brav-2000

title: Inference in Long-Horizon Event Studies: A Bayesian Approach with Application to Initial Public Offerings tags: [bayesian, event-study, empirical-finance, ipo, posterior-predictive, sur, gibbs-sampler, shrinkage, long-horizon, griddy-gibbs] sources: [] updated: 2026-06-01 kind: paper author: Alon Brav date: 2000-10-01 url: https://www.jstor.org/stable/222545

Summary

Long-horizon buy-and-hold returns are non-normal (right-skewed) and cross-sectionally dependent when firms cluster in calendar time. Both biases cause conventional t-tests to over-reject. Brav proposes a Bayesian predictive approach: fit a seemingly unrelated regression (SUR) model with an equicorrelation structure and lognormal shrinkage priors on firm residual standard deviations (SDs); simulate the predictive distribution of the sample mean by compounding single-period draws; use the predictive density as the null for inference. Applied to 1,521 initial public offerings (IPOs, 1975–1984), the characteristic-based model is not rejected while the Fama-French three-factor (FF3F) model is decisively rejected — its factor loadings imply far higher expected returns than were realised.

Key Claims

Standard t-tests in long-horizon event studies are misspecified due to (i) right-skewed compounded returns and (ii) positive cross-sectional dependence from unpriced industry factors.
The nonparametric bootstrap (Ikenberry-Lakonishok-Vermaelen 1995) is too narrow by ~~30%: it ignores cross-sectional correlation (accounts for ~half the gap) and uses replacement firms with lower residual SDs than IPOs (~~10.4% vs. ~15.7% monthly).
SUR setup: $Y = F\iota + V$ , residuals $V \sim \text{MVN}(0, \Sigma)$ (multivariate normal), $\Sigma = SRS$ with $S$ a diagonal SD matrix and $R$ an equicorrelation matrix with common $\rho$ per industry.
Lognormal Empirical Bayes prior on $\sigma_i$ : $\log(\sigma_i) \sim N(\bar{s}, \delta_\sigma)$ centered at the within-industry grand mean; shrinkage toward industry average exploits the premise that same-industry firms have similar residual variation.
Common correlation $\rho$ : uniform prior restricted to ensure positive definiteness; posterior $\rho \approx 2.5$ – $2.7\%$ for computer/data services industry; small but materially widens the predictive density tails ( $\pm 10$ – $12$ percentage points, pp).
Griddy-Gibbs for non-conjugate conditionals of $\rho$ and $\sigma_i$ (non-standard forms due to the $S/R$ decomposition).
Small sample (113 computer/data services IPOs): characteristic model not rejected; predictive 5th–95th percentile = [−37%, +50%].
Full sample (1,521 IPOs): characteristic model not rejected (observed −4.9% within [−14%, +16%]); FF3F rejected (observed −47.9% vs. 5th percentile −18.5%).
The methodology is well-specified: rejection rates across 250 random samples of 200 firms match nominal 5% and 10% levels for both the characteristic and the factor model.

Concepts Introduced or Extended

Entities Mentioned

Alon Brav

Quotes

"The methodology employs a Bayesian 'predictive' approach, essentially a goodness-of-fit criterion, based on the idea that good models among those in consideration should make predictions close to what has been observed in the data."

My Take

A technically solid paper that cleanly diagnoses why the bootstrap fails in long-horizon event studies and proposes a principled Bayesian fix. The connection to posterior predictive checking (Box 1980, Gelman-Meng-Stern 1996) is natural and well-executed. The equicorrelation assumption within industries is restrictive but tractable; the industry-by-industry decomposition for the full sample is a pragmatic engineering solution. The substantive finding — characteristic model OK, FF3F rejected — is influential in the IPO underperformance debate and is robust to shrinkage assumptions. One tension: the paper uses Empirical Bayes (prior centered at sample grand mean) rather than a genuinely informative prior, which slightly blurs the Bayesian/frequentist boundary.