stock prices and fundamentals: a macroeconomic perspective

Stock Prices and Fundamentals: A Macroeconomic PerspectiveAuthor(s): Michael T. KileySource: The Journal of Business, Vol. 77, No. 4 (October 2004), pp. 909-936Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/10.1086/422629 .

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#04409 UCP: BN article # 770411

Michael T. KileyFederal Reserve Board

Stock Prices and Fundamentals:A Macroeconomic Perspective*

‘‘‘You can write about anything you like,’ aneconomics professor once told me as he ex-plained the term-paper assignment, ‘as longas it’s not about the stockmarket.’ Economistswere famous for saying silly things aboutstocks, he said. It’s better just to avoid thewhole subject’’ so said. N. Gregory Mankiw1

In the late 1990s, the U.S. stock market tookoff, leaving conventional valuation benchmarkssuch as dividend yields or P/E ratios very farfrom historical averages. While recent turbulencein equity markets has brought market valuesdown notably from their peaks, the market valueof U.S. firms remained very high relative to val-uation benchmarks through 2001. Several recentanalyses have suggested that the old benchmarksno longer apply because the U.S. economy hasentered a period of faster growth and lower re-quired returns, two changes that imply a largerun-up in equity markets in the familiar Gordon(1962) growth model. This paper considers suchshifts in ‘‘fundamentals’’ in a standard dynamicgeneral-equilibrium model with production and

(Journal of Business, 2004, vol. 77, no. 4)B 2004 by The University of Chicago. All rights reserved.0031-8248/2004/7704-0010$10.00

909

* This research was facilitated by the excellent research as-sistance of Ojas Desai, Betsy Vrankovich, and Joanna Wares.This research has benefited at various stages from comments byBill Emmons, Eileen Mauskopf, John Roberts, Karl Whelan,Stephen Wright, an anonymous referee, and participants inseveral seminars. Responsibility for any errors lies solely withthe author. The views expressed herein are the author’s and donot reflect those of the Federal Reserve Board or its staff. Contactthe author at [email protected]. In Fortune, November 8, 1999, ‘‘The Dow Will Hit

36,000! (Someday).’’

This paper comparesthe predictions for themarket value of firmsfrom the Gordongrowth model withthose from a dynamicgeneral-equilibriummodel. The predictionsfor movements in themarket value of firmsfollowing shifts inpreferences, growthprospects, and risk arequantitatively andqualitatively differentacross the models.While previous re-search illustrated how adrop in the required re-turn or an increase inthe growth rate of theeconomy can explainthe run-up in equityvalues in the 1990s inthe Gordon growthmodel, the general-equilibrium model sug-gests that such resultsare misleading.



#04409 UCP: BN article # 770411

concludes that consideration of general equilibrium and productiondecisions alters—quantitatively and qualitatively—the ability of fastergrowth prospects or declining equity premiums to explain the run-up inthe market value of firms. This conclusion arises because faster growthprospects do not increase the ratio of market value to output in a pro-duction economy (in contrast to the Gordon model result). A decline inthe required return to equity or the equity premium provides much lessboost to asset prices in the production economy, and under some con-ditions no boost to equity values whatsoever. In the Gordon growthmodel, the stock price equals the present discounted value of dividends.Discussions applying this model to the aggregate stock market—andthere are many—assume that a number of important variables that de-termine the market value of firms are exogenous. For example, previousresearch typically assumed that any changes in the growth rate ofearnings, the return to equity or risk-free assets, or the dividend share ofearnings occur independent of each other. Such discussions may bemisleading because these variables are not exogenous parameters;rather, the interaction of savings and investment opportunities and thepace of technological progress jointly determine these variables.

The model presented in this paper, a general-equilibrium modelwith nonexpected utility preferences, is familiar to most economistsand provides a framework in which to think about the links betweentechnology, investment, and asset markets. However, the model hasnot been used in discussions of how shifts in technology, preferences,or risk affect equity values (with a few exceptions since the workingpaper version of this analysis first appeared, notably McGrattan andPrescott 2001). In part, this may reflect the tendency of models used infinance applications to ignore macroeconomic issues of savings andinvestment or general-equilibrium effects more broadly. For example,the production- or investment-based asset-pricing model of Cochrane(1991, 1996) notes that arbitrage considerations imply that the returnto investment in equities should equal the return to investment inphysical capital. Therefore, a decline in the required return to equityshould be associated with an increase in investment (which lowers thereturn to physical capital with short-run decreasing returns). Such aninvestment effect is considered later and found wanting in the data ofthe late 1990s. More important, the general-equilibrium model con-siders how changes in fundamentals lead to shifts in typical valuationbenchmarks, such as the dividend-price ratio, once the joint determi-nation of asset prices, dividends, investment, and savings are explic-itly modeled. For example, a lower required return to equity maylower the dividend-price ratio, a well-known Gordon growth modelresult; but this decline may occur in part because dividends fall, hencethe degree to which equity prices may justifiably rise following such ashift is more muted in general equilibrium. The recent examination of

910 Journal of Business



#04409 UCP: BN article # 770411

the effects of the demographic shifts associated with the baby boom byAbel (2000) in an overlapping-generations general-equilibrium modelis an example of the general-equilibrium approach taken here.2

Another factor that may have dissuaded economists from analyzingthe market value of firms using the approach adopted here can begleaned from the opening quote: It is inherently difficult to tie high-frequency movements in equity markets to observable fundamentals;therefore, economists avoid talking about the stock market. Theexercises that follow illustrate the implications of unobserved shifts infundamentals for the economy beyond equity markets by consideringa general-equilibrium model of production; the discussion of theseauxiliary implications should prove useful in any attempt to gauge theplausibility of different hypotheses regarding how shifts in requiredreturns or increases in growth affect the market value of firms.Finally, one provocative recent explanation offered in Hall (2001)

attributes the run-up in the market value of firms to a surge in the ac-cumulated stock of intangible capital (where such capital reflects thevalue of business practices, intellectual capital, or other investments notmeasured in physical capital). This idea has a ring of plausibility, andongoing research efforts have attempted to further examine how wellintangible investments help explain the late 1990s boom in equity values.However, some studies (e.g., Bond and Cummins 2000 and Cummins2002) suggested that any increase in intangible investment has beenmuch too modest to explain the recent behavior of the stock market (onboth the upswing and downswing). Given these controversies, the anal-ysis here focuses on the plausibility of stories derived from the Gordongrowth model and the alternative implications of changing growth ratesor required returns that come from a simple general-equilibrium model.Section 1 discusses recent research that examined the market value

of firms in the Gordon growth model and other approaches. Section 2presents the model with production, and section 3 presents the modelsolution and discusses the link between this model and the Lucas (1978)asset-pricing model. Section 4 discusses how shifts in preferences, tech-nology and risk affect the market value of firms in the different models.

I. Recent Research on the Market Value of Firms

A brief review of recent experience is useful to set the stage. Figure 1presents the ratio of trend earnings, defined as the Hodrick-Prescotttrend value, to equity prices for the Standard and Poor’s Composite

2. Other examples of asset-pricing issues examined in models with production include Basu(1987), Jermann (1998), and Tallarini (2000). Each of these contributions focuses on questionsregarding asset returns that fall outside the scope of this paper. Moreover, the analysis thatfollows presents simple formulas governing fluctuations. The analyses in previous contributionsemphasize numerical solution techniques that make interpretation more difficult.

911Stock Prices and Fundamentals



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Stock Price Index (from Shiller 2000, updated through 2001; data areyearly averages).3 In 2000, this ratio fell to the lowest level everrecorded, 3% (over a sample that spans 1871 to 2001). Prior to 1998,the only foray below 4% had occurred in 1929. Moreover, the weak-ness in equity prices in 2001 boosted the ratio of trend earnings toprices only marginally to a level near the 1997 value. The high value ofequity prices relative to earnings led Shiller (2000) to suggest thatequities have been overvalued since the mid-1990s.

Another perspective on the high level of the U.S. stock market liesin a comparison of the market value of firms to the assets owned byfirms. Under the assumption that the securities issued by firms areclaims to their stock of physical capital, and assuming that physicalcapital is near its long-run level (because adjustment costs are modest,for example) and the economy is competitive, the value of the stock ofphysical capital should equal the value of the securities issued byfirms.4 Figure 2 graphs the market value of firms in the business sector

Fig. 1.—Ratio of trend earnings to equity prices, 1871–2001

3. Themonthly data fromwhich these yearly averages are computed can be downloaded fromRobert Shiller’s webpage (http://www.econ.yale.edu/~shiller/data.htm). This page contains theinformation on earnings, stock prices, dividends, and the Consumer Price Index (which is used incomputing real returns and deflating certain nominal levels as discussed later).4. Actually, complications in the tax code make the relationship a bit more complex, but

the changes in the tax code in the last 5 years are not significant enough to explain the surgein equity markets, and I follow other authors (e.g., Hall 2001, Smithers and Wright 2000, andMcGrattan and Prescott 2001) in ignoring taxes.




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Fig. 2.—The market value of firms and physical capital, 1948–2000: (a) Marketvalue and physical capital, (b) ratio.

a

b




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and the current cost of physical capital stock held by the businesssector over the postwar period (in real terms, deflated by the ConsumerPrice Index with a base year of 2000), along with their ratio (Tobin’sQ) in the bottom panel.5 In 1990, the ratio of market value to physicalcapital equaled its postwar average (over 1948–1995). By 1999, thisratio had risen to nearly 2O times its historical average, far beyond anyother such deviation, and the weakness in equity values in 2000brought Q down to 2 times its historical average. (The value in 2001cannot be computed because capital stock data for that year are un-available, but equity price movements since 2000 imply that Q hasfallen further). The unprecedented divergence of the market value offirms from valuation benchmarks is the stylized fact examined in themodels that follow.

Most recent discussions of the surge in the market value of firms inthe 1990s have used the standard present value relation equating themarket value of firms (V ) to the present discounted value of dividends(D), the Gordon (1962) model:

V tð Þ ¼X1j¼1

D t þ jð Þ1þ rð Þ j

where r is the discount rate (which is assumed to be constant). Equating themarket value of firms to the present discounted value of dividends ignoresdebt; most commentators have taken the more narrow view and focusedsolely on the equity value of firms. Later, I examine the market valueof firms including debt when I consider the implications of parameterchanges in a standard general-equilibrium model, and I henceforth abuselanguage and interchangeably refer to the market value of firms and equityvalues. This focus seems appropriate given the overall run-up in themarket value of firms documented in figure 2.

5. The data on output, investment, and capital stocks used in this study cover the businesssector of the U.S. economy. The value of the financial securities issued by the business sectoris taken from the flow of funds accounts of the Federal Reserve Board. The market value offirms equals the market value of outstanding equities plus the value of financial liabilitiesless financial assets. Alternatives to the CPI as the deflator do not alter the results discussed.The same deflator should be used when comparing the value of physical capital and themarket value of firms to ensure that movements in the deflated series capture movements inreal terms measured in common units. The choice of deflator is unimportant for movementsin Q (because it is a ratio). Of course, for other issues, it is very important to keep track ofrelative prices and hence employ the information in the national accounts on relative pricemovements. For a simple example where such effects are important and references to somerelated literature, see Kiley (2001b), which provides an analysis of the contribution of rapidtechnological advance in the high-tech equipment-making sector to aggregate economicgrowth.




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A particularly simple version of the Gordon growth model assumesthat D grows at a constant rate g, in which case,

V tð Þ ¼ D t þ 1ð Þr � g

and the dividend-price ratio is given by

D t þ 1ð ÞV tð Þ ¼ r � g:

It is also of interest to consider the earnings-price ratio implied by thismodel because, especially in recent years, firms have turned to alternativemeans of ‘‘paying dividends,’’ such as share repurchases (e.g., Liang andSharpe 1999) that do not show up in dividend measures and hence distortthe dividend-price ratio. The change in earnings equals the required returnmultiplied by reinvested earnings

�E t þ 1ð Þ ¼ r E tð Þ � D tð Þ½ �:

Dividing both sides by earnings, inserting the equality between earningsgrowth and dividend growth (in the long run) yields the equilibriumdividend-payout ratio, which implies the earnings-price ratio is

E t þ 1ð ÞV tð Þ ¼ r:

According to these formulas, the dividend-price ratio is a decreasingfunction of the growth rate of dividends and an increasing function ofthe required return to equity, and the earnings-price ratio equals thereturn to equity. Over the 1948–1994 period, the average ex poste realreturn to equity was 8.6% and the average earnings-price ratio was8.6%, in line with the model prediction.Recent earnings-price ratios have been below these averages: As

discussed in figure 1, trend earnings have been near or at historiclows relative to prices. The high level of equity prices relative todividends and earnings, combined with the high value of Tobin’s Qshown in figure 2, led numerous commentators and academics to askwhether equity markets are overvalued or if the old yardsticks nolonger apply. Perhaps the phrase most typically associated with thisdebate is ‘‘irrational exuberance,’’ a phrase claimed by Shiller (2000)in his presentation of a range of psychological factors that may ex-plain an irrational bubble in asset prices. Campbell and Shiller (1998)present much of the quantitative analysis behind Shiller’s concerns, inparticular, that a low dividend-price ratio is a signal that equities are




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overvalued and the medium-term outlook for equity returns is poor.This conclusion follows from a careful analysis that shows howprevious episodes with below average dividend-price ratios have beenfollowed by mean reversion in this ratio. Further, they demonstratethat this mean reversion arises from an adjustment in prices notdividends, implying that a low value for D=V leads to below-averageincreases in equity values.

Heaton and Lucas (1999) consider whether changes in funda-mentals such as stock market participation, risk aversion, or timepreference may have lowered the required return to equity and re-sulted in a lower equilibrium level of the dividend-price or earnings-price ratio; overall, they conclude that even large changes in theseparameters can explain at most half the decreased ratio of dividends toequity prices, again suggesting some bubble component. The analysisof Heaton and Lucas is similar to that which follows in that theseauthors employ a general-equilibrium model; however, the model theyconsider is of an endowment economy (i.e., an economy with anexogenous output and dividend stream), so Heaton and Lucas do notexamine the implications of changing fundamentals on production andinvestment, which is important in this paper. The analysis in a pro-duction economy illustrates how investment, dividends, and returnsreact to shifts in fundamentals, considerations absent from the analysisin earlier work.6

Other research suggested that the current low value of the dividend-price ratio does not signal overvaluation of equities. Siegel (1999)suggests that the required return to equity may have fallen from itshistoric average of 9% because new technologies in financial serviceshave lowered transaction costs. He suggests that the return to investorshistorically has been close to 5%—with the difference from the 9%return on a broad equity index representing transaction costs—and theelimination of these transaction costs implies that, in the future, thereturn to equity will be 5%. In addition, Siegel argues that broad marketequity indexes now are more heavily skewed toward fast-growth in-dustries, hence the strength in earnings growth in the years up to 1999is likely to continue, necessitating a higher value of g in the previouspresent-value calculation. For example, simply lowering r to 5% low-ers the earnings-price ratio to 5.

Glassman and Hassett (1999) have gone considerably further andargued that the large equity premium observed historically reflected

6. Roberts (1999) is a partial exception; he examines the response of investment, divi-dends, and stock prices to shifts in required returns and productivity in a model withexogenously fixed interest rates, abstracting from the saving and output effects of Suchshifts. His analysis does not consider what shifts in preferences or risk may alter requiredreturns or distinguish between risky and riskless assets. Nonetheless, this paper has benefitedfrom access to Roberts’ preliminary draft.




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unwarranted pessimism regarding the riskiness of stocks and thatthe equity premium dropped below historical averages. The real returnto commercial paper over 1948–1995 averaged about 2.1%, nearly7 percentage points below the return to equity. It is well-known thatconsiderable effort and modifications of typical asset-pricing modelsare required to generate such a large equity premium (Cochrane1997), leading Glassman and Hassett to conclude that, perhaps, sucha large premium will not be required in the future. While their pre-sentation is somewhat stylistic and geared toward a general audi-ence, more academic commentaries have presented similar musings,albeit less forcefully (such as Cochrane 1997 and Heaton and Lucas1999).

In a model very similar to that presented here, McGrattan andPrescott (2001) also argue that financial markets have not overvaluedU.S. firms. Their presentation relies on a standard stochastic growthmodel whose primary difference from the model here is its failure tomatch the historical equity premium (a well-known failure of suchmodels since Mehra and Prescott 1985). The results in their paper aremore similar than different to those here, despite these authors’ dif-ferent presentation. In particular, while McGrattan and Prescott devi-ate from the presentation that follows in some details, their primaryconclusion is that the market value of firms should reflect the valueof firms’ productive assets. The level of these productive assets isa decreasing function of the required return to equity (among otherfactors). Since the required return to equity implied by their model liesfar below the historical average return, both the justified stock ofproductive assets and the justified market value of firms should beabout twice the value of the GDP, and this is the value they report forthe late 1990s. Hence, the stock market is not overvalued. Implicit inthis analysis is the conclusion that the stock market has been under-valued for nearly every period in U.S. history prior to the late 1990s.7

In contrast, the analysis that follows takes as given the historicalrelationships observed between the market value of firms and othereconomic variables and explores whether the changes in conditions

7. McGrattan and Prescott’s analysis assumes that the ratio of the market value of firms tothe value of their productive assets, Tobin’s Q, should equal 1. While their construction of Qdiffers from that in figure 2, its time-series movements and relationship between currentvalues and historical averages are similar. And McGrattan and Prescott’s assertion thatfinancial markets are not overvalued in 2000 implies that the earlier period was one ofpersistent undervaluation. Historically, Q typically was much less than 1, a fact that might beexplained by other factors, including features of the tax code (e.g., the investment tax creditcould not be used for purchases of used capital, depreciation schedules for tax purposes treatnew and used capital differently). It is also important to note that the average Q fluctuatedsignificantly about its long-run average, and in some periods (e.g., the 1970s) the average Qfell significantly for reasons that economic models have difficulty explaining (reflectingperhaps the obverse of the factors operating in the 1990s).




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typically appealed to as justifications for higher market values canjustify a stock market run-up. McGrattan and Prescott do not considerwhat changes in the economy could generate the equity performance ofthe 1990s.

II. A General-Equilibrium Model

A representative agent, dynamic general-equilibrium model providesa simple framework within which one can examine the impact offundamentals on a broad range of economic variables, including themarket value of firms, investment, output, and the capital stock. Theframework adopted here differs from most macroeconomic analysesby adopting preferences that are not separable across states of nature;this specification (nonexpected utility), following Epstein and Zin(1989) and Weil (1990), allows a separation between risk aversion andintertemporal substitution and hence can better match asset-pricingregularities. The specification and solution of the model with thesepreferences may be unfamiliar to some and of independent interest.The determination of asset prices in the model will be familiar (e.g.,Campbell, Lo, and MacKinlay 1997 or Cochrane 2001). The key in-sights provided by the model relate to the general-equilibrium deter-mination of consumption, investment, and dividends.

A. Consumer Preferences

The representative consumer’s preferences (U ) are defined recursivelyby

Ut ¼ lnCt þh

1� hð Þ 1� mð Þ lnEt e 1�hð Þ 1�mð ÞUtþ1

n o;m > 0; 0 < h < 1;

ð1Þ

where E{} is the mathematical expectations operator, C represents con-sumption, and the remaining symbols represent parameters of the utilityfunction. This recursive definition of preferences allows for a separation ofthe intertemporal elasticity of substitution (which equals 1 in equation (1))and the coefficient of relative risk aversion (m) as in Epstein and Zin (1989)and Weil (1990). When m equals 1, the recursion in equation (1) collapsesto the standard expected utility case, in which the coefficient of relative riskaversion equals the inverse of the intertemporal elasticity of substitution(i.e., 1); when m differs from 1, the recursion in equation (1) implies thatpreferences are not separable across states and the coefficient of relativerisk aversion differs from the inverse of the intertemporal elasticity ofsubstitution. Notably,m greater than 1 implies that consumers are more riskaverse than under expected utility.




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B. Production Technology

Firms produce output (Y ) with capital (K ). The production functionis the familiar AK production function used in simple endogenousgrowth models

Yt ¼ AtKt: ð2Þ

In equation (2), A is an exogenous productivity parameter, whose stochasticproperties are discussed later. This production function, while quite specialin not possessing even short-run decreasing returns to capital, generatesparticularly simple solutions for quantity and asset price fluctuations andhas the property that economic growth occurs endogenously when capitalaccumulation is permitted. A production function with decreasing returnsto capital yields the same results for the questions of interest as the AKproduction function.8

C. Resource Constraints

The resource constraints in the economy are relatively standard. Pro-duction equals consumption plus investment:

Yt ¼ Ct þ It; ð3Þ

The capital accumulation constraint allows for adjustment costsassociated with the installation of capital.9 Adjustment costs drive awedge between the value of the capital stock owned by firms and themarket value of firms, reflecting the scarcity value attached to installedcapital when capital installation is costly.10 Moreover, the model withvery high adjustment costs is equivalent to a model without capitalaccumulation, as in the Lucas (1978) endowment economy.A general specification of adjustment costs is that of Lucas and Prescott

(1971), who consider a capital accumulation equation of the form

Ktþ1 ¼ JIt

Kt

� �Kt; ð4Þ

8. It is simple to show that, in the model that follows with adjustment costs to investment,modifying the production function to Yt ¼ AtK

at L

1�at leaves all the basic results unchanged.

Kiley (2001a) presents an analysis of different issues using this alternative production functionand contains the solution formulas that can be applied to the questions addressed here. Morebroadly, previous work with stochastic growth models (e.g., Tallarini 2000) or work buildingoff the analysis here (e.g., Lafourcade 2001) indicate that the qualitative results here are fairlygeneral, although some modifications of the competitive model here may slightly alter theresults. See the summary for suggestions on how model modifications may help general-equilibrium models better explain equity price developments in the late 1990s.9. Such adjustment costs are standard in investment models (e.g., Lucas 1967, Hayashi

1982).10. Such a wedge is potentially important for the questions at hand, as an increase in this

wedge could explain a run-up in the market value of firms relative to the replacement valueof their capital stock as shown in figure 2. Abel (2000) also emphasizes this distinction.




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where J [�] is increasing and concave. The concavity of the installationfunction J [�] captures the notion of adjustment costs by introducingdiminishing returns to the intensity of investment. Lucas and Prescott(1971) demonstrate how strict concavity of J [�] slows capital stock ad-justment relative to a frictionless benchmark (in which J [�] is linear).Following earlier treatments, the depreciation rate (y) is defined as the levelof investment relative to the capital stock (I/K ) such that the capital stock isunchanged (i.e., y equals J�1[1], using standard notation for an inversefunction). To obtain closed-form solutions, two (mutually exclusive andconvenient) forms of the installation function are assumed:

JIt

Kt

� �¼ It

Kt

þ 1� yð Þ; 0 < y � 1 ð5aÞ

JIt

Kt

� �¼ It

Kt

� �d

; 0 < d � 1: ð5bÞ

These functions satisfy the properties assumed for J [�]. In equation (5a),adjustment costs equal zero (i.e., equation (5a) is the standard accumula-tion identity) and y corresponds to the depreciation rate. In equation (5b),adjustment costs are important (i.e., J [�] is strictly concave) and the degreeof adjustment costs is determined by parameter d. ( In particular, it is animplication of the first-order condition for investment derived later that theelasticity of investment with respect to Tobin’s Q equals 1= 1�ð dÞ). Notethat the definition of the depreciation rate combined with equation (5b)implies that the specification with adjustment costs assumes full depreci-ation. A spate of work adopted equation (5b) because this form is knownto deliver closed-form solutions (e.g., Basu 1987 and Hercowitz andSampson 1991) and captures investment adjustment costs, thereby al-lowing for fluctuations in Tobin’s Q away from one in model simulations(e.g., Abel 2000).11

11. Closed-form solutions for output, consumption, investment, and asset price fluctua-tions are dependent on the specific functional forms used for the preference specification inequation (1), the production function in equation (2), and the adjustment cost specification inequation (4). More generally, closed-form solutions for these variables can be found for anadjustment cost function of the form J ½ It

KT� ¼ ½ 1� yð Þ þ yð It

yKtÞ1�f� 1

1�f ; 0 < y � 1; f � 0. Inthis case, the production function must be a constant-elasticity-of-substitution function ofcapital and labor and preferences must be of the expected-utility, constant-intertemporal-elasticity-of-substitution form, where the elasticity of substitution between capital and laborand the intertemporal elasticity of substitution must be linked to the adjustment cost pa-rameter f (this result is a trivial reformulation of one in Benhabib and Rustichini 1994). Thesesolutions do not allow for nonexpected utility and hence cannot plausibly entertain thechanges in the equity premium discussed here. Nonetheless, the basic thrust of all the resultshere are unchanged within this class of model. Moreover, the results would hold more broadlyin stochastic growth models solved via numerical techniques (e.g., Tallarini 2000).




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III. The Competitive Equilibrium

The competitive equilibrium of the economy can most easily be foundby considering a social planner’s problem (as is often the case, e.g.,Sargent 1987). The competitive allocation of consumption and in-vestment is the solution of a benevolent social planner’s maximizationof utility, equation (1), subject to the technological and resource con-straints, equations (2) to (5).The first-order conditions for consumption, investment and next

period’s capital stock are

BUj

BCj

¼ E j; Et ¼1

Ct

; Etþ1 ¼1

Ctþ1

e 1�hð Þ 1�mð ÞUtþ1

Et e 1�hð Þ 1�mð ÞUtþ1f gð6Þ

E t ¼ J 0It

Kt

� �qt; ð7Þ

qt ¼ hEt E tþ1Atþ1 þ qtþ1 JItþ1

Ktþ1

� �� J 0

Itþ1

Ktþ1

� �Itþ1

Ktþ1

� �� : ð8Þ

Equation (6) defines the marginal utility of consumption, andequation (7) defines the marginal value of an additional unit of capitalin period t + 1 (the multiplier on either equation (5a) or (5b), qt ). Notethat it is clear from equation (7) that Tobin’s Q corresponds to theratio of the Lagrange multiplier on the capital accumulation equation(5a) or (5b) (given by q) and the Lagrange multiplier on the aggregateresource constraint equation (3) (given by E) and hence equals J 0 �½ ��1

,an intuitive result as this corresponds to the value of installed capitalrelative to uninstalled capital. This implies that Tobin’s Q alwaysequals 1 without adjustment costs (case (5a)) and the elasticity of I/Kwith respect to Tobin’s Q equals 1= 1� dð Þ in the case with adjustmentcosts. Equation (8) (in combination with equation (6)) equates themarginal rate of substitution between current and future consumptionto the return to postponed consumption (which involves both themarginal product of capital in production and the marginal product ofinvestment in capital accumulation). This is the intertemporal conditionfor optimality.Generally, the nonlinear equations that characterize the optimal al-

location (equations (2) through (8)) do not possess closed-form so-lutions; however, in the current case, the assumptions regardingfunctional forms yield a solution via what Long and Plosser (1983)term ‘‘dumb luck.’’ Dumb luck consists of a method of undeterminedcoefficients: Guess a form of the decision rules for consumption andinvestment and verify that a solution of this form satisfies all the




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first-order conditions and constraints. By-products of this procedureare the decision rules in terms of the underlying parameters governingpreferences and technology.

To implement this procedure, one needs good guesses for the de-cision rules. In the case without adjustment costs, such a guess issimple, as it is well-known that, in similar problems where consumersreceive only capital income, consumption is proportional to thecapital stock. In the case with adjustment costs, the contributions ofLong and Plosser (1983) and Hercowitz and Sampson (1991) suggestthat a good guess is that consumption and investment are a constantfraction of output.12 Inserting these guesses into the first-order con-ditions and some algebra yield the solutions for both cases, shown inbox 1.

Box 1. Solutions for quantities in the case without adjustmentcosts:

Ct ¼ 1� hð Þ Yt þ 1� yð ÞKt½ �; It ¼ hYt � 1� hð Þ 1� yð ÞKt; ðI:aÞ

Yt ¼ AtKt; ðI:bÞ

Ktþ1 ¼ h Yt þ 1� yð ÞKt½ � ðI:cÞ

Solutions for quantities in the case with adjustment costs:

Ct ¼1� h

1� h 1� dð Þ Yt; It ¼hd

1� h 1� dð Þ Yt; ðII:aÞ

Yt ¼ AtKt; ðII:bÞ

Ktþ1 ¼ K1�dt Idt ðII:cÞ

These solutions have intuitive properties. For example, in the casewithout adjustment costs, a change in productivity (A) has a greatereffect (in percentage terms) on investment, as capital is accumulated,than on consumption, leading to greater variability in investment thanconsumption for plausible specifications of the process governing A. Inthe case with adjustment costs, the frictions in capital installation lowerthe incentives to invest; hence, investment and consumption respondequally, in percentage terms, to any shift in A.

12. It would seem that, since the model with adjustment costs has no labor income,consumption should be proportional to wealth in every period. In fact, as will be shown later,this remains true in the model with adjustment costs; the constant saving-rate consumptionrule arises because investment is proportional to wealth in the adjustment cost model.




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Moreover, since the solutions for investment and consumption areindependent of risk aversion, the time path of all quantities is inde-pendent of risk aversion. Nonexpected utility does not alter thebusiness cycle or growth properties of the model at all, regardless ofthe degree of risk-aversion. This result will prove quite useful next incalibrating the model to match growth and asset-pricing regularities.

A. Asset Pricing

Non-state-separable preferences (Epstein-Zin-Weil preferences) werefirst applied to asset-pricing issues, as a perusal of the references makesclear. The analytical characterization of quantity dynamics allows asimple characterization of asset returns, which is crucial in any exam-ination of movements in the market value of firms.Following the usual practice (e.g., Campbell et al. 1997; Cochrane

2001), assets can be priced with knowledge of a pricing kernel or sto-chastic discount factor M. Specifically, the return to an asset j is deter-mined by the following equation:

1 ¼ Et Rjtþ1Mtþ1

� �; ð9Þ

where Rjtþ1is the return on asset j between period t and period t þ 1. The

stochastic discount factor M is given by the ratio of the marginal utility ofconsumption in period t þ 1 to the marginal utility of consumption inperiod t:

Mtþ1 ¼BUt

BCtþ1

,BUt

BCt

¼ hCt

Ctþ1

e 1�hð Þ 1�mð ÞUtþ1

Et e 1�hð Þ 1�mð ÞUtþ1f g: ð10Þ

In the expected utility case (m equal to 1), equation (10) simplifies to thefamiliar log-utility case, where the stochastic discount factor is the dis-counted inverse of consumption growth.First, consider the implications of the model for the risk-free rate:

Rearranging equation (9) shows that the risk-free rate equals the inverseof the expected value of the stochastic discount factor:

Rjtþ1 ¼

1

Et Mtþ1f g : ð11Þ

To determine the expectation in equation (11), the stochastic process forproductivity must be specified. Two different cases are considered, againcorresponding to a case without adjustment costs of investment and a casewith adjustment costs. In each of these cases, the process for A and theremaining parameters is chosen to yield an identical, random-walk process




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for the log-level of consumption in which the innovation has a normaldistribution. It is easy to show that utility is distributed normally when thelog of consumption has a normal distribution and find the expectations inequations (9) to (11).13

To derive the return to equity (i.e., the return to a claim to capital),consider a decentralized version of the model, in which firms undertakeinvestment and issue shares to finance this investment. For simplicity,one share is traded as a claim to the economy’s capital stock, with valueVt at the end of period t (following the payment of dividends, so Vt is theex-dividend price of the share). The return to an investment in this shareis Vtþ1 þ Dtþ1ð Þ=Vt, where D represents the dividend payment (whichin turn equals the firm’s revenue minus investment, Y � I ). Using thestandard arguments, the value of the share equals the value of the capitalstock in terms of consumption. In the model without adjustment costs,the relative price of capital (in terms of consumption, Tobin’s Q) isalways 1. In the model with adjustment costs, the price of investment interms of consumption is 1, but the capital adjustment costs implied byequation (5b) mean that the price of capital in terms of consumption(Tobin’s Q) differs from one and equals

Qt ¼BKtþ1

BIt

� ��1

¼ 1

d

It

Kt

� �1�d

:

The return to equity is therefore

Retþ1 ¼

Vtþ1 þ Dtþ1

Vt

¼ Qtþ1Ktþ2 þ Dtþ1

Qt Ktþ1

¼ Atþ1 þ 1� y; case að Þ

¼ 1

hYtþ1

Yt; case bð Þ

Taking expectations of this equation yields the expected return to equity.Box 2 summarizes the stochastic processes for productivity, consumption,and asset returns in both cases; note that, since consumption follows thesame stochastic process in each case, the asset returns are the same ineach case.

13. It is clear from assumptions (I.d) and (II.d) in box 2 and the formulas in box 1 that thenatural logarithm of consumption is normally distributed. To confirm that utility is thennormally distributed, examine equation (1); as the log of consumption is the only stochasticterm, utility is normally distributed. With this knowledge (and the fact that E exf g equalsemþ0:5s when x is normally distributed with mean m and variance s), a method of unde-termined coefficients can be trivially applied to equation (1) to find the stochastic processgoverning utility. Kiley (2001a) contains more relevant algebra.




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Box 2. Stochastic Processes and Asset ReturnsStochastic process in the case without adjustment costs (case a):

ln At þ 1� yð Þ½ � ¼ ln Aa þ 1� yð Þ½ � þ et; et � N 0;j2

ðI:dÞ

Stochastic process in the case with adjustment costs (case b):

lnAt ¼ d lnAb þ 1� dð ÞlnAt�1 þ et; et � N 0;j2

ðII:dÞ

Consumption process for cases a and b:

lnCt ¼ g þ lnCt�1 þ et; et � N 0;j2

;

g ¼ ln Aa þ 1� yð Þ½ � þ lnh ¼ d lnAb þ d lnhd

1� h 1� dð Þ

Risk-free gross return:

Rftþ1 ¼

1

hegþ

12�m

o2 :

Return to equity:

EtRetþ1 ¼

1

hegþ

12o2 :

Equity premium:

ln EtRetþ1=R

ftþ1

� �¼ mj2:

The properties of these asset returns are reasonable: The risk-freerate is decreasing in risk aversion (as investors who are more riskaverse are willing to pay more for the safety of a risk-free real return)and the equity premium is increasing in risk aversion. Importantly, thereturn to equity is independent of risk aversion; this return is deter-mined by the discounted value of dividends, and risk aversion affectsonly the risk-free rate. The ability of the model to match the equitypremium through high degrees of risk aversion without altering thedynamic properties of quantity variables proves very useful in cali-brating the model to match both consumption dynamics and assetreturns. In particular, business cycle modelers consider high degrees ofrisk aversion implausible because a high degree of risk aversion wouldlead to a strong consumption-smoothing motive when risk aversion andintertemporal substitution are tightly linked (as in Rouwenhorst 1995 orJermann 1998). In the model of this paper, such strong consumption-smoothing motives do not arise because risk aversion and intertemporal




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substitution are separated.14 In any event, most explanations of theequity premium require high degrees of risk aversion (Campbell et al.1997; Cochrane 2000), and most of the studies cited by these authors donot go as far as the model here by considering the joint behavior ofconsumption and asset returns driven by some exogenous shock pro-cess. Moreover, by separating intertemporal substitution and risk aver-sion, the model here encounters no problems matching both the equitypremium and the risk-free rate for plausible discount factors (a problemcommon to other models, such as Weil 1989; Campbell et al. 1997).

B. The Lucas Endowment Model

An important special case of the model occurs when capital is fixed,which is the model with adjustment costs that are arbitrarily large (thecase b, d equal to zero case). In this case, we normalize the constantcapital stock to 1, so that consumption simply equals the productivityprocess (A). Choosing this productivity process to match the con-sumption process in the other versions of the model (given in box 2)yields identical processes for consumption and asset returns acrossmodels. However, in this case the price of the equity claim equalsh= 1� hð Þð ÞCt.This model is the Lucas (1978) asset-pricing model under the utility

specification (equation (1)). Note that the solutions for the price ofequity and return to equity are the same as the solution under log-utility (e.g., Sargent 1987, p. 96), but the risk-free rate is differentwhen the coefficient of relative risk aversion differs from 1.

C. Calibration

The closed-form solutions allow for analytic results, but parametervalues are also assigned to gain some insight into the quantitative natureof the predictions. Over the 1948–1995 period, the average change inthe log of nondurable and services consumption (1996 chain-weightedprices) was 0.032(g) and the variance of this change was 0.00015(j2).Given these parameter values and a historical (gross) real return toequity of 1.086, the formula for the return to equity in box 2 implies thatthe discount factor (h) must equal 0.9508. The historical real risk-freereturn averaged 1.021, implying an equity premium of 0.062 (in logterms) and a coefficient of relative risk aversion (m) of 411. This is verylarge but does not have the implications that lead macroeconomists todismiss large degrees of risk aversion in the current model, as discussedalready. The parameters governing capital accumulation (y and d ) are

14. Tallarini (2000) shows, through a range of numerical simulations, near independenceof quantity fluctuations from risk aversion in a related model that must be solved using thenumerical discounted linear exponential quadratic gaussian control techniques of Hansenand Sargent (1995).




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set so that the ratio of the market value of firms to business investmentroughly matches the average over 1948–1995 (9.35), implying that yequals 0.078 and d equals 0.107.15 These values are plausible values forthe depreciation rate and the elasticity of the investment-to-capital ratiowith respect to Tobin’s Q 1= 1� dð Þ ¼ 1:12ð Þ, although the latter is a bithigher than some estimates in the literature.

IV. The Implications of Shifts in Preferences or Technology

Given the various versions of the model and the calibrated parametervalues reported previously, the implications of shifts in preferences(changes in risk aversion and time preference) and shifts in technology(average growth rate and the variance of growth innovations) can beanalyzed. These types of parameter shifts are considered because mostdiscussions of the run-up in equity values in recent years either ex-plicitly (e.g., Heaton and Lucas 1999) or implicitly (e.g., Glassman andHassett 1999) appeal to similar factors.

A. Shifts in Preferences

First consider the implications of shifts in preferences. For example,discussions that suggest that the run-up in equity values in recent yearsstems from declines in the required return to equity are potentiallyconsistent with a decrease in risk aversion or the discount rate. In theGordon growth model, a lower value of the required return to equitygenerates a run-up in the ratio of equity value to dividends (whichequals 1= r � gð Þ, where r is the return to equity) and earnings; such arun-up occurred in the 1990s (as shown in figure 1), and this type ofreasoning appears to be standard practice.Turning to the implications of the model, table 1 reports the effects of

shifts in preferences for three cases: the Lucas endowment model, themodel without adjustment costs, and the model with adjustment costs.The top panel reports the impact of lower risk aversion: a higher risk-free rate and a lower equity premium across the board. In fact, if oneentertained large shifts in risk aversion, the equity premium could belowered dramatically. However, the lower equity premium stems en-tirely from the higher risk-free rate. The return to equity, the ratio of themarket value offirms to output (V/Y ), and the dividend-price ratio (D/Y )are unchanged. In this model, the return to a claim to consumption in thefuture depends on intertemporal substitution, not risk aversion.The results are identical for this shift in all three models. Lower risk

aversion and a lower equity premium need not lead to a run-up in the

15. The ratio of the market value of firms to investment equals QtKtþ1=It in both models(with and without adjustment costs). Using the capital accumulation equations and thedefinition of Q, this ratio equals eg= eg � 1þ yð Þ in case a and 1/d in case b.




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market value of firms, as the lower equity premium can arise from anincrease in the risk-free rate. This result stands in sharp contrast to thestandard discussion, which observes that the historical return to equity hasbeen higher than would be justified if risk-aversion is low and attributesthe run-up in equity values to a fading of the equity premium. The modelhere clearly illustrates that such a fading may have no effect on equityvaluations, as it could occur through an increase in the risk-free rate.

The lower panel reports the effect of a lower discount rate accompaniedby an appropriate adjustment to technology (A) to leave growth unaltered.Under this shift, the economy moves to lower risk-free and equity returns(with an unchanged equity premium) and experiences a run-up in marketvalue relative to output (and a drop in the dividend-price ratio). Note,however, that in the endowment economy the ratio of dividends to outputremains constant, but in the production economies the ratio of dividendsto output (D/Y ) falls, as the ratio of investment to output (I/Y ) rises. Thedecline in the ratio of dividends to output accompanying a decrease in thediscount rate implies that the run-up in market value relative to output ismuted relative to the Gordon growth model effect or the effect in theendowment economy, a potentially quantitatively important result absentfrom models that abstract from capital accumulation. The rise in the ratioof investment to output reflects the increased saving that accompanies alower discount rate, and increased savings/investment is a key driver in theincrease in the market value of firms relative to output.

To summarize, a shift in preferences that lowers the required return toequity can lead to a run-up in the ratio of the market value of firms.However, lower risk aversion need not lower the required return to

TABLE 1 Effect of Changes in Preferences on Asset Returns and Market Value

Variable Endowment Model A. No Adjustment Costs B. Adjustment Costs

Lower Risk Aversion (�m< 0)

Rtþ1 f + + +Rtþ1e 0 0 0lnðEtRtþ1e=Rtþ1 f Þ � � �Vt=Yt 0 0 0Dt=Vt 0 0 0Dt=Yt 0 0 0

It=Yt n.a. 0 0

Lower Discount Rate (�h> 0)

Rtþ1 f � � �Rtþ1e � � �lnðEtRtþ1e=Rtþ1 f Þ 0 0 0Vt=Yt + + +Dt=Vt � � �Dt=Yt 0 � �It=Yt n.a. + +




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equity, and higher savings/investment is a key driver of the market valueof firms in the models with capital accumulation.

B. Shifts in Technology

Now consider the effects of faster growth or a lower variance ofproductivity innovations. The prospect of faster growth is often men-tioned in discussions of the run-up in the market value of firms, in partbecause of the very good growth performance of the U.S. economy inthe late 1990s. A lower variance may also be supported by recent data,as argued for some parts of the GDP by McConnell and Perez-Quiros(2000), or could be interpreted as a way to model increased portfoliodiversification, as argued in Heaton and Lucas (1999). If the lowervariance decreased the required return to equity or faster growth boostedthe growth rate, the run-up in market values relative to dividends pre-dicted by the Gordon growth model would be substantial.Table 2 reports the implications of shifts in technology in the model

for the three cases: the Lucas endowment model, the model withoutadjustment costs, and the model with adjustment costs. The top panelreports the impact of a decline in aggregate variability. The risk-freereturn rises, the equity return falls, and the risk premium declines in allthree cases. However, the decline in the equity return is not accompa-nied by a run-up in themarket value offirms in any of the models. This isbecause the decline in the equity return solely reflects a Jensen’s in-equality effect; expected continuously compounded returns to equityEtln Rtþ1eð Þð Þ are unaffected, as are savings, investment, capital, andmarket value. The decline in the equity premium reflects the decrease in

TABLE 2 Effect of Changes in Technology on Asset Returns and Market Value

Variable Endowment Model A. No Adjustment Costs B. Adjustment Costs

Lower Variance (�j 2< 0)

Rtþ1 f + + +Rtþ1e � � �lnðEtRtþ1e=Rtþ1 f Þ � � �Vt=Yt 0 0 0Dt=Vt 0 0 0Dt=Yt 0 0 0

It=Yt n.a. 0 0

Faster Growth (�g> 0)

Rtþ1 f + + +Rtþ1e + + +lnðEtRtþ1e=Rtþ1 f Þ 0 0 0Vt=Yt 0 � 0Dt=Vt 0 0 0Dt=Yt 0 � 0It=Yt n.a. + 0




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aggregate risk associated with lower aggregate variability and could bequantitatively substantial (a point examined later) but occurs through anincrease in the risk-free rate and hence does not boost the market value.

The lower panel reports the effects of faster growth. In each model,faster growth raises the risk-free and equity return and leaves un-changed the equity premium. In the endowment economy, the increasein the required return to equity offsets the effect of faster growth on thepresent discounted value of dividends, and the market value is unaf-fected by the shift. In the model with adjustment costs (case b), themarket value is similarly unaffected because the higher required returnoffsets the effect of faster growth; note also that savings and investmentare unaffected by the faster pace of growth with adjustment costs be-cause the incentive to lower savings in the face of a higher futureconsumption stream is offset by the effect of higher returns on savings.The lack of any effect of faster growth on savings is the key to the zeroeffect on the market value, as the market value is proportional to in-vestment in the model with adjustment costs. This link between themarket value and investment in the general-equilibrium model is sen-sible, reflecting the Q-literature argument that a high market valuereflects good investment opportunities (although such arguments areoften partial equilibrium in nature).

The model without adjustment costs contains an even more startlingresult: The market value of firms, relative to output, falls when theeconomy moves to a faster average growth rate. In the model, fastergrowth spurs higher savings, higher investment, and hence lowerdividends. The decline in the level of dividends and the increase in therequired return to equity actual lead to a lower present discounted valueof dividends relative to output (despite the faster growth in dividends)and a lower ratio of market value to output.

To summarize, lower aggregate variability lowers the equity pre-mium, but has no effect on the ratio of the market value of firms tooutput or the dividend-price ratio. Similarly, faster growth prospectsleave the market value to output ratio unchanged or lower, because ofthe negative effects that arise from higher required returns, an increasein investment, and a lower dividend share of output.

C. Quantitative Example

The preceding analysis suggests that it is quite difficult to generate asubstantial run-up in the market value of firms in the models of thispaper, relative to the results one might derive from the Gordongrowth model, because of the links among saving, investment, divi-dends, asset returns, preferences, and technology. Unlike in the Gordongrowth model, the risk-free return and dividend share are not exoge-nous in general equilibrium. As an illustrative exercise, consider theeffects of a number of quantitatively ‘‘plausible’’ shifts in technology




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and preferences. In particular, consider the effects of the followingsimultaneous changes:

1. Lower aggregate volatility by 0.00008 (so that j2 equals 0.00007);the variance of innovations in nondurables and services consump-tion growth over 1985–1999 was 0.00007, which change generatesthis lower value for consumption variability;

2. Lower the discount rate to generate a return to equity of 0.04, thevalue suggested by Glassman and Hassett, requiring h equal to0.9928. In addition, the change in time preference is accompaniedby a shift in technology that leaves growth unaltered.16

Note that, in the models used in this paper, only the discount rate changegenerates an increase in the ratio of the market value of firms to output ordividends, and this increase is larger than would be the case if growth wereallowed to rise, because faster growth leaves unchanged or lowers the ratioof market value to output (table 2).The effect of these changes in the Gordon growth model is simple

to calculate: The new value of the dividend-price ratio is 0.008, andthe new value of the earnings-price ratio is 0.04. If this value wereextrapolated to recent experience, equities would be fairly valued, onaverage, over the recent time period, repeating a popular claim. Theview from the general-equilibrium model is quite different. First,consider expected returns: The return to equity equals 0.04 by con-struction, and the equity premium falls by more than half, to 0.029.This large decline in the equity premium reflects the large shift inaggregate risk associated with the stable macroeconomy over the lastdecade and a half. As discussed earlier, the lower level of risk, by itself,generates the large drop in the equity premium under the changesoutlined in 1 and 2, but has no effect on the market value of firms.Under the changes induced by 1 and 2, the dividend-price ratio

implied by the general-equilibrium models is the same as that in theGordon growth model, but the run-up in the market value of firmsgenerated by the burst of savings and investment is muted by the in-crease in investment; in simpler terms, the dividend-price ratio fallsboth because of an increase in market value and a decrease in divi-dends. Turning to the quantity implications of the shift in time pref-erence, the ratio of market value to investment declines in the modelwithout adjustment costs and is unchanged in the model with adjust-ment costs. As shown in figure 3, the ratio of market value to invest-ment or savings skyrocketed since the mid-1990s, which is inconsistent

16. Given the formulas for g in case a and b in box 2, the changes in Aa and Ab that leave gunchanged for the new value of h are easy to compute. Note that values for Aa and Ab havenot been discussed in the calibration section, as their sole effect is on average growth (g) andg is chosen directly.




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with the models of this paper.17 Similarly, figure 4 reveals that the shareof business investment in business output is not high by historicalstandards currently (at least not beyond the range of normal cyclicalvariation); in fact, the 2001 value equaled the average since 1948 andwas below the average over more recent decades. Apparently, firms donot believe that investment in projects with low returns are accepted byshareholders and have not increased investment strongly. Hence, thesurge in the market value of firms in the late 1990s, while qualitativelyconsistent with the notion that the required return to equity has fallen,does not appear to be consistent with the implications of a typicalgeneral-equilibrium model when the implications outside of financialmarkets are considered.

These results are not sensitive to the assumption that the growtheffects of a lower discount rate are offset by a shift in technology (A); asmentioned previously, faster growth either lowers the ratio of marketvalue to output or leaves this ratio unchanged and raises the investment

Fig. 3.—Ratio of market value to investment or saving

17. All ratios involving series from the National Income and Product Accounts (NIPA)involve the nominal values of these series, as the market values are reported in nominalterms, and ratios of series from the NIPAs derived from chain-weighted series do notaccurately reflect the changes in spending in these categories (reflecting the nonadditivity ofchain-weighted series).




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share of output, implying once again that investment should increasemore than market value following a fall in the discount rate.

V. Summary

The relationship between the market value of firms and fundamentalsin a production economy is different than the relationship between themarket value of firms and fundamentals in typical calculations usingthe Gordon growth model. Research using the this model has sug-gested that the recent surge in the market value of the business sectoris not necessarily a signal of investors’ ‘‘irrational exuberance’’ butrather reflects a decline in the equity premium or an increase in growth.Such claims are quite reasonable in the Gordon growth model. How-ever, the Gordon model was meant to describe a relationship between asingle firm’s earnings, dividends, and required returns, not the general-equilibrium determination of interest rates, investment and growthprospects.Consideration of general-equilibrium effects overturns the intuition

many glean from the Gordon growth model. The risk-free rate is notexogenous and hence changes in aggregate risk or investor’s riskaversion that lower the equity premium need not lower equity returns;the models of this paper suggest that, under sensible conditions, therisk-free rate rises in response to such shifts. Factors that lower the

Fig. 4.—Investment share of business output, 1948–2001




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required return to equity spur saving and hence capital accumulation.The process of capital accumulation requires increased investment andhence greater retained earnings and lower dividends. Because of thisprocess, the increase in the market value of firms stemming from ashift in the required return to equity in a production economy is lowerthan the increase in the Gordon model. And the market value of firmsrelative to investment/savings tends to fall, or at least not rise, in themodels of this paper when required returns drop. The data clearly donot suggest that firms increase investment in response to a shift to lowrequired returns. Further, the model illustrated how the links betweengrowth, savings, and investment imply that faster growth can actuallylower the ratio of the market value of firms to output, a prediction ofopposite sign from the Gordon growth model.

This discussion implies that the model of this paper fails to explainwhy the market value of firms rose so dramatically, relative to just aboutany imaginable gauge of fundamentals, in the late 1990s. This failure,while unsatisfying at some level, suggests a reorganization of thinkingaway from the simple Gordon growth model calculations that can befound in Heaton and Lucas (1999) or International Monetary Fund(1999). One approach may be to build other factors into the type ofmodel presented here. For example, Lafourcade (2001) considers howimperfect competition may alter the results slightly. In particular, thepresence of monopoly power drives a wedge between the marginal andaverage Q (from Hayashi 1982), creating an avenue along which someof the results regarding how market values, dividends, and investmentrespond to changes in fundamentals can differ from the competitivebenchmark of this investigation. However, Lafourcade’s conclusionsare very similar, especially once firm entry is allowed to drive profits tozero in the long run (as in this case, the long run effects are essentiallythose contained here and the short-run effects differ only marginally).An alternative route may be one mentioned (but not pursued) inMcGrattan and Prescott (2001), who suggest that technological changesthat raise the capital intensity of production (perhaps including intan-gible capital) could be followed by a run-up in market values. To theextent such a shift benefits physical capital, a surge in physical in-vestment may be expected, and many of the results of this paper re-garding the general-equilibrium response of investment and dividendsapply. However, such a shift benefiting intangible capital may not havesuch clearly measurable consequences; hence, further investigationsalong the lines of Hall (2001), Bonds and Cummins (2000), andCummins (2002) would prove informative. Finally, some very recentresearch has begun to explore whether capital market features that makefinancing costs lower during booms may better explain large fluctua-tions in equity market values (e.g., Caballero and Hammour 2002 andJermann and Quadrini 2002).




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As an alternative, perhaps the trail pursued in Shiller (2000), whoemphasizes psychological factors, will prove fruitful in explaining therise in the market value of firms in the late 1990s. Such investigationsshould also focus on whether deviations of asset prices from funda-mentals provide some opportunity for perceptive investors to makeunusual returns or whether the nature of such fluctuations makes suchefforts only marginally profitable.

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