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«JUNIOR CAN’T BORROW: A NEW PERSPECTIVE ON THE EQUITY PREMIUM PUZZLE George M. Constantinides John B. Donaldson Rajnish Mehra ABSTRACT Ongoing ...»

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Forthcoming Quarterly Journal of Economics



George M. Constantinides

John B. Donaldson

Rajnish Mehra


Ongoing questions on the historical mean and standard deviation of the return on equities and bonds and on the

equilibrium demand for these securities are addressed in the context of a stationary, overlapping-generations economy in which consumers are subject to a borrowing constraint. The key feature captured by the OLG economy is that the bulk of the future income of the young consumers is derived from their wages forthcoming in their middle age, while the bulk of the future income of the middle-aged consumers is derived from their savings in equity and bonds. The young would like to borrow and invest in equity but the borrowing constraint prevents them from doing so. The middle-aged choose to hold a diversified portfolio that includes positive holdings of bonds and this explains the demand for bonds. Without the borrowing constraint, the young borrow and invest in equity, thereby decreasing the mean equity premium and increasing the rate of interest.

JEL Classifications: D91, E21, G11, G12 Keywords: equity premium, borrowing constraints, limited stock market participation, lifecycle portfolio investment.

∗ We thank Andrew Abel, John Cochrane, Roger Craine, Domenico Cuoco, Steven Davis, the editor Edward Glaeser, John Heaton, Thore Johnsen, Hayne Leland, Robert Lucas, the late Merton Miller, Kevin Murphy, Nick Souleles, Nancy Stokey, Jonathan Parker, Raaj Sah, Raman Uppal, three anonymous referees, participants at numerous conferences and seminars for helpful comments. We are particularly indebted to Edward Prescott for numerous helpful insights and advice on the calibration of our model. We also thank Yu-Hua Chu, Yubo Wang, and Lior Mezly for computational assistance.

The usual caveat applies. Constantinides acknowledges financial support from the Center for Research in Security Prices, the University of Chicago. Mehra acknowledges financial support from the Academic Senate of the University of California. Donaldson acknowledges financial support from the Faculty Research fund of the Graduate School of Business, Columbia University.


The question as to why the historical equity premium is so high and the real rate of interest is so low was addressed in Mehra and Prescott [1985]. They demonstrated that the equilibrium of a reasonably parameterized, representative-consumer exchange economy is able to furnish a mean annual premium of equity return over the riskless rate of, at most, 0.35 percent, in contrast to its historical level of 6 percent in U.S. data. Furthermore, the equilibrium annual riskless rate of interest is consistently too high, about 4 percent, as opposed to the observed 1 percent in U.S. data.1 Further, in econometric tests the conditional Euler equations of per capita consumption, is also rejected by Hansen and Singleton [1982], Hansen and Jagannathan [1991], Ferson and Constantinides [1991] and others.

Several generalizations of key features of the Mehra and Prescott [1985] model have been proposed to better reconcile observations with theory. These include alternative assumptions on preferences,2 modified probability distributions to admit rare but disastrous events,3 incomplete markets,4 and market imperfections;5 none have fully resolved the anomalies. Cochrane and This point is emphasized in Weil [1989].

For example, Abel [1990], Benartzi and Thaler [1995], Boldrin, Christiano and Fisher [2001], Campbell and Cochrane [1999], Constantinides [1990], Daniel and Marshall [1997], Epstein and Zin [1991], and Ferson and Constantinides [1991].

See, Rietz [1988] and Mehra and Prescott [1988].

For example, Bewley [1982], Constantinides and Duffie [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]. Empirical papers that investigate the role of incomplete markets on asset prices include Brav, Constantinides and Geczy [2001], Cogley [1999], Jacobs [1999], and VissingHansen [1992], and Kocherlakota [1996] provide excellent surveys of this literature.

The novelty of this paper lies in incorporating a life-cycle feature to study asset pricing.

The idea is appealingly simple. The attractiveness of equity as an asset depends on the correlation between consumption and equity income. If equity pays off in states of high marginal utility of consumption, it will command a higher price, (and consequently a lower rate of return),

–  –  –

consumption varies inversely with consumption, equity will command a high rate of return if it pays off in states when consumption is high, and vice versa.6 A key insight of our paper is that as the correlation of equity income with consumption changes over the life cycle of an individual, so does the attractiveness of equity as an asset.

Consumption can be decomposed into the sum of wages and equity income. A young person looking forward in his life has uncertain future wage and equity income; furthermore, the correlation of equity income with consumption will not be particularly high, as long as stock and wage income are not highly correlated. This is empirically the case, as documented by Davis and Jorgensen [2001].

For example, Aiyagari and Gertler [1991], Alvarez and Jerman [2000], Bansal and Coleman [1996], Basak and Cuoco [1998], Brav and Geczy [1995], Danthine, Donaldson and Mehra [1992], He and Modest [1995], Heaton and Lucas [1996], Luttmer [1996], McGrattan and Prescott [2000,2001], and Storesletten, Telmer and Yaron [1999]. Empirical papers that investigate the role of limited participation, as a manifestation of market imperfections, on asset prices include Attanasio, Banks and Tanner [1998], Brav and Geczy [1995], Brav, Constantinides and Geczy [2001], Cogley [1999], Jacobs [1999], Mankiw and Zeldes [1991], and Vissing-Jorgensen [2001].

This is precisely the reason why high-beta stocks in the simple CAPM framework have a high rate of return. In that model, the return on the market is a proxy for consumption. High-beta stocks pay off when the market return is high, i.e. when marginal utility is low, hence their price is (relatively) low and their rate of return high.

Willen [2000]. Equity will thus be a hedge against fluctuations in wages and a “desirable” asset to hold as far as the young are concerned.

The same asset (equity) has a very different characteristic for the middle aged. Their wage uncertainty has largely been resolved. Their future retirement wage income is either zero or deterministic and the innovations (fluctuations) in their consumption occur from fluctuations in equity income. At this stage of the life cycle, equity income is highly correlated with consumption. Consumption is high when equity income is high, and equity is no longer a hedge against fluctuations in consumption; hence, for this group, it requires a higher rate of return.

The characteristics of equity as an asset therefore change, depending on who the predominant holder of the equity is. Life cycle considerations thus become crucial for asset pricing. If equity is a “desirable” asset for the marginal investor in the economy, then the observed equity premium will be low, relative to an economy where the marginal investor finds it unattractive to hold equity. The deus ex machina is the stage in the life cycle of the marginal investor.

In this paper, we argue that the young, who should be holding equity in an economy without frictions and with complete contracting, are effectively shut out of this market because of borrowing constraints. They are characterized by low wages; ideally, they would like to smooth lifetime consumption by borrowing against future wage income (consuming a part of the loan and investing the rest in higher return equity). However, as is well recognized, they are prevented from doing so because human capital alone does not collateralize major loans in modern economies for reasons of moral hazard and adverse selection.

In the presence of borrowing constraints, equity is thus exclusively priced by the middleaged investors since the young are effectively excluded from the equity markets and we observe a high equity premium. If the borrowing constraint is relaxed, the young will borrow to purchase equity, thereby raising the bond yield. The increase in the bond yield induces the middle-aged to shift their portfolio holdings from equity to bonds. The increase in the demand for equity by the young and the decrease in the demand for equity by the middle-aged work in opposite directions.

On balance, the effect is to increase both the equity and the bond return while simultaneously shrinking the equity premium. Furthermore, the relaxation of the borrowing constraint reduces the net demand for bonds and the risk free rate puzzle re-emerges.

In order to systematically illustrate these ideas, we construct an overlapping-generations (OLG) exchange economy in which consumers live for three periods. In the first period, a period of human capital acquisition, the consumer receives a relatively low endowment income. In the second period, the consumer is employed and receives wage income subject to large uncertainty.

In the third period, the consumer retires and consumes the assets accumulated in the second period. We explore the implications of a borrowing constraint by deriving and contrasting the stationary equilibria in two versions of the economy. In the borrowing-constrained version, the young are prohibited from borrowing and from selling equity short. The borrowingunconstrained economy differs from the borrowing-constrained one only in that the borrowing constraint and the short-sale constraint are absent.

Our model introduces two forms of market incompleteness. First, consumers of one generation are prohibited from trading claims against their future wage income with consumers of another generation.7 Second, consumers of one generation are prohibited from trading bonds and equity with consumers of an unborn generation. Our model suppresses a third and potentially important form of market incompleteness that arises from the inability of an age cohort of consumers to insure via pooling the risks of their persistent, heteroscedastic idiosyncratic income shocks.8 Specifically, we model each generation of consumers with a representative consumer.

This assumption is justified only if there exists a complete set of claims through which heterogeneous consumers within a generation can pool their idiosyncratic income shocks. Absent a complete set of such claims, consumer heterogeneity in the form of uninsurable, persistent and heteroscedastic idiosyncratic income shocks, with counter-cyclical conditional variance, has the potential to resolve empirical difficulties encountered by representative-consumer models.9 Nevertheless, consumer heterogeneity within a generation is downplayed in our model in order to isolate and explore the implications of heterogeneity across generations in a parsimonious paradigm.

The paper is organized as follows. The economy and equilibrium are defined in Section II. In Section III, we discuss the calibration of the economy. In Section IV, we present and Being homogeneous within their generation, consumers have no incentive to trade claims with consumers of their own generation.

This perspective is emphasized in Storesletten Telmer and Yaron [1999]. They provide empirical evidence that shocks to the wage income process indeed have these properties and introduce this type of shocks in their model. They find that the interaction of life cycle effects and the uninsurable wage income shocks plays an important role in generating their results. Although they have a borrowing constraint in their model, as we do, it is the uninsurable wage income shocks that drive their results by deterring the young consumers from investing in equity. By contrast, in our model, it is the borrowing constraint exclusively that deters the young consumers from investing in equity.

See, Mehra and Prescott [1985], Mankiw [1986] and Constantinides and Duffie [1996].

discuss the equilibrium results in both the borrowing-constrained and the unconstrained economies for a plausible range of parameter values. Extensions are discussed in Section V.

Section VI concludes the paper. Technical aspects on the definition of equilibrium, existence of equilibrium, and the numerical calculations are detailed in the appendices available from the authors.

–  –  –

We consider an overlapping-generations, pure exchange economy.10 Each generation lives for three periods as young, middle-aged, and old. Three is the minimal number of periods that captures the heterogeneity of consumers across age groups, which we wish to emphasize: the borrowing-constrained young, the saving middle-aged, and the dis-saving old. In the calibration, each period is taken to represent twenty years. We model each generation of consumers with a representative consumer. As explained in the introduction, consumer heterogeneity within a generation is downplayed in our model in order to isolate and explore the implications of heterogeneity across generations in a parsimonious paradigm.

There is one consumption good in each period and it perishes at the end of the period.

Wages, consumption, dividends and coupons, as well as the prices of the bonds and equity are There is a long tradition of OLG models in the literature. Auerbach and Kotlikoff [1987] employ a deterministic OLG model in their study of fiscal policy. Rios-Rull [1994] employs a stochastic OLG model in his investigation of the role of market incompleteness on equilibrium allocations. Kurz and Motolese [2000] use the framework to examine rational beliefs. See also Cocco, Gomes, and Maenhout [1998], Huggett [1996], Jagannathan and Kocherlakota [1996], and Storesletten [2000].

denominated in units of the consumption good.

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