Mehra and Prescott (Journal of Monetary Economics 1985) identified the phenomenon that the historical real returns of stocks over government bonds are anomalously high, which has become known as the “equity premium puzzle.” Subsequent researchers seeking to resolve the puzzle have focused on factors that require adjustments to the empirical side of the puzzle (for example, they have looked at sample time periods and mean reversion or aversion), alternative theoretical frameworks (for instance, they have researched preferences, disaster states, survivorship bias, incomplete markets, and market imperfection), or other rationales. The authors extend the framework of Constantinides, Donaldson, and Mehra (Quarterly Journal of Economics 2002), which focused on market imperfection.

Practitioners may find this research useful in identifying the middle-aged consumer as the primary driver of investment returns. Investment products and strategies can be geared to address the preferences of the habit-forming consumer with the most assets to invest.

Constantinides et al. (hereafter CDM) proposed an overlapping-generations model that assumed that the borrowing-constrained younger generation is prevented from owning equity and that middle-aged consumers save more by holding more bonds and less equity (because their retirement income is expected to be zero or deterministic and their future consumption is highly correlated with equity income). The older generation is assumed to hold neither equity nor bonds. CDM concluded that middle-aged consumers’ savings decisions have a dominant impact on equity and bond returns. If the younger generation were unconstrained, the net effect of them being allowed to borrow to purchase equity would be an increase in equity returns and bond returns, which would shrink the equity premium. But it is assumed instead that the young are prevented from borrowing and that all assets are accumulated during middle age and consumed in old age.

The authors incorporate habit formation into the overlapping-generations economy and suggest that the habit-formation process contributes to the middle-aged consumer demanding more bonds and less equity. The growth rate in aggregate savings increases as habit persistence increases under both borrowing-unconstrained and borrowing-constrained economies, but the growth rate is greater in a borrowing-constrained economy. An even higher demand for bonds (yielding a lower risk-free rate) and a lower demand for equity (yielding a higher required return for holding equity) lead to a higher equity premium than that presented in CDM.

The authors discuss related works on habit formation in the equity premium puzzle. They then analyze the optimum savings of habit-forming middle-aged consumers under a borrowing-constrained economy and the positive effect habit formation has on middle-aged consumers’ savings. Using comparative static analyses and calibrations, they show that incorporating habit-formation preferences into a three-period overlapping-generations model has a positive impact on the savings level of middle-aged consumers.

Under a borrowing-constrained economy, the young are prevented from borrowing to make equity investments; thus, both equity returns and bond returns are exclusively determined by habit-forming middle-aged investors. The authors derive the optimum savings level of the middle-aged generation by solving the maximization problem of the discounted utility over the consumer life cycle and then show the positive impact of habit-formation preferences on the optimum savings level of middle-aged consumers.

A total of 54 different versions of the economy are considered in the calibrations, with different ranges of parameters set for both borrowing-constrained and borrowing-unconstrained economies. The authors derive these versions by changing the coefficient of relative risk aversion and the habit-forming parameter by various increments. The annualized return is defined as the geometric average over a 20-year holding period.

The authors provide a theoretical perspective that seeks to explain a puzzle identified by previous researchers. The conclusions are predicated on several assumptions and are tied to the real world by stating that the young are prevented from borrowing against future labor income because human capital alone does not collateralize major loans as a result of moral hazard and adverse selection.

This research may have been more useful to practitioners if more empirical data had been applied and discussed. It is unclear what would constitute an acceptable and explainable historical equity premium to reconcile empirical data to theoretical calibrations.