Rare Disasters and Asset Markets in the Twentieth Century
Source: Barro, R. J. (2006) · Quarterly Journal of Economics 121(3), 823–866 · doi:10.1162/qjec.121.3.823
TL;DR
Revives Rietz's (1988) idea that low-probability economic disasters — large, rare contractions in output and consumption (wars, depressions) — can resolve the equity-premium puzzle. Calibrating disaster frequency and size from twentieth-century data across 35 countries, Barro shows a standard consumption-based model with reasonable risk aversion (γ ≈ 4) matches the high equity premium, low risk-free rate, and volatile stock returns.
The question
Mehra–Prescott (1985) showed standard models need implausibly high risk aversion to explain why equities out-earn government bills by ~7%/year. Rietz (1988) proposed rare disasters as the fix, but the profession dismissed it as relying on counterfactually high disaster probabilities/sizes. Barro's contribution is to measure twentieth-century disasters empirically and ask whether a tractable, conventional model calibrated to them can match the asset-pricing facts.
The model
A Lucas (1978) representative-agent fruit-tree economy with exogenous, i.i.d. shocks to productivity growth; time-additive, isoelastic (CRRA) preferences and complete markets (later extended to allow capital formation).
Each year, a small probability p of a disaster: a contraction of size b in consumption/output. Equity is a secure claim on output; the "risk-free" government bill suffers partial default in disaster states.
Disasters make the threat of catastrophic loss raise the required equity premium and depress the bill rate (precautionary saving), without extreme preferences.
Key predictions
Calibrated disaster process (from WWI, the Great Depression, WWII, and post-war emerging-market collapses): disaster probability p ≈ 1.5–2% per year (baseline p = 1.7%), with per-capita-GDP declines distributed over 15–64% (mean contraction size ≈ 0.29 raw, ≈ 0.35 adjusting for 2.5%/yr trend growth); based on 35 countries.
Headline result: with the historical disaster-size distribution, a coefficient of relative risk aversion of γ ≈ 4.3 generates a levered equity premium of 0.07 at the baseline p = 0.017 (γ ≈ 3.3 if b is fixed at 0.5; γ ≈ 10 if b = 0.25). Equivalently, at γ = 4 the required p is about 0.022.
Contrast with the disaster-free model: at γ = 4, σ = 0.02 the standard model delivers a premium of only 0.0016 versus 0.07 observed, and a counterfactually high real bill rate (~0.127). Disasters fix both.
Also rationalizes the high volatility of stock returns, a high price-earnings ratio (~59 near baseline), and low expected real interest rates during major wars (e.g., WWII).
Empirical status
A calibration/theory paper, not a regression study; its disaster distribution is drawn from realized twentieth-century contractions. It launched the modern rare-disasters literature (Gabaix 2012 variable disasters; Wachter 2013) and is widely cited as the disciplined revival of Rietz. The "peso problem" it embodies — that the priced risk may not appear in any given short sample — is itself a central caution for empirical asset pricing.
Limitations
Results hinge on the assumed disaster probability and size distribution, which are inherently hard to estimate from rare events (and partly extrapolated across countries).
Treats disasters as i.i.d. with constant intensity; later work (Gabaix, Wachter) argues time-varying disaster risk is needed to match return predictability/volatility dynamics.
Distinguishing rare-disaster risk from behavioral or long-run-risk explanations of the premium is empirically difficult.
Key references
Rietz, T. (1988) — The Equity Risk Premium: A Solution — Journal of Monetary Economics
Mehra, R. & Prescott, E. (1985) — The Equity Premium: A Puzzle — Journal of Monetary Economics
