M AY / J U N E 1 9 9 6
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 thank Satyajit Chatterjee; Pamela Labadie; and the participants of seminars at the University of Texas, the Federal Reserve Bank of Dallas, and the World Bank for helpful comments on an earlier draft of this article. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. in the rate of inflation raises the long-run Inflation, level of real activity for economies whose initial rate of inflation is relatively low. For Financial economies experiencing moderate initial rates of inflation, the same kind of change Markets, in inflation seems to have no significant effect on long-run real activity. However, and Capital for economies whose initial inflation rates are fairly high, further increases in infla- Formation tion significantly reduce the long-run level of output. Any successful theory of how Sangmok Choi, Bruce D. inflation affects real activity must account Smith, and John H. Boyd for these nonmonotonicities. Along the same lines, Bruno and consensus among economists seems Easterly (1995) demonstrate that a num- to be that high rates of inflation ber of economies have experienced sus- A cause “problems,” not just for some tained inflations of 20 percent to 30 per- individuals, but for aggregate economic cent without suffering any apparently performance. There is much less agree- major adverse consequences. However, ment about what these problems are and once the rate of inflation exceeds some how they arise. We propose to explain critical level (which Bruno and Easterly how inflation adversely affects an economy estimate to be about 40 percent), signifi- by arguing that high inflation rates tend to cant declines occur in the level of real ac- exacerbate a number of financial market tivity. This seems consistent with the re- frictions. In doing so, inflation interferes sults of Bullard and Keating. with the provision of investment capital, Evidence is also accumulating that in- as well as its allocation.1 Such interference flation adversely affects the allocative func- is then detrimental to long-run capital for- tion of capital markets, depressing the level mation and to real activity. Moreover, high of activity in those markets and reducing enough rates of inflation are typically ac- investors’ rates of return. Again, however, companied by highly variable inflation and these effects seem highly nonlinear. In a by variability in rates of return to saving cross-sectional analysis, for example, Boyd, on all kinds of financial instruments. We Levine, and Smith (1995) divide countries argue that, by exacerbating various finan- into quartiles according to their average cial market frictions, high enough rates of rates of inflation. The lowest inflation inflation force investors’ returns to display quartile has the highest level of financial this kind of variability. It seems difficult market activity, and the highest inflation then to prevent the resulting variability in quartile has the lowest level of financial returns from being transmitted into real market activity. However, the two middle activity. quartiles display only very minor differ- Unfortunately, for our understanding ences. Thus for the financial system, as for 1 of these phenomena, the effects of perma- real activity, there seem to be threshold ef- This explanation has been artic- ulated in a number of recent nent increases in the inflation rate for fects associated with the inflation rate. papers. See, for example, long-run activity seem to be quite compli- Moreover, as we will show, high rates Azariadis and Smith (forthcom- cated and to depend strongly on the initial of inflation tend to depress the real returns ing), Boyd and Smith (forth- level of the inflation rate. For example, equity-holders receive and to increase coming), and Schreft and Bullard and Keating (forthcoming) find their variability. In Korea and Taiwan, Smith (forthcoming and that a permanent, policy-induced increase there were fairly pronounced jumps in the 1994).
F E D E R A L R E S E RV E B A N K O F ST. L O U I S MAY / J U N E 1 9 9 6
rate of inflation in 1988 and 1989, respec- lower rates of interest and therefore must tively. In each country, before those dates, do something to keep them from seeking inflation’s effects on rates of return to eq- external finance. The specific response uity, rate of return volatility, and transac- here is that markets ration credit, and tions volume appear to be insignificant. more severe rationing accompanies higher After the dates in question, these effects inflation. This rationing then limits the are generally highly significant. Thus it availability of investment capital and re- seems possible that—to adversely affect duces the long-run level of real activity. In the financial system—inflation must be addition, when credit rationing is suffi- “high enough.” ciently severe, it induces endogenously Why does inflation affect financial arising volatility in rates of return to sav- markets and real activity this way? We ings. This volatility must be transmitted to produce a theoretical model in which— real activity and, hence, to the rate of in- consistent with the evidence—higher in- flation. Variable inflation therefore neces- flation reduces the rate of return received sarily accompanies high enough rates of by savers in all financial markets. By itself inflation, as we observe in practice. this effect might be enough to reduce sav- This story, of course, does not explain ings and hence the availability of invest- why these effects are strongest at high— ment capital. However, we do not believe and not at low—rates of inflation. The ex- that this explanation by itself is very plau- planation for this lies in the fact that—at sible, for two reasons. First, to explain the low rates of inflation—our analysis sug- nonmonotonicities we have noted, the sav- gests that credit market frictions are poten- ings function would have to bend back- tially innocuous. Thus at low rates of infla- ward. Little or no empirical evidence ex- tion, credit rationing might not emerge at ists to support this notion. Second, almost all, and none of the mechanisms men- all empirical evidence suggests that sav- tioned in the previous paragraph would be ings is not sufficiently sensitive to rates of operative. In this case our economy would 2 The same phenomena we re- return to make this a plausible mechanism act as if it had no financial market frictions. port here occur in the presence for inflation to have large effects. Thus an When this occurs, our model possesses a of a costly state verification alternative mechanism is needed. standard Mundell-Tobin effect that makes problem (Boyd and Smith forth- We present a model in which inflation higher inflation lead to higher long-run lev- coming), or in a model where reduces real returns to savings and, via this els of real activity.3 However, once inflation spatial separation and limited mechanism, exacerbates an informational exceeds a certain critical level, credit ra- communication affect the finan- friction afflicting the financial system. The tioning must be observed, and higher rates cial system (Schreft and Smith forthcoming and 1994). particular friction modeled is an adverse of inflation can have the adverse conse- selection problem in capital markets. How- quences noted above. 3 In particular, in the absence of ever, the specific friction seems not to be Finally, our analysis suggests that a financial market frictions, our central to the results we obtain.2 What is certain kind of “development trap” phe- model reduces to one in which central is that the severity of the financial nomenon is ubiquitous, particularly at higher rates of inflation (easier market friction is endogenous and varies relatively high rates of inflation.4 We often monetary policy) stimulates real output growth. This occurs positively with the rate of inflation. observe that economies whose perfor- in a variety of monetary growth In this specific model, higher rates of mance looks fairly similar at some point models: see Mundell (1965); inflation reduce savers’ real rates of return in time—like Argentina and Canada circa Tobin (1965); Diamond and lower the real rates of interest that 1940—strongly diverge in terms of their (1965); or especially Azariadis borrowers pay. By itself, this effect makes subsequent development. Although (1993) (for an exposition); more people want to be borrowers and this is clearly often because of differences Sidrauski (1967); and Shell, fewer people want to be savers. However, in government policies, presumably many Sidrauski, and Stiglitz (1969). people who were not initially getting governments confront similar policy op- 4 See Azariadis and Drazen credit represent “lower quality borrowers” tions. One would thus like to know (1990) for one of the original or, in other words, higher default risks. In- whether intrinsically similar economies theoretical expositions of devel- vestors will be uninterested in making can experience divergent economic perfor- opment traps. more loans to lower quality borrowers at mance for purely endogenous reasons.
F E D E R A L R E S E RV E B A N K O F ST. L O U I S
10 MAY/ J U N E 1 9 9 6
The answer in models with financial mar- tical in its size and composition. We de- ket frictions is that this can occur fairly scribe the latter below and index time pe- easily: When the severity of an economy’s riods by t = 0, 1, .... financial market frictions is endogenous, it At each date, a single final commodity is possible that—for endogenous reasons— is produced via a technology that utilizes the friction is perceived to be more or homogeneous physical capital and labor as less severe. If it is perceived to be more inputs. An individual producer employing
(less) severe, financial markets provide less Kt units of capital and Nt units of labor at t
(more) investment capital. The result is a produces F(Kt,Nt) units of final output. reduced (enhanced) level of real economic For purposes of exposition, we will as- performance. This validates the original sume that F has the constant elasticity of perception that the friction was (was not) substitution form severe. Thus, as we show, development trapsshould be expected to be quite (1) F(K,N) = [aK +bN ]1/ , common. The remainder of the article proceeds and we will assume throughout that < 0 as follows: In the first section we lay out a holds.5 Defining k º K/N to be the capital- theoretical model that illustrates the argu- labor ratio, it will often be convenient to ments just given, while in the second sec- work with the intensive production func- tion we describe an equilibrium of the tion f(k) º F(k,1). Clearly, here model. In the third section we discuss how inflation affects the level of real activity (1¢) f(k) = [ak +b]. when the financial market friction is not operative, while in the fourth section we Finally, to keep matters notationally take up the same issue when it is. In the simple, we assume that capital depreciates fifth section we examine when the friction completely in one period.6 will or will not be operative and derive the Each generation consists of two types theoretical implications we have already of agents. Type 1 agents—who constitute a discussed. In the sixth section we show fraction Î (0,1) of the population—are that an array of empirical evidence sup- endowed with one unit of labor when ports these implications. In the final sec- young and are retired when old. We as- tion we offer our conclusions. sume that all young-period labor is sup- plied inelastically. In addition, type 1 5 agents have access to a linear technology If r ³ 0, our analysis is a spe- cial case of that in Azariadis A SIMPLE for storing consumption goods whereby ILLUSTRATIVE MODEL and Smith (forthcoming). We one unit stored at t yields x > 0 units of therefore restrict attention here The purpose of this section is to pre- consumption at t + 1. to r < 0. The assumption that sent a model that illustrates how inflation Type 2 agents represent a fraction r < 0 holds implies that the interacts with a particular financial market 1 - of each generation. These agents elasticity of substitution be- friction. This friction is purposely kept supply one unit of labor inelastically when tween capital and labor is less very simple in order to highlight the eco- old and have no young-period labor en- than unity. Empirical evidence nomic mechanisms at work. Later we will dowment.7 In addition, type 2 agents have supports such a supposition. argue that these mechanisms are operative no access to the technology for storing 6 It is easy to verify that this as- very generally in economies where finan- goods. They do, on the other hand, have sumption implies no real loss of cial markets are characterized by informa- access to a technology that converts one generality. tional asymmetries. unit of final output at t into one unit of 7 This assumption implies that all + capital at t 1. Only type 2 agents have capital investment must be ex- access to this technology. The Environment ternally financed, as will soon be We imagine that any agent who owns apparent. This provides the link The economy is populated by an infi- capital at t can operate the final goods pro- between financial market condi- nite sequence of two period lived, overlap- duction process at that date. Thus type 2 tions and capital formation that ping generations. Each generation is iden- agents are producers in old age. It entails is at the heart of our analysis.
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
11 M AY / J U N E 1 9 9 6
no loss of generality to assume that all endowed with one unit of labor (supplied
such agents run the production process inelastically) and with K0 > 0 units of capi- and work for themselves in their second tal. No other agents are endowed at any period. date with capital or consumption goods. With respect to agents’ objective func- tions, it is simplest to assume that all agents care only about old-age consump- Trading tion and that they are risk neutral.8 These Three kinds of transactions occur in assumptions are easily relaxed. this economy. First, final goods and ser- The central feature of the analysis is vices are bought and sold competitively.
the presence of an informational friction We let pt denote the dollar price at t of a affecting the financing of capital invest- unit of final output. Second, producers ments. In particular, we assume that each hire the labor of young type 1 agents in a agent is privately informed about his own competitive labor market, paying the real
type. We also assume that nonmarket ac- wage rate wt at t. And third, young tivities, such as goods storage, are unob- (nondissembling) type 1 workers save servable, while all market transactions are their entire labor income, which they sup- publicly observed. Thus, to emphasize, an ply inelastically in capital markets, thereby 8 Risk neutrality implies that agent’s type and storage activity are private acquiring claims on type 2 agents—and there are no potential gains information, while all market transac- possibly on some dissembling type 1 from the use of lotteries in the tions—in both labor and credit markets— agents—and claims on the government, presence of private information. are common knowledge. This set of as- such as money or national debt. The 9 The hallmark of models of sumptions is intended to keep the model we present here is not rich enough credit rationing based on ad- informational asymmetry in our model to capture any distinction between differ- verse selection or moral hazard very simple: Since type 2 agents cannot ent types of financial claims, such as debt is that different agents have dif- work when young, they cannot credibly or equity.10 We thus think of young agents ferent probabilities of loan re- claim to be type 1. However, type 1 agents as simply acquiring a generalized claim payment and hence regard the might claim to be type 2 when young. We against producers of capital. It entails no interest rate dimensions of a now describe what happens if they do so. loss of generality to think of financial mar- loan contract differently. See, for instance, Stiglitz and Weiss If a type 1 agent wishes to claim to be ket activity as being intermediated, say (1981) or Bencivenga and type 2, he cannot work when young, and through banks, mutual funds, or pension Smith (1993). Ours is the sim- he must borrow the same amount as type 2 funds. We assume there is free entry into plest possible version of such a agents do. Since type 1 agents are incapable the activity of intermediation. We also let scenario: Type 2 agents repay of producing physical capital, it will ulti- Rt+1 be the real gross rate of return earned loans with probability one, mately be discovered that they have mis- by intermediaries between t and t + 1 on
while type 1 agents default represented their type. To avoid punish- (nondefaulted) investments, and we let rt+1 with the same probability. ment, we assume that a dissembling type 1 be the real gross rate of return earned by Matters are somewhat different agent absconds with his loan, becoming young savers. After describing government in models of credit rationing autarkic and financing old-age consump- policy, we return to a description of equi- based on a costly state verifica- tion by storing the proceeds of his borrow- librium conditions in these markets. tion problem in financial mar- kets. See, for instance, ing. Dissembling type 1 agents never repay loans. Notice, however, that since type 2 Williamson (1986 and 1987) The Government and Labadie (1995). We will agents cannot store goods, they will never discuss such models briefly in choose to abscond, and hence they always We let Mt denote the outstanding per the conclusion. repay their loans.9 Obviously, lenders will capita money supply at t. At t = 0 the initial want to avoid making loans to dissembling old agents are endowed with the initial per 10 For models of informational > frictions that do generate debt type 1 agents. How they do so is the sub- capita money supply, M 1 0. Thereafter, and equity claims, see Boot and ject of the section on equilibrium condi- the money supply evolves according to Thakor (1993), Dewatripont tions in financial markets. and Tirole (1994), Chang It remains to describe the initial con- (2) Mt+1 = Mt , (1986), or Boyd and Smith ditions of our economy. At t = 0 there is an (1995a and b). initial old generation where each agent is where > 0 is the exogenously given gross
FE D E R A L R E S E RV E B A N K O F S T. L O U I S
12 MAY/ J U N E 1 9 9 6
rate of money creation. We assume that the (4) Kt+1 = bt + t. government makes a once and for all choice of at t = 0: In steady-state equilib- Let Lt denote the quantity of young ria the (gross) rate of inflation will equal . labor hired by a representative producer at Our ultimate purpose is to examine t. Each such producer combines this with how different choices of affect finan- his own unit of labor to obtain Nt = Lt + 1 cial markets and, through this channel, units of labor services. Then the producer’s capital formation. To make our results as profits, net of loan repayments, are stark as possible, we assume that the gov- F(Kt,Lt+1) - wtLt - Rtbt 1 since an interest ernment uses the proceeds of money cre- obligation of Rt bt 1 was incurred at t - 1. ation to finance a subsidy to private capital Producers wish to maximize old-period in- formation. It should then be transparent come. At t, bt 1 is given by past credit ex- that any adverse effects of inflation are a tensions, so that the only remaining choice result of the presence of inflation alone variable is Lt. Profits are maximized when and not what the revenue from the in-
flation tax is used for. More specifically, (5) wt = F2(Kt,Lt +1) = F2(Kt/Nt,1) then, we assume that any monetary injec- (1- )/ tions (withdrawals) occur via lump-sum = f(kt) - kt f ¢(kt)=b(akt + b) transfers to young agents claiming to be type 2. Genuine type 2 agents will use º w(kt) these transfers entirely to invest in capital; hence government policy here consists of a where kt º Kt /Nt is the capital labor ratio. capital subsidy program financed by print- Equation 5 asserts the standard result that ing money. If we let t denote the real labor earns its marginal product. value of the transfer received by young For future reference, it will be useful type 2 agents at t, and we let t Î [0,1] de- to have an expression for the consump- 2 note the fraction of dissembling type 1 tion, ct, of old type 2 agents at t. Clearly agents in the time t population, then the 2 government budget constraint implies that (6) ct = F1(×)Kt + F2(×)(Lt + 1) - wtLt - Rtbt- 1 the real value of transfers, per capita, equals the real value, per capita, of = [F1(×) - Rt]bt- 1 + wt + F1(×) t- 1. seigniorage revenue. Thus The first equality in equation 6 follows
(3) [(1 - ) + t] t = (Mt - Mt- 1)/pt from Euler’s law, while the second follows from equations 3, 4, and 5. Equation 6 must hold at all dates. If we let mt º Mt/pt asserts that old producers have income denote time t real balances, equations 2 equal to the marginal product of their own and 3 imply that labor, plus the value of the capital paid
for through transfer payments [F1(×) t 1],
(3¢) [(1 - ) + t] t = [( - 1)/ ]mt. plus the net income obtained from capital attained through borrowing [(F (×) - R )b ]. EQUILIBRIUM 1 t t 1 CONDITIONS
Financial Markets 11 Factor Markets For a canonical adverse selec- Intermediaries face a fairly standard tion model, see Rothschild and
Let bt denote the real value of borrowing adverse selection problem in financial Stiglitz (1976). 11 by young type 2 agents at t. These agents markets. If they lend to a dissembling 12 It is easy to verify that nondis- 12 also receive a transfer t. All resources ob- type 1 agent, the loan will not be repaid. sembling type 1 agents will not tained by these individuals are used to fund Hence it is desirable not to lend to these wish to borrow if Rt+1 ³ capital investments at t. Each old producer agents, but at the same time such agents max(rt+1,x). This condition at t + 1 will hence have the capital stock cannot be identified ex ante. Intermedi- will hold in equilibrium.
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
13 MAY/ J U N E 1 9 9 6
aries will hence structure financial con- of funds at each date are simply the sav- tracts to deter type 1 agents from dissem- ings of young type 1 agents, which in per
bling or, in other words, to induce self- capita terms are wt. Uses of funds are
selection (only type 2 agents choose to ac- loans to borrowers [(1 - )bt per capita],
cept funding). plus real balances (mt per capita), plus per
Using typical assumptions in econ- capita storage (st). Thus equality between omies with adverse selection, we assume sources and uses of funds obtains if and that intermediaries announce financial only if
contracts consisting of a loan quantity bt,
and an interest rate (or return to the (9) w(kt) = (1 - )bt + mt + st.
intermediary) of Rt+1. Each intermediary announces such a contract, taking the The fourth condition is that type 2 contracts offered by other intermediaries agents will be willing to borrow if and as given. Hence we seek a Nash equilib- only if rium set of financial contracts. On the de- posit side we assume that intermediaries (10) F1(Kt,Nt) = F1(Kt/Nt,1) = f¢(kt) (1 )/ behave competitively (that is, each inter- = a[a+bk ] ³ Rt+1 = rt+1 mediary assumes it can raise all the funds it wants at the going rate of return on holds14. Equation 10 implies that type 2
savings rt+1). agents perceive nonnegative profits from One objective of intermediaries is to borrowing. And finally, type 1 agents are induce self-selection. This requires that willing to supply funds to intermediaries if type 1 agents prefer to work when young and only if the return they receive is at and save their young-period income rather least as large as the return available on al-
than to borrow bt, receive the transfer t, ternative savings instruments (money and and abscond. If they work when young storage). This requires that
and save the proceeds, their utility is rt+1wt.
If they borrow bt, obtain the transfer t, (11a) rt+1 ³ pt/pt+1
and abscond, their utility is x(bt+ t). Hence
self-selection requires that (11b) rt+1 ³ x.
(7) rt+1wt ³ x(bt+ t). We will want agents to hold money in equilibrium. Hence equation 11a must al- 13 13 See Rothschild and Stiglitz Standard arguments establish that equa- ways hold with equality. We will assume (1976), or in this specific tion 7 holds in any Nash equilibrium and that equation 11b is a strict inequality; context, Azariadis and Smith that all type 1 agents are deterred from dis- hence in equilibrium st = 0 (storage is (forthcoming). sembling. Hence t = 0 holds at all dates. dominated in rate of return). Equation 11b
14 In addition, since there is free entry is validated, at least near steady states, by See equation 6. into intermediation, all intermediaries the assumption that 15 An additional requirement of must earn zero profits in equilibrium.
equilibrium is that intermedi- Since t = 0, this simply requires that (a1) 1/x > . aries perceive no incentive to “pool” dissembling type 1 15 (8) Rt+1 = rt+1. We will henceforth impose equation a1. agents with type 2 agents and to charge an interest rate An equilibrium in financial markets that compensates for the de- Some Implications faults by dissembling type 1 now requires that five conditions be satis- agents. Azariadis and Smith fied. First, given rt+1 and t, the quantity of We now know that in equilibrium all (forthcoming) show that there funds obtained in the marketplace by each young type 1 agents supply their labor to is no such incentive if type 2 agent must satisfy equation 7. Sec- producers. Hence labor market clearing re-
f¢(kt+1) £ rt+1/(1-l ) ond, equation 8 must hold. Third, sources quires that the per capita labor demand of
holds for all t. and uses of funds must be equal. Sources producers [(1 - )Lt] equals the per capita
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
14 M AY / J U N E 1 9 9 6 labor supply of young type 1 agents ( ). We can now reduce our search for an Therefore, equilibrium to the problem of finding a
sequence {kt, mt} that satisfies equations
(12) Lt = /(1 - ). 14, 15¢, and 16¢at all dates, with k0 > 0 given as an initial condition. We now
It is an immediate implication that Nt = 1 make an additional comment. If equation
+ Lt = 1/(1 - ) and that 15¢is a strict inequality at any date, young type 2 agents perceive positive
(13) kt º Kt/Nt = (1 - )Kt. profits to be made from borrowing and hence will want to borrow an arbitrarily
In addition, under equation a1, st = 0 holds, large amount. Because this is not possible, so that equation 9 becomes if equation 15¢is a strict inequality, their borrowing must be constrained. The rele-
(9¢) (1 - )bt = w(kt) - mt. vant constraint is equation 7. In this case
equation 7 at equality determines bt,
Now note that kt+1 = (1 - )Kt+1 = and equation 16¢will hold with equality.
(1 - )(bt+ t). Using this fact in equation In equilibrium, at least one of the condi- 9¢, we obtain tions (equations 15¢or 16¢) must thus hold with equality. If equation 15¢is an
(9²) kt+1 = w(kt) - mt - (1 - ) t. equality, the equilibrium coincides with standard equilibria that obtain in similar
Finally, we know that t = 0. Using this economies with no informational asym- fact in equation 1¢and substituting the re- metries.16 In this case we say the equilib- sult into equation 9² yields rium is Walrasian. If equation 15¢holds as a strict inequality, then equation 16¢is
(14) kt+1 = w(kt) - mt/ . an equality. We refer to this situation as credit rationing. It is also possible to derive some fur- ther implications from the preceding dis- cussion. Equations 10 and 11a at equality, WALRASIAN EQUILIBRIA imply that We now describe sequences that sat- isfy equations 14 and 15¢at equality. For
(15) f¢(kt+1) ³ rt+1 = pt/pt+1. the present we do not impose equation 16¢: This amounts to assuming that agents’
We can now use the identity pt/pt+1 º types are publicly observed. In the section
(Mt+1/pt+1)(pt/Mt)(Mt/Mt+1) º mt+1/ mt to on the endogeneity of financial market fric- write equation 15 as tions, we ask when such sequences will also satisfy equation 16 or, in other words,
(15¢) f¢(kt+1) ³ mt+1/ mt. when Walrasian resource allocations can be sustained even in the presence of the infor- Finally, equation 7 must hold in equilib- mational asymmetry. We begin with steady- rium. Substituting equation 4 into equa- state equilibria, and then briefly describe tion 7, and using Kt+1 = kt+1/(1 - ), we ob- the nature of equilibrium paths that ap- tain the equivalent condition proach the steady state. Because the mater- 16 See, for example, Diamond ial in this section is quite standard,17 we at- (1965), Tirole (1985),
(16) rt+1w(kt) ³ xkt+1/(1- ). tempt to present it fairly concisely. or Azariadis (1993, chapter 26.2).
Equation 11a also implies an alternative 17 Steady States See, for instance, Diamond form of equation 16: (1965), Tirole (1985), or In a steady state kt and mt are constant. Azariadis (1993, chapter
(16¢)[mt+1/ mt]w(kt) ³ xkt+1/(1- ). Hence equation 15¢at equality reduces to 26.2).
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
15 M AY / J U N E 1 9 9 6
(17) f¢(k) = 1/ = pt/pt+1, It is easy to show that the monetary steady state is a saddle or, in other words, while equation 14 becomes that there is only one choice of m0 that averts a hyperinflation where money asymp- (18) m = [ w(k) - k]. totically loses all value. Thus nonhyperin- flationary equilibria are determinate (only It is immediately apparent from equa- one possible equilibrium path approaching tion 17 that increases in the rate of money the monetary steady state exists), and it growth (and inflation), , increase the is possible to show that the steady state is steady-state capital-labor ratio, per capita necessarily approached monotonically. output, and productivity of labor. This is Walrasian equilibria therefore cannot dis- true for all rates of money growth satisfying play economic fluctuations in output, real equation a1. Because the empirical evidence returns to investors, or the rate of inflation. cited in the introduction strongly suggests that higher inflation can lead to higher long- run levels of real activity only if initial rates Summary of inflation are relatively low, it is clear that Walrasian equilibria are unique. our model cannot confront the whole array Growth traps are therefore impossible. of empirical experience in the absence of the Moreover, Walrasian equilibria do not informational asymmetry. display economic fluctuations. Finally, For future reference, it will be conve- Walrasian equilibria have the feature that nient to give an explicit form for the capi- increases in the long-run rate of inflation tal stock (or variables related to it) as a lead to higher long-run levels of real activ- function of the money growth rate. To this ity and productivity. end we define the variable
(19) z º (b/a)k º w(k ) / k f (k ). EQUILIBRIA WITH t t t t t CREDIT RATIONING
It is readily verified that zt is simply the ra- In this section we investigate se- tio of labor’s share to capital’s share: The as- quences {kt,mt} that satisfy equations 14 sumption that < 0 implies that zt is an in- and 16¢at equality at all dates. In the sec- creasing function of kt. Hence movements tion on the endogeneity of financial mar- in zt simply reflect similar movements in kt. ket frictions, we then examine when a
It is easy to check that f (kt) = Walrasian equilibrium or an equilibrium 1/ - (1- )/ 1/ (1- )/ a [1+(b/a)kt ] º a (1+zt) . with credit rationing will actually obtain. Then, if we let z*( ) denote the value of z As before, we begin with steady-state equi- satisfying equation 17 for each , we have libria. that
(20) z*( ) = [a 1/ (1/ )] /(1- ) - 1. Steady States
When kt and mt are constant, equation Equations 19 and 20 give the capital stock 16¢at equality implies that the steady-state in a Walrasian steady state. capital-labor ratio satisfies
(21) w(k)/k = x /(1 - ). Dynamics Equations 14 and 15¢at equality de- Equation 21 says that the capital stock is scribe how the economy evolves given determined by how financial markets con- k0 and m0: the initial capital-labor ratio trol borrowing to induce self-selection. and initial real balances. The initial price The rate of inflation matters because it af- level is endogenous, and so m0 º M0/p0 fects the rate of return that nondissem- is endogenous. bling type 1 agents receive on their sav-
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
16 MAY / J U N E 1 9 9 6
18 ings. As inflation rises, this return falls, Figure 1 with the consequence that the utility of working and saving declines. To prevent Determination of z type 1 agents from dissembling, the utility Under Credit Rationing of doing so must also fall. Equation 21 de- H(z) scribes the consequences for the per capita capital stock. It will be convenient to transform equation 21 as follows: First note that it can be written as x a- 1/ s 1- l (21¢)[w(k)/kf¢(k)]f¢(k) = x /(1 - ).
Second, given equation 19 and our previous H(z) observations about f¢(k), it is easy to verify z (s ) -r s that [w(k)/kf¢(k)]f¢(k) = a1/ z(1+z)(1- )/ . zz ( ) This observation allows us to rewrite the equilibrium condition equation 21¢as all solutions to equation 22 yield positive levels of real balances. (22) a 1/ [x /(1 - )] Result 1 is proved in the Appendix. = z(1+z)(1 )/ º H(z). As the Appendix establishes, the function H(z) defined in equation 22 has Equation 22 determines the steady-state the configuration depicted in Figure 1. equilibrium value(s) of z as a function of In particular, the long-run inflation rate . Equation 19 then gives the steady-state per capita capi- tal stock. Steady-state real balances are de- 18 In this analysis, inflation is in- termined from equation 14 with k and m and H attains a unique maximum at z = - . versely related to the return on constant: Thus, if real balances and hence to the return on savings. However, the intuition underlying our results 1/ (23) m = [ w(k) - k]. (26) H(- ) ³ a [x /(1 - )] is not dependent on real bal- ances earning the same real re- Equation 21 permits us to rewrite equa- equation 22 has a solution, which is de- turn as other savings instru- tion 23 as picted in Figure 1. If < ˆ where ments. Higher inflation will also reduce the return on savings in (23¢) m = k{[x /(1 - )] - 1}. ˆ = [(1 - )/x]a1/ H(- ), economies where nominal inter- est rate ceilings bind or where For future reference, it will be convenient there will be exactly two solutions to equa- binding reserve requirements _ to define the function A( ) by tion 22 that are denoted by _z( ) and z( ) subject intermediaries to infla- in Figure 1. tionary taxation. Binding inter- est rate ceilings and reserve re- º - > £ ˆ (24) A( ) [x /(1 )] . The conditions A( ) 1 and quirements are very common in are equivalent to developing countries and are We can now state our first result. hardly unknown in the United (a3) (1 - )/ x < £ ˆ. States. Finally, our empirical re- RESULT 1. Define ˆ by sults do support the notion that We henceforth assume that equation a3 higher inflation does reduce the holds. We also assume that real returns received by in- vestors (see the section on Then if £ ˆ, there exists a solution to equa - (a4) 1/x³ ˆ some empirical evidence). tion 22. If, in addition, 19 Clearly 1/x > (1-l )/l x can so that equation a3 implies satisfaction of hold only if l > 0.5. Equation (a2) A( ) > 1 equation a1.19 a4 obviously implies this.
F E D E R A L R E S E RV E B A N K O F ST. L O U I S
17 MAY/ J U N E 1 9 9 6
Figure 2 The Effects of Higher Inflation The Consequences of The consequences of an increase in Higher Inflation the steady-state inflation rate are depicted in Figure 2. Evidently, an increase in H(z) raises z( ) and reduces z( ) or, in other words
- 1/ x holds. The same statements apply to k. a s 2 1- l Hence, in the low- (high-) capital-stock
- 1/ x steady state, an increase in the inflation rate a s 1 1- l raises (lowers) the steady-state capital H(z) stock. These effects occur because an in- z (s ) z (s ) zz (s ) zz (s ) crease in reduces the steady-state return 1 2 s > s 2 1 2 1 on savings. Other things equal, this lowers the utility of honest type 1 agents and would cause them to misrepresent their type. To Figure 3 preserve self-selection w(k) must rise rela- Inflation and its Consequences tive to (b+ ) = k/(1 - ). In the low- (high-) Under Credit Rationing capital-stock steady state, this requires that k rise (fall). Thus higher inflation exacer- ˆzz (s ) 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 zˆ ( ) any solutions to that equa- tion. Evidently, there can be no solution to equation 22 if the government sets above ˆ. For satisfying equation a3, clearly we have A(s )=1 ˆ
£ ˆ Evidently, when , there are two so- Of particular interest in this context is lutions to equation 22. This multiplicity of the possibility that an increase in the long- candidate equilibria derives from the way run rate of inflation can reduce the long-run that financial markets respond to the pres- capital stock, real activity, and productivity. ence of the adverse selection problem. To in- Such consequences are often observed em- duce self-selection at any given value of , pirically when inflation increases, particu- + w(k) and (b ) must be linked. One way larly when the initial rate of inflation is rela- that self-selection can occur is for w(k) and tively high. This outcome is observed in the + (b ) both to be low; this requires that z be high-capital-stock steady state. We now + low. Alternatively, w(k) and (b ) can both want to know which, if either, steady state be relatively high; this requires that z be can be approached under credit rationing. high. The possibility that there is more than one way for financial markets to address an informational asymmetry has a generality Dynamics beyond this particular model, as shown by
Boyd and Smith (forthcoming) or Schreft Given an initial capital-labor ratio, k0,
and Smith (forthcoming and 1994). and an initial level of real balances, m0,
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
18 MAY / JU N E 1 9 9 6 equations 14 and 16¢at equality govern Summary the subsequent evolution of k and m . t t When financial market frictions bind, The Appendix establishes our second there can be two steady-state equilibria dif- result. fering in their levels of real development. RESULT 2. (a) The low-capital-stock steady Both steady states can potentially be ap- proached. A continuum of paths approach- state is a saddle. All {kt,mt} sequences ap - proaching it do so monotonically. (b) The ing the high-capital-stock steady state ex- high-capital-stock steady state is a sink if ˆ ists so that the operation of financial is not too large. markets creates an indeterminacy. If the steady-state inflation rate is high enough, Result 2a implies that both the high- all such paths display endogenously arising and the low-capital-stock steady states can volatility in real activity, real returns, and potentially be approached. To approach inflation. In this sense high inflation also the low-capital-stock steady state, m0 must engenders variable inflation. be chosen to lie on a “saddle path;” that is, there is a unique choice of m0 that allows the economy to approach the low-capital- THE ENDOGENEITY stock steady state. OF FINANCIAL Result 2b implies that, for some open MARKET FRICTIONS set of values of k0, there is a whole inter- In the section on Walrasian equilibria, val of choices of m0 that allow the high- capital-stock steady state to be ap- we described equilibria under the assump- proached. The requirement of avoiding a tion that information about borrower type is hyperinflation thus no longer implies publicly available. In the section on equilib- ria with credit rationing, we described can- what m0 must be. Monetary equilibria have become indeterminate. A continuum didate equilibria under the assumption that equation 16¢holds as an equality. In this of possible equilibrium values of m0 exist and hence so does a continuum of possi- section we ask when equation 16¢will and ble equilibrium paths approaching the will not be an equality in equilibrium. When high-capital-stock steady state. This is a it is, credit rationing will occur. When it consequence of the informational friction is not, self-selection occurs even with afflicting capital markets. Walrasian allocations. In the former situa- Not only is the informational asym- tion, financial market frictions are severe metry a source of indeterminacy, it is a enough to affect the allocation of invest- potential source of endogenous economic ment capital for entirely endogenous rea- volatility as well. We now establish that sons. In the latter situation, it transpires— such volatility must be observed near the again for entirely endogenous reasons—that high-capital-stock steady state whenever financial market frictions are not severe the rate of inflation is sufficiently high. enough to affect allocations. One of our At high rates of inflation, the economy main results is that when the steady-state in- must thus pay a price to avoid the flation rate is high enough, financial market low-capital-stock steady state: This price frictions must matter and credit rationing is the existence of endogenous volatility must occur. Thus high enough rates of infla- in real activity, inflation, and asset tion imply that market frictions must ad- returns. versely affect the extension of credit and capital formation as well. RESULT 3. Suppose that is sufficiently close to ˆ. Then all paths approaching the When Are Walrasian Allocations high-capital-stock steady state do so nonmo - notonically. Consistent With Self-Selection? When do candidate Walrasian equilib-
Result 3 is proved in the Appendix. ria (sequences {kt,mt} satisfying equations
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
19 M AY / JU N E 1 9 9 6
Figure 4a Figure 4b Multiple Steady States The Steady-State Equilibrium ˆzz(s ), z*(s ) Correspondence (Case 1) zˆ(s ), z*(s ) zˆ(s ) z*(s ) ˆz(s ) z*(s )
a - 1/ s s- sˆ s a - 1/ s s- sˆ s
14 and 15¢at equality) also satisfy equa- are inconsistent with self-selection and do tion 16¢?For simplicity of exposition, we not constitute legitimate equilibria. focus our discussion on steady states. Walrasian steady states satisfy equa- tion 16¢when equation 17 holds and when Credit Rationing the implied value of k satisfies We now ask the opposite question: When do solutions to equation 16¢at equal- (29) [w(k)/kf¢(k)]f¢(k) ³ x /(1 - ). ity satisfy equation 15¢? Since f¢(k) = a1/ (1 +z)(1- )/ , clearly they do so if and only if We have already established that [w(k)/kf¢(k)] = a1/ z(1+z)(1- )/ ; hence equation 29 is equivalent to In particular, equation 31 asserts that credit * - 1/ (30) H[z ( )] ³ a [x /(1 - )]. can be rationed if and only if the solution to equation 22 yields a lower capital stock than We now demonstrate our fourth result. would obtain under a Walrasian allocation. This observation has the following implica- RESULT 4. Equation 30 is satisfied if and tion: The smaller (larger) solution to equa- only if holds. tion 16¢at equality is an equilibrium if and only if We now put all Result 4 is proved in the Appendix. these facts together. The result asserts that Walrasian alloca- tions are consistent with self-selection if and only if the steady-state value of z The Steady-State Equilibrium under full information lies between the Correspondence values of z solving equation 16¢at equality. When this condition is satisfied, the Wal- Here we describe the full set of steady- rasian allocation continues to constitute an state equilibria for each potential choice of equilibrium, even in the presence of the . We begin by depicting z*( ) and zˆ ( ) informational asymmetry. Endogenous fac- simultaneously in Figure 4a and b. It is tors allow the friction to be sufficiently easy to check that z*( ) is an increasing mild that it does not affect the allocation function, and that z*(a 1/ ) = 0. Combining of investment capital. Thus, when this with our previous results about the Walrasian allocations correspondence zˆ ( ), it follows that there are equilibrium allocations. When are three possible configurations of the Walrasian allocations steady-state equilibrium correspondence.
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
20 M AY / J U N E 1 9 9 6
We now briefly discuss each case. The first steady-state inflation exceeds a critical case is the one of primary interest to us. level ( ) informational frictions must inter- fere with the operation of capital markets. Case 1. Suppose that Since zz*( ) > z( ) for all > , both z( ) and z( ) constitute legitimate equilib- ria with credit rationing. For Î( , ˆ), there are thus again two steady-state equi- Then we have the configuration depicted in libria. Our previous results indicate that Figure 4a.20 The lociz*( ) and zˆ ( ) inter- one is a sink and one a saddle; hence both sect twice at and .21 can potentially be approached. In the high- For < ,z*( )
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
21 M AY / J U N E 1 9 9 6
Figure 5a Figure 5b Multiple Steady States The Steady-State Equilibrium ˆzz (s ), z*( ) Correspondence (Case 2) ˆzz(s ), z*( )
ˆzz( ) ˆzz( )
z*( ) z*( )
a - 1/ - a- 1/ -
steady-state equilibria, just as in Case 1. ticular, if (see the Appen- ˆ * However, here for Î [ , ],z( ) z ( ) dix), there are three distinct possibilities:_ holds, so that neither the Walrasian nor • [max { , (1- )/ x }, ]. He r e one the credit rationing allocations are legiti- steady-state equilibrium exists with credit mate steady states. Hence steady-state rationing and one exists without. Paths equilibria exist if and only if Î [ , ]. approaching both steady states do so The steady-state equilibrium corre- monotonically. Increases in (within this spondence for Case 2 is depicted in Figure interval) raise the capital stock in each 5b. In this case no branch of the corre- steady state.26 spondence exists for which z (and k) are • 27 Here there are two decreasing in . Thus this case cannot eas- steady-state equilibria, each displaying ily capture the empirical observations cited credit rationing. Dynamical equilibrium in the introduction. paths approaching each steady state may do so monotonically. In the higher of the steady Case 3. states, increases in the steady-state inflation Here holds for all . It rate are detrimental to capital formation and follows that there are no steady-state equi- the long-run level of real activity. libria for any value of . • Here there continue to be two steady-state equilibria with credit ra- tioning Now equilibrium paths Discussion approaching the high-capital-stock steady Of the various possible configurations state necessarily display endogenous fluc- of the steady-state equilibrium correspon- tuations. This is the price paid for avoid- dence, only that in Case 1 seems like it ing convergence to the low-capital-stock 26 However, increases in can can easily confront empirical findings like steady state. Moreover, if low levels of real still result in a reduction in the those of Bullard and Keating (forthcom- activity are to be avoided, high rates of steady-state capital stock if ing) and Bruno and Easterly (1995). We money growth induce volatility in all eco- they induce transitions from the therefore regard this as the most interest- nomic variables, including the inflation Walrasian to the credit rationing ing case and explore it somewhat further. rate. High rates of inflation are then asso- regime. The current analysis As shown in Result 3, some critical ciated with variable rates of inflation. provides no guidance as to value ( c) of the money growth rate exists,_ when such transitions might or with < ˆ such thatforall max { , }, might not occur. c c equilibrium paths approaching the high- An Example 27 Obviously we are assuming capital-stock steady state necessarily dis- We now present a set of parameter val- here that play endogenous oscillation. Then, in par- ues satisfying equations a4, A19 (implying
F E D E R A L R E S E RV E B A N K O F ST. L O U I S
22 MAY/ J U N E 1 9 9 6
Table 1 labor’s share exceeding capital’s share, as is true empirically. Regressions from Stock Market Data*: United States SOME EMPIRICAL EVIDENCE (1) The theoretical analysis of the previ- † RVt = .00 + .01 V(t) + 2.9 GIP(t) – .05 INF(t) ous sections yields several predictions that ‡ ‡ (.01)(.003) (3.8) (.02) can be tested empirically. R2 = .03, DW = 1.97, Q(60) = 77.7 1. Increases in the steady-state rate (2) of inflation reduce the real returns in-
RRt = –.01 – .01 RR(t–1) – .35 V(t) + .10 RRAT(t) – 2.9 INF(t) vestors receive. (.20)(.05) (.10)‡ (.12) (1.1)‡ 2. Such increases can lead to greater R2 = .09, Q(60) = 56.2 inflation variability and also to greater (3) variability in the returns on all assets. 3. Higher long-run rates of inflation NRt = –.01 – .01 NR(t–1) – .34 V(t) + .10 RRAT(t) – 1.9 INF(t) (.20) (.05) (.10)‡ (.13) (1.1)‡ raise steady-state output levels for R2 = .06, Q(60) = 56.4 economies whose rate of inflation is ini- tially low enough.28 For economies with (4) initially high rates of inflation ( ³ ) fur- Vt = .01 + .19 RRAT(t) – 2.87 GIP(t) + 2.26 INF(t) ther increases in inflation must reduce ‡ ‡ (.1) (.08) (37.6) (.73) long-run output levels, unless the econ- R2 = .02, DW = 1.99, Q(60) = 71.5 omy is in a development trap. 4. When higher inflation is detri- * Monthly, 1958-93. mental to long-run output levels, inflation † Denotes that a Cochrane-Orcutt procedure has been employed. adversely affects the level of activity in fi- ‡ Denotes significance at the 5 percent level or higher. nancial markets.
Standard errors are in parentheses. As we have noted, many of these re- sults are empirically well-supported in the DW: Durbin-Watson statistic existing literature. For example, it is well- Q: Ljung-Box Q statistic known that higher rates of inflation are typically accompanied by greater inflation variability, as shown in Friedman (1992). that we have a Case 1 economy), A24¢, Similarly, the third implication listed above A26¢(implying that intermediaries have is consistent with the empirical evidence no incentive to pool different agent types presented by Bullard and Keating (forth- in any steady-state equilibrium),_ and A27 coming) and Bruno and Easterly (1995), [implying that (1- )/ x < ]. One set of which we summarized in the introduction. 28 parameter values satisfying these condi- We now address evidence for the remain- As we have seen, this is true tions is given by ˆ =2, = - 1, x = 1/32, = ing propositions. along either branch of the steady-state equilibrium corre- = 63/64, and a 1/16. For these parameter Table 1 presents the results of four re- spondence if The state- values, equation a3 reduces to Î (0.508, gressions using stock market data for the ment in the text does require 29 2). These parameter values imply, paren- United States over the period 1958–93. some qualification, though. In thetically, that the government can allow The dependent variables are the growth particular, as noted above, if the money supply to grow as rapidly as rate of the real value of transactions on the higher inflation causes the 100 percent per period, or could contract New York Stock Exchange (RV); real re- economy to shift from the Wal- the money supply by as much as 49 per- turns on the Standard & Poor’s 500 Index, rasian to the credit rationed cent per period. They also imply an empir- inclusive of dividends (RR); nominal re- equilibrium for then an ically plausible elasticity of substitution turns on the Standard & Poor’s Index, in- increase in the inflation rate can between capital and labor of 0.5. It is also clusive of dividends (NR); and the stan- cause long-run output to fall. easy to check that, for all > (1 - )/ x, dard deviation of daily returns on the 29 Data sources are listed in the the high-capital-stock steady state has Standard & Poor’s Index (V). The explana- Appendix.
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
23 M AY / J U N E 1 9 9 6
Figure 6 Table 2 Ratio of the Value of Stock Market Transactions to GDP: United States Regressions from Stock Market Data*: Total Value of Shares Traded/GDP Ch i l e 4.5 (1) 4.0 RVt = .00 + .75 GIP(t) – .30 INF(t) † 3.5 (.02) (.20) (1.5) R2 = .10, DW = 2.24, Q(33) = 25.5 3.0 (2)
2.5 RRt = .00 + .22 RR(t–1) – .02 RRAT(t) – 2.56 INF(t) (.01) (.08)† (.007)† (.68)† 2.0 R2 = .19, Q(33) = 19.9
1.5 (3)
NRt = .00 + .17 NR(t–1) – .02 RRAT(t) – 1.30 INF(t) 1.0 (.01)(.09)† (.007)† (.66)† R2 = .09, Q(33) = 19.7 0.5 0.0 2.5 5.0 7.5 10.0 12.5 15.0 * Monthly, 1981-91. Inflation (%) † Denotes significance at the 5 percent level or higher.
Standard errors are in parentheses. Figure 7 DW: Durbin-Watson statistic
Ratio of the Value of Stock Market Transactions to GDP: Q: Ljung-Box Q statistic Chile Total Value of Shares Traded/GDP larger set that we estimated. Finally, all 0.10 data are reported as deviations from their sample means,30 and pass standard station- 0.09 arity tests in that form. In some regres- 0.08 sions we corrected for serial correlation using a Cochrane-Orcutt procedure. 0.07 As is apparent from Table 1, higher rates 0.06 of inflation significantly reduce the growth rate of stock market transactions. As pre- 0.05 dicted by theory, higher inflation thus atten- 0.04 uates financial market activity. In addition, as the inflation rate rises, the real return re- 0.03 ceived by investors falls significantly.31 In- 0.02 deed, over this time period even nominal re- turns to investors appear to be negatively 0.01 8.0 12.0 16.0 20.0 24.0 28.0 32.0 associated with inflation. Finally, higher in- Inflation (%) flation increases the volatility of stock re- turns. All of these results are consistent with the predictions of our model. tory variable of interest is the rate of infla- Figure 6 depicts the ratio of the value of tion in the Consumer Price Index (INF). stock market transactions (on the New York Other explanatory variables are also em- Stock Exchange) to gross domestic product 30 We also ran the regressions re- ployed. However, the results appear to be (GDP), plotted against the rate of inflation. ported without removing the quite robust to the inclusion of other ex- Apparently, higher inflation rates also tend sample means. This led to no dif- planatory variables. These regressions were to reduce the level of financial market activ- ferences in results. selected as being representative of a much ity using this particular measure.
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
24 MAY/ J U N E 1 9 9 6
Table 3 Table 4
Regressions from Regressions from Stock Market Data*: Stock Market Data*: Ko r e a Tai w a n A. 1982-87 A. 1983-88
(1) (1)
RVt = .01 + .12 V(t) – .008 GIP(t) – .12 INF(t) RVt = - .02 + 1.1 GIP(t) + 9.1 INF(t) (.05)(.13) (.008) (.1) (.05) (.52)† (6.5) R2 = .04, DW = 2.3, Q(24) = 33.2 R2 = .08, DW = 1.8, Q(24) = 13.4 (2) (2)
RRt = .00 – .17 RR(t–1) + .25 V(t) – 1.69 RRAT(t) – 2.32 INF(t) RRt = .00 + .23 RR(t–1) – .01 RRAT(t) – 7.3 INF(t) (.72)(.12) (1.9) (4.50) (4.50) (.02)(.13)† (.01) (8.5) R2 = .03, Q(24) = 17.6 R2 = .18, Q(24) = 19.6 (3) † Vt = .04 + .29 RRAT(t) – .01 GIP(t) – .11 INF(t) B. 1988-94 (.11) (.42) (.005)‡ (.42) (1) R2 = .39, DW = 2.34, Q(24) = 15.6 ‡ RVt = –.03 + .5 GIP(t) – 7.1 INF(t) (.05)(.50) (4.0)† B. 1988-94 R2 = .11, DW = 1.88, Q(21) = 14.1 (1) (2)
RVt = .00 + .34 V(t) + .02 GIP(t) – .28 INF(t) RRt = .00 + .36 RR(t–1) – .01 RRAT(t) – 18.7 INF(t) (.07)(.16)‡ (.01)‡ (.13)‡ (.01)(.11)† (.01) (10.1)† R2 = .11, DW = 2.15, Q(27) = 29.4 R2 = .21, Q(24) = 26.8 (2) (3)
RRt = –.19 – .18 RR(t–1) + 1.9 V(t) – 6.5 RRAT(t) – 9.77 INF(t) NRt = .00 + .35 NR(t–1) – .01 RRAT(t) – 17.8 INF(t) (.77)(.11) (1.74) (3.55)‡ (3.86)‡ (.01) (.11)† (.01) (10.1)† R2 = .11, Q(27) = 34.8 R2 = .17, Q(24) = 25.4 (3) * Monthly. 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)‡ † Denotes significance at the 5 percent level or higher. R2 = .10, Q(27) = 32.1 ‡ Denotes that a Cochrane-Orcutt procedure has been employed. (4) Standard errors are in parentheses. † Vt = –.01 + .33 RRAT(t) – .01 GIP(t) + .40 INF(t) DW: Durbin-Watson statistic (.04) (.36) (.006)‡ (.38) Q: Ljung-Box Q statistic R2 = .08, DW = 1.95, Q(24) = 33.0
* Monthly. market transactions on the Santiago Stock † Denotes that a Cochrane-Orcutt procedure has been employed. Exchange, and RRAT is the real interest
‡ Denotes significance at the 5 percent level or higher. rate on 30–89 day bank deposits. A lack of daily data prevents us from examining Standard errors are in parentheses. the volatility of stock market returns. As DW: Durbin-Watson statistic in the case of the United States, we see 31 Boudoukh and Richardson Q: Ljung-Box Q statistic that higher rates of inflation significantly (1993), using a much longer reduce investors’ real and nominal rates time series, also find that higher Table 2 reports the results of estimat- of return on the stock exchange. The rates of inflation have reduced ing similar regressions using stock market point estimate suggests that higher infla- real stock market returns in the data from Chile. Here RV represents the tion also depresses the growth rate of United States and in the United growth rate of the real value of stock market transactions, although here the Kingdom.
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
25 MAY/ J U N E 1 9 9 6
Figure 8 year (1982) is excluded as an outlier. Tables 3 and 4 report analogous regres- Ratio of the Value of Stock Market sion results for Korea and Taiwan. Here we Transactions to GDP: Korea proceed somewhat differently, since both Total Value of Shares Traded/GDP Korea and Taiwan experienced fairly pro- 0.8 nounced jumps in their rates of inflation in 1988 and 1989, respectively. In particular, 0.7 in Korea the average monthly inflation rate 0.6 was 0.27 percent over the period 1982–87, while from 1988–94 it was 0.54 percent. In 0.5 Taiwan, the average monthly rate of infla- tion over the period 1983–88 was 0.07 per- 0.4 cent, but jumped to 0.33 percent from 0.3 1989–93. These increases are apparent in Figures 8 and 9, respectively. 0.2 In view of these marked changes in the inflation rate, we proceeded as follows. 0.1 For each country we divided the sample 0.0 and ran regressions analogous to those re- 2 4 6 8 10 ported above. For Korea the results are re- Inflation (%) ported in Table 3. Over the low inflation period (1982–87), inflation has no signifi- cant effects on the real return on equity, its Figure 9 volatility, or on the growth rate of stock Ratio of the Value of Stock Market market transactions. However, during the Transactions to GDP: Taiwan period of higher inflation, increases in the Total Value of Shares Traded/GDP rate of inflation lead to statistically signifi- 7 cant reductions in the growth rate of transactions and the real and nominal re- 6 turn on equity. With respect to the volatil- ity of market returns, our point estimates 5 again suggest that inflation leads to higher volatility, but the inflation coefficient is 4 not significantly different from zero. Figure 8 represents Korea’s ratio of the 3 value of stock market transactions to GDP and its rate of inflation. Clearly, in the 2 higher inflation period of 1988–93, the negative relationship between market ac- 1 tivity and the rate of inflation is highly pronounced. This is not the case for the 0 low-inflation period 1982–87. Here then -1 0 1 2 3 4 5 we see some evidence for threshold effects: Inflation (%) Inflation seems to have significant adverse consequences only after it exceeds some point estimate is not significantly different critical level. from zero. Table 4 repeats the same regression Figure 7 depicts the ratio of the value procedure for Taiwan, but lack of daily of stock market transactions to GDP for data prevents us from constructing a Chile, plotted against its rate of inflation. volatility of returns measure. Here we see a Again we perceive a negative relationship, similar pattern to that for Korea. During particularly if the one single-digit inflation the period of low inflation (1983–88), the
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
26 M AY / J U N E 1 9 9 6
Table 5
Comparisons Across Countries: Simple Correlations of Market and Macrovariables with the Inflation Rate (INF)
Country/Period U.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 –.20 RR –.25 –.15 –.06 –.20 –.12 –.23 V –.05 — –.09 –.12 —— GIP –.02 –.10 –.14 –.03 –.12 –.24 RRAT –.70 –.67 –.95 –.91 –.99 –.99
*Average monthly inflation rate 0.27 percent. ‡ Average monthly inflation rate 0.07 percent. † Average monthly inflation rate 0.54 percent. § Average monthly inflation rate 0.33 percent. effect of inflation on the growth rate of of inflation tend to reduce the real rates of real stock market activity is insignificant return received by savers in a variety of mar- and similarly for the real returns on equity. kets.32 When credit is rationed, this reduc- However, in the period of high inflation, tion in returns worsens informational fric- both the growth rate of real equity market tions that interfere with the operation of the activity and the real returns on equity financial system. Once inflation exceeds a were adversely effected by inflation in a certain critical rate, a potential consequence statistically significant way. Nominal eq- is that the financial system provides less in- uity returns are negatively associated with vestment capital, resulting in reduced capi- inflation, with a t-value of about 1.6. Here tal formation and long-run levels of real ac- we see further evidence that inflation may tivity. Such forces need not operate at low be detrimental only after it exceeds some rates of inflation, providing an explanation threshold level. of why the consequences of higher inflation Figure 9 displays Taiwan’s value of seem to be so much more severe once infla- stock market transactions to GDP ratio, as tion exceeds some threshold level. well as its inflation rate. Clearly, this mea- In addition, high enough rates of infla- sure does not suggest that inflation has tion force endogenously arising economic been detrimental to the level of equity volatility to be observed. Thus, as we ob- market activity. serve, high inflation induces inflation vari- Table 5 shows simple correlations of ability and variability in rates of return on the financial variables with the inflation all savings instruments. Theory predicts rate for each of the countries and subperi- that this volatility should be transmitted to ods. These results are quite consistent with real activity as well. the regression results. On the whole, this Obviously, these results have been ob- empirical evidence seems to support our tained in the context of a highly stylized model’s predictions. We have even seen ev- and simplified model of the financial sys- idence that inflation’s adverse conse- tem. How general are they? We believe quences may only be observed if the rate they are quite general. Boyd and Smith of inflation is sufficiently high. (forthcoming) produce a model of a finan- cial system that is subject to a costly state verification problem, one where investors CONCLUSIONS provide some internal financing of their 32 Further evidence on this point Both our theoretical analysis and our own investment projects. Again, two mon- appears in Boyd, Levine, and empirical evidence indicate that higher rates etary steady-state equilibria exist and both Smith (1995).
FE D E R A L R E S E RV E B A N K O F S T. L O U I S
27 M AY / J U N E 1 9 9 6
can potentially be approached. Thus devel- Boudoukh, Jacob, and Matthew Richardson. “Stock Returns and Inflation: opment trap phenomena arise. In the A Long-Horizon Perspective,” American Economic Review (December steady state with higher levels of real ac- 1993), pp. 1,346–55. tivity, higher inflation interferes with the Boyd, John H.; Ross Levine; and Bruce D. Smith. “Inflation and Finan- provision of internal finance, thereby exac- cial Market Performance.” Manuscript. Federal Reserve Bank of erbating the costly state verification prob- Minneapolis, 1995. lem. As a result, greater inflation reduces _____ and Smith, Bruce D. “Capital Market Imperfections in a Mone- the long-run level of real activity, the level tary Growth Model.” Economic Theory (forthcoming). of financial market activity, and real re- turns to savers. Moreover, as is the case _____ and _____. “The Evolution of Debt and Equity Markets in Economic Development.” Manuscript. Federal Reserve Bank of here, high enough rates of inflation force Minneapolis, 1995a. endogenously generated economic volatil- ity to emerge. And, interestingly, Boyd and _____ and _____. “The Use of Debt and Equity in Optimal Finan- Smith (forthcoming) obtain a result that is cial Contracts.” Manuscript. Federal Reserve Bank of Minneapolis, not available here: Once inflation exceeds 1995b. a critical level, it is possible that only the Bruno, Michael, and William Easterly. “Inflation Crises and Long-Run low-activity steady state can be ap- Growth.” Manuscript. The World Bank, 1995. proached. Inflation rates exceeding this Bullard, James, and John Keating. “The Long-Run Relationship Between level can then force the kinds of crises dis- Inflation and Output in Postwar Economics,” Journal of Monetary Eco - cussed by Bruno and Easterly (1995). Re- nomics (forthcoming). lated results are obtained by Schreft and Smith (forthcoming and 1994) in models Champ, Bruce; Bruce D. Smith; and Stephen D. Williamson. “Currency Elasticity and Banking Panics: Theory and Evidence,” Canadian Journal where financial market frictions take the of Economics (forthcoming). form of limited communication, as in Townsend (1987) and Champ, Smith, and Chang, Chun. “Capital Structure as Optimal Contracts.” Manuscript. Williamson (forthcoming). University of Minnesota, 1986. A shortcoming of all of the models Dewatripont, Mathias, and Jean Tirole. “A Theory of Debt and Equity: Di- mentioned—including ours—is that they versity of Securities and Manager-Shareholder Congruence,” Quarterly do not give rise to distinct and/or interest- Journal of Economics (November 1994), pp. 1,027–54. ing roles for debt and equity markets. Em- Diamond, Peter A. “National Debt in a Neoclassical Growth Model,” pirical evidence suggests that both kinds American Economic Review (December 1965), pp. 1,126–50. of markets are adversely affected by high inflation.33 This is a natural topic for fu- Friedman, Milton. Money Mischief: Episodes in Monetary History. Harcourt- ture investigation. Brace-Jovanovich, 1992. Labadie, Pamela. “Financial Intermediation and Monetary Policy in a General Equilibrium Banking Model,” Journal of Money, Credit and Banking (November 1995), pp. 1,290–1,315. REFERENCES Mundell, Robert. “Growth, Stability, and Inflationary Finance,” Journal of Azariadis, Costas. Intertemporal Macroeconomics. Oxford: Basil Political Economy (April 1965), pp. 97–109. Blackwell, 1993. Rothschild, Michael, and Joseph Stiglitz. “Equilibrium in Competitive _____ and Allan Drazen. “Threshold Externalities in Economic Develop- Insurance Markets: An Essay on the Economics of Imperfect Informa- ment,” Quarterly Journal of Economics (May 1990), pp. 501–26. tion,” Quarterly Journal of Economics (November 1976), pp. 629–650. _____ and Bruce D. Smith. “Private Information, Money and Growth: Indeterminacy, Fluctuations, and the Mundell-Tobin Effect,” Journal of Schreft, Stacey L., and Bruce D. Smith. “The Effects of Open Market Op- Economic Growth (forthcoming). erations in a Model of Intermediation and Growth.” Manuscript. Cornell University, 1994. Bencivenga, Valerie R., and Bruce D. Smith. “Some Consequences of Credit Rationing in an Endogenous Growth Model,” Journal of _____ and _____. “Money, Banking, and Capital Formation,” Jour - Economic Dynamics and Control (January-March 1993), nal of Economic Theory (forthcoming). pp. 97–122. Shell, Karl; Miguel Sidrauski; and Joseph Stiglitz. “Capital Gains, 33 See Boyd, Levine, and Smith Boot, Arnoud W. A., and Anjan V. Thakor. “Security Design,” Journal of Income, and Saving,” Review of Economic Studies (January 1969), (1995). Finance (September 1993), pp. 1,349–78. pp. 15–26.
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
28 MAY/ J U N E 1 9 9 6
Sidrauski, Miguel. “Inflation and Economic Growth,” Journal of Political Economy (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 (October 1965), 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, and Equilibrium 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.
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
29 MAY / J U N E 1 9 9 6
Appendix
PROOF OF RESULT 1 It is well-known from Azariadis (1993, It will be useful to begin by describing chapter 6.4) that a steady state is a saddle some properties of the function H(z) º if T( ) > 1 + D( ). A steady state is a sink z(1+z)(1- )/ . Clearly, H(0) = 0, and if |D( )| < 1 and 1 D( ) < T( ) < 1 + D( ). We now state the following prelimi- (A1) lim H(z) = 0 z ¥ nary result. is established by an application of L’Hopital’s LEMMA 1. At the low (high) capital stock rule. Moreover, clearly, steady state, D( ) > (<) 1 holds.
(A2) zH (z)/ H(z) =1 +[(1 - )/ ][z/( 1 +z)]. Proof. It is straightforward to show that
Thus H (z) ³ (<) 0 holds if and only if (A4) D( ) = (1 - )/[1 zˆ( )]. z ³ (<) - . It follows from these observations Since z( ) - [z( ) > - ],D( )>(<)1 that equation 22 has a solution if and only holds at the low- (high-) capital-stock if equation 26 holds. This is readily verified steady state. to be equivalent to ³ ˆ,with ˆ defined by It is now possible to demonstrate the equation 25. following. When equation 22 has a solution, the as- sociated value of k can be obtained from LEMMA 2. At the low- (high-) capital-stock equation 19. Equation 23 then produces m. steady state, T( ) > (<) 1 + D( ) holds. Ev i d e n t l y , m is positive if and only if A( ) > 1. Proof. As is readily verified,
PROOF OF RESULT 2 (A5) T( ) = 2 - A( ) + A( )D( ).
Using equation 14 to replace kt+1 in Thus T( ) > (<) 1 + D( ) holds if and equation 16 gives the relation only if
2 (A3) mt 1 = A( )m t [x /(1 )]m t / w(kt). (A6) [A( ) - 1]D( ) > (<) [A( ) - 1].
Equations 14 and A3 govern the evolution A( ) > 1 and Lemma 1 implies that of the sequence {kt,mt}. Near a steady state > (<) holds at the low- (high-) capital- this evolution is described by a linear ap- stock steady state. proximation of these two equations. Letting (k,m) denote any pair of steady-state equi- Lemma 2 implies that the low-capital- librium values for the capital-labor ratio and stock steady state is a saddle. Paths ap- real balances, this linear approximation is proaching it necessarily do so monoton- given by (kt+1- k,mt+1- m)¢=J(kt- k,mt- m)¢, ically if T( ) > 0 at that steady state. But where J is the Jacobian matrix T( ) > 0 follows from equation A5 and Lemma1. Thus Result 2(a) is established. l w¢(k) 1 / Lemmas 1 and 2 also imply that the J high-capital-stock steady state is a sink if [(1 -l )/x][A( 1]2w¢(k) 2 A( (A7) T( ) > - 1 - D( ) Let T( ) and D( ) denote the trace and de- terminant, respectively, of J, where we ex- holds at that steady state. By equation A5, plicitly denote their dependence on . equation A7 is equivalent to
F E D E R A L R E S E RV E B A N K O F ST. L O U I S
30 MAY/ J U N E 1 9 9 6
Appendix
(A7¢) D( ) > [A( ) - 3]/[A( ) + 1]. = ˆ and hence by continuity, that it holds for sufficiently near ˆ. In particular, Equation A4 implies that equation A7¢ necessarily holds if 3 ³ A( ), which in turn is implied by 3 ³ A( ˆ) The high-capital- stock steady state is thus a sink, if ˆ is not {2- [x / (1 - )] ˆ }/[x / (1 - ) ˆ ] too large. while
PROOF OF RESULT 3
It is well-known that paths approach- Thus equation A11 holds for near ˆ if ing a steady state do so nonmonotonically if T( )2 < 4D( ) holds, as in Azariadis (A12) 2 [x / (1 - )] ˆ <[x / (1 - )] ˆ . (1993, chapter 6.4). We first establish the following. But equation A12 is implied by A(ˆ)>1. This establishes the result. LEMMA 3. T( ) > 0 holds if is sufficiently close to ˆ. PROOF OF RESULT 4
Proof. From equation A5, T( ) > 0 holds if z( ) and z( ) both satisfy
(A8) 2 > A( )[1 - D( )] H(z) = a 1/ [x /(1 - )]. where at the high-capital-stock steady state Thus z*( ) satisfies equation 30 if and only if holds. As is ap- (A9) D( ) = (1 - ) / [1 z( )]. parent from Figure1, this will be the case if and only if Thus RESULT 6 It follows that equation A8 necessarily holds for large enough values of . z*( ) intersects zˆ ( ) at most twice. Lemma 3 implies that T( )2 < 4D( ) holds for large enough if and only if Proof. z*( ) satisfies
(A10) T( ) 2 D( ). (A13) [1 + z*( )](1- )/ º a- 1/ / .
Substituting equation A5 into equation A10 Multiplying both sides of equation A13 by and rearranging terms yields the equivalent z*( ) gives the equivalent condition condition (A13¢) H[z*( )] = a- 1/ z*( )/ . (A10¢) 2[1 D( )] Moreover, whenever z*( ) = zˆ ( ), we have A( )[1 D( )][1 D( )] (A14) H[z*( )] = H[zˆ( )] or, since D( ) < 1, º a 1/ [x / (1 - )]. (A11) [2 A( )] / A( )< D( ). Equations A13¢and A14 imply that We now show that equation A11 holds for z*( ) = zˆ ( ) if and only if
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
31 MAY / JU N E 1 9 9 6
Appendix
Case 1 (A15¢) a- 1/(1- ) = /(1- ) + [x/(1- )] (2- )/(1- ) Q ( ) º Q( ).
The function Q( ) is depicted in the Q ( ) Figure. It is readily demonstrated that Q(a- 1/ ) > a- 1/(1- ) and that Q¢( ) ³ 0 holds if and only if a - 1/(1- ) (A16) ³ [- (1- )/x(2- )]0.5.
There are therefore three possibilities.
a - 1/ Case 1. Suppose that
Case 2 (A17) a 1/ < [- (1 - )/x(2 - )]0.5 Q ( ) and that Q ( ) (A18) Q{[- (1 - )/x(2 - )]0.5} < a- 1/(1- ).
Then equation A15¢has exactly two a - 1/(1- ) solutions, as shown in the Figure. It fol- lows that z*( ) intersects zˆ ( ) exactly twice.
Case 2. a - 1/ Suppose that equation A17 holds but that equation A18 fails. Then there is at most one intersection of z*( ) and zˆ ( ), Case 3 as shown in the Figure. Q ( ) Case 3. Q ( ) Suppose that equation A17 fails. Then Q ( ) ³ 0 holds for all ³ a 1/ . There are no intersections of z*( ) and zˆ ( ), as the Figure shows. a - 1/(1- ) These three cases exhaust the set of possibilities and establish the result.
EXISTENCE OF STEADY- - 1/ a STATE EQUILIBRIA Result 6 implies that steady-state equi- libria exist, in general, if and only if sat- (A15) z*( ) = [x/(1 - )] 2. isfies equation a3 and equations A17 and A18 hold. It will be useful to have a suffi- Equation A15 is readily shown to be cient condition implying that equations equivalent to the condition A17 and A18 are satisfied. From Figure 4a,
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
32 M AY / JU N E 1 9 9 6
Appendix it is apparent that z*( ) intersects or equivalently, if zˆ( ) if z* (ˆ ) >- . We now describe when this condition holds. (A22¢) zˆ ( ) ³ (1 - )a1/r H[zˆ ( )]º x 2.
RESULT 7. z* (ˆ ) >- holds if and only if Equation A22¢holds at the high-capital- stock steady state if (A19) ˆ >[- (1 - )/x]0.5. (A23) z( )/ 2 ³ x. Proof. Equations 20 and 25 imply that z*( ) > - holds if and only if Since the left-hand side of equation A23 is decreasing in , A23 holds for all (A20) (a 1/ )2[x/(1 - )] £ ˆ if < - [(1- )(1 )/ ]2. (A24) z( ˆ)/x³ ˆ 2. Equation A20 is easily shown to be equiv- alent to equation A19. or equivalently, if
Thus equation A19 implies the existence (A24¢) - /x ³ ˆ 2. of multiple steady states for all satisfying equation a3. Equation A22¢holds at the low-capital- stock steady state if
PROOF OF RESULT 5 (A25) z( )/ 2 ³ x .
This result has already been estab- Clearly, a sufficient condition for equation lished when credit rationing obtains. Thus A25 is that we must establish that m > 0 holds at the Walrasian steady state. From equation 18, (A26) z( )³ x ˆ 2. in a Walrasian steady state Since z( )=[x/(1 - )] 2 it follows that (A21) m = k{ [w(k)/k] - 1}. (A26¢) 2 ³ (1 - ) ˆ 2 Since z*( )Î [z( ),z( )], we also have that w(k)/k ³ x /(1 - ). Hence A( ) > 1 is sufficient for equation A22¢to hold at the implies that m > 0 holds. low-capital-stock steady state. To summarize, equation A22¢holds at z( ) and z( ) for all Î [ , ˆ ]if equations IMPOSSIBILITY OF A24¢and A26¢hold. POOLING Azariadis and Smith (forthcoming) RESULT 8 prove that there is never an incentive if and only if for an intermediary to pool type 2 and dissembling type 1 agents in a Walrasian (1 )/ (A27) ˆ ³- (1 - ) ´ equilibrium. They also prove that there is no such incentive under credit ration- (1 )/ 1 + (1 - )/x 2 . ing if { [ ]} (A22) 1 ³ (1 - )f (k) holds if and 1/ (1 )/ = (1 - )a [1 + zˆ ( )] only if
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
33 MAY / J U N E 1 9 9 6
Appendix
(A28) (1 - )/x < [- (1 - )/x(2 - )]0.5 dard & Poor’s Statistics, SBBI Yearbook, various dates.) and V: Standard deviation of returns on the daily Standard & Poor’s (A29) ˆ £- (1 - )(1- )/ ´ index. (SBBI Yearbook, various dates.) {1+[(1- )/x 2]}- (1- )/ INF: Rate of inflation in the CPI. (Bureau of Labor Statistics.) GIP: Growth rate of industrial pro- Proof. It is easy to verify that duction index. (Federal Re- (1- )/ xÎ [ , ] if and only if serve Industrial Production Indices.) (A30) Q[(1 - )/x ] £ a - 1/(1- ) RRAT: Three-month Treasury bill rate, in real terms. (Federal Reserve holds. Using the definition of Q, it is Bulletin, various dates.) straightforward to show that equation A30 is equivalent to 2. Chile Sources. (A30¢) - a1/ x/(1- ) (1- )(1- )/ [ ] All data are from the Boletoin mensual ³ - (1- )(1- )/ ´ (Banco Central de Chile). They are avail- able monthly from 1981–91. 1 + (1- )/x 2 - (1- )/ . { [ ]} RV: Growth rate of the real value of But, as is apparent from equation 25, transactions on the Santiago equation A30¢is equivalent to equation Stock Exchange. A27. RR: Real return to equity, inclusive It can be shown that (1- )x ³ of dividend yields. holds if and only if Q¢[(1-l )/xl ] < 0 and NR: Nominal returns to equity, in- Q[(1-l )/xl ] ³ a- 1/(1- ) are satisfied. The clusive of dividend yields. former condition is equation A28, the lat- INF: Rate of change in the CPI. ter is equation A29. RRAT: Real rate of interest on 30- to 89-day bank deposits.
DATA SOURCES 3. Korea 1. United States All monthly data are available from Monthly data are available over the 1982–94. period 1958–93. Sources. Sources. RV: Growth rate of the real value of RV: Growth rate of real value of transactions on the Korea transactions on the New York Stock Exchange. (Securities Stock Exchange. (New York Statistics Monthly, Korea Stock Stock Exchange Factbook, vari- Exchange, various dates.) ous dates.) RR: Real returns to equity, inclusive RR: Real returns on the Standard & of dividend yields. (Securities Poor’s 500 index, inclusive of Statistics Monthly, Korea Stock dividend yields. (Standard & Exchange, various dates.) Poor’s Statistics, SBBI Yearbook, NR: Nominal returns to equity, in- various dates.) clusive of dividend yields. (Se - NR: Nominal returns on the Stan- curities Statistics Monthly, dard & Poor’s 500 index, inclu- Korea Stock Exchange, various sive of dividend yields. (Stan- dates.)
F E D E R A L R E S E RV E B A N K O F ST. L O U I S
34 MAY/ J U N E 1 9 9 6
Appendix
V: Standard deviation of daily re- Sources. turns. (Securities Statistics RV: Growth rate of the real value of Monthly, Korea Stock Ex- stock transactions in the Tai- change, various dates.) wan area. (Financial Statistics INF: Rate of growth of the CPI. Monthly, Central Bank of (Economic Statistics Yearbook, China, various dates.) Bank of Korea, various RR: Real returns, inclusive of divi- dates.) dend yields. (Financial Statis - GIP: Growth rate of industrial pro- tics Monthly, Central Bank of duction. (Economic Statistics China, various dates.) Yearbook, Bank of Korea, vari- NR: Nominal returns, inclusive of ous dates.) dividend yields. (Financial Sta - RRAT: Three-month corporate bill tistics Monthly, Central Bank of rate, in real terms. China, various dates.) INF: Growth rate of CPI. (Monthly 4. Taiwan Statistics of the Republic of All data are available monthly from China, Central Bank of China, 1983–93. various dates.)
F E D E R A L R E S E RV E B A N K O F S T. L O U I S
35