The equity premium: A puzzle

This 1985 Journal of Monetary Economics paper by Rajnish Mehra and Edward C. Prescott documents that over the ninety-year period 1889-1978, the average real annual return on the Standard and Poor’s 500 Composite Index was 6.98 percent while the average real return on short-term, virtually default-free securities was only 0.80 percent, an average equity premium of 6.18 percent (standard error 1.76 percent), and asks whether this gap can be accounted for by a class of general-equilibrium pure-exchange models that abstract from transactions costs, liquidity constraints, and other frictions absent from the Arrow-Debreu framework (Sections 1-2, pp. 145-147, 155-156). Using a variant of Lucas’s (1978) exchange-economy model – modified so that the growth RATE, rather than the level, of the (single) representative household’s consumption endowment follows a two-state Markov process, in order to accommodate the sustained, non-stationary growth actually observed in U.S. per capita consumption – the authors calibrate the consumption process to match the historical mean, standard deviation, and first-order serial correlation of U.S. consumption growth, then search over the whole empirically defensible range of risk-aversion (0 to 10) and time-discount parameters to see what combinations of average risk-free rate and average equity premium the model can produce (Sections 3-4, pp. 150-155). They find that the model can generate a maximum average equity premium of only 0.35 percent – compared with the 6.18 percent observed – and that this conclusion is robust to measurement error in inflation, to the level of temporal aggregation, to alternative specifications of the consumption process (including higher moments), and to introducing financial leverage on the modeled firm or extending the model to allow production and capital accumulation (Section 4, pp. 155-158). The intuition, as the authors explain it, is that in a growing economy the levels of risk aversion needed to generate a six-percent premium also imply implausibly high average real interest rates, since sufficiently risk-averse agents discount future (higher) consumption so heavily that the model-implied risk-free rate rises far above the 0.80 percent actually observed (Section 1, pp. 146-147; Section 5, p. 157). The paper concludes that the puzzle can equally well be framed as asking why the risk-free rate was so low rather than why the equity return was so high, and conjectures that resolving it will most likely require an equilibrium model with some friction or market incompleteness – rather than a complete-markets Arrow-Debreu economy – doubting that either investor heterogeneity or non-time-additive preferences alone will suffice (Section 5, pp. 157-159).

Rajnish Mehra | Macro Paper Warehouse

The equity premium: A puzzle