostall empirical evidence suggests that sav-ings is not sufficiently sensitive to rates ofreturn to make this a plausible mechanismfor inflation to have large effects. Thus analternative mechanism is needed.

We present a model in which inflationreduces real returns to savings and, via thismechanism, exacerbates an informationalfriction afflicting the financial system. Theparticular friction modeled is an adverseselection problem in capital markets. How-ever, the specific friction seems not to becentral to the results we obtain.2 What iscentral is that the severity of the financialmarket friction is endogenous and variespositively with the rate of inflation.

In this specific model, higher rates ofinflation reduce savers’ real rates of returnand lower the real rates of interest thatborrowers pay. By itself, this effect makesmore people want to be borrowers andfewer people want to be savers. However,people who were not initially gettingcredit represent “lower quality borrowers”or, in other words, higher default risks. In-vestors will be uninterested in makingmore loans to lower quality borrowers at

lower rates of interest and therefore mustdo something to keep them from seekingexternal finance. The specific responsehere is that markets ration credit, andmore severe rationing accompanies higherinflation. This rationing then limits theavailability of investment capital and re-duces the long-run level of real activity. Inaddition, when credit rationing is suffi-ciently severe, it induces endogenouslyarising volatility in rates of return to sav-ings. This volatility must be transmitted toreal activity and, hence, to the rate of in-flation. Variable inflation therefore neces-sarily accompanies high enough rates ofinflation, as we observe in practice.

This story, of course, does not explainwhy these effects are strongest at high—and not at low—rates of inflation. The ex-planation for this lies in the fact that—atlow rates of inflation—our analysis sug-gests that credit market frictions are poten-tially innocuous. Thus at low rates of infla-tion, credit rationing might not emerge atall, and none of the mechanisms men-tioned in the previous paragraph would beoperative. In this case our economy wouldact as if it had no financial market frictions.When this occurs, our model possesses astandard Mundell-Tobin effect that makeshigher inflation lead to higher long-run lev-els of real activity.3 However, once inflationexceeds a certain critical level, credit ra-tioning must be observed, and higher ratesof inflation can have the adverse conse-quences noted above.

Finally, our analysis suggests that acertain kind of “development trap” phe-nomenon is ubiquitous, particularly at relatively high rates of inflation.4 We oftenobserve that economies whose perfor-mance looks fairly similar at some point in time—like Argentina and Canada circa1940—strongly diverge in terms of theirsubsequent development. Although this is clearly often because of differencesin government policies, presumably manygovernments confront similar policy op-tions. One would thus like to knowwhether intrinsically similar economiescan experience divergent economic perfor-mance for purely endogenous reasons.

2 The same phenomena we re-port here occur in the presenceof a costly state verificationproblem (Boyd and Smith forth-coming), or in a model wherespatial separation and limitedcommunication affect the finan-cial system (Schreft and Smithforthcoming and 1994).

3 In particular, in the absence offinancial market frictions, ourmodel reduces to one in whichhigher rates of inflation (easiermonetary policy) stimulatesreal output growth. This occursin a variety of monetary growthmodels: see Mundell (1965);Tobin (1965); Diamond(1965); or especially Azariadis(1993) (for an exposition);Sidrauski (1967); and Shell,Sidrauski, and Stiglitz (1969).

4 See Azariadis and Drazen(1990) for one of the originaltheoretical expositions of devel-opment traps.

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The answer in models with financial mar-ket frictions is that this can occur fairlyeasily: When the severity of an economy’sfinancial market frictions is endogenous, itis possible that—for endogenous reasons—the friction is perceived to be more or less severe. If it is perceived to be more(less) severe, financial markets provide less(more) investment capital. The result is areduced (enhanced) level of real economicperformance. This validates the originalperception that the friction was (was not)severe. Thus, as we show, developmenttrapsshould be expected to be quite common.

The remainder of the article proceedsas follows: In the first section we lay out atheoretical model that illustrates the argu-ments just given, while in the second sec-tion we describe an equilibrium of themodel. In the third section we discuss howinflation affects the level of real activitywhen the financial market friction is notoperative, while in the fourth section wetake up the same issue when it is. In thefifth section we examine when the frictionwill or will not be operative and derive thetheoretical implications we have alreadydiscussed. In the sixth section we showthat an array of empirical evidence sup-ports these implications. In the final sec-tion we offer our conclusions.

A SIMPLE ILLUSTRATIVE MODEL

The purpose of this section is to pre-sent a model that illustrates how inflationinteracts with a particular financial marketfriction. This friction is purposely keptvery simple in order to highlight the eco-nomic mechanisms at work. Later we willargue that these mechanisms are operativevery generally in economies where finan-cial markets are characterized by informa-tional asymmetries.

The EnvironmentThe economy is populated by an infi-

nite sequence of two period lived, overlap-ping generations. Each generation is iden-

tical in its size and composition. We de-scribe the latter below and index time pe-riods by t = 0, 1, ....

At each date, a single final commodityis produced via a technology that utilizeshomogeneous physical capital and labor asinputs. An individual producer employingKt units of capital and Nt units of labor at tproduces F(Kt,Nt) units of final output.For purposes of exposition, we will as-sume that F has the constant elasticity ofsubstitution form

(1) F(K,N) = [aK +bN ]1/ ,

and we will assume throughout that < 0holds.5 Defining k ≡ K/N to be the capital-labor ratio, it will often be convenient towork with the intensive production func-tion f(k) ≡ F(k,1). Clearly, here

(1′) f(k) = [ak +b].

Finally, to keep matters notationallysimple, we assume that capital depreciatescompletely in one period.6

Each generation consists of two typesof agents. Type 1 agents—who constitute afraction ∈(0,1) of the population—areendowed with one unit of labor whenyoung and are retired when old. We as-sume that all young-period labor is sup-plied inelastically. In addition, type 1agents have access to a linear technologyfor storing consumption goods wherebyone unit stored at t yields x > 0 units ofconsumption at t + 1.

Type 2 agents represent a fraction 1 − of each generation. These agentssupply one unit of labor inelastically whenold and have no young-period labor en-dowment.7 In addition, type 2 agents haveno access to the technology for storinggoods. They do, on the other hand, haveaccess to a technology that converts oneunit of final output at t into one unit ofcapital at t + 1. Only type 2 agents haveaccess to this technology.

We imagine that any agent who ownscapital at t can operate the final goods pro-duction process at that date. Thus type 2agents are producers in old age. It entails

5 If ρ ≥0, our analysis is a spe-cial case of that in Azariadisand Smith (forthcoming). Wetherefore restrict attention hereto ρ <0. The assumption that ρ <0 holds implies that theelasticity of substitution be-tween capital and labor is lessthan unity. Empirical evidencesupports such a supposition.

6 It is easy to verify that this as-sumption implies no real loss ofgenerality.

7 This assumption implies that allcapital investment must be ex-ternally financed, as will soon beapparent. This provides the linkbetween financial market condi-tions and capital formation thatis at the heart of our analysis.

no loss of generality to assume that allsuch agents run the production processand work for themselves in their secondperiod.

With respect to agents’ objective func-tions, it is simplest to assume that allagents care only about old-age consump-tion and that they are risk neutral.8 Theseassumptions are easily relaxed.

The central feature of the analysis isthe presence of an informational frictionaffecting the financing of capital invest-ments. In particular, we assume that eachagent is privately informed about his owntype. We also assume that nonmarket ac-tivities, such as goods storage, are unob-servable, while all market transactions arepublicly observed. Thus, to emphasize, anagent’s type and storage activity are privateinformation, while all market transac-tions—in both labor and credit markets—are common knowledge. This set of as-sumptions is intended to keep theinformational asymmetry in our modelvery simple: Since type 2 agents cannotwork when young, they cannot crediblyclaim to be type 1. However, type 1 agentsmight claim to be type 2 when young. Wenow describe what happens if they do so.

If a type 1 agent wishes to claim to betype 2, he cannot work when young, andhe must borrow the same amount as type 2agents do. Since type 1 agents are incapableof producing physical capital, it will ulti-mately be discovered that they have mis-represented their type. To avoid punish-ment, we assume that a dissembling type 1agent absconds with his loan, becomingautarkic and financing old-age consump-tion by storing the proceeds of his borrow-ing. Dissembling type 1 agents never repayloans. Notice, however, that since type 2agents cannot store goods, they will neverchoose to abscond, and hence they alwaysrepay their loans.9 Obviously, lenders willwant to avoid making loans to dissemblingtype 1 agents. How they do so is the sub-ject of the section on equilibrium condi-tions in financial markets.

It remains to describe the initial con-ditions of our economy. At t = 0 there is aninitial old generation where each agent is

endowed with one unit of labor (suppliedinelastically) and with K0 > 0 units of capi-tal. No other agents are endowed at anydate with capital or consumption goods.

TradingThree kinds of transactions occur in

this economy. First, final goods and ser-vices are bought and sold competitively.We let pt denote the dollar price at t of aunit of final output. Second, producershire the labor of young type 1 agents in acompetitive labor market, paying the realwage rate wt at t. And third, young(nondissembling) type 1 workers savetheir entire labor income, which they sup-ply inelastically in capital markets, therebyacquiring claims on type 2 agents—andpossibly on some dissembling type 1agents—and claims on the government,such as money or national debt. Themodel we present here is not rich enoughto capture any distinction between differ-ent types of financial claims, such as debtor equity.10 We thus think of young agentsas simply acquiring a generalized claimagainst producers of capital. It entails noloss of generality to think of financial mar-ket activity as being intermediated, saythrough banks, mutual funds, or pensionfunds. We assume there is free entry intothe activity of intermediation. We also letRt+1 be the real gross rate of return earnedby intermediaries between t and t + 1 on(nondefaulted) investments, and we let rt+1

be the real gross rate of return earned byyoung savers. After describing governmentpolicy, we return to a description of equi-librium conditions in these markets.

The GovernmentWe let Mt denote the outstanding per

capita money supply at t. At t = 0 the initialold agents are endowed with the initial percapita money supply, M 1 > 0. Thereafter,the money supply evolves according to

(2) Mt+1 = Mt ,

where > 0 is the exogenously given gross

8 Risk neutrality implies thatthere are no potential gainsfrom the use of lotteries in thepresence of private information.

9 The hallmark of models ofcredit rationing based on ad-verse selection or moral hazardis that different agents have dif-ferent probabilities of loan re-payment and hence regard theinterest rate dimensions of aloan contract differently. See,for instance, Stiglitz and Weiss(1981) or Bencivenga andSmith (1993). Ours is the sim-plest possible version of such ascenario: Type 2 agents repayloans with probability one,while type 1 agents defaultwith the same probability.Matters are somewhat differentin models of credit rationingbased on a costly state verifica-tion problem in financial mar-kets. See, for instance,Williamson (1986 and 1987)and Labadie (1995). We willdiscuss such models briefly inthe conclusion.

10 For models of informational frictions that do generate debtand equity claims, see Boot andThakor (1993), Dewatripontand Tirole (1994), Chang(1986), or Boyd and Smith(1995a and b).

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rate of money creation. We assume that thegovernment makes a once and for allchoice of at t = 0: In steady-state equilib-ria the (gross) rate of inflation will equal .

Our ultimate purpose is to examinehow different choices of affect finan-cial markets and, through this channel,capital formation. To make our results asstark as possible, we assume that the gov-ernment uses the proceeds of money cre-ation to finance a subsidy to private capitalformation. It should then be transparentthat any adverse effects of inflation are aresult of the presence of inflation aloneand not what the revenue from the in-flation tax is used for. More specifically,then, we assume that any monetary injec-tions (withdrawals) occur via lump-sumtransfers to young agents claiming to betype 2. Genuine type 2 agents will usethese transfers entirely to invest in capital;hence government policy here consists of acapital subsidy program financed by print-ing money. If we let t denote the realvalue of the transfer received by youngtype 2 agents at t, and we let t ∈ [0,1] de-note the fraction of dissembling type 1agents in the time t population, then thegovernment budget constraint implies thatthe real value of transfers, per capita,equals the real value, per capita, ofseigniorage revenue. Thus

(3) [(1 − ) + t] t = (Mt − Mt−1)/pt

must hold at all dates. If we let mt ≡ Mt/pt

denote time t real balances, equations 2and 3 imply that

(3′) [(1 − ) + t] t = [( −1)/ ]mt.

EQUILIBRIUMCONDITIONSFactor Markets

Let bt denote the real value of borrowingby young type 2 agents at t. These agentsalso receive a transfer t. All resources ob-tained by these individuals are used to fundcapital investments at t. Each old producerat t + 1 will hence have the capital stock

(4) Kt+1 = bt + t.

Let Lt denote the quantity of younglabor hired by a representative producer att. Each such producer combines this withhis own unit of labor to obtain Nt = Lt + 1units of labor services. Then the producer’sprofits, net of loan repayments, areF(Kt,Lt+1) − wtLt − Rtbt 1 since an interestobligation of Rt bt 1 was incurred at t − 1.Producers wish to maximize old-period in-come. At t, bt 1 is given by past credit ex-tensions, so that the only remaining choicevariable is Lt. Profits are maximized when

(5) wt = F2(Kt,Lt +1) = F2(Kt/Nt,1)

= f(kt) − kt f ′(kt)=b(akt + b)(1− )/

≡ w(kt)

where kt ≡ Kt /Nt is the capital labor ratio.Equation 5 asserts the standard result thatlabor earns its marginal product.

For future reference, it will be usefulto have an expression for the consump-tion, c2

t, of old type 2 agents at t. Clearly

(6) c2t = F1(⋅)Kt + F2(⋅)(Lt + 1) − wtLt − Rtbt−1

= [F1(⋅) − Rt]bt−1 + wt + F1(⋅) t−1.

The first equality in equation 6 followsfrom Euler’s law, while the second followsfrom equations 3, 4, and 5. Equation 6 asserts that old producers have incomeequal to the marginal product of their ownlabor, plus the value of the capital paid for through transfer payments [F1(⋅) t 1],plus the net income obtained from capital attained through borrowing [(F1(⋅) − Rt)bt 1].

Financial MarketsIntermediaries face a fairly standard

adverse selection problem in financial markets.11 If they lend to a dissemblingtype 1 agent, the loan will not be repaid.12

Hence it is desirable not to lend to theseagents, but at the same time such agentscannot be identified ex ante. Intermedi-

11 For a canonical adverse selec-tion model, see Rothschild andStiglitz (1976).

12 It is easy to verify that nondis-sembling type 1 agents will notwish to borrow if Rt+1 ≥max(rt+1,x). This conditionwill hold in equilibrium.

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aries will hence structure financial con-tracts to deter type 1 agents from dissem-bling or, in other words, to induce self-selection (only type 2 agents choose to ac-cept funding).

Using typical assumptions in econ-omies with adverse selection, we assumethat intermediaries announce financialcontracts consisting of a loan quantity bt,and an interest rate (or return to the intermediary) of Rt+1. Each intermediaryannounces such a contract, taking thecontracts offered by other intermediariesas given. Hence we seek a Nash equilib-rium set of financial contracts. On the de-posit side we assume that intermediariesbehave competitively (that is, each inter-mediary assumes it can raise all the fundsit wants at the going rate of return on savings rt+1).

One objective of intermediaries is toinduce self-selection. This requires thattype 1 agents prefer to work when youngand save their young-period income ratherthan to borrow bt, receive the transfer t,and abscond. If they work when youngand save the proceeds, their utility is rt+1wt.If they borrow bt, obtain the transfer t,and abscond, their utility is x(bt+ t). Henceself-selection requires that

(7) rt+1wt ≥ x(bt+ t).

Standard arguments13 establish that equa-tion 7 holds in any Nash equilibrium andthat all type 1 agents are deterred from dis-sembling. Hence t = 0 holds at all dates.

In addition, since there is free entryinto intermediation, all intermediariesmust earn zero profits in equilibrium.Since t = 0, this simply requires that

(8) Rt+1 = rt+1.

An equilibrium in financial marketsnow requires that five conditions be satis-fied. First, given rt+1 and t, the quantity offunds obtained in the marketplace by eachtype 2 agent must satisfy equation 7. Sec-ond, equation 8 must hold. Third, sourcesand uses of funds must be equal. Sources

of funds at each date are simply the sav-ings of young type 1 agents, which in percapita terms are wt. Uses of funds areloans to borrowers [(1 − )bt per capita],plus real balances (mt per capita), plus percapita storage (st). Thus equality betweensources and uses of funds obtains if andonly if

(9) w(kt) = (1 − )bt + mt + st.

The fourth condition is that type 2agents will be willing to borrow if andonly if

(10) F1(Kt,Nt) = F1(Kt/Nt,1) = f ′(kt)

= a[a+bk ](1 )/ ≥ Rt+1 = rt+1

holds14. Equation 10 implies that type 2agents perceive nonnegative profits fromborrowing. And finally, type 1 agents arewilling to supply funds to intermediaries ifand only if the return they receive is atleast as large as the return available on al-ternative savings instruments (money andstorage). This requires that

(11a) rt+1 ≥ pt/pt+1

(11b) rt+1 ≥ x.

We will want agents to hold money inequilibrium. Hence equation 11a must al-ways hold with equality. We will assumethat equation 11b is a strict inequality;hence in equilibrium st = 0 (storage isdominated in rate of return). Equation 11bis validated, at least near steady states, bythe assumption that

(a1) 1/x > .

We will henceforth impose equation a1.1 5

Some ImplicationsWe now know that in equilibrium all

young type 1 agents supply their labor toproducers. Hence labor market clearing re-quires that the per capita labor demand ofproducers [(1 − )Lt] equals the per capita

13 See Rothschild and Stiglitz(1976), or in this specificcontext, Azariadis and Smith(forthcoming).

14 See equation 6.

15 An additional requirement ofequilibrium is that intermedi-aries perceive no incentive to“pool” dissembling type 1agents with type 2 agents and to charge an interest ratethat compensates for the de-faults by dissembling type 1agents. Azariadis and Smith(forthcoming) show that thereis no such incentive iff ′(kt+1) ≤ rt+1/(1−λ)holds for all t.

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labor supply of young type 1 agents ( ).Therefore,

(12) Lt = /(1 − ).

It is an immediate implication that Nt = 1+ Lt = 1/(1 − ) and that

(13) kt ≡ Kt/Nt = (1 − )Kt.

In addition, under equation a1, st = 0 holds,so that equation 9 becomes

(9′) (1 − )bt = w(kt) − mt.

Now note that kt+1 = (1 − )Kt+1 =(1 − )(bt+ t). Using this fact in equation9′, we obtain

(9″) kt+1 = w(kt) − mt − (1 − ) t.

Finally, we know that t = 0. Using thisfact in equation 1 ′ and substituting the re-sult into equation 9″ yields

(14) kt+1 = w(kt) − mt/ .

It is also possible to derive some fur-ther implications from the preceding dis-cussion. Equations 10 and 11a at equality,imply that

(15) f ′(kt+1) ≥ rt+1 = pt/pt+1.

We can now use the identity pt/pt+1 ≡(Mt+1/pt+1)(pt/Mt)(Mt/Mt+1) ≡ mt+1/ mt towrite equation 15 as

(15′) f ′(kt+1) ≥ mt+1/ mt.

Finally, equation 7 must hold in equilib-rium. Substituting equation 4 into equa-tion 7, and using Kt+1 = kt+1/(1 − ), we ob-tain the equivalent condition

(16) rt+1w(kt) ≥ xkt+1/(1− ).

Equation 11a also implies an alternativeform of equation 16:

(16′) [mt+1/ mt]w(kt) ≥ xkt+1/(1− ).

We can now reduce our search for anequilibrium to the problem of finding asequence {kt, mt} that satisfies equations14, 15 ′, and 16′ at all dates, with k0 > 0given as an initial condition. We nowmake an additional comment. If equation15′ is a strict inequality at any date,young type 2 agents perceive positiveprofits to be made from borrowing andhence will want to borrow an arbitrarilylarge amount. Because this is not possible,if equation 15′ is a strict inequality, theirborrowing must be constrained. The rele-vant constraint is equation 7. In this caseequation 7 at equality determines bt,and equation 16′ will hold with equality.In equilibrium, at least one of the condi-tions (equations 15′ or 16 ′) must thushold with equality. If equation 15′ is anequality, the equilibrium coincides withstandard equilibria that obtain in similareconomies with no informational asym-metries.16 In this case we say the equilib-rium is Walrasian. If equation 15′ holdsas a strict inequality, then equation 16′ isan equality. We refer to this situation ascredit rationing.

WALRASIAN EQUILIBRIAWe now describe sequences that sat-

isfy equations 14 and 15′ at equality. Forthe present we do not impose equation 16′:This amounts to assuming that agents’types are publicly observed. In the sectionon the endogeneity of financial market fric-tions, we ask when such sequences willalso satisfy equation 16 or, in other words,when Walrasian resource allocations can besustained even in the presence of the infor-mational asymmetry. We begin with steady-state equilibria, and then briefly describethe nature of equilibrium paths that ap-proach the steady state. Because the mater-ial in this section is quite standard,17 we at-tempt to present it fairly concisely.

Steady StatesIn a steady state kt and mt are constant.

Hence equation 15′ at equality reduces to

16 See, for example, Diamond(1965), Tirole (1985), or Azariadis (1993, chapter26.2).

17 See, for instance, Diamond(1965), Tirole (1985), orAzariadis (1993, chapter26.2).

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(17) f ′(k) = 1/ = pt/pt+1,

while equation 14 becomes

(18) m = [ w(k) − k].

It is immediately apparent from equa-tion 17 that increases in the rate of moneygrowth (and inflation), , increase thesteady-state capital-labor ratio, per capitaoutput, and productivity of labor. This istrue for all rates of money growth satisfyingequation a1. Because the empirical evidencecited in the introduction strongly suggeststhat higher inflation can lead to higher long-run levels of real activity only if initial ratesof inflation are relatively low, it is clear thatour model cannot confront the whole arrayof empirical experience in the absence of theinformational asymmetry.

For future reference, it will be conve-nient to give an explicit form for the capi-tal stock (or variables related to it) as afunction of the money growth rate. To thisend we define the variable

(19) zt ≡ (b/a)kt ≡ w(kt) / kt f (kt).

It is readily verified that zt is simply the ra-tio of labor’s share to capital’s share: The as-sumption that < 0 implies that zt is an in-creasing function of kt. Hence movementsin zt simply reflect similar movements in kt.

It is easy to check that f (kt) =a1/ [1+(b/a)kt

− ](1− )/ ≡ a1/ (1+zt)(1− )/ .Then, if we let z*( ) denote the value of zsatisfying equation 17 for each , we havethat

(20) z*( ) = [a 1/ (1/ )] /(1− ) − 1.

Equations 19 and 20 give the capital stockin a Walrasian steady state.

DynamicsEquations 14 and 15 ′ at equality de-

scribe how the economy evolves given k0 and m0: the initial capital-labor ratioand initial real balances. The initial pricelevel is endogenous, and so m0 ≡ M0/p0

is endogenous.

It is easy to show that the monetarysteady state is a saddle or, in other words,that there is only one choice of m0 thataverts a hyperinflation where money asymp-totically loses all value. Thus nonhyperin-flationary equilibria are determinate (onlyone possible equilibrium path approachingthe monetary steady state exists), and it is possible to show that the steady state isnecessarily approached monotonically.Walrasian equilibria therefore cannot dis-play economic fluctuations in output, realreturns to investors, or the rate of inflation.

SummaryWalrasian equilibria are unique.

Growth traps are therefore impossible.Moreover, Walrasian equilibria do not display economic fluctuations. Finally,Walrasian equilibria have the feature thatincreases in the long-run rate of inflationlead to higher long-run levels of real activ-ity and productivity.

EQUILIBRIA WITH CREDIT RATIONING

In this section we investigate se-quences {kt,mt} that satisfy equations 14and 16′ at equality at all dates. In the sec-tion on the endogeneity of financial mar-ket frictions, we then examine when aWalrasian equilibrium or an equilibriumwith credit rationing will actually obtain.As before, we begin with steady-state equi-libria.

Steady StatesWhen kt and mt are constant, equation

16′ at equality implies that the steady-statecapital-labor ratio satisfies

(21) w(k)/k = x /(1 − ).

Equation 21 says that the capital stock isdetermined by how financial markets con-trol borrowing to induce self-selection.The rate of inflation matters because it af-fects the rate of return that nondissem-bling type 1 agents receive on their sav-

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16

ings. As inflation rises, this return falls,18

with the consequence that the utility ofworking and saving declines. To preventtype 1 agents from dissembling, the utilityof doing so must also fall. Equation 21 de-scribes the consequences for the per capitacapital stock.

It will be convenient to transformequation 21 as follows: First note that itcan be written as

(21′) [w(k)/kf ′(k)]f ′(k) = x /(1 − ).

Second, given equation 19 and our previousobservations about f ′(k), it is easy to verifythat [w(k)/kf ′(k)]f ′ (k) = a1/ z(1+z)(1− )/ .This observation allows us to rewrite theequilibrium condition equation 21′ as

(22) a 1/ [x /(1 − )] = z(1+z)(1 )/ ≡ H(z).

Equation 22 determines the steady-stateequilibrium value(s) of z as a function ofthe long-run inflation rate . Equation 19then gives the steady-state per capita capi-tal stock. Steady-state real balances are de-termined from equation 14 with k and mconstant:

(23) m = [ w(k) − k].

Equation 21 permits us to rewrite equa-tion 23 as

(23′) m = k{[x /(1 − )] − 1}.

For future reference, it will be convenientto define the function A( ) by

(24) A( ) ≡ [x /(1 − )] .

We can now state our first result.

RESULT 1. Define ˆ by

Then if ≤ ˆ, there exists a solution to equa -tion 22. If, in addition,

(a2) A( ) > 1

all solutions to equation 22 yield positive levelsof real balances.Result 1 is proved in the Appendix.

As the Appendix establishes, the function H(z) defined in equation 22 hasthe configuration depicted in Figure 1. In particular,

and H attains a unique maximum at z = − .Thus, if

(26) H(− ) ≥ a 1/ [x /(1 − )]

equation 22 has a solution, which is de-picted in Figure 1. If < ˆ where

ˆ = [(1 − )/x]a1/ H(− ),

there will be exactly two solutions to equa-tion 22 that are denoted by z_( ) and z

_( )

in Figure 1.The conditions A( ) > 1 and ≤ ˆ

are equivalent to

(a3) (1 − )/ x < ≤ ˆ.

We henceforth assume that equation a3holds. We also assume that

(a4) 1/x≥ ˆ

so that equation a3 implies satisfaction ofequation a1.19

18 In this analysis, inflation is in-versely related to the return onreal balances and hence to thereturn on savings. However, theintuition underlying our resultsis not dependent on real bal-ances earning the same real re-turn as other savings instru-ments. Higher inflation will alsoreduce the return on savings ineconomies where nominal inter-est rate ceilings bind or wherebinding reserve requirementssubject intermediaries to infla-tionary taxation. Binding inter-est rate ceilings and reserve re-quirements are very common indeveloping countries and arehardly unknown in the UnitedStates. Finally, our empirical re-sults do support the notion thathigher inflation does reduce thereal returns received by in-vestors (see the section onsome empirical evidence).

19 Clearly 1/x > (1−λ)/λx canhold only if λ >0.5. Equationa4 obviously implies this.

MAY/ JU N E 1 9 9 6


17

Figure 1

Determination of z Under Credit RationingH(z)

z (σ) −ρ zz (σ)

H(z)

a−1/

1−xλ σ

Evidently, when ≤ ˆ, there are two so-lutions to equation 22. This multiplicity ofcandidate equilibria derives from the waythat financial markets respond to the pres-ence of the adverse selection problem. To in-duce self-selection at any given value of ,w(k) and (b+ ) must be linked. One waythat self-selection can occur is for w(k) and(b+ ) both to be low; this requires that z below. Alternatively, w(k) and (b+ ) can bothbe relatively high; this requires that z behigh. The possibility that there is more thanone way for financial markets to address aninformational asymmetry has a generalitybeyond this particular model, as shown byBoyd and Smith (forthcoming) or Schreftand Smith (forthcoming and 1994).

The Effects of Higher InflationThe consequences of an increase in

the steady-state inflation rate are depictedin Figure 2. Evidently, an increase in raises z( ) and reduces z( ) or, in otherwords

holds. The same statements apply to k.Hence, in the low- (high-) capital-stocksteady state, an increase in the inflation rateraises (lowers) the steady-state capitalstock. These effects occur because an in-crease in reduces the steady-state returnon savings. Other things equal, this lowersthe utility of honest type 1 agents and wouldcause them to misrepresent their type. Topreserve self-selection w(k) must rise rela-tive to (b+ ) = k/(1 − ). In the low- (high-)capital-stock steady state, this requires thatk rise (fall). Thus higher inflation exacer-bates informational asymmetries, with im-plications for the capital stock that are ad-verse in the high-capital-stock steady state.

Figure 3 depicts the solutions to equa-tion 22 as a function of , where we de-note by z( ) any solutions to that equa-tion. Evidently, there can be no solution toequation 22 if the government sets above ˆ . For satisfying equation a3,clearly we have

Of particular interest in this context isthe possibility that an increase in the long-run rate of inflation can reduce the long-runcapital stock, real activity, and productivity.Such consequences are often observed em-pirically when inflation increases, particu-larly when the initial rate of inflation is rela-tively high. This outcome is observed in thehigh-capital-stock steady state. We nowwant to know which, if either, steady statecan be approached under credit rationing.

Dynamics

Given an initial capital-labor ratio, k0,and an initial level of real balances, m0,

MAY/ JU N E 1 9 9 6


18

Figure 2

The Consequences ofHigher InflationH(z)

z (σ1) z (σ2) zz (σ2) zz (σ1)σ2 > σ1

H(z)

a−1/

1−xλ σ2

a−1/

1−xλ σ1

Figure 3

Inflation and its Consequences Under Credit Rationing

zz (σ)

A(σ)=1 ˆ

equations 14 and 16′ at equality governthe subsequent evolution of kt and mt.The Appendix establishes our second result.

RESULT 2. (a) The low-capital-stock steadystate is a saddle. All {kt,mt} sequences ap -proaching it do so monotonically. (b) Thehigh-capital-stock steady state is a sink if ˆis not too large.

Result 2a implies that both the high-and the low-capital-stock steady states canpotentially be approached. To approachthe low-capital-stock steady state, m0 mustbe chosen to lie on a “saddle path;” that is,there is a unique choice of m0 that allowsthe economy to approach the low-capital-stock steady state.

Result 2b implies that, for some openset of values of k0, there is a whole inter-val of choices of m0 that allow the high-capital-stock steady state to be ap-proached. The requirement of avoiding ahyperinflation thus no longer implieswhat m0 must be. Monetary equilibriahave become indeterminate. A continuumof possible equilibrium values of m0 existand hence so does a continuum of possi-ble equilibrium paths approaching thehigh-capital-stock steady state. This is aconsequence of the informational frictionafflicting capital markets.

Not only is the informational asym-metry a source of indeterminacy, it is apotential source of endogenous economicvolatility as well. We now establish thatsuch volatility must be observed near thehigh-capital-stock steady state wheneverthe rate of inflation is sufficiently high. At high rates of inflation, the economymust thus pay a price to avoid the low-capital-stock steady state: This priceis the existence of endogenous volatilityin real activity, inflation, and asset returns.

RESULT 3. Suppose that is sufficientlyclose to ˆ. Then all paths approaching thehigh-capital-stock steady state do so nonmo -notonically.

Result 3 is proved in the Appendix.

SummaryWhen financial market frictions bind,

there can be two steady-state equilibria dif-fering in their levels of real development.Both steady states can potentially be ap-proached. A continuum of paths approach-ing the high-capital-stock steady state ex-ists so that the operation of financialmarkets creates an indeterminacy. If thesteady-state inflation rate is high enough,all such paths display endogenously arisingvolatility in real activity, real returns, andinflation. In this sense high inflation alsoengenders variable inflation.

THE ENDOGENEITY OF FINANCIAL MARKET FRICTIONS

In the section on Walrasian equilibria,we described equilibria under the assump-tion that information about borrower type ispublicly available. In the section on equilib-ria with credit rationing, we described can-didate equilibria under the assumption thatequation 16′ holds as an equality. In this section we ask when equation 16′ will and will not be an equality in equilibrium. Whenit is, credit rationing will occur. When it is not, self-selection occurs even with Walrasian allocations. In the former situa-tion, financial market frictions are severeenough to affect the allocation of invest-ment capital for entirely endogenous rea-sons. In the latter situation, it transpires—again for entirely endogenous reasons—thatfinancial market frictions are not severeenough to affect allocations. One of ourmain results is that when the steady-state in-flation rate is high enough, financial marketfrictions must matter and credit rationingmust occur. Thus high enough rates of infla-tion imply that market frictions must ad-versely affect the extension of credit andcapital formation as well.

When Are Walrasian AllocationsConsistent With Self-Selection?

When do candidate Walrasian equilib-ria (sequences {kt,mt} satisfying equations

MAY/ JU N E 1 9 9 6


19

14 and 15′ at equality) also satisfy equa-tion 16′? For simplicity of exposition, wefocus our discussion on steady states.

Walrasian steady states satisfy equa-tion 16′ when equation 17 holds and whenthe implied value of k satisfies

(29) [w(k)/kf ′(k)]f ′(k) ≥ x /(1 − ).

We have already established that[w(k)/kf ′(k)] = a1/ z(1+z)(1− )/ ; henceequation 29 is equivalent to

(30) H[z*( )] ≥ a−1/ [x /(1 − )].

We now demonstrate our fourth result.

RESULT 4. Equation 30 is satisfied if andonly if holds.

Result 4 is proved in the Appendix.The result asserts that Walrasian alloca-tions are consistent with self-selection ifand only if the steady-state value of zunder full information lies between thevalues of z solving equation 16′ at equality.When this condition is satisfied, the Wal-rasian allocation continues to constitute anequilibrium, even in the presence of theinformational asymmetry. Endogenous fac-tors allow the friction to be sufficientlymild that it does not affect the allocationof investment capital. Thus, when

Walrasian allocationsare equilibrium allocations. When

Walrasian allocations

are inconsistent with self-selection and donot constitute legitimate equilibria.

Credit RationingWe now ask the opposite question:

When do solutions to equation 16′ at equal-ity satisfy equation 15′? Since f ′(k) = a1/ (1+z)(1− )/ , clearly they do so if and only if

In particular, equation 31 asserts that creditcan be rationed if and only if the solution toequation 22 yields a lower capital stock thanwould obtain under a Walrasian allocation.This observation has the following implica-tion: The smaller (larger) solution to equa-tion 16′ at equality is an equilibrium if andonly if We now put allthese facts together.

The Steady-State EquilibriumCorrespondence

Here we describe the full set of steady-state equilibria for each potential choice of

. We begin by depicting z*( ) and z( )simultaneously in Figure 4a and b. It iseasy to check that z*( ) is an increasingfunction, and that z*(a 1/ ) = 0. Combiningthis with our previous results about thecorrespondence z( ), it follows that thereare three possible configurations of thesteady-state equilibrium correspondence.

MAY/ JU N E 1 9 9 6


20

Figure 4a

zz(σ), z*(σ)

Multiple Steady States

a −1/ σ−σ

z (σ) z*(σ)

Figure 4b

a −1/ σ− σσ

σ

The Steady-State EquilibriumCorrespondence (Case 1)

z(σ)z*(σ)

z (σ), z*(σ)

σσ

We now briefly discuss each case. The firstcase is the one of primary interest to us.

Case 1. Suppose that

Then we have the configuration depicted inFigure 4a.20 The lociz*( ) and z( ) inter-sect twice at and .21

For < ,z*( )< zz( )holds. Hence neither the Walrasian situation nor thecredit rationing situation constitutes a le-gitimate equilibrium. Then if < , thereare no monetary steady states.

For ∈[ , ],z*( )∈[z( ),z( )] holds.It follows that the Walrasian steady state isconsistent with self-selection whenever

∈[ , ] and hence is a true steady-stateequilibrium. At the same time, z( ) ≤ z*( )also holds. Thus z( ) is a legitimate steadystate with credit rationing. Clearly, z( )> z*( ) holds for all ∈[ , ] and hence z( ) is not a legitimate steady state for

< . Thus, for ∈[ , ] exactly twosteady-state equilibria exist: one withcredit rationing and one without. Our pre-vious results imply that both steady statesare saddles and hence that both can poten-tially be approached.22 If credit rationingarises, the result will be that the capitalstock is depressed. The capital stock islow, and therefore w(k) must be low rela-tive to (b + ) = k/(1 − ). This forces in-termediaries to ration credit to induce self-selection. Credit rationing can thus arisefor fully endogenous reasons.

Suppose that two intrinsically identi-cal economies23 with ∈[ , ] land in dif-ferent steady states. The economy with alow capital stock will experience credit ra-tioning, while that with a high capitalstock does not. Thus the better-developedeconomy will appear to have a better func-tioning financial system, as in fact it does.However, the inefficient functioning ofcapital markets in the poorer economy is apurely endogenous outcome.

When > holds, z*( )< z( ) holdsas well. Hence Walrasian outcomes are nolonger consistent with self-selection andthey cannot be equilibria. Thus, when

steady-state inflation exceeds a criticallevel ( ) informational frictions must inter-fere with the operation of capital markets.

Since zz*( ) > z( ) for all > , both z( ) and z( ) constitute legitimate equilib-ria with credit rationing. For ∈( , ˆ ),there are thus again two steady-state equi-libria. Our previous results indicate thatone is a sink and one a saddle; hence bothcan potentially be approached. In the high-(low-) capital-stock steady state, credit ra-tioning appears to be less (more) severe.

To summarize, in this case for ∈( , ˆ) potentially two steady-state

equilibria exist. In one credit market fric-tions are relatively severe; in the otherthey are less so.

We have thus far not insisted that asteady-state equilibrium have a positivelevel of real balances. Keeping this condi-tion in mind, we present our fifth result.

RESULT 5. Suppose thatA( ) > 1 holds. Thenany steady state has positive real balances.

Result 5 is proved in the Appendix.24

In this case, then, the steady-stateequilibrium correspondence is given bythe solid locus in Figure 4b. For ≤ ,the steady-state equilibrium value of z,and hence of k, increases with . Thus, forlow initial rates of inflation, increases in result in higher steady-state capital stocksand output levels (unless increases in re-sult in a shift from a Walrasian equilib-rium to an equilibrium with credit ra-tioning). However, for > , equilibrialying along the upper branch of this locuswill have z (and hence k) decreasing as increases. Thus, at high initial inflationrates, increases in can reduce long-runoutput levels. This situation is very consis-tent with the empirical evidence reviewedin the introduction.25

Case 2. (Figure 5a).In this case z*( ) and z( ) (generi-

cally) have two intersections, as they didpreviously. In addition, for < there areno steady-state equilibria, as in Case 1.Similarly, for ∈[ , ] there are two

20 Equation 32 holds if and only ifequation A19 holds, as estab-lished in the Appendix sectionon the existence of steady-stateequilibria. Thus A19 gives aprimitive condition under whichCase 1 obtains.

21 The Appendix section that cov-ers Result 6 proves that thereare at most two intersectionsand that there are exactly twointersections in this particularcase.

22 The existence of two saddles ispossible because dynamicalequilibria follow different laws ofmotion depending on whether aWalrasian regime or a regime ofcredit rationing pertains.

23 Except, possibly, for their initialcapital stocks.

24 Strictly speaking, in any steadystate with credit rationing, it isnecessary that intermediariesperceive no arbitrage opportuni-ties associated with “pooling”type 2 and dissembling type 1agents (see footnote 11). The Appendix establishes thatintermediaries perceive no such incentive, for any value of ∈[ , ], so long as

l x ≤ 2 and 2 ≥(1 − λ) ˆ 2 both are satisfied.

25 For both outcomes to be consis-tent with positive levels of realbalances, it is necessary that

holds. TheAppendix establishes that

holds if either equations A27 or A28and A29 are satisfied.

MAY/ JU N E 1 9 9 6


21

steady-state equilibria, just as in Case 1.However, here for ∈[ , ˆ ],z( ) z*( )holds, so that neither the Walrasian northe credit rationing allocations are legiti-mate steady states. Hence steady-stateequilibria exist if and only if ∈[ , ].

The steady-state equilibrium corre-spondence for Case 2 is depicted in Figure5b. In this case no branch of the corre-spondence exists for which z (and k) aredecreasing in . Thus this case cannot eas-ily capture the empirical observations citedin the introduction.

Case 3.Here holds for all . It

follows that there are no steady-state equi-libria for any value of .

DiscussionOf the various possible configurations

of the steady-state equilibrium correspon-dence, only that in Case 1 seems like itcan easily confront empirical findings likethose of Bullard and Keating (forthcom-ing) and Bruno and Easterly (1995). Wetherefore regard this as the most interest-ing case and explore it somewhat further.

As shown in Result 3, some criticalvalue ( c) of the money growth rate exists,with c< ˆ such thatforall max {

_, c},

equilibrium paths approaching the high-capital-stock steady state necessarily dis-play endogenous oscillation. Then, in par-

ticular, if (see the Appen-dix), there are three distinct possibilities:

• [max { , (1- )/ x },_

]. H e re onesteady-state equilibrium exists with creditrationing and one exists without. Paths approaching both steady states do so monotonically. Increases in (within thisinterval) raise the capital stock in eachsteady state.26

• 27 Here there are twosteady-state equilibria, each displayingcredit rationing. Dynamical equilibriumpaths approaching each steady state may doso monotonically. In the higher of the steadystates, increases in the steady-state inflationrate are detrimental to capital formation andthe long-run level of real activity.

• Here there continue to betwo steady-state equilibria with credit ra-tioning Now equilibrium pathsapproaching the high-capital-stock steadystate necessarily display endogenous fluc-tuations. This is the price paid for avoid-ing convergence to the low-capital-stocksteady state. Moreover, if low levels of realactivity are to be avoided, high rates ofmoney growth induce volatility in all eco-nomic variables, including the inflationrate. High rates of inflation are then asso-ciated with variable rates of inflation.

An ExampleWe now present a set of parameter val-

ues satisfying equations a4, A19 (implying

26 However, increases in canstill result in a reduction in thesteady-state capital stock ifthey induce transitions from theWalrasian to the credit rationingregime. The current analysisprovides no guidance as towhen such transitions might ormight not occur.

27 Obviously we are assuminghere that

MAY/ JU N E 1 9 9 6


22

Figure 5a

Multiple Steady States

a −1/ −

z*( )

Figure 5b

a−1/ −

The Steady-State EquilibriumCorrespondence (Case 2)

zz ( )

z*( )

zz ( )

zz (σ), z*( )zz (σ), z*( )

that we have a Case 1 economy), A24′,A26′ (implying that intermediaries haveno incentive to pool different agent typesin any steady-state equilibrium), and A27[implying that (1- )/ x <

_]. One set of

parameter values satisfying these condi-tions is given by ˆ =2, = −1, x = 1/32, =63/64, and a = 1/16. For these parametervalues, equation a3 reduces to ∈ (0.508,2). These parameter values imply, paren-thetically, that the government can allowthe money supply to grow as rapidly as100 percent per period, or could contractthe money supply by as much as 49 per-cent per period. They also imply an empir-ically plausible elasticity of substitutionbetween capital and labor of 0.5. It is alsoeasy to check that, for all > (1 − )/ x,the high-capital-stock steady state has

labor’s share exceeding capital’s share, as istrue empirically.

SOME EMPIRICAL EVIDENCE

The theoretical analysis of the previ-ous sections yields several predictions thatcan be tested empirically.

1. Increases in the steady-state rateof inflation reduce the real returns in-vestors receive.

2. Such increases can lead to greaterinflation variability and also to greatervariability in the returns on all assets.

3. Higher long-run rates of inflationraise steady-state output levels foreconomies whose rate of inflation is ini-tially low enough.28 For economies withinitially high rates of inflation ( ≥ ) fur-ther increases in inflation must reducelong-run output levels, unless the econ-omy is in a development trap.

4. When higher inflation is detri-mental to long-run output levels, inflationadversely affects the level of activity in fi-nancial markets.

As we have noted, many of these re-sults are empirically well-supported in theexisting literature. For example, it is well-known that higher rates of inflation aretypically accompanied by greater inflationvariability, as shown in Friedman (1992).Similarly, the third implication listed aboveis consistent with the empirical evidencepresented by Bullard and Keating (forth-coming) and Bruno and Easterly (1995),which we summarized in the introduction.We now address evidence for the remain-ing propositions.

Table 1 presents the results of four re-gressions using stock market data for theUnited States over the period 1958–93.29

The dependent variables are the growthrate of the real value of transactions on theNew York Stock Exchange (RV); real re-turns on the Standard & Poor’s 500 Index,inclusive of dividends (RR); nominal re-turns on the Standard & Poor’s Index, in-clusive of dividends (NR); and the stan-dard deviation of daily returns on theStandard & Poor’s Index (V). The explana-

28 As we have seen, this is truealong either branch of thesteady-state equilibrium corre-spondence if The state-ment in the text does requiresome qualification, though. Inparticular, as noted above, ifhigher inflation causes theeconomy to shift from the Wal-rasian to the credit rationedequilibrium for then anincrease in the inflation rate cancause long-run output to fall.

29 Data sources are listed in theAppendix.

MAY/ JU N E 1 9 9 6


23

Regressions from Stock Market Data*:United States

(1)RVt

† = .00 + .01 V(t) + 2.9 GIP(t) – .05 INF(t)(.01)(.003)‡ (3.8) (.02)‡

R2 = .03, DW = 1.97, Q(60) = 77.7

(2)RRt = –.01 – .01 RR(t–1) – .35 V(t) + .10 RRAT(t) – 2.9 INF(t)

(.20)(.05) (.10)‡ (.12) (1.1)‡

R2 = .09, Q(60) = 56.2

(3)NRt = –.01 – .01 NR(t–1) – .34 V(t) + .10 RRAT(t) – 1.9 INF(t)

(.20) (.05) (.10)‡ (.13) (1.1)‡

R2 = .06, Q(60) = 56.4

(4)Vt = .01 + .19 RRAT(t) – 2.87 GIP(t) + 2.26 INF(t)

(.1) (.08)‡ (37.6) (.73)‡

R2 = .02, DW = 1.99, Q(60) = 71.5

Table 1

* Monthly, 1958-93.

† Denotes that a Cochrane-Orcutt procedure has been employed.

‡ Denotes significance at the 5 percent level or higher.

Standard errors are in parentheses.

DW: Durbin-Watson statistic

Q: Ljung-Box Q statistic

tory variable of interest is the rate of infla-tion in the Consumer Price Index (INF).Other explanatory variables are also em-ployed. However, the results appear to bequite robust to the inclusion of other ex-planatory variables. These regressions wereselected as being representative of a much

larger set that we estimated. Finally, alldata are reported as deviations from theirsample means,30 and pass standard station-arity tests in that form. In some regres-sions we corrected for serial correlationusing a Cochrane-Orcutt procedure.

As is apparent from Table 1, higher ratesof inflation significantly reduce the growthrate of stock market transactions. As pre-dicted by theory, higher inflation thus atten-uates financial market activity. In addition,as the inflation rate rises, the real return re-ceived by investors falls significantly.31 In-deed, over this time period even nominal re-turns to investors appear to be negativelyassociated with inflation. Finally, higher in-flation increases the volatility of stock re-turns. All of these results are consistent withthe predictions of our model.

Figure 6 depicts the ratio of the value ofstock market transactions (on the New YorkStock Exchange) to gross domestic product(GDP), plotted against the rate of inflation.Apparently, higher inflation rates also tendto reduce the level of financial market activ-ity using this particular measure.

30 We also ran the regressions re-ported without removing thesample means. This led to no dif-ferences in results.

MAY/ JU N E 1 9 9 6


24

Regressions from Stock Market Data*:C h i l e

(1)RVt = .00 + .75 GIP(t) – .30 INF(t)

(.02) (.20)† (1.5)R2 = .10, DW = 2.24, Q(33) = 25.5

(2)RRt = .00 + .22 RR(t–1) – .02 RRAT(t) – 2.56 INF(t)

(.01) (.08)† (.007)† (.68)†

R2 = .19, Q(33) = 19.9

(3)NRt = .00 + .17 NR(t–1) – .02 RRAT(t) – 1.30 INF(t)

(.01)(.09)† (.007)† (.66)†

R2 = .09, Q(33) = 19.7

Table 2

* Monthly, 1981-91.

† Denotes significance at the 5 percent level or higher.




Figure 6

Ratio of the Value of Stock Market Transactions to GDP:United States

Total Value of Shares Traded/GDP

4.5

4.0

3.5

3.0

2.5

1.0

0.5

1.5

2.0

0.0 2.5 5.0 7.5 10.0 12.5 15.0

Inflation (%)

Figure 7

Ratio of the Value of Stock Market Transactions to GDP:Chile


0.10

0.09

0.08

0.07

0.06

0.03

0.02

0.01

0.04

0.05

8.0 12.0 16.0 20.0 24.0 28.0 32.0

Inflation (%)

Table 2 reports the results of estimat-ing similar regressions using stock marketdata from Chile. Here RV represents thegrowth rate of the real value of stock

market transactions on the Santiago StockExchange, and RRAT is the real interestrate on 30–89 day bank deposits. A lackof daily data prevents us from examiningthe volatility of stock market returns. Asin the case of the United States, we seethat higher rates of inflation significantlyreduce investors’ real and nominal rates of return on the stock exchange. Thepoint estimate suggests that higher infla-tion also depresses the growth rate ofmarket transactions, although here the

31 Boudoukh and Richardson(1993), using a much longertime series, also find that higherrates of inflation have reducedreal stock market returns in theUnited States and in the UnitedKingdom.

MAY/ JU N E 1 9 9 6


25

Regressions from Stock Market Data*:K o r e aA. 1982-87

(1)RVt = .01 + .12 V(t) – .008 GIP(t) – .12 INF(t)

(.05)(.13) (.008) (.1)R2 = .04, DW = 2.3, Q(24) = 33.2

(2)RRt = .00 – .17 RR(t–1) + .25 V(t) – 1.69 RRAT(t) – 2.32 INF(t)

(.72)(.12) (1.9) (4.50) (4.50)R2 = .03, Q(24) = 17.6

(3)Vt

† = .04 + .29 RRAT(t) – .01 GIP(t) – .11 INF(t)(.11) (.42) (.005)‡ (.42)

R2 = .39, DW = 2.34, Q(24) = 15.6

B. 1988-94

(1)RVt = .00 + .34 V(t) + .02 GIP(t) – .28 INF(t)

(.07)(.16)‡ (.01)‡ (.13)‡

R2 = .11, DW = 2.15, Q(27) = 29.4

(2)RRt = –.19 – .18 RR(t–1) + 1.9 V(t) – 6.5 RRAT(t) – 9.77 INF(t)

(.77)(.11) (1.74) (3.55)‡ (3.86)‡

R2 = .11, Q(27) = 34.8

(3)NRt = –.23 – .23 NR(t–1) + 2.5 V(t) – 5.43 RRAT(t) – 7.11 INF(t)

(.73)(.11)‡ (1.72) (3.36) (3.63)‡

R2 = .10, Q(27) = 32.1

(4)Vt

† = –.01 + .33 RRAT(t) – .01 GIP(t) + .40 INF(t)(.04) (.36) (.006)‡ (.38)

R2 = .08, DW = 1.95, Q(24) = 33.0

Table 3

* Monthly.

† Denotes that a Cochrane-Orcutt procedure has been employed.

‡ Denotes significance at the 5 percent level or higher.




Regressions from Stock Market Data*:Ta i w a nA. 1983-88

(1)RVt = −.02 + 1.1 GIP(t) + 9.1 INF(t)

(.05) (.52)† (6.5)R2 = .08, DW = 1.8, Q(24) = 13.4


(.02)(.13)† (.01) (8.5)R2 = .18, Q(24) = 19.6

B. 1988-94

(1)RVt

‡ = –.03 + .5 GIP(t) – 7.1 INF(t)(.05)(.50) (4.0)†

R2 = .11, DW = 1.88, Q(21) = 14.1


(.01)(.11)† (.01) (10.1)†

R2 = .21, Q(24) = 26.8

(3)NRt = .00 + .35 NR(t–1) – .01 RRAT(t) – 17.8 INF(t)

(.01) (.11)† (.01) (10.1)†

R2 = .17, Q(24) = 25.4

Table 4

* Monthly.

† Denotes significance at the 5 percent level or higher.

‡ Denotes that a Cochrane-Orcutt procedure has been employed.




point estimate is not significantly differentfrom zero.

Figure 7 depicts the ratio of the valueof stock market transactions to GDP forChile, plotted against its rate of inflation.Again we perceive a negative relationship,particularly if the one single-digit inflation

year (1982) is excluded as an outlier.Tables 3 and 4 report analogous regres-

sion results for Korea and Taiwan. Here weproceed somewhat differently, since bothKorea and Taiwan experienced fairly pro-nounced jumps in their rates of inflation in1988 and 1989, respectively. In particular,in Korea the average monthly inflation ratewas 0.27 percent over the period 1982–87,while from 1988–94 it was 0.54 percent. InTaiwan, the average monthly rate of infla-tion over the period 1983–88 was 0.07 per-cent, but jumped to 0.33 percent from1989–93. These increases are apparent inFigures 8 and 9, respectively.

In view of these marked changes inthe inflation rate, we proceeded as follows.For each country we divided the sampleand ran regressions analogous to those re-ported above. For Korea the results are re-ported in Table 3. Over the low inflationperiod (1982–87), inflation has no signifi-cant effects on the real return on equity, itsvolatility, or on the growth rate of stockmarket transactions. However, during theperiod of higher inflation, increases in therate of inflation lead to statistically signifi-cant reductions in the growth rate oftransactions and the real and nominal re-turn on equity. With respect to the volatil-ity of market returns, our point estimatesagain suggest that inflation leads to highervolatility, but the inflation coefficient isnot significantly different from zero.

Figure 8 represents Korea’s ratio of thevalue of stock market transactions to GDPand its rate of inflation. Clearly, in thehigher inflation period of 1988–93, thenegative relationship between market ac-tivity and the rate of inflation is highlypronounced. This is not the case for thelow-inflation period 1982–87. Here thenwe see some evidence for threshold effects:Inflation seems to have significant adverseconsequences only after it exceeds somecritical level.

Table 4 repeats the same regressionprocedure for Taiwan, but lack of dailydata prevents us from constructing avolatility of returns measure. Here we see asimilar pattern to that for Korea. Duringthe period of low inflation (1983–88), the

MAY/ JU N E 1 9 9 6


26

Figure 8

Ratio of the Value of Stock Market Transactions to GDP: Korea


0.8

0.6

0.5

0.4

0.3

0.0

0.1

0.2

2 4 6 8 10Inflation (%)

0.7

Figure 9

Ratio of the Value of Stock Market Transactions to GDP: Taiwan


7

6

5

4

3

1

0

2

-1 0 1 2 3 4 5Inflation (%)

effect of inflation on the growth rate ofreal stock market activity is insignificantand similarly for the real returns on equity.However, in the period of high inflation,both the growth rate of real equity marketactivity and the real returns on equitywere adversely effected by inflation in astatistically significant way. Nominal eq-uity returns are negatively associated withinflation, with a t-value of about 1.6. Herewe see further evidence that inflation maybe detrimental only after it exceeds somethreshold level.

Figure 9 displays Taiwan’s value ofstock market transactions to GDP ratio, aswell as its inflation rate. Clearly, this mea-sure does not suggest that inflation hasbeen detrimental to the level of equitymarket activity.

Table 5 shows simple correlations ofthe financial variables with the inflationrate for each of the countries and subperi-ods. These results are quite consistent withthe regression results. On the whole, thisempirical evidence seems to support ourmodel’s predictions. We have even seen ev-idence that inflation’s adverse conse-quences may only be observed if the rateof inflation is sufficiently high.

CONCLUSIONSBoth our theoretical analysis and our

empirical evidence indicate that higher rates

of inflation tend to reduce the real rates ofreturn received by savers in a variety of mar-kets.32 When credit is rationed, this reduc-tion in returns worsens informational fric-tions that interfere with the operation of thefinancial system. Once inflation exceeds acertain critical rate, a potential consequenceis that the financial system provides less in-vestment capital, resulting in reduced capi-tal formation and long-run levels of real ac-tivity. Such forces need not operate at lowrates of inflation, providing an explanationof why the consequences of higher inflationseem to be so much more severe once infla-tion exceeds some threshold level.

In addition, high enough rates of infla-tion force endogenously arising economicvolatility to be observed. Thus, as we ob-serve, high inflation induces inflation vari-ability and variability in rates of return onall savings instruments. Theory predictsthat this volatility should be transmitted toreal activity as well.

Obviously, these results have been ob-tained in the context of a highly stylizedand simplified model of the financial sys-tem. How general are they? We believethey are quite general. Boyd and Smith(forthcoming) produce a model of a finan-cial system that is subject to a costly stateverification problem, one where investorsprovide some internal financing of theirown investment projects. Again, two mon-etary steady-state equilibria exist and both

32 Further evidence on this pointappears in Boyd, Levine, andSmith (1995).

MAY/ JU N E 1 9 9 6


27

Comparisons Across Countries: Simple Correlations of Market andMacrovariables with the Inflation Rate (INF)

Country/PeriodU.S. Chile Korea* Korea† Taiwan‡ Taiwan§

Variable 1958-93 1981-91 1982-87 1988-94 1983-88 1989-93

RV –.06 –.02 –.12 –.19 –.12 –.20RR –.25 –.15 –.06 –.20 –.12 –.23V –.05 — –.09 –.12 — —GIP –.02 –.10 –.14 –.03 –.12 –.24RRAT –.70 –.67 –.95 –.91 –.99 –.99

Table 5

* Average monthly inflation rate 0.27 percent.† Average monthly inflation rate 0.54 percent.

‡ Average monthly inflation rate 0.07 percent.§ Average monthly inflation rate 0.33 percent.

can potentially be approached. Thus devel-opment trap phenomena arise. In thesteady state with higher levels of real ac-tivity, higher inflation interferes with theprovision of internal finance, thereby exac-erbating the costly state verification prob-lem. As a result, greater inflation reducesthe long-run level of real activity, the levelof financial market activity, and real re-turns to savers. Moreover, as is the casehere, high enough rates of inflation forceendogenously generated economic volatil -ity to emerge. And, interestingly, Boyd andSmith (forthcoming) obtain a result that isnot available here: Once inflation exceedsa critical level, it is possible that only thelow-activity steady state can be ap-proached. Inflation rates exceeding thislevel can then force the kinds of crises dis-cussed by Bruno and Easterly (1995). Re-lated results are obtained by Schreft andSmith (forthcoming and 1994) in modelswhere financial market frictions take theform of limited communication, as inTownsend (1987) and Champ, Smith, andWilliamson (forthcoming).

A shortcoming of all of the modelsmentioned—including ours—is that theydo not give rise to distinct and/or interest-ing roles for debt and equity markets. Em-pirical evidence suggests that both kindsof markets are adversely affected by highinflation.33 This is a natural topic for fu-ture investigation.

REFERENCESAzariadis, Costas. Intertemporal Macroeconomics. Oxford: Basil

Blackwell, 1993.

_____ and Allan Drazen. “Threshold Externalities in Economic Develop-ment,” Quarterly Journal of Economics (May 1990), pp. 501–26.

_____ and Bruce D. Smith. “Private Information, Money and Growth:Indeterminacy, Fluctuations, and the Mundell-Tobin Effect,” Journal ofEconomic Growth (forthcoming).

Bencivenga, Valerie R., and Bruce D. Smith. “Some Consequences of Credit Rationing in an Endogenous Growth Model,” Journal of Economic Dynamics and Control (January-March 1993), pp. 97–122.

Boot, Arnoud W. A., and Anjan V. Thakor. “Security Design,” Journal ofFinance (September 1993), pp. 1,349–78.

Boudoukh, Jacob, and Matthew Richardson. “Stock Returns and Inflation:A Long-Horizon Perspective,” American Economic Review (December1993), pp. 1,346–55.

Boyd, John H.; Ross Levine; and Bruce D. Smith. “Inflation and Finan-cial Market Performance.” Manuscript. Federal Reserve Bank of Minneapolis, 1995.

_____ and Smith, Bruce D. “Capital Market Imperfections in a Mone-tary Growth Model.” Economic Theory (forthcoming).

_____ and _____. “The Evolution of Debt and Equity Markets inEconomic Development.” Manuscript. Federal Reserve Bank of Minneapolis, 1995a.

_____ and _____. “The Use of Debt and Equity in Optimal Finan-cial Contracts.” Manuscript. Federal Reserve Bank of Minneapolis,1995b.

Bruno, Michael, and William Easterly. “Inflation Crises and Long-RunGrowth.” Manuscript. The World Bank, 1995.

Bullard, James, and John Keating. “The Long-Run Relationship BetweenInflation and Output in Postwar Economics,” Journal of Monetary Eco -nomics (forthcoming).

Champ, Bruce; Bruce D. Smith; and Stephen D. Williamson. “CurrencyElasticity and Banking Panics: Theory and Evidence,” Canadian Journalof Economics (forthcoming).

Chang, Chun. “Capital Structure as Optimal Contracts.” Manuscript. University of Minnesota, 1986.

Dewatripont, Mathias, and Jean Tirole. “A Theory of Debt and Equity: Di-versity of Securities and Manager-Shareholder Congruence,” QuarterlyJournal of Economics (November 1994), pp. 1,027–54.

Diamond, Peter A. “National Debt in a Neoclassical Growth Model,”American Economic Review (December 1965), pp. 1,126–50.

Friedman, Milton. Money Mischief: Episodes in Monetary History. Harcourt-Brace-Jovanovich, 1992.

Labadie, Pamela. “Financial Intermediation and Monetary Policy in aGeneral Equilibrium Banking Model,” Journal of Money, Credit andBanking (November 1995), pp. 1,290–1,315.

Mundell, Robert. “Growth, Stability, and Inflationary Finance,” Journal ofPolitical Economy (April 1965), pp. 97–109.

Rothschild, Michael, and Joseph Stiglitz. “Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Informa-tion,” Quarterly Journal of Economics (November 1976), pp. 629–650.

Schreft, Stacey L., and Bruce D. Smith. “The Effects of Open Market Op-erations in a Model of Intermediation and Growth.” Manuscript. CornellUniversity, 1994.

_____ and _____. “Money, Banking, and Capital Formation,” Jour -nal of Economic Theory (forthcoming).

Shell, Karl; Miguel Sidrauski; and Joseph Stiglitz. “Capital Gains, Income, and Saving,” Review of Economic Studies (January 1969), pp. 15–26.

33 See Boyd, Levine, and Smith(1995).

MAY/ JU N E 1 9 9 6


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Sidrauski, Miguel. “Inflation and Economic Growth,” Journal of PoliticalEconomy (December 1967), pp. 796–810.

Stiglitz, Joseph, and Andrew Weiss. “Credit Rationing in Markets with Imperfect Information,” American Economic Review (June 1981), pp. 393–410.

Tirole, Jean. “Asset Bubbles and Overlapping Generations,” Econometrica(November 1985), pp. 1,499–1,528.

Tobin, James. “Money and Economic Growth,” Econometrica (October1965), pp. 671–84.

Townsend, Robert M. “Economic Organization with Limited Communica-tion,” American Economic Review (December 1987), pp. 954–71.

Williamson, Stephen D. “Costly Monitoring, Financial Intermediation, andEquilibrium Credit Rationing,” Journal of Monetary Economics (Septem-ber 1986), pp. 159–79.

_____. “Costly Monitoring, Loan Contracts, and Equilibrium Credit Rationing,” Quarterly Journal of Economics (February 1987), pp. 135–45.

MAY/ JU N E 1 9 9 6


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MAY/ JU N E 1 9 9 6


30

PROOF OF RESULT 1It will be useful to begin by describing

some properties of the function H(z) ≡z(1+z)(1− )/ . Clearly, H(0) = 0, and

(A1) lim H(z) = 0z ∞

is established by an application of L’Hopital’srule. Moreover, clearly,

(A2) z H (z) /H(z) = 1 + [(1 − ) / ] [z/ ( 1+z)].

Thus H (z) ≥ (<) 0 holds if and only if z ≥ (<) − .

It follows from these observations that equation 22 has a solution if and onlyif equation 26 holds. This is readily verifiedto be equivalent to ≥ ˆ ,with ˆ defined byequation 25.

When equation 22 has a solution, the as-sociated value of k can be obtained fro mequation 19. Equation 23 then produces m.E v i d e n t l y, m is positive if and only if A( ) > 1 .

PROOF OF RESULT 2

Using equation 14 to replace kt+1 inequation 16 gives the relation

(A3) mt 1 = A( )m t [x /(1 )]m t2 / w(kt).

Equations 14 and A3 govern the evolutionof the sequence {kt,mt}. Near a steady statethis evolution is described by a linear ap-proximation of these two equations. Letting(k,m) denote any pair of steady-state equi-librium values for the capital-labor ratio andreal balances, this linear approximation isgiven by (kt+1−k,mt+1−m)′= J(kt−k,mt−m)′,where J is the Jacobian matrix

λw′(k) 1 /J

[(1 −λ)/x][A( 1]2w′(k) 2 A(

Let T( ) and D( ) denote the trace and de-terminant, respectively, of J, where we ex-plicitly denote their dependence on .

It is well-known from Azariadis (1993,chapter 6.4) that a steady state is a saddleif T( ) > 1 + D( ). A steady state is a sinkif |D( )| < 1 and 1 D( ) < T( ) < 1 +D( ).

We now state the following prelimi-nary result.

LEMMA 1. At the low (high) capital stocksteady state, D( ) > (<) 1 holds.

Proof. It is straightforward to show that

(A4) D( ) = (1 − )/[1 z( )].

Since z( ) − [z( ) > − ],D( )>(<)1 holds at the low- (high-) capital-stocksteady state.

It is now possible to demonstrate thefollowing.

LEMMA 2. At the low- (high-) capital-stocksteady state, T( ) > (<) 1 + D( ) holds.

Proof. As is readily verified,

(A5) T( ) = 2 − A( ) + A( )D( ).

Thus T( ) > (<) 1 + D( ) holds if andonly if

(A6) [A( ) − 1]D( ) > (<) [A( ) − 1].

A( ) > 1 and Lemma 1 implies that > (<) holds at the low- (high-) capital-stock steady state.

Lemma 2 implies that the low-capital-stock steady state is a saddle. Paths ap-proaching it necessarily do so monoton-ically if T( ) > 0 at that steady state. ButT( ) > 0 follows from equation A5 andLemma1. Thus Result 2(a) is established.

Lemmas 1 and 2 also imply that thehigh-capital-stock steady state is a sink if

(A7) T( ) > −1 − D( )

holds at that steady state. By equation A5,equation A7 is equivalent to

Appendix

MAY/ JU N E 1 9 9 6


31

(A7′) D( ) > [A( ) − 3]/[A( ) + 1].

Equation A4 implies that equation A7′necessarily holds if 3 ≥ A( ), which in turnis implied by 3 ≥ A( ˆ ) The high-capital-stock steady state is thus a sink, if ˆ is nottoo large.

PROOF OF RESULT 3

It is well-known that paths approach-ing a steady state do so nonmonotonicallyif T( )2 < 4D( ) holds, as in Azariadis(1993, chapter 6.4). We first establish thefollowing.

LEMMA 3. T( ) > 0 holds if is sufficientlyclose to ˆ .

Proof. From equation A5, T( ) > 0 holds if

(A8) 2 > A( )[1 − D( )]

where at the high-capital-stock steady state

(A9) D( ) = (1 − ) / [1 z( )].

Thus

It follows that equation A8 necessarilyholds for large enough values of .

Lemma 3 implies that T( )2 < 4D( )holds for large enough if and only if

(A10) T( ) 2 D( ).

Substituting equation A5 into equation A10and rearranging terms yields the equivalentcondition

(Α10′) 2[1 D( )]

Α( )[1 D( )][1 D( )]

or, since D( ) < 1,

(A11) [2 A( )] / A( )< D( ).

We now show that equation A11 holds for

= ˆ and hence by continuity, that it holdsfor sufficiently near ˆ . In particular,

{2−[x / (1 − )] ˆ }/[x / (1 − ) ˆ ]

while

Thus equation A11 holds for near ˆ if

(A12) 2 [x / (1 − )] ˆ < [x / (1 − )] ˆ .

But equation A12 is implied by A( ˆ )>1.This establishes the result.

PROOF OF RESULT 4

z( ) and z( ) both satisfy

H(z) = a 1/ [x /(1 − )].

Thus z*( ) satisfies equation 30 if andonly if holds. As is ap-parent from Figure1, this will be the caseif and only if

RESULT 6

z*( ) intersects z( ) at most twice.

Proof. z*( ) satisfies

(A13) [1 + z*( )](1− )/ ≡ a−1/ / .

Multiplying both sides of equation A13 byz*( ) gives the equivalent condition

(A13′) H[z*( )] = a−1/ z*( )/ .

Moreover, whenever z*( ) = z( ), we have

(A14) H[z*( )] = H[z( )]

≡ a 1/ [x / (1 − )].

Equations A13′ and A14 imply that z*( ) = z( ) if and only if

Appendix

MAY/ JU N E 1 9 9 6


32

(A15) z*( ) = [x/(1 − )] 2.

Equation A15 is readily shown to beequivalent to the condition

(A15′) a−1/(1− ) = /(1− ) + [x/(1− )] (2− )/(1− )

≡ Q( ).

The function Q( ) is depicted in theFigure. It is readily demonstrated that Q(a−1/ ) > a−1/(1− ) and that Q′( ) ≥ 0 holdsif and only if

(A16) ≥ [− (1− )/x(2− )]0.5.

There are therefore three possibilities.

Case 1.Suppose that

(A17) a 1/ < [− (1 − )/x(2 − )]0.5

and that

(A18) Q{[− (1 − )/x(2 − )]0.5} < a−1/(1− ).

Then equation A15′ has exactly two solutions, as shown in the Figure. It fol-lows that z*( ) intersects z( ) exactlytwice.

Case 2.Suppose that equation A17 holds but

that equation A18 fails. Then there is atmost one intersection of z*( ) and z( ), as shown in the Figure.

Case 3.Suppose that equation A17 fails. Then

Q ( ) ≥ 0 holds for all ≥ a 1/ . There are nointersections of z*( ) and z( ), as the Figureshows.

These three cases exhaust the set ofpossibilities and establish the result.

EXISTENCE OF STEADY-STATE EQUILIBRIA

Result 6 implies that steady-state equi-libria exist, in general, if and only if sat-isfies equation a3 and equations A17 andA18 hold. It will be useful to have a suffi-cient condition implying that equationsA17 and A18 are satisfied. From Figure 4a,

Appendix

Case 1

Q ( )

a −1/

Q ( )

a −1/(1− )

Case 2

Q ( )

a −1/

Q ( )

a −1/(1− )

Case 3

Q ( )

a −1/

Q ( )

a −1/(1− )

MAY/ JU N E 1 9 9 6


33

it is apparent that z*( ) intersects z( ) if z* ( ˆ ) >− . We now describe whenthis condition holds.

RESULT 7. z*( ˆ ) >− holds if and only if

(A19) ˆ >[− (1 − )/x]0.5.

Proof. Equations 20 and 25 imply thatz*( ) > − holds if and only if

(A20) (a 1/ )2[x/(1 − )]< − [(1− )(1 )/ ]2.

Equation A20 is easily shown to be equiv-alent to equation A19.

Thus equation A19 implies the existenceof multiple steady states for all satisfyingequation a3.

PROOF OF RESULT 5

This result has already been estab-lished when credit rationing obtains. Thuswe must establish that m > 0 holds at theWalrasian steady state. From equation 18,in a Walrasian steady state

(A21) m = k{ [w(k)/k] − 1}.

Since z*( )∈[z( ),z( )], we also havethat w(k)/k ≥ x /(1 − ). Hence A( ) > 1implies that m > 0 holds.

IMPOSSIBILITY OF POOLING

Azariadis and Smith (forthcoming)prove that there is never an incentive for an intermediary to pool type 2 anddissembling type 1 agents in a Walrasianequilibrium. They also prove that thereis no such incentive under credit ration-ing if

(A22) 1 ≥ (1 − )f (k)

= (1 − )a1/ [1 + z( )](1 )/

or equivalently, if

(A22′) z( ) ≥ (1 − )a1/ρH[z( )]≡ x 2.

Equation A22′ holds at the high-capital-stock steady state if

(A23) z( )/ 2 ≥ x.

Since the left-hand side of equation A23 is decreasing in , A23 holds for all

≤ ˆ if

(A24) z( ˆ )/x≥ ˆ 2.

or equivalently, if

(A24′) − /x ≥ ˆ 2.

Equation A22′ holds at the low-capital-stock steady state if

(A25) z( )/ 2 ≥ x .

Clearly, a sufficient condition for equationA25 is that

(A26) z( )≥x ˆ 2.

Since z( )=[x /(1 − )] 2 it follows that

(A26′) 2 ≥(1 − ) ˆ 2

is sufficient for equation A22′ to hold at thelow-capital-stock steady state.

To summarize, equation A22′ holds atz( ) and z( ) for all ∈[ , ˆ ]if equationsA24′ and A26′ hold.

RESULT 8if and only if

(A27) ˆ ≥− (1 − )(1 )/ ×

{1 + [(1 − )/x 2]} (1 )/ .

holds if andonly if

Appendix

MAY/ JU N E 1 9 9 6


34

(A28) (1 − )/x < [− (1 − )/x(2 − )]0.5

and

(A29) ˆ ≤− (1 − )(1− )/ ×

{1+[(1− )/x 2]}−(1− )/

Proof. It is easy to verify that (1− )/ x∈[ , ] if and only if

(A30) Q[(1 − )/x ] ≤ a−1/(1− )

holds. Using the definition of Q, it isstraightforward to show that equation A30is equivalent to

(A30′) −a1/ [x/(1− )] (1− )(1− )/

≥ − (1− )(1− )/ ×

{1 + [(1− )/x 2]}−(1− )/ .

But, as is apparent from equation 25, equation A30′ is equivalent to equationA27.

It can be shown that (1− )x ≥holds if and only if Q′[(1−λ)/xλ] < 0 andQ[(1−λ)/xλ] ≥ a−1/(1− ) are satisfied. Theformer condition is equation A28, the lat-ter is equation A29.

DATA SOURCES1. United States

Monthly data are available over theperiod 1958–93.Sources.

RV: Growth rate of real value oftransactions on the New YorkStock Exchange. (New YorkStock Exchange Factbook, vari-ous dates.)

RR: Real returns on the Standard &Poor’s 500 index, inclusive ofdividend yields. (Standard &Poor’s Statistics, SBBI Yearbook,various dates.)

NR: Nominal returns on the Stan-dard & Poor’s 500 index, inclu-sive of dividend yields. (Stan-

dard & Poor’s Statistics, SBBIYearbook, various dates.)

V: Standard deviation of returnson the daily Standard & Poor’sindex. (SBBI Yearbook, variousdates.)

INF: Rate of inflation in the CPI.(Bureau of Labor Statistics.)

GIP: Growth rate of industrial pro-duction index. (Federal Re-serve Industrial Production Indices.)

RRAT: Three-month Treasury bill rate,in real terms. (Federal ReserveBulletin, various dates.)

2. ChileSources.

All data are from the Boletoin mensual(Banco Central de Chile). They are avail-able monthly from 1981–91.

RV: Growth rate of the real value oftransactions on the SantiagoStock Exchange.

RR: Real return to equity, inclusiveof dividend yields.

NR: Nominal returns to equity, in-clusive of dividend yields.

INF: Rate of change in the CPI.RRAT: Real rate of interest on 30- to

89-day bank deposits.

3. KoreaAll monthly data are available from

1982–94.Sources.

RV: Growth rate of the real value oftransactions on the KoreaStock Exchange. (SecuritiesStatistics Monthly, Korea StockExchange, various dates.)

RR: Real returns to equity, inclusiveof dividend yields. (SecuritiesStatistics Monthly, Korea StockExchange, various dates.)

NR: Nominal returns to equity, in-clusive of dividend yields. (Se -curities Statistics Monthly,Korea Stock Exchange, variousdates.)

Appendix

MAY/ JU N E 1 9 9 6


35

V: Standard deviation of daily re-turns. (Securities StatisticsMonthly, Korea Stock Ex-change, various dates.)

INF: Rate of growth of the CPI.(Economic Statistics Yearbook,Bank of Korea, various dates.)

GIP: Growth rate of industrial pro-duction. (Economic StatisticsYearbook, Bank of Korea, vari-ous dates.)

RRAT: Three-month corporate billrate, in real terms.

4. TaiwanAll data are available monthly from

1983–93.

Sources.RV: Growth rate of the real value of

stock transactions in the Tai-wan area. (Financial StatisticsMonthly, Central Bank ofChina, various dates.)

RR: Real returns, inclusive of divi-dend yields. (Financial Statis -tics Monthly, Central Bank ofChina, various dates.)

NR: Nominal returns, inclusive ofdividend yields. (Financial Sta -tistics Monthly, Central Bank ofChina, various dates.)

INF: Growth rate of CPI. (MonthlyStatistics of the Republic ofChina, Central Bank of China,various dates.)

Appendix

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