JUNIOR CAN'T BORROW: A NEW PERSPECTIVE ON THE … QJE.pdftheless, consumer heterogeneity withina generation is down-played in our model in order to isolate and explore the implications

JUNIOR CANrsquoT BORROW A NEW PERSPECTIVEON THE EQUITY PREMIUM PUZZLE

GEORGE M CONSTANTINIDES

JOHN B DONALDSON

RAJNISH MEHRA

Ongoing questions on the historical mean and standard deviation of thereturn on equities and bonds and on the equilibrium demand for these securitiesare addressed in the context of a stationary overlapping-generations economy inwhich consumers are subject to a borrowing constraint The key feature capturedby the OLG economy is that the bulk of the future income of the young consumersis derived from their wages forthcoming in their middle age while the bulk of thefuture income of the middle-aged consumers is derived from their savings inequity and bonds The young would like to borrow and invest in equity but theborrowing constraint prevents them from doing so The middle-aged choose tohold a diversied portfolio that includes positive holdings of bonds and thisexplains the demand for bonds Without the borrowing constraint the youngborrow and invest in equity thereby decreasing the mean equity premium andincreasing the rate of interest

I INTRODUCTION

The question as to why the historical equity premium is sohigh and the real rate of interest is so low was addressed inMehra and Prescott [1985] They demonstrated that the equilib-rium of a reasonably parameterized representative-consumerexchange economy is able to furnish a mean annual premium ofequity return over the riskless rate of at most 035 percent incontrast to its historical level of 6 percent in U S data Further-more the equilibrium annual riskless rate of interest is consis-tently too high about 4 percent as opposed to the observed 1percent in U S data1 Further in econometric tests the condi-

We thank Andrew Abel John Cochrane Roger Craine Domenico CuocoSteven Davis the editor Edward Glaeser John Heaton Thore Johnsen HayneLeland Robert Lucas the late Merton Miller Kevin Murphy Nicholas SoulelesNancy Stokey Jonathan Parker Raaj Sah Raman Uppal three anonymousreferees and participants at numerous conferences and seminars for helpfulcomments We are particularly indebted to Edward Prescott for numerous helpfulinsights and advice on the calibration of our model We also thank Yu-Hua ChuYubo Wang and Lior Mezly for computational assistance The usual caveatapplies Constantinides acknowledges nancial support from the Center for Re-search in Security Prices the University of Chicago Mehra acknowledges nan-cial support from the Academic Senate of the University of California Donaldsonacknowledges nancial support from the Faculty Research fund of the GraduateSchool of Business Columbia University

1 This point is emphasized in Weil [1989]

copy 2002 by the President and Fellows of Harvard College and the Massachusetts Institute ofTechnologyThe Quarterly Journal of Economics February 2002

269

tional Euler equation of per capita consumption is also rejected byHansen and Singleton [1982] Hansen and Jagannathan [1991]Ferson and Constantinides [1991] and others

Several generalizations of key features of the Mehra andPrescott [1985] model have been proposed to better reconcileobservations with theory These include alternative assumptionson preferences2 modied probability distributions to admit rarebut disastrous events3 incomplete markets4 and market imper-fections5 none have fully resolved the anomalies Cochrane andHansen [1992] and Kocherlakota [1996] provide excellent surveysof this literature

The novelty of this paper lies in incorporating a life-cyclefeature to study asset pricing The idea is appealingly simple Theattractiveness of equity as an asset depends on the correlationbetween consumption and equity income If equity pays off instates of high marginal utility of consumption it will command ahigher price (and consequently a lower rate of return) than if itspayoff is in states where marginal utility is low Since the mar-ginal utility of consumption varies inversely with consumptionequity will command a high rate of return if it pays off in stateswhen consumption is high and vice versa6

A key insight of our paper is that as the correlation of equityincome with consumption changes over the life cycle of an indi-vidual so does the attractiveness of equity as an asset Consump-

2 For example Abel [1990] Benartzi and Thaler [1995] Boldrin Christianoand Fisher [2001] Campbell and Cochrane [1999] Constantinides [1990] Daniel andMarshall [1997] Epstein and Zin [1991] and Ferson and Constantinides [1991]

3 See Reitz [1988] and Mehra and Prescott [1988]4 For example Bewley [1982] Constantinides and Dufe [1996] Detemple

and Serrat [1996] Heaton and Lucas [1997 2000] Krusell and Smith [1998]Lucas [1994] Mankiw [1986] Marcet and Singleton [1999] Mehra and Prescott[1985] Storesletten Telmer and Yaron [1999] and Telmer [1993] Empiricalpapers that investigate the role of incomplete markets on asset prices includeBrav Constantinides and Geczy [2002] Cogley [1999] Jacobs [1999] and Vis-sing-Jorgensen [2002]

5 For example Aiyagari and Gertler [1991] Alvarez and Jermann [2000]Bansal and Coleman [1996] Basak and Cuoco [1998] Brav and Geczy [1995]Danthine Donaldson and Mehra [1992] He and Modest [1995] Heaton andLucas [1996] Luttmer [1996] McGrattan and Prescott [2000 2001] and Stores-letten Telmer and Yaron [1999] Empirical papers that investigate the role oflimited participation as a manifestation of market imperfections on asset pricesinclude Attanasio Banks and Tanner [2002] Brav and Geczy [1995] BravConstantinides and Geczy [2002] Cogley [1999] Jacobs [1999] Mankiw andZeldes [1991] and Vissing-Jorgensen [2002]

6 This is precisely the reason why high-beta stocks in the simple CAPMframework have a high rate of return In that model the return on the market isa proxy for consumption High-beta stocks pay off when the market return is highie when marginal utility is low hence their price is (relatively) low and their rateof return high

270 QUARTERLY JOURNAL OF ECONOMICS

tion can be decomposed into the sum of wages and equity incomeA young person looking forward in his life has uncertain futurewage and equity income furthermore the correlation of equityincome with consumption will not be particularly high so long asstock and wage income are not highly correlated This is empiri-cally the case as documented by Davis and Willen [2000] Equitywill thus be a hedge against uctuations in wages and a ldquodesir-ablerdquo asset to hold as far as the young are concerned

The same asset (equity) has a very different characteristic forthe middle-aged Their wage uncertainty has largely been re-solved Their future retirement wage income is either zero ordeterministic and the innovations (uctuations) in their con-sumption occur from uctuations in equity income At this stageof the life cycle equity income is highly correlated with consump-tion Consumption is high when equity income is high and equityis no longer a hedge against uctuations in consumption hencefor this group it requires a higher rate of return

The characteristics of equity as an asset therefore changedepending on who the predominant holder of the equity is Life-cycle considerations thus become crucial for asset pricing If eq-uity is a ldquodesirablerdquo asset for the marginal investor in the econ-omy then the observed equity premium will be low relative to aneconomy where the marginal investor nds it unattractive to holdequity The deus ex machina is the stage in the life cycle of themarginal investor

In this paper we argue that the young who should be holdingequity in an economy without frictions and with complete con-tracting are effectively shut out of this market because of bor-rowing constraints They are characterized by low wages ideallythey would like to smooth lifetime consumption by borrowingagainst future wage income (consuming a part of the loan andinvesting the rest in higher return equity) However as is wellrecognized they are prevented from doing so because humancapital alone does not collateralize major loans in modern econo-mies for reasons of moral hazard and adverse selection

In the presence of borrowing constraints equity is thus ex-clusively priced by the middle-aged investors since the young areeffectively excluded from the equity markets and we observe ahigh equity premium If the borrowing constraint is relaxed theyoung will borrow to purchase equity thereby raising the bondyield The increase in the bond yield induces the middle-aged toshift their portfolio holdings from equity to bonds The increase in

271JUNIOR CANrsquoT BORROW

the demand for equity by the young and the decrease in thedemand for equity by the middle-aged work in opposite direc-tions On balance the effect is to increase both the equity and thebond return while simultaneously shrinking the equity premiumFurthermore the relaxation of the borrowing constraint reducesthe net demand for bonds and the risk-free rate puzzlereemerges

In order to systematically illustrate these ideas we constructan overlapping-generations (OLG) exchange economy in whichconsumers live for three periods In the rst period a period ofhuman capital acquisition the consumer receives a relatively lowendowment income In the second period the consumer is em-ployed and receives wage income subject to large uncertainty Inthe third period the consumer retires and consumes the assetsaccumulated in the second period We explore the implications ofa borrowing constraint by deriving and contrasting the stationaryequilibria in two versions of the economy In the borrowing-constrained version the young are prohibited from borrowing andfrom selling equity short The borrowing-unconstrained economydiffers from the borrowing-constrained one only in that the bor-rowing constraint and the short-sale constraint are absent

Our model introduces two forms of market incompletenessFirst consumers of one generation are prohibited from tradingclaims against their future wage income with consumers of an-other generation7 Second consumers of one generation are pro-hibited from trading bonds and equity with consumers of anunborn generation Our model suppresses a third and potentiallyimportant form of market incompleteness that arises from theinability of an age cohort of consumers to insure via pooling therisks of their persistent heteroskedastic idiosyncratic incomeshocks8 Specically we model each generation of consumerswith a representative consumer This assumption is justied onlyif there exists a complete set of claims through which heteroge-

7 Being homogeneous within their generation consumers have no incentiveto trade claims with consumers of their own generation

8 This perspective is emphasized in Storesletten Telmer and Yaron [1999]They provide empirical evidence that shocks to the wage income process indeedhave these properties and introduce this type of shocks in their model They ndthat the interaction of life-cycle effects and the uninsurable wage income shocksplay an important role in generating their results Although they have a borrow-ing constraint in their model as we do it is the uninsurable wage income shocksthat drive their results by deterring the young consumers from investing inequity By contrast in our model it is the borrowing constraint exclusively thatdeters the young consumers from investing in equity


neous consumers within a generation can pool their idiosyncraticincome shocks Absent a complete set of such claims consumerheterogeneity in the form of uninsurable persistent and het-eroskedastic idiosyncratic income shocks with countercyclicalconditional variance has the potential to resolve empirical dif-culties encountered by representative-consumer models9 Never-theless consumer heterogeneity within a generation is down-played in our model in order to isolate and explore theimplications of heterogeneity across generations in a parsimoni-ous paradigm

The paper is organized as follows The economy and equilib-rium are dened in Section II In Section III we discuss thecalibration of the economy In Section IV we present and discussthe equilibrium results in both the borrowing-constrained andthe unconstrained economies for a plausible range of parametervalues Extensions are discussed in Section V Section VI con-cludes the paper Technical aspects on the denition of equilib-rium existence of equilibrium and the numerical calculationsare detailed in the appendixes available from the authors

II THE ECONOMY AND EQUILIBRIUM

We consider an overlapping-generations pure exchangeeconomy10 Each generation lives for three periods as youngmiddle-aged and old Three is the minimal number of periodsthat captures the heterogeneity of consumers across age groupswhich we wish to emphasize the borrowing-constrained youngthe saving middle-aged and the dissaving old In the calibrationeach period is taken to represent twenty years We model eachgeneration of consumers with a representative consumer As ex-plained in the introduction consumer heterogeneity within ageneration is downplayed in our model in order to isolate andexplore the implications of heterogeneity across generations in aparsimonious paradigm

9 See Mehra and Prescott [1985] Mankiw [1986] and Constantinides andDufe [1996]

10 There is a long tradition of OLG models in the literature Auerbach andKotlikoff [1987] employ a deterministic OLG model in their study of scal policyRios-Rull [1994] employs a stochastic OLG model in his investigation of the roleof market incompleteness on equilibrium allocations Kurz and Motolese [2000]use the framework to examine rational beliefs See also Cocco Gomes andMaenhout [1998] Huggett [1996] Jagannathan and Kocherlakota [1996] andStoresletten [2000]


There is one consumption good in each period and it perishesat the end of the period Wages consumption dividends andcoupons as well as the prices of the bonds and equity are denomi-nated in units of the consumption good

There are two types of securities in the model bonds andequity Both are innitely lived We think of bonds as a proxy forlong-term government debt Each bond pays a xed coupon of oneunit of the consumption good in every period in perpetuity11 Thesupply of bonds is xed at b units The aggregate coupon paymentis b in every period and represents a portion of the economyrsquoscapital income We denote by qt

b the ex-coupon bond price inperiod t

One perfectly divisible equity share is traded It is the claimto the net dividend stream d t the sum total of all private capitalincome (stocks corporate bonds and real estate) We denote by q t

e

the ex-dividend share price in period t With the supply of equityxed at one share in perpetuity the issue and repurchase ofequities and bonds is implicitly accounted for by the fact that theequity is dened as the claim to the net dividend We do not modelthe method by which rms determine and nance the net divi-dendmdashrms are exogenous to the exchange economy

The consumer born in period t receives deterministic wageincome w0 0 in period t when young stochastic wage incomewt 1 1

1 0 in period t 1 1 when middle aged and zero wageincome in period t 1 2 when old By making the wage incomeprocess of the middle-aged consumer exogenous we abstract fromthe labor-leisure trade-off Claims on a consumerrsquos future wageincome are not traded

A consumer born in period t enters life with zero endowmentof the equity and bond The consumer purchases zt 0

e shares ofstock and z t 0

b bonds when young The consumer adjusts theseholdings to zt 1

e and z t 1b respectively when middle aged Since we

rule out bequests the consumer liquidates hisher entire portfoliowhen old12 Thus z t 2

e 5 0 and zt 2b 5 0

We study and contrast two versions of the economy In theunconstrained economy consumers are permitted to borrow by

11 We also report the shadow price of a one-period (twenty-year) bond in zeronet supply Note that it is infeasible to introduce a one-year bond in this economybecause the length of one period is assumed to be twenty years

12 Ruling out bequests provides a parsimonious way to emphasize the effectof a borrowing constraint on consumersrsquo life-cycle behavior This admittedlycontroversial assumption is extensively discussed in Section V


shorting the bonds They are also permitted to short the shares ofstock (Negative holdings of either the bonds or equity are inter-preted as short positions) In the constrained economy the con-sumers are forbidden to borrow by shorting the bonds It isirrelevant whether or not we allow the consumers to short theequity because a restriction on shorting the equity is nonbindingfor the particular range of parameters value with which we cali-brate the economies

We denote by ct j the consumption in period t 1 j( j 5 0 12) of a consumer born in period t The budget constraint of theconsumer born in period t is

(1) ct0 1 zt0b qt

b 1 z t0e qt

e w0

when young

(2) ct1 1 zt1b q t 1 1

b 1 z t1e qt 1 1

e wt 1 11 1 zt0

b ~ qt 1 1b 1 b 1 z t0

e ~ qt 1 1e 1 dt 1 1

when middle-aged and

(3) ct2 zt1b ~ qt 1 2

b 1 b 1 z t1e ~ qt 1 2

e 1 dt 1 2

when oldWe also impose the constraints

(4) c t0 $ 0 ct1 $ 0 and ct2 $ 0

that rule out negative consumption and personal bankruptcyThey are sometimes referred to as positive-net-worth constraints

Underlying the economy is an increasing sequence It t 5 01 of information sets available to consumers in period tThe information set It contains the wage income and dividendhistories up to and including period t It also contains the con-sumption bond investment and stock investment histories of allconsumers up to and including period t 2 1 Most of this infor-mation turns out to be redundant in the particular stationaryequilibria explored in Section III

Consumption and investment policies are such that decisionsmade in period t depend only on information available in period tFormally a consumption and investment policy of the consumerborn in period t is dened as the collection of the It-measurable(ct 0 zt 0

b zt 0e ) the It 1 1-measurable (ct 1z t 1

b zt 1e ) and the It 1 2-

measurable ct 2 The consumer born in period t has expected utility


(5) E ~ Oi 5 0

2

b iu ~ cti u It

where b is the constant subjective discount factorIn period t the old consumers sell their holdings in equity

and bonds and consume the proceeds By market clearing thedemand for equity and bonds by the young and middle-agedconsumers must equal the xed supply of equity and bonds

(6) zt0e 1 zt 2 11

e 5 1

and

(7) z t0b 1 zt 2 11

b 5 b

We conclude the description of the economy by specifying thejoint stochastic process of the wage income and dividend Asnoted earlier the wage income of the young is a constant w0 andthe wage income of the old is equal to zero Instead of specifyingthe joint process of the wage income of the middle-aged consumerand the dividend (wt

1 dt) we choose to specify the joint processof the aggregate income and the wages of the middle-aged( ytw t

1) where the aggregate income yt is dened as

(8) yt 5 w0 1 w t1 1 b 1 dt

Our denition of aggregate income includes the (constant) couponpayment on government debt13 For simplicity we model the jointprocess of the (detrended) aggregate income and the wage incomeof the middle-aged as a time-stationary Markov chain with anondegenerate unique stationary probability distribution14 In

13 This denition appears to differ from the standard denition of the GDPwhich does not include the coupon payment on government debt We justify ourdenition of the GDP as follows In a more realistic model that takes into accountthe taxation of wages and dividend by the government to service its debt w0 1w t

1 1 dt stands for the sum of the after-tax wages and dividend The sum of thebefore-tax wages and dividend is obtained by adding b to the after-tax wages anddividend as in equation (8) In any case the interest on government debt in theUnited States is about 3 percent of the GDP and the calibration remains essen-tially unchanged whether the denition of the GDP includes the term b or not

14 In the spirit of Lucas [1978] the model abstracts from growth andconsiders an economy that is stationary in levels The average growth in totaloutput is thus zero Mehra and Prescott [1985] however study an economy thatis stationary in growth rates and has a unit root in levels In their model the effectof the latter generalization is to increase the mean return on all nancial assetsrelative to what would prevail ceteris paribus in a stationary-in-levels economybut the return differentials across different securities are not much affected Theintuition is as follows with growth creating preordained increases in future


the calibration yt and wt1 assume two values each The four

possible realizations of the pair ( ytw t1) are represented by the

state variable st 5 j j 5 1 4 We denote the corresponding4 3 4 transition probability matrix as P

We consider stationary rational expectations equilibria as inLucas [1978] Equilibrium is dened as the set of consumptionand investment policies of the consumers born in each period andthe It-measurable bond and stock prices qt

b and qte in all periods

such that (a) each consumerrsquos consumption and investment policymaximizes the consumerrsquos expected utility from the set of admis-sible policies while taking the price processes as given and (b)bond and equity markets clear in all periods15

It is beyond the scope of this paper to characterize the full setof such equilibria It turns out however that in the borrowing-unconstrained economy there exists a stationary rational expec-tations equilibrium in which decisions made in period t and pricesin period t are measurable with respect to the current state st 5j j 5 1 4 and the one-period lagged state These additionalstate variables are present because in every period a middle-agedconsumer participates in the securities market and hisher ac-tions are inuenced by the securities acquired when young

In the borrowing-constrained economy and for the particularrange of parameters that we calibrate the economy there exists astationary rational expectations equilibrium in which the youngconsumers do not participate in the equity and bond marketsDecisions made in period t and prices in period t are measurablewith respect to the current state st 5 j j 5 1 4 alone

consumption relative to the present investors require greater mean returns fromall securities across the board in order to be induced to postpone consumption Thepoint of all this is that our life-cycle considerations can be examined in eithercontext we choose the stationary-in-levels because it is marginally simpler com-putationally and better matches observed mean return data It is also consistentwith zero population growth another feature of our model We have constructedan analogous model where both output and population grow (output stochasti-cally) The general results of this paper are duplicated in that setting as wellGeneralizations to incorporate production could be done along the lines in Donald-son and Mehra [1984] and Prescott and Mehra [1980]

15 The characterization of the equilibrium and the proof of existence of astationary equilibrium are in Appendix A of the unabridged version of this paperavailable from the authors The numerical routine for calculating the equilibriumin both the borrowing-constrained and the unconstrained economies is outlined inAppendix C of the same paper


Lagged state variables are absent because middle-aged consum-ers do not participate in the securities market when young16

Since our main results depend crucially on the assumptionthat borrowing is ruled out this assumption merits careful ex-amination The borrowing constraint may be challenged becausein reality consumers have the opportunity to purchase equities onmargin and purchase index futures with small initial and main-tenance margins They may also borrow indirectly by purchasingthe equity of highly levered rms and by purchasing index op-tions We investigate these possibilities in the context of theequilibrium of borrowing-constrained economies In Section V wereport that a very small margin sufces to deter a borrowing-unconstrained young consumer from purchasing equity on mar-gin index futures and highly levered forms of equity Essen-tially a young consumer is unwilling to sacrice even a smallamount of immediate consumption to put up as margin for thepurchase of equity

For both versions of the model the common stylized assump-tions made on the income processes enable us to capture threekey aspects of reality in a parsimonious way17 First the wageincome received by the young and the old is small compared withthe income received by the middle-aged Therefore the youngwould like to borrow against future income and the middle-agedwould like to save However the young cannot borrow because ofthe borrowing constraint Second the major future income uncer-tainty is faced by the young It turns out that in the equilibriumof most of our borrowing-constrained economies the equity pre-mium has low correlation with the wage income that the youngexpect to receive in their middle age The young would like toborrow and invest in equity but the borrowing constraint pre-vents them from doing so Third the saving middle-aged face nowage uncertainty18 Therefore they save by investing in a port-

16 See Appendix B of the unabridged version of this paper for the proof ofexistence of an equilibrium and discussion

17 The simplifying assumption that the wage income of the young is de-terministic and common across the young of the same generation may be re-laxed to allow this income to be stochastic and different across the young of thesame generation Whereas this generalization would certainly increase the real-ism (and complexity) of the model it would not change the basic message of ourpaper as long as a sufciently large fraction of the young were to remainborrowing-constrained

18 The simplifying assumption that the wage income of the old is zero maybe relaxed to allow for pension income and social security benets This incomeand benets are deterministic from the perspective of the middle-aged consumers


folio of equities and bonds driven primarily by the motive ofdiversication of risk

III CALIBRATION

Period utility is assumed to be of the form

(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1

where a 0 is the (constant) relative risk aversion coefcient Weadopt a conventional specication of preferences in order to focusattention on a different issuemdashthe role of the borrowing con-straint in the context of an overlapping-generations economymdashaswell as to make our results directly comparable to the priorliterature

We present results for values of a 5 4 and 6 We set b 5 044for a period of length 20 years This corresponds to an annualsubjective discount factor of 096 which is standard in the mac-roeconomic literature19

The calibration of the joint Markov process on the wageincome of the middle-aged consumers w1 and the aggregateincome y is simplied considerably by the observation that theequilibrium security prices in the borrowing-constrained econ-omy are linear scale multiples of the wage and income variablesThis follows from the homogeneity introduced by the constant-RRA preferences20

This property of equilibrium security prices implies that theequilibrium joint probability distribution of the bond and equityreturns is invariant to the level of the exogenous macroeconomicvariables for a xed y w1 correlation structure Rather thedistribution depends on a set of fundamental ratios and correla-tions (i) the average share of income going to labor E[w1 1w0]E[ y] (ii) the average share of income going to the labor of the

when incorporated into our analysis they increase the demand for equity by themiddle-aged and reduce the mean equity premium Specically the mean equitypremium decreases approximately by the factor 1 2 x where x is the fraction ofconsumption of the old consumers that is derived from these benets

19 In the OLG literature there has been a trend toward calibrating themodels with the subjective discount factor b greater than one Unlike in an innitehorizon setting in an OLG framework b 1 is not necessary for the existence ofequilibrium Hence we also investigate the equilibrium in economies with annualsubjective discount factor equal to 104 The results are insensitive to the value ofthe subjective discount factor

20 For the unconstrained economy this statement is proved in Lemma A1Appendix A of the unabridged version of this paper available from the authors


young w0E[ y] (iii) the average share of income going to intereston government debt bE[ y] (iv) the coefcient of variation of thetwenty-year wage income of the middle aged s (w1)E(w1) (v)the coefcient of variation of the twenty-year aggregate incomes ( y)E( y) (vi) the twenty-year autocorrelation of the labor in-come corr(w t

1 w t 2 11 ) (vii) the twenty-year autocorrelation of the

aggregate income corr( ytyt 2 1) and (viii) the twenty-year cross-correlation corr( ytwt

1)Accordingly we calibrate the model on ranges of the above

moments (i)ndash(viii) There are enough degrees of freedom to permitthe construction of a 4 3 4 transition matrix that exhibits aparticular type of symmetry Specically the joint process onincome ( y) and wage of the middle-aged (w1) is modeled as asimple Markov chain with transition matrix

(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H

p 1 D f 2 D H ss H f 2 D p 1 DH s p f

4

where the condition

(11) f 1 p 1 s 1 H 5 1

ensures that the row sums of the elements of the transitionmatrix are one There are nine parameters to be determinedY1E[ y] Y2E[ y] w1

1E[ y] w21E[ y] f p s D and H21 These

parameters are chosen to satisfy the eight target moments andthe condition (11) As it turns out these parameters are such thatall the elements of the transition matrix are positive

The single most serious challenge to the calibration is theestimation of the above unconditional moments Recall that thewage income of the middle-aged and the aggregate income aretwenty-year aggregates Thus even a century-long time seriesprovides only ve nonoverlapping observations resulting in largestandard errors of the point estimates Standard econometric

21 In Tables II III and VI the matrix parameters corresponding to theindicated panels are as follows f 5 05298 p 5 00202 s 5 00247 H 5 04253and D 5 001 (top left) f 5 08393 p 5 00607 s 5 00742 H 5 00258 and D 5003 (top right) f 5 05496 p 5 00004 s 5 00034 H 5 04466 and D 5 003(bottom left) f 5 08996 p 5 00004 s 5 00034 H 5 00966 and D 5 003(bottom right) We do not report our choice of Y W etc because the returns in thiseconomy are scale invariant and thus these values are not uniquely determined


methods designed to extract more information from the timeseries such as the utilization of overlapping observations or thetting of high-frequency high-order time-series models onlymarginally increase the effective number of nonoverlapping ob-servations and leave the standard errors large

We thus rely in large measure on an extensive sensitivityanalysis with the range of values considered as follows

i The average share of income going to labor E[w1 1w0]E[y] In the U S economy this ratio is about 66 to75 depending on the historical period and the manner ofadjusting capital income

The model considered in this paper however is implic-itly concerned only with the fraction of the populationthat owns nancial assets at least at some stage of theirlife cycle and it is the labor income share of that groupthat should matter For the time period for which theequity premium puzzle was originally stated about 25percent of the population held nancial assets [Mankiwand Zeldes 1991 Blume and Zeldes 1993] that fractionhas risen to its current level of about 40 percent In ourborrowing-constrained economy the fraction of the popu-lation owning nancial assets is 33 midway between theaforementioned estimates We acknowledge howeverthat age is not the sole determinant of ownership ofnancial assets Nevertheless it is likely that the shareof income to labor is probably lower for the security-owning class than the population at large In light ofthese comments we set the ratio E[w1 1 w0]E[y] in thelower half of the documented range (66 70)

ii The average share of income going to the labor of theyoung w0E[y] This share is set in the range (16 20)sufciently small to guarantee that the young have thepropensity to borrow and render the borrowing constraintbinding in the borrowing-constrained economy

Our model presumes a high ratio of expected middle-aged income to the income of the young one that impliesa 45 percent per year annual real wage growth (twenty-year time period) Campbell et al [2001] report that theage prole of labor income is much less upwardly slopedfor less well-educated groups (see their Figure 1) Wewould argue that this group is less likely to own stocks orlong-term government bonds so that we are in effect


modeling the age proles of labor income only of thewell-educated stockholding class Assuming no trend infactor shares overall labor income will grow at the samerate as national income which is about 3 percent Assum-ing that the 50 percent of the population who do not ownstock experience only a 15 percent per year (as suggestedby the Campbell et al gure) average increase in wageincome the wage growth of the more highly educatedstockholding class must then be in the neighborhood of45 percent per year which is what we assume

We have constructed a model in which there are stock-holders and nonstockholders with the latter experiencingslower labor income growth The general results of thepresent paper are unaffected by this generalization

iii The average share of income going to interest on govern-ment debt bE[y] This is set at 03 consistent with theU S historical experience

iv The coefcient of variation of the twenty-year wage in-come of the middle-aged s (w1)E(w1) The comparativereturn distributions generated by the constrained andthe unconstrained versions of the model depend cruciallyon this coefcient Ideally we would like the calibrationto reect the fact that the young face large idiosyncraticuncertainty in their future labor income generated byuncertainty in the choice of career and on their relativesuccess in their chosen career Nevertheless consumerheterogeneity within a generation is disallowed in ourformal model in order to isolate and explore the implica-tions of heterogeneity across generations in a parsimoni-ous way

We are unaware of any study that estimates the coef-cient of variation of the twenty-year (or annual) wageincome of the middle aged s (w1)E(w1) Creedy [1985]in a study of select ldquowhite-collarrdquo professions in theUnited Kingdom estimates that the annual coefcients (w)E(w) is in the range 031ndash057 in a study of womenCox [1984] estimates the coefcient to be about 025Gourinchas and Parker [forthcoming] estimate the an-nual cross-sectional coefcient of variation to be about05 Considering the above estimates we calibrate thecoefcient of variation to be 025


v The coefcient of variation of the twenty-year aggregateincome s (y)E(y) This coefcient captures the variationin detrended twenty-year aggregate income In the U Seconomy the log of the detrended (Hodrick-Prescott l-tered) quarterly aggregate income is highly autocorre-lated and has standard deviation of about 18 percentThis information provides little guidance in choosing thecoefcient of variation of the twenty-year aggregate in-come We consider the values 020 and 025

vi The 20-year autocorrelations and cross-correlation of thelabor income of the middle-aged and the aggregate in-come corr(ytwt) corr(yt yt 2 1) and corr(w t

1 w t 2 11 ) Lack-

ing sufcient time-series data to estimate the twenty-year autocorrelations and cross correlation we presentresults for a variety of autocorrelation and cross-correla-tion structures

In Table I we report empirical estimates of the mean andstandard deviation of the annualized twenty-year holding-periodreturn on the SampP 500 total return series and on the IbbotsonU S Government Treasury Long-Term bond yield For yearsprior to 1926 the series was augmented using Shillerrsquos SampP 500series and the twenty-year geometric mean of the one-year bondreturns Real returns are CPI adjusted The annualized mean (onequity or the bond) return is dened as the sample mean of[log20-year holding period return]20 The annualized standarddeviation of the (equity or bond) return is dened as the samplestandard deviation of [log20-year holding period return] = 20The annualized mean equity premium is dened as the differenceof the mean return on equity and the mean return on the bondThe standard deviation of the premium is dened as the samplestandard deviation of [log20-year nominal equity return 2logthe 20-year nominal bond return] = 20 Estimates on returnscover the sample period 11889 ndash121999 with 92 overlappingobservations and the sample period 11926 ndash121999 with 55 over-lapping observations We do not report standard errors as theseare large on nominal returns we have only four and on realreturns we have only two nonoverlapping observations

In Table I the real mean equity return is 6ndash7 percent with astandard deviation of 13ndash15 percent the mean bond return isabout 1 percent and the mean equity premium is 5ndash6 percentSince the equity in our model is the claim not just to corporate


dividends but also to all risky capital in the economy the meanequity premium that we aim to match is about 3 percent

IV RESULTS AND DISCUSSION

The properties of the stationary equilibria of the calibratedeconomies are reported in Tables II and III In Table II we setRRA 5 6 s ( y)E[ y] 5 020 and s (w1)E[w1] 5 025 and inTable III we set RRA 5 4 s ( y)E[ y] 5 025 and s (w1)E[w1] 5 025

Our terminology is the same for both the constrained and theunconstrained economies The one-period (twenty-year) bond isreferred to as the bond The bond is in zero net supply and itsprice is dened as the private valuation of the bond by themiddle-aged consumer22 The consol bond which is in positive netsupply is referred to as the consol

22 Specically it is the shadow price of the bond determined by the marginalrate of substitution of the middle-aged consumer It would be meaningless to report

TABLE I

Real returns (in percent)

11889ndash121999 11926ndash121999

Equity Bond Premium Equity Bond Premium

MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521

Nominal returns (in percent)

11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521

We report empirical estimates of the mean and standard deviation of the annualized twenty-yearholding-period-returnon the SampP 500 total return series and on the Ibbotson U S Government TreasuryLong-Term Bond yield For years prior to 1926 the series was augmented using Shillerrsquos SampP 500 series andthe twenty-year geometric mean of the one-yearbond returns Real returns are CPI adjusted The annualizedmean (on equity or the bond) return is dened as the sample mean of the [log20-year holding periodreturn]20 The annualized standard deviation of the (equity or bond) return is dened as the samplestandard deviation of the [log20-year holding period return]= 20 The mean equity premium is dened asthe difference of the mean return on equity and the mean return on the bond The standard deviation of thepremium is dened as the sample standard deviation of the [log20-year nominal return on equity 2 logthe20-year nominal return on the bond]= 20 Estimates on returns cover the sample period 11889ndash121999with 92 overlapping observations and the sample period 11926ndash121999 with 55 overlapping observations


For all securities the annualized mean return is dened asmean of log20-year holding period return20 The annualizedstandard deviation of the (equity bond or consol) return is de-

the private valuation of the bond by the young consumer because the young consumerwould like to sell the bond short (borrow) but the borrowing constraint is binding Theprivate valuation of the bond by the young consumer is also well dened We havecalculated both private valuations of the bond and they agree to the second decimalpoint Essentially the two traded securities the equity and the consol come close tocompleting the market and the private valuation of the (one-period) bond by the youngand the middle-aged practically coincide even though the bond is not traded in theequilibrium

TABLE II

Correlation ( yw1 ) 5 01

Low serial autocorrof y and of w1 (01)

High serial autocorrof y and of w1 (08)

Borrowingconstrained

Borrowingunconstrained



MEAN EQUITY RET 84 102 94 122STD OF EQUITY RET 230 420 265 265MEAN BOND RET 51 90 67 111STD OF BOND RET 154 276 208 119MEAN PRMBOND 34 11 26 10STD PRMBOND 184 316 128 25MEAN CONSOL RET 37 99 45 111STD OF CONSOL RET 191 276 190 119MEAN PRMCONSOL 47 03 49 10STD PRMCONSOL 105 52 101 92MARGIN 2 1 M 530 NA 170 NACORR(w1 d) 2 043 2 043 2 042 2 042CORR(w1 PRMBOND) 2 002 000 013 058


MEAN EQUITY RET 79 127 83 139STD OF EQUITY RET 186 298 149 162MEAN BOND RET 58 113 69 129STD OF BOND RET 152 258 106 126MEAN PRMBOND 21 14 14 09STD PRMBOND 126 134 98 104MEAN CONSOL RET 61 118 67 129STD OF CONSOL RET 167 266 103 128MEAN PRMCONSOL 18 056 16 10STD PRMCONSOL 72 38 74 12MARGIN 2 1 M 827 NA 156 NACORR(w1 d) 035 055 036 091CORR(w1 PRMBOND) 005 2 004 019 013

We set RRA 5 6 s ( y)E[ y] 5 020 and s (w1)E[w1] 5 025 The variables are dened in the main textof the paper The consol bond is in positive net supply and the one-period (twenty-year) bond is in zero netsupply


ned as the standard deviation of [log20-year holding periodreturn] = 20 The mean annualized equity premium return overthe bond return ldquoMEAN PRMBONDrdquo is dened as the differ-ence between the mean return on equity and the mean return onthe bond The standard deviation of the premium of equity returnover the bond return ldquoSTD PRMBONDrdquo is dened as the stan-dard deviation of [log20-year nominal equity return 2 logthe20-year nominal bond return] = 20 The mean premium of equityreturn over the consol return ldquoMEAN PRMCONSOLrdquo and the

TABLE III













standard deviation of the premium of equity return over theconsol return ldquoSTD PRMCONSOLrdquo are dened in a similarmanner

The single most important observation across all the casesreported in Tables IIndashIV is that the mean (20-year or consol) bondreturn roughly doubles when the borrowing constraint is relaxedThis observation is robust to the calibration of the correlation andautocorrelation of the labor income of the middle-aged with theaggregate income In these examples the borrowing constraintgoes a long way albeit not all the way toward resolving therisk-free rate puzzle This of course is the rst part of the thesisof our paper if the young are able to borrow they do so andpurchase equity the borrowing activity of the young raises thebond return thereby exacerbating the risk-free rate puzzle

The second observation across all the borrowing-constrainedcases reported in Tables II and III is that the minimum meanequity premium over the twenty-year bond is about half thetarget of 3 percent Furthermore the premium decreases whenthe borrowing constraint is relaxed in some cases quite substan-tially This is the second part of the thesis of our paper if theyoung are able to borrow the increase in the bond return inducesthe middle-aged to shift their portfolio holdings in favor of the

TABLE IV

State 1 State 2 State 3 State 4 Unconditional

PROBABILITY 0275 0225 0225 0275 1CONSUMPTION OF THE

YOUNG 19000 19000 19000 19000 19000CONSUMPTION OF THE

MIDDLE-AGED 36967 33003 27335 28539 31591CONSUMPTION OF THE

OLD 62232 26594 71864 31058 47834MEAN EQUITY RETURN 47 54 129 110 84MEAN BOND RETURN 25 08 74 92 51MEAN PRMBOND 22 46 55 21 34MEAN CONSOL

RETURN 23 2 14 47 88 37MEAN PRMCONSOL 24 69 82 25 47MARGIN 2 1 M 1212 386 178 373 530

We set RRA 5 6 s ( y)E[ y] 5 020 s (w1)E[w1] 5 025 corr(ytyt 2 1) 5 corr(wt1wt 2 1

1 ) 5 01 andcorr(ytwt) 5 01 The variables are dened in the main text of the paper The consol bond is in positive netsupply and the one-period (twenty-year) bond is in zero net supply


bond the increase in the demand for equity by the young and thedecrease in the demand for equity by the middle-aged work inopposite directions on balance the effect is to increase the returnon both equity and the bond while simultaneously shrinking theequity premium Although the mean equity premium decreasesin all the cases when the borrowing constraint is relaxed theamount by which the premium decreases is the largest in the toppanels of Tables II and III in which the labor income of themiddle-aged and aggregate income are negatively correlated

The third observation across all the cases reported in TablesIIndashIII is that the correlation of the labor income of themiddle-aged and the equity premium over the twenty-year bondcorr(w1 PRMBOND) is much smaller in absolute value23 thanthe exogenously imposed correlation of the labor income of themiddle-aged and the dividend corr(w1 d) Thus equity is attrac-tive to the young because of the large mean equity premium andthe low correlation of the premium with the wage income of themiddle-aged thereby corroborating another important dimensionof our model In equilibrium it turns out that the correlation ofthe wage income of the middle-aged and the equity return islow24 The young consumers would like to invest in equity be-cause equity return has low correlation with their future con-sumption if their future consumption is derived from their futurewage income However the borrowing constraint prevents themfrom purchasing equity on margin Furthermore since the youngconsumers are relatively poor and have an incentive to smooththeir intertemporal consumption they are unwilling to decreasetheir current consumption in order to save by investing in equityTherefore the young choose not participate in the equity market

The fourth observation is that the borrowing constraint re-sults in standard deviations of the annualized twenty-year eq-uity and bond returns which are lower than in the unconstrainedcase and which are comparable to the target values in Table I

In Table IV we present the consumption of the young mid-dle-aged and old and the conditional rst moments of the returnsat the four states of the borrowing-constrained economy Theeconomy is calibrated as in the rst two columns of the top left

23 This is consistent with the low correlation between the return on equityand wages reported by Davis and Willen [2000]

24 The low correlation of the wage income of the middle-aged and the equityreturn is a property of the equilibrium and obtains for a wide range of values of theassumed correlation of the wage income of the middle-aged and the dividend


panel of Table II and corresponds to the case where RRA 5 6s ( y)E[ y] 5 020 s (w1)E[w1] 5 025 corr( ytyt 2 1) 5corr(w t

1 w t 2 11 ) 5 01 and corr( ytwt) 5 01 This is our base case

As expected the young simply consume their endowment whichin our model is constant across states The consumption of themiddle-aged is also smooth The consumption of the old is sur-prisingly variable it is this variability that induces the middle-aged to invest partly in bonds despite the high mean premium ofequity over bonds The conditional rst moments of the returnsare substantially different across the states

V EXTENSIONS

V1 Limited Consumer Participation in the Capital Markets

Our life-cycle economy induces a type of limited participa-tion that of young consumers in the stock market and that of oldconsumers in the labor market However all consumers partici-pate in the capital markets in two out of the three phases of thelife cycle as savers in their middle age and as dissavers in theirold age25 In this section we introduce a second type of consumersthe passive consumers who never participate in the capital mar-kets The passive consumers are introduced in order to accommo-date albeit in an ad hoc fashion a different type of limitedparticipation of consumers in the capital markets that addressedin Mankiw and Zeldes [1991] Blume and Zeldes [1993] andHaliassos and Bertaut [1995] We refer to the consumers whoparticipate in capital markets in two out of the three phases of thelife cycle as active consumers

In calibrating this alternative economy we assume that 60percent of the consumers are passive and 40 percent are activeSince only two-thirds of the active consumers participate in thecapital markets in any period the percentage of the population (ofactive and passive consumers) that participate in the capitalmarkets in any period is 26 percent

We assume that both passive and active consumers receivewage income $19000 when young and $0 when old The passiveconsumers receive income $33000 when middle-aged The activeconsumers receive income either $90125 or $34125 when mid-dle-aged The results are presented in Table V and are contrasted

25 For the unconstrained version all ages participate


to our ldquoprimerdquo case in Table II the upper left panel The resultsare essentially unchangedmdashthe premium is somewhat highermdashattesting to the robustness of the model along this dimension oflimited participation

V2 Bequests

A simple way to relax the no-bequest assumption is to inter-pret the ldquoconsumptionrdquo of the old as the sum of the old consumersrsquoconsumption and their bequests As long as bequests skip ageneration and are received by the borrowing-unconstrained mid-dle-aged as is often the case the young remain borrowing-con-strained and our results remain intact

More generally we distinguish between the old consumersrsquoactual consumption and their bequestsmdashthe joy of giving Weintroduce a utility function for the old consumers that is separa-ble over actual consumption and bequests Furthermore we spec-ify that the old consumers are satiated at a low level of actualconsumption Such a model would imply that the middle-agedconsumers would save primarily to bequeath wealth rather thanto consume in their old age This interpretation is interesting inits own right and makes the OLG model consistent with theempirical observation that the correlation between the (actual)consumption of the old and the stock market return is low

TABLE V

MEAN EQUITY RETURN 174STD OF EQUITY RETURN 476MEAN BOND RETURN 126STD OF BOND RETURN 435MEAN PRMBOND 48STD PRMBOND 235MEAN CONSOL RETURN 97STD OF CONSOL RETURN 452MEAN PRMCONSOL 77STD PRMCONSOL 122MARGIN 2 1 M 927CORR(w1 d) 2 042CORR(w1 PRMBOND) 2 003

The serial autocorrelation of y and of w1 is 01 The table presents the borrowing-constrained case Weset RRA 5 6 s ( y)E[ y] 5 020 s (w1)E[w1] 5 025 W(0)E[ y] 5 019 wpassive(1)E[ y] 5 020E[wactive(1)]E[ y] 5 025 W(2)E[ y] 5 0 and the proportion of active consumers 40 percent The variablesare dened in the main text of the paper The consol bond is in positive net supply and the one-period(twenty-year) bond is in zero net supply


V3 Margin Requirements

A novel feature of our paper is that the limited stock marketparticipation by the young consumers arises endogenously as theresult of an assumed borrowing constraint The young because oftheir steep earnings and consumption prole would not choosevoluntarily to reduce their period 0 consumption in order to savein the form of equity They would however be willing to borrowagainst their future labor income to buy equity and increase theirperiod 0 consumption but this is precluded by the borrowingconstraint The restriction on borrowing against future laborincome is realistic We have motivated it by recognizing thathuman capital alone does not collateralize major loans in moderneconomies for reasons of moral hazard and adverse selectionHowever the restriction on borrowing to invest in equity may bechallenged on the grounds that in reality consumers have theopportunity to purchase equity and stock index futures on marginand purchase a home with a 15 percent down payment Weinvestigate these possibilities in the context of the equilibrium ofthe borrowing-constrained economies

We dene M to be the dollar amount that a consumer canborrow for one (twenty-year) period with one dollar down pay-ment and invest M 1 1 dollars in equity on margin That is themargin requirement is 1(M 1 1) which is approximately equalto M 2 1 for large M We report the maximum value of M that stilldeters young investors from purchasing equity on margin TablesIIndashIV display the value of M in the equilibrium of all the borrow-ing-constrained economies In all cases M exceeds the value of55 a young consumer is unwilling to sacrice even one dollar ofimmediate consumption to put up as margin for the purchase ofequity worth $56 This demonstrates that our results remainunchanged if the borrowing constraint to purchase equity isreplaced by even a small margin requirement of 2 percent

V4 Firm Leverage

We also investigate the possibility that investors evade themargin requirement by purchasing the equity of a levered rmwhere the ldquormrdquo is the claim to the dividend process A simplevariation of the above calculations shows that a margin require-ment of 4 percent sufces to deter the borrowing-constrainedyoung from purchasing the levered equity even if the debt-to-


equity ratio is 11 We conclude that our results remain effectivelyunchanged even if we recognize the ability of rms to borrow

V5 Other Market Congurations

So far we have assumed that the equity and the consol bondare in positive net supply while the one-period (twenty-year)bond is in zero net supply Here we consider a variation of theeconomy in which the equity and the one-period (twenty-year)bond are in positive net supply while the consol bond is in zeronet supply We calibrate the economy using the same parametersas those used in Table II The properties of the equilibrium arepresented in Table VI and are contrasted with the properties ofthe equilibrium in Table II It is clear that the major conclusion ofthe paper remains robust to this variation of the economy the

TABLE VI








MEAN EQUITY RET 69 92 81 107STD OF EQUITY RET 181 429 249 267MEAN BOND RET 46 82 62 90STD OF BOND RET 153 293 208 190MEAN PRMBOND 23 11 19 17STD PRMBOND 107 313 86 178MARGIN 2 1 M 178 NA 170 NACORR(w1 d) 2 043 2 043 2 043 2 043CORR(w1 PRMBOND) 2 0004 2 0004 003 067


MEAN EQUITY RET 74 118 79 102STD OF EQUITY RET 167 314 116 158MEAN BOND RET 55 104 67 92STD OF BOND RET 152 262 104 147MEAN PREMBOND 19 14 12 09STD PRMBOND 89 167 64 153MARGIN 2 1 M 827 NA 156 NACORR(w1 d) 035 035 036 036CORR(w1 PRMBOND) 007 075 037 005



borrowing constraint increases the equity premium Further-more security returns in the constrained economy remain uni-formly below their unconstrained counterparts

VI CONCLUDING REMARKS

We have addressed ongoing questions on the historical meanand standard deviation of the returns on equities and bonds andon the equilibrium demand for these securities in the context of astationary overlapping-generations economy in which consumersare subject to a borrowing constraint The particular combinationof these elements captures the effect of the borrowing constrainton the investorsrsquo saving and dissaving behavior over their lifecycle We nd in all cases that the imposition of the borrowingconstraint reduces the risk-free rate and increases the risk pre-mium in some cases quite signicantly However the standarddeviation of the security returns remains too low relative to thedata On a qualitative basis our results mirror effects in thelarger society the decline in the premium documented in Blan-chard [1992] has been contemporaneous with a substantial in-crease in individual indebtedness

The model is intentionally sparse in its assumptions in orderto convey the basic message in the simplest possible way It canbe enriched in various ways that enhance its realism For exam-ple we may increase the number of generations from three tosixty representing consumers of ages twenty to eighty in annualincrements In such a model we expect that the youngest con-sumers are borrowing-constrained for a number of years andinvest neither in equity nor in bonds thereafter they invest in aportfolio of equity and bonds with the proportion of equity intheir portfolio decreasing as they grow older and the attractive-ness of equity diminishes It is possible to increase the endow-ment of young consumers to reect intergenerational transfersand make the endowment of the young random and differentacross consumers These changes will have pricing implicationsto the extent that the young investors who are currently infra-marginal in the equity and bond markets become marginal Wecan model the pension income and social security benets of theold consumers It is possible to introduce heterogeneity of con-sumers within a generation We can model GDP growth as astationary process as in Mehra [1988] rather than modeling (de-trended) GDP level as a stationary process We can specify dis-


tinct production sectors endogenize production endogenize thelabor-leisure trade-off and model the government sector in amore realistic manner than we have done in the paper Wesuspect that in all these cases the essential message of our paperwill survive the borrowing constraint has the effect of lowering theinterest rate and raising the equity premium

UNIVERSITY OF CHICAGO GRADUATE SCHOOL OF BUSINESS AND NATIONAL BUREAU

OF ECONOMIC RESEARCH

COLUMBIA UNIVERSITY

UNIVERSITY OF CALIFORNIA AT SANTA BARBARA AND UNIVERSITY OF CHICAGO

GRADUATE SCHOOL OF BUSINESS

REFERENCES

Abel Andrew B ldquoAsset Prices under Habit Formation and Catching up with theJonesesrdquo American Economic Review Papers and Proceedings LXXX (1990)38ndash42

Aiyagari S Rao and Mark Gertler ldquoAsset Returns with Transactions Costs andUninsured Individual Riskrdquo Journal of Monetary Economics XXVII (1991)311ndash331

Auerbach Alan J and Laurence J Kotlikoff Dynamic Fiscal Policy (CambridgeMA Cambridge University Press 1987)

Alvarez Fernando and Urban Jermann ldquoAsset Pricing When Risk Sharing IsLimited by Defaultrdquo Econometrica XLVIII (2000) 775ndash797

Attanasio Orazio P James Banks and Sarah Tanner ldquoAsset Holding and Con-sumption Volatilityrdquo Journal of Political Economy (2002) forthcoming

Bansal Ravi and John W Coleman ldquoA Monetary Explanation of the EquityPremium Term Premium and Risk-Free Rate Puzzlesrdquo Journal of PoliticalEconomy CIV (1996) 1135ndash1171

Basak Suleyman and Domenico Cuoco ldquoAn Equilibrium Model with RestrictedStock Market Participationrdquo Review of Financial Studies XI (1998)309ndash341

Benartzi Shlomo and Richard H Thaler ldquoMyopic Loss Aversion and the EquityPremium Puzzlerdquo Quarterly Journal of Economics CX (1995) 73ndash92

Bewley Truman F ldquoThoughts on Tests of the Intertemporal Asset Pricing Mod-elrdquo Working paper Northwestern University 1982

Blanchard Olivier ldquoThe Vanishing Equity Premiumrdquo Working paper Massachu-setts Institute of Technology 1992

Blume Marshall E and Stephen P Zeldes ldquoThe Structure of Stock Ownership inthe U Srdquo Working paper University of Pennsylvania 1993

Boldrin Michele Lawrence J Christiano and Jonas D M Fisher ldquoHabit Persis-tence Asset Returns and the Business Cyclerdquo American Economic ReviewXCI (2001) 149ndash166

Brav Alon George M Constantinides and Christopher C Geczy ldquoAsset Pricingwith Heterogeneous Consumers and Limited Participation Empirical Evi-dencerdquo Journal of Political Economy (2002) forthcoming

Brav Alon and Christopher C Geczy ldquoAn Empirical Resurrection of the SimpleConsumption CAPM with Power Utilityrdquo Working paper University of Chi-cago 1995

Campbell John Y Joao Cocco Francisco Gomes and Pascal J Maenhout ldquoIn-vesting Retirement Wealth A Lifecycle Modelrdquo in Risk Aspects of Investment-Based Social Security Reform John Y Campbell and Martin Feldstein eds(Chicago IL University of Chicago Press 2001)

Campbell John Y and John H Cochrane ldquoBy Force of Habit A Consumption-Based Explanation of Aggregate Stock Market Behaviorrdquo Journal of PoliticalEconomy CVII (1999) 205ndash251


Cocco Joao F Francisco J Gomes and Pascal J Maenhout ldquoConsumption andPortfolio Choice over the Life-Cyclerdquo Working paper Harvard University1998

Cogley Timothy ldquoIdiosyncratic Risk and the Equity Premium Evidence from theConsumer Expenditure Surveyrdquo Working paper Arizona State University1999

Cochrane John H and Lars Peter Hansen ldquoAsset Pricing Explorations forMacroeconomicsrdquo in NBER Macroeconomics Annual Olivier J Blanchardand Stanley Fischer eds (Cambridge MA MIT Press 1992)

Constantinides George M ldquoHabit Formation A Resolution of the Equity Pre-mium Puzzlerdquo Journal of Political Economy XCVIII (1990) 519ndash543

Constantinides George M and Darrell Dufe ldquoAsset Pricing with HeterogeneousConsumersrdquo Journal of Political Economy CIV (1996) 219ndash240

Cox David ldquoInequality in the Lifetime Earnings of Womenrdquo Review of Economicsand Statistics LXIV (1984) 501ndash504

Creedy John Dynamics of Income Distribution (Oxford UK Basil Blackwell1985)

Daniel Kent and David Marshall ldquoThe Equity Premium Puzzle and the Risk-Free Rate Puzzle at Long Horizonsrdquo Macroeconomic Dynamics I (1997)452ndash484

Danthine Jean-Pierre John B Donaldson and Rajnish Mehra ldquoThe EquityPremium and the Allocation of Income Riskrdquo Journal of Economic Dynamicsand Control XVI (1992) 509ndash532

Davis Stephen J and Paul Willen ldquoUsing Financial Assets to Hedge LaborIncome Risk Estimating the Benetsrdquo Working paper University of Chicago2000

Detemple Jerome B and Angel Serrat ldquoDynamic Equilibrium with LiquidityConstraintsrdquo Working paper University Chicago 1996

Donaldson John B and Rajnish Mehra ldquoComparative Dynamics of an Equilib-rium Intertemporal Asset Pricing Modelrdquo Review of Economic Studies LI(1984) 491ndash508

Epstein Larry G and Stanley E Zin ldquoSubstitution Risk Aversion and theTemporal Behavior of Consumption and Asset Returns An Empirical Analy-sisrdquo Journal of Political Economy XCIX (1991) 263ndash286

Ferson Wayne E and George M Constantinides ldquoHabit Persistence and Dura-bility in Aggregate Consumptionrdquo Journal of Financial Economics XXIX(1991) 199ndash240

Gourinchas Pierre-Olivier and Jonathan A Parker ldquoConsumption over the Life-cyclerdquo Econometrica forthcoming

Haliassos Michael and Carol C Bertaut ldquoWhy Do So Few Hold Stocksrdquo Eco-nomic Journal CV (1995) 1110ndash1129

Hansen Lars Peter and Ravi Jagannathan ldquoImplications of Security MarketData for Models of Dynamic Economiesrdquo Journal of Political Economy XCIX(1991) 225ndash262

Hansen Lars Peter and Kenneth J Singleton ldquoGeneralized Instrumental Vari-ables Estimation of Nonlinear Rational Expectations Modelsrdquo EconometricaL (1982) 1269ndash1288

He Hua and David M Modest ldquoMarket Frictions and Consumption-Based AssetPricingrdquo Journal of Political Economy CIII (1995) 94ndash117

Heaton John and Deborah J Lucas ldquoEvaluating the Effects of IncompleteMarkets on Risk Sharing and Asset Pricingrdquo Journal of Political EconomyCIV (1996) 443ndash487

Heaton John and Deborah J Lucas ldquoMarket Frictions Savings Behavior andPortfolio Choicerdquo Journal of Macroeconomic Dynamics I (1997) 76ndash101

Heaton John and Deborah J Lucas ldquoPortfolio Choice and Asset Prices TheImportance of Entrepreneurial Riskrdquo Journal of Finance LV (2000)1163ndash1198

Huggett Mark ldquoWealth Distribution in Life-Cycle Economiesrdquo Journal of Mone-tary Economics XXXVIII (1996) 469ndash494

Jacobs Kris ldquoIncomplete Markets and Security Prices Do Asset-Pricing PuzzlesResult from Aggregation Problemsrdquo Journal of Finance LIV (1999)123ndash163


Jagannathan Ravi and Narayana R Kocherlakota ldquoWhy Should Older PeopleInvest Less in Stocks Than Younger Peoplerdquo Federal Bank of MinneapolisQuarterly Review XX (1996) 11ndash23

Kocherlakota Narayana R ldquoThe Equity Premium Itrsquos Still a Puzzlerdquo Journal ofEconomic Literature XXXIV (1996) 42ndash71

Krusell Per and Anthony A Smith ldquoIncome and Wealth Heterogeneity in theMacroeconomyrdquo Journal of Political Economy CVI (1998) 867ndash896

Kurz Mordecai and Maurizio Motolese ldquoEndogenous Uncertainty and MarketVolatilityrdquo Working paper Stanford University 2000

Lucas Deborah J ldquoAsset Pricing with Undiversiable Risk and Short SalesConstraints Deepening the Equity Premium Puzzlerdquo Journal of MonetaryEconomics XXXIV (1994) 325ndash341

Lucas Robert E ldquoAsset Prices in an Exchange Economyrdquo Econometrica XLVI(1978) 1429ndash1445

Luttmer Erzo G J ldquoAsset Pricing in Economies with Frictionsrdquo EconometricaLXIV (1996) 1439ndash1467

Mankiw N Gregory ldquoThe Equity Premium and the Concentration of AggregateShocksrdquo Journal of Financial Economics XVII (1986) 211ndash219

Mankiw N Gregory and Stephen P Zeldes ldquoThe Consumption of Stockholdersand Nonstockholdersrdquo Journal of Financial Economics XXIX (1991) 97ndash112

Marcet Albert and Kenneth J Singleton ldquoEquilibrium Asset Prices and Savingsof Heterogeneous Agents in the Presence of Portfolio Constraintsrdquo Macroeco-nomic Dynamics III (1999) 243ndash277

McGrattan Ellen R and Edward C Prescott ldquoIs the Stock Market OvervaluedrdquoFederal Reserve Bank of Minneapolis Quarterly Review XXIV (2000) 20ndash 40

McGrattan Ellen R and Edward C Prescott ldquoTaxes Regulations and AssetPricesrdquo Working paper Federal Reserve Bank of Minneapolis 2001

Mehra Rajnish ldquoOn the Existence and Representation of Equilibrium in anEconomy with Growth and Nonstationary Consumptionrdquo International Eco-nomic Review XXIX (1988) 131ndash135

Mehra Rajnish and Edward C Prescott ldquoThe Equity Premium A PuzzlerdquoJournal of Monetary Economics XV (1985) 145ndash161

Mehra Rajnish and Edward C Prescott ldquoThe Equity Premium A SolutionrdquoJournal of Monetary Economics XXII (1988) 133ndash136

Prescott Edward C and Rajnish Mehra ldquoRecursive Competitive EquilibriumThe Case of Homogeneous Householdsrdquo Econometrica XLVIII (1980)1365ndash1379

Rietz Thomas A ldquoThe Equity Risk Premium A Solutionrdquo Journal of MonetaryEconomics XXII (1988) 117ndash131

Rios-Rull Jose-Victor ldquoOn the Quantitative Importance of Market Complete-nessrdquo Journal of Monetary Economics XXXIV (1994) 463ndash496

Storesletten Kjetil ldquoSustaining Fiscal Policy through Immigrationrdquo Journal ofPolitical Economy CVIII (2000) 300ndash323

Storesletten Kjetil Chris I Telmer and Amir Yaron ldquoAsset Pricing with Idio-syncratic Risk and Overlapping Generationsrdquo Working paper Carnegie Mel-lon University 1999

Telmer Chris I ldquoAsset-Pricing Puzzles and Incomplete Marketsrdquo Journal ofFinance XLIX (1993) 1803ndash1832

Vissing-Jorgensen Annette ldquoLimited Stock Market Participationrdquo Journal ofPolitical Economy (2002) forthcoming

Weil Philippe ldquoThe Equity Premium Puzzle and the Risk-Free Rate PuzzlerdquoJournal of Monetary Economics XXIV (1989) 401ndash421


tional Euler equation of per capita consumption is also rejected byHansen and Singleton [1982] Hansen and Jagannathan [1991]Ferson and Constantinides [1991] and others

Several generalizations of key features of the Mehra andPrescott [1985] model have been proposed to better reconcileobservations with theory These include alternative assumptionson preferences2 modied probability distributions to admit rarebut disastrous events3 incomplete markets4 and market imper-fections5 none have fully resolved the anomalies Cochrane andHansen [1992] and Kocherlakota [1996] provide excellent surveysof this literature

The novelty of this paper lies in incorporating a life-cyclefeature to study asset pricing The idea is appealingly simple Theattractiveness of equity as an asset depends on the correlationbetween consumption and equity income If equity pays off instates of high marginal utility of consumption it will command ahigher price (and consequently a lower rate of return) than if itspayoff is in states where marginal utility is low Since the mar-ginal utility of consumption varies inversely with consumptionequity will command a high rate of return if it pays off in stateswhen consumption is high and vice versa6

A key insight of our paper is that as the correlation of equityincome with consumption changes over the life cycle of an indi-vidual so does the attractiveness of equity as an asset Consump-

2 For example Abel [1990] Benartzi and Thaler [1995] Boldrin Christianoand Fisher [2001] Campbell and Cochrane [1999] Constantinides [1990] Daniel andMarshall [1997] Epstein and Zin [1991] and Ferson and Constantinides [1991]

3 See Reitz [1988] and Mehra and Prescott [1988]4 For example Bewley [1982] Constantinides and Dufe [1996] Detemple

and Serrat [1996] Heaton and Lucas [1997 2000] Krusell and Smith [1998]Lucas [1994] Mankiw [1986] Marcet and Singleton [1999] Mehra and Prescott[1985] Storesletten Telmer and Yaron [1999] and Telmer [1993] Empiricalpapers that investigate the role of incomplete markets on asset prices includeBrav Constantinides and Geczy [2002] Cogley [1999] Jacobs [1999] and Vis-sing-Jorgensen [2002]

5 For example Aiyagari and Gertler [1991] Alvarez and Jermann [2000]Bansal and Coleman [1996] Basak and Cuoco [1998] Brav and Geczy [1995]Danthine Donaldson and Mehra [1992] He and Modest [1995] Heaton andLucas [1996] Luttmer [1996] McGrattan and Prescott [2000 2001] and Stores-letten Telmer and Yaron [1999] Empirical papers that investigate the role oflimited participation as a manifestation of market imperfections on asset pricesinclude Attanasio Banks and Tanner [2002] Brav and Geczy [1995] BravConstantinides and Geczy [2002] Cogley [1999] Jacobs [1999] Mankiw andZeldes [1991] and Vissing-Jorgensen [2002]

6 This is precisely the reason why high-beta stocks in the simple CAPMframework have a high rate of return In that model the return on the market isa proxy for consumption High-beta stocks pay off when the market return is highie when marginal utility is low hence their price is (relatively) low and their rateof return high

























e









e 5 0 and zt 2b 5 0







(1) ct0 1 zt0b qt

b 1 z t0e qt

e w0

when young

(2) ct1 1 zt1b q t 1 1

b 1 z t1e qt 1 1

e wt 1 11 1 zt0

b ~ qt 1 1b 1 b 1 z t0

e ~ qt 1 1e 1 dt 1 1


(3) ct2 zt1b ~ qt 1 2

b 1 b 1 z t1e ~ qt 1 2

e 1 dt 1 2


(4) c t0 $ 0 ct1 $ 0 and ct2 $ 0








(5) E ~ Oi 5 0

2

b iu ~ cti u It



(6) zt0e 1 zt 2 11

e 5 1

and

(7) z t0b 1 zt 2 11

b 5 b




(8) yt 5 w0 1 w t1 1 b 1 dt

























III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES


























































































e









e 5 0 and zt 2b 5 0







(1) ct0 1 zt0b qt

b 1 z t0e qt

e w0

when young

(2) ct1 1 zt1b q t 1 1

b 1 z t1e qt 1 1

e wt 1 11 1 zt0

b ~ qt 1 1b 1 b 1 z t0

e ~ qt 1 1e 1 dt 1 1


(3) ct2 zt1b ~ qt 1 2

b 1 b 1 z t1e ~ qt 1 2

e 1 dt 1 2


(4) c t0 $ 0 ct1 $ 0 and ct2 $ 0








(5) E ~ Oi 5 0

2

b iu ~ cti u It



(6) zt0e 1 zt 2 11

e 5 1

and

(7) z t0b 1 zt 2 11

b 5 b




(8) yt 5 w0 1 w t1 1 b 1 dt

























III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES




















































































e









e 5 0 and zt 2b 5 0







(1) ct0 1 zt0b qt

b 1 z t0e qt

e w0

when young

(2) ct1 1 zt1b q t 1 1

b 1 z t1e qt 1 1

e wt 1 11 1 zt0

b ~ qt 1 1b 1 b 1 z t0

e ~ qt 1 1e 1 dt 1 1


(3) ct2 zt1b ~ qt 1 2

b 1 b 1 z t1e ~ qt 1 2

e 1 dt 1 2


(4) c t0 $ 0 ct1 $ 0 and ct2 $ 0








(5) E ~ Oi 5 0

2

b iu ~ cti u It



(6) zt0e 1 zt 2 11

e 5 1

and

(7) z t0b 1 zt 2 11

b 5 b




(8) yt 5 w0 1 w t1 1 b 1 dt

























III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES














































































e









e 5 0 and zt 2b 5 0







(1) ct0 1 zt0b qt

b 1 z t0e qt

e w0

when young

(2) ct1 1 zt1b q t 1 1

b 1 z t1e qt 1 1

e wt 1 11 1 zt0

b ~ qt 1 1b 1 b 1 z t0

e ~ qt 1 1e 1 dt 1 1


(3) ct2 zt1b ~ qt 1 2

b 1 b 1 z t1e ~ qt 1 2

e 1 dt 1 2


(4) c t0 $ 0 ct1 $ 0 and ct2 $ 0








(5) E ~ Oi 5 0

2

b iu ~ cti u It



(6) zt0e 1 zt 2 11

e 5 1

and

(7) z t0b 1 zt 2 11

b 5 b




(8) yt 5 w0 1 w t1 1 b 1 dt

























III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES







































































e









e 5 0 and zt 2b 5 0







(1) ct0 1 zt0b qt

b 1 z t0e qt

e w0

when young

(2) ct1 1 zt1b q t 1 1

b 1 z t1e qt 1 1

e wt 1 11 1 zt0

b ~ qt 1 1b 1 b 1 z t0

e ~ qt 1 1e 1 dt 1 1


(3) ct2 zt1b ~ qt 1 2

b 1 b 1 z t1e ~ qt 1 2

e 1 dt 1 2


(4) c t0 $ 0 ct1 $ 0 and ct2 $ 0








(5) E ~ Oi 5 0

2

b iu ~ cti u It



(6) zt0e 1 zt 2 11

e 5 1

and

(7) z t0b 1 zt 2 11

b 5 b




(8) yt 5 w0 1 w t1 1 b 1 dt

























III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES





































































(1) ct0 1 zt0b qt

b 1 z t0e qt

e w0

when young

(2) ct1 1 zt1b q t 1 1

b 1 z t1e qt 1 1

e wt 1 11 1 zt0

b ~ qt 1 1b 1 b 1 z t0

e ~ qt 1 1e 1 dt 1 1


(3) ct2 zt1b ~ qt 1 2

b 1 b 1 z t1e ~ qt 1 2

e 1 dt 1 2


(4) c t0 $ 0 ct1 $ 0 and ct2 $ 0








(5) E ~ Oi 5 0

2

b iu ~ cti u It



(6) zt0e 1 zt 2 11

e 5 1

and

(7) z t0b 1 zt 2 11

b 5 b




(8) yt 5 w0 1 w t1 1 b 1 dt

























III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES



































































(5) E ~ Oi 5 0

2

b iu ~ cti u It



(6) zt0e 1 zt 2 11

e 5 1

and

(7) z t0b 1 zt 2 11

b 5 b




(8) yt 5 w0 1 w t1 1 b 1 dt

























III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES






















































































III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES











































































III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES




































































III CALIBRATION


(9) u ~ c 5 ~ 1 2 a 2 1 ~ c1 2 a 2 1














(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES








































































(10)

~ Y1 w11

~ Y1 w21

~ Y2 w11

~ Y2 w21

~ Y1 w11 ~ Y1 w2

1 ~ Y2 w11 ~ Y2 w2

1

3f p s H


4

where the condition

(11) f 1 p 1 s 1 H 5 1






















1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES


















































































1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES











































































1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES





































































1 w t 2 11 ) Lack-










TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES








































































TABLE I


11889ndash121999 11926ndash121999


MEAN 615 082 534 671 014 658STD 1395 740 1432 1579 725 1521


11889ndash121999 11926ndash121999


MEAN 920 386 534 1055 397 658STD 1388 727 1432 1447 849 1521





TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES





































































TABLE II














TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES




































































TABLE III
















TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES






































































TABLE IV




















V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES













































































V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES






































































V EXTENSIONS








V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES




































































V2 Bequests



TABLE V







V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES






































































V4 Firm Leverage






TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES






































































TABLE VI





















COLUMBIA UNIVERSITY



REFERENCES











































































COLUMBIA UNIVERSITY



REFERENCES






































































COLUMBIA UNIVERSITY



REFERENCES












































































































































Documents

JUNIOR CAN'T BORROW: A NEW PERSPECTIVE ON THE … QJE.pdftheless, consumer heterogeneity withina generation is down-played in our model in order to isolate and explore the implications