Methodology
Reverse Event Study
A reverse event study measures the ripple of a known event onto firms that were never part of it. The event hits one focal firm, and you read the abnormal returns of its connected but uninvolved neighbours, competitors, suppliers, customers, industry and country peers, to see who the shock spreads to and whether it hurts them or helps them.
Take a known event on firm A, build a portfolio of connected bystander firms B, and run the ordinary abnormal-return machinery on them instead of on A. The sign is the whole point: a significantly negative bystander CAR is contagion, a positive one is a competitive effect where the neighbours capture what A loses. This is distinct from the genuinely inverse problem of inferring an unknown event date from observed returns, which is what the Event Date Identifier handles.
Two things called a reverse event study
The phrase "reverse event study" is used for two designs that share almost nothing beyond the word "reverse". Before you read further, or read anyone else's paper, settle which one is meant.
Spillover is not the inverse problem: do not conflate the two. Sense (1), the established design this page covers, is the cross-firm spillover study: the event date is known and the object of study is the set of bystander firms. Sense (2) is the truly inverse problem: the abnormal returns are known but the event date is unknown, and you work backwards to date it. That second problem is not a spillover study at all, it is what the Event Date Identifier (/edi) app solves. When you meet "reverse event study" in the literature, check which sense the author intends. See also the spillover row on Other event study types.
The estimator: same abnormal-return machinery, new target
There is no new statistics in a spillover study. You reuse the exact market-model or CAPM abnormal-return engine described under Expected return models, and simply point it at the bystanders instead of the focal firm. Three steps.
Step 1, abnormal returns on each bystander. For bystander firm \(i\), fit a normal-return model over a pre-event estimation window, then take the abnormal return as the observed return minus the expected return, and cumulate it over the event window into a firm-level CAR:
\[ AR_{i,t} = R_{i,t} - E\!\left[R_{i,t}\mid X_t\right], \qquad CAR_i = \sum_{t=t_1}^{t_2} AR_{i,t} \]
Step 2, aggregate and read the sign. Average the bystander CARs into a cumulative average abnormal return \(\overline{CAAR}\). A significantly negative value is evidence of contagion, a significantly positive value is evidence of a competitive effect. Lang and Stulz (1992) is the canonical demonstration that both signs genuinely appear in the data.
Step 3, explain the sign with a cross-sectional regression. Regress the firm-level CARs on the link and moderator variables to understand why the sign came out the way it did:
\[ CAR_i = \gamma_0 + \gamma_1\,\text{Concentration}_i + \gamma_2\,\text{Leverage}_i + \gamma_3\,\text{LinkStrength}_i + \varepsilon_i \]
Reading the sign
Negative bystander CAR means contagion: the event revealed shared risk or bad news the whole group carries. Positive bystander CAR means competition: the neighbours capture demand, market share or rents that the focal firm loses. The magnitude tells you how much, the sign tells you which story.
What moves the sign
Concentration. Measured by a Herfindahl index. The competitive, positive effect dominates in concentrated, low-leverage industries, while contagion dominates in competitive, high-leverage ones (Lang and Stulz, 1992).
Leverage. Highly levered peers are more contagion-prone, because they share the financial fragility the event exposes (Lang and Stulz, 1992).
Link strength. The percent of sales or purchases tied to the focal firm. Hertzel et al. (2008) use exactly this to isolate suppliers and customers along the supply chain: the tighter the link, the stronger the effect.
Why clustering breaks naive tests
This is the hard part of the design, and the part that separates a credible spillover study from a spurious one.
Every bystander shares the same event date, so their abnormal returns are cross-sectionally correlated at that date: one common shock moves the whole portfolio together. Tests that assume the firms are independent treat that single correlated jump as many independent pieces of evidence, so they over-reject massively and report "significance" that is not there. The chain is: shared event date, cross-sectional correlation, over-rejection. Three remedies address it, and all are in the Significance tests menu:
- Portfolio / calendar-time aggregation. Form one portfolio of bystanders per event and test the portfolio's abnormal return, so the correlation is absorbed into a single time series.
- The BMP standardized cross-sectional test (Boehmer, Musumeci and Poulsen, 1991), robust to event-induced variance.
- The Kolari and Pynnonen (2010) adjustment, which extends BMP to correct explicitly for the cross-sectional correlation that clustering creates. Their headline result: even low cross-correlation is serious once returns are event-clustered.
Applications
The same estimator answers very different questions depending on the trigger event and who the bystanders are. The canonical sign in each case, and its interpretation, follows from the contagion-versus-competition logic above. This page preserves the plain-language CAPM/AR/abnormal-volatility framing and the mergers, antitrust and environmental-regulation examples from the earlier version, and adds the verified sign for each.
| Trigger event on firm A | Bystanders B | Typical sign | Interpretation |
|---|---|---|---|
| Bankruptcy filing | Industry rivals | Mixed | Contagion in competitive, levered industries; competition in concentrated ones (Lang and Stulz, 1992). |
| Horizontal merger, M&A | Rival producers | Often positive | Rivals gain if the merger signals collusion or higher prices, a test of the collusion hypothesis, though Eckbo's (1983) own evidence points to efficiency rather than collusion. |
| Antitrust action | Rivals of the accused | Sign flips vs merger | Blocking a merger reverses the rival gain (Eckbo, 1983). |
| Financial distress | Suppliers and customers | Negative | Supply-chain contagion, strongest where link strength is high (Hertzel et al., 2008). |
| Earnings release | Same-industry peers | Information transfer | Peers re-rate on the news content even with no own-firm news (Foster, 1981; Firth, 1976). |
| Regulatory or environmental change | Peer firms, country peers | Context-dependent | Shared regulatory exposure pulls one way, differential compliance cost the other. |
For how these designs sit inside empirical finance and accounting research, see Academic research.
Key references
| Reference | Why it matters here |
|---|---|
| Lang, L. H. P., & Stulz, R. M. (1992). Contagion and competitive intra-industry effects of bankruptcy announcements: An empirical analysis. Journal of Financial Economics, 32(1), 45–60. Link | The canonical contagion-versus-competition paper, and the source of the concentration and leverage moderators. |
| Hertzel, M. G., Li, Z., Officer, M. S., & Rodgers, K. J. (2008). Inter-firm linkages and the wealth effects of financial distress along the supply chain. Journal of Financial Economics, 87(2), 374–387. Link | Supply-chain spillover to suppliers and customers, and the basis for the link-strength moderator. |
| Foster, G. (1981). Intra-industry information transfers associated with earnings releases. Journal of Accounting and Economics, 3(3), 201–232. Link | Seminal information-transfer evidence underpinning the earnings-release row. |
| Firth, M. (1976). The impact of earnings announcements on the share price behaviour of similar type firms. The Economic Journal, 86(342), 296–306. Link | Early, pre-Foster documentation of cross-firm information transfer on earnings news. |
| Eckbo, B. E. (1983). Horizontal mergers, collusion, and stockholder wealth. Journal of Financial Economics, 11(1–4), 241–273. Link | Rival abnormal returns as a test of the collusion hypothesis, underpinning the merger and antitrust rows. |
| Boehmer, E., Musumeci, J., & Poulsen, A. B. (1991). Event-study methodology under conditions of event-induced variance. Journal of Financial Economics, 30(2), 253–272. Link | The BMP standardized cross-sectional test, a core tool for the clustered-bystander setting. |
| Kolari, J. W., & Pynnonen, S. (2010). Event study testing with cross-sectional correlation of abnormal returns. The Review of Financial Studies, 23(11), 3996–4025. Link | Extends BMP to correct for the cross-sectional correlation induced by event-date clustering, the problem at the heart of spillover studies. |