Before We Start…

Assignment Release and Submission Schedule

Overview

Where we are in the research pipeline

Today we add two specialized tools for finance research: event studies for measuring market reactions to specific events, and Fama–MacBeth regressions for testing whether firm characteristics systematically predict returns over time.

Overview

Today’s learning objectives

• Understand the logic of event studies as a causal inference tool for measuring stock price reactions
• Define estimation and event windows, estimate expected return models, and calculate cumulative abnormal returns (CARs)
• Compare the Market Model and Fama–French 3-Factor Model as benchmarks for expected returns
• Understand the Fama–MacBeth two-step procedure for cross-sectional asset pricing tests
• Recognize when to use event studies vs. Fama–MacBeth vs. the panel methods from L4
• Appreciate recent methodological advances connecting event studies to causal inference

From DiD to Event Studies

What’s new, what’s familiar

From DiD to Event Studies

When to use what

Each method makes different assumptions to construct the counterfactual. No single method dominates — the right choice depends on the research question and data structure.

From DiD to Event Studies

Why event studies work — The efficient market hypothesis

Event studies rely on a version of the semi-strong form of market efficiency (Fama 1970):

Stock prices quickly incorporate all publicly available information. When new information arrives, prices adjust rapidly — abnormal returns are concentrated in a short window around the event.

Event Study Methodology

Step 1: Define the event

Event date: September 18, 2015

• EPA issues Notice of Violation — a public, well-dated, exogenous shock
• This is what makes Dieselgate a clean event: clear date, public information, limited anticipation

What makes a “good” event for event studies?

• Precise timing: The exact date of information arrival is known
• Surprise content: The event contains genuinely new information
• No confounding events: Other major news does not coincide with the event date
• Limited information leakage: Insider trading or rumours have not pre-empted the announcement

Event Study Methodology

Step 1: Define the windows

Event Study Methodology

Step 2: The Market Model

The simplest expected return model:

\[R_{i,t} = \alpha_i + \beta_i R_{m,t} + \varepsilon_{i,t}\]

Event Study Methodology

Step 2: Estimation window — Fitting the model

What happens in the estimation window?

• We estimate \(\hat{\alpha}_i\) and \(\hat{\beta}_i\) using OLS on [−120, −30] only
• These parameters capture the firm’s “normal” relationship with the market
• The estimation window must be before the event to avoid contamination

Intuition

If VW stock typically moves 1.2% for every 1% move in the DAX (\(\hat{\beta} = 1.2\)), and earns an extra 0.01% per day on average (\(\hat{\alpha} = 0.0001\)), then on any given day we can predict what VW “should” have returned — absent any firm-specific news.

Event Study Methodology

Step 2: Choosing a benchmark model

For short-window studies, the model choice typically does not matter much. We will verify this by comparing Market Model and FF3 results in A5.

Event Study Methodology

Step 3: The Fama–French 3-Factor Model

\[R_{i,t} - R_{f,t} = \alpha_i + \beta_{mkt}(R_{m,t} - R_{f,t}) + \beta_{smb}\, SMB_t + \beta_{hml}\, HML_t + \varepsilon_{i,t}\]

Event Study Methodology

Step 4: Abnormal returns — The “surprise”

\[AR_{i,t} = R_{i,t} - \hat{E}[R_{i,t}]\]

• \(R_{i,t}\): What the stock actually returned on day \(t\)
• \(\hat{E}[R_{i,t}]\): What we predicted it would return, given the market
• \(AR_{i,t}\): The abnormal return — the part unexplained by normal market movements

Sanity check

In the estimation window, the mean abnormal return should be approximately zero — because we estimated the model on that data. If \(\bar{AR} \neq 0\) in the estimation window, something has gone wrong. This is the event study equivalent of checking OLS residuals.

Event Study Methodology

Step 4: Interpreting abnormal returns

On September 18, 2015, VW’s actual return was far below what its beta and the market return would predict.The large negative \(AR\) is the market’s verdict on Dieselgate.

Event Study Methodology

Step 5: Cumulative abnormal returns (CAR)

\[CAR_i[0, +5] = \sum_{t=0}^{5} AR_{i,t}\]

Why cumulate?

• Markets may take several days to fully digest complex information
• Day 0 captures the initial shock; days +1 to +5 capture revisions, analyst coverage, contagion effects, and information cascading through the market
• A single day’s AR might miss the full story — CAR captures the total price impact

Event Study Methodology

The classic event study plot

This is the visual equivalent of the DiD plot you saw in L4 — but at daily frequency with the “treatment” being the scandal announcement.

Event Study Methodology

Expected results from Dieselgate

Event Study Methodology

Statistical testing

Once you have CARs, you need to test whether they are statistically significant:

Event Study Methodology

Cross-sectional analysis — “Who was hit hardest?”

After computing CARs, we can ask: what firm characteristics predict larger (or smaller) reactions?

\[CAR_i[0, +5] = \gamma_0 + \gamma_1 \text{German}_i + \gamma_2 \text{Size}_i + \gamma_3 \text{ROA}_i + \gamma_4 \text{Leverage}_i + u_i\]

• This is a cross-sectional OLS regression — connecting back to L3
• The dependent variable is the CAR you just calculated
• \(\gamma_1\) captures the differential reaction for German firms
• \(\gamma_2\) through \(\gamma_4\) test whether firm characteristics (size, profitability, leverage) amplify or dampen the reaction

This is exactly what you did in A3 — but now you understand the full pipeline from raw returns to CARs to cross-sectional tests.

Event Study Methodology

Practical considerations and pitfalls

Common challenges

• Thin trading: Stocks that trade infrequently may have stale prices, biasing AR calculations
• Event date ambiguity: Was the “real” event the EPA notice on September 18, or the media coverage on September 19, or earlier rumours? Sensitivity analysis with different event dates helps
• Overlapping events: If another major announcement coincides with the event, the AR will capture both
• Small samples: With few treated firms, statistical power is low and outliers are influential
• Event window length: Shorter windows are cleaner but may miss delayed reactions; longer windows introduce noise

Event Study Methodology

Summary of event studies

New Frontiers

Reframing event studies as causal inference

The classic event study asks: “What would this stock have returned absent the event?”

That is fundamentally a counterfactual question — the same question DiD asks, just at daily frequency. Goldsmith-Pinkham and Lyu (2025) make this connection explicit:

The traditional abnormal return \(AR_{i,t} = R_{i,t} - \hat{E}[R_{i,t}]\) is really an estimate of the average treatment effect on the treated — where the “treatment” is the event and the “counterfactual” comes from the factor model.

New Frontiers

When does the benchmark model matter?

Two dimensions determine how much trouble you face:

The intuition

• Daily factor premiums are tiny (~0.02%). Over a 5-day window, misspecification error is negligible
• But compound that over 250 trading days → up to 5 percentage points of bias
• With many randomly timed events, factor realizations average out. With a single event, you are exposed to whatever the factors happened to do on that specific day
• Dieselgate is a single event — we should be aware of this limitation, even though our short window provides protection

New Frontiers

When it goes wrong — A concrete example

Acemoglu et al. (2016) study firms connected to Timothy Geithner around his nomination as Treasury Secretary (November 21, 2008):

New Frontiers

When it goes wrong — A concrete example

Acemoglu et al. (2016) study firms connected to Timothy Geithner around his nomination as Treasury Secretary (November 21, 2008):

New Frontiers

When it goes wrong — A concrete example

Acemoglu et al. (2016) study firms connected to Timothy Geithner around his nomination as Treasury Secretary (November 21, 2008):

New Frontiers

Alternative counterfactual approaches

Instead of assuming you know the right factor model, let the data construct the counterfactual:

New Frontiers

Takeaway for your thesis

The good news: A5 uses a short event window [0,+5] and compares two benchmark models. If both tell the same story, your results are robust to the concerns raised by this new literature.

Fama–MacBeth Regression

From event reactions to systematic patterns

Event studies ask: “Did this specific event move stock prices?”

A different question: “Do certain firm characteristics systematically predict returns across time?”

Fama–MacBeth Regression

The problem with pooled OLS

Cross-sectional correlation of residuals

When you pool all firm-month observations and run OLS, you implicitly assume residuals are independent across firms within the same period. But…

• Firms are hit by common shocks (recessions, market crashes, policy changes)
• On a bad day, most firms have negative residuals simultaneously
• This means residuals within the same time period are correlated

Fama–MacBeth Regression

The Fama–MacBeth idea

Fama and MacBeth (1973) proposed an elegant two-step solution:

Step 1: For each month t, run a cross-sectional regression

Collect T slope coefficients \(\hat{\gamma}_{1,1}, \hat{\gamma}_{1,2}, \ldots, \hat{\gamma}_{1,T}\)

Step 2: Average the T coefficients and use their time-series variation for inference

\(\bar{\gamma}_1 = \frac{1}{T} \sum_{t=1}^{T} \hat{\gamma}_{1,t} \quad \text{and} \quad SE(\bar{\gamma}_1) = \frac{s(\hat{\gamma}_{1,t})}{\sqrt{T}}\)

Fama–MacBeth Regression

Step 1: Cross-sectional regressions

For each time period \(t\) (e.g. each month):

\[R_{i,t} = \gamma_{0,t} + \gamma_{1,t}\, X_{i,t-1} + \varepsilon_{i,t}\]

Fama–MacBeth Regression

Step 2: Time-series average

\[\bar{\gamma}_1 = \frac{1}{T} \sum_{t=1}^{T} \hat{\gamma}_{1,t}\]

The average slope across all periods is our estimate of the systematic relationship between the characteristic and returns — the risk premium, if you are thinking in asset pricing terms.

Fama–MacBeth Regression

Step 3: Standard errors

\[SE(\bar{\gamma}_1) = \frac{s(\hat{\gamma}_{1,t})}{\sqrt{T}}\]

where \(s(\hat{\gamma}_{1,t})\) is the standard deviation of the \(T\) estimated slopes.

Fama–MacBeth Regression

Visualizing the distribution of slopes

What the distribution tells you

• Slopes tightly clustered around a positive value → strong, stable evidence that the characteristic predicts returns
• Slopes widely dispersed around zero → no reliable relationship; sometimes positive, sometimes negative
• Slopes with a clear positive mean but large variance → the relationship exists on average but is noisy period-by-period

This distribution is the core diagnostic of Fama–MacBeth. It shows you not just the average effect, but how consistent it is over time.

Fama–MacBeth Regression

Applications in published research

Fama–MacBeth is everywhere in asset pricing and corporate finance:

• Original CAPM tests: Fama and MacBeth (1973) tested whether market beta explains cross-sectional return variation
• Fama–French factor tests: Do SMB and HML factors carry a risk premium?
• ESG and returns: Does environmental or social performance predict returns?
• Liquidity premiums: Do less-liquid stocks earn higher returns?
• Anomaly research: Size, value, momentum, profitability, investment — nearly all tested via FM

If you read a finance paper that reports “Fama–MacBeth regressions,” you now know exactly what the authors did and why.

Fama–MacBeth Regression

Limitations

• Errors-in-variables (EIV): The first-stage coefficients \(\hat{\gamma}_{1,t}\) are estimated with error, which attenuates the second-stage average toward zero. The Shanken correction adjusts for this, but adds complexity, see Kim (1995) and Shanken (1992).
• Persistence in characteristics: FM assumes cross-sections are relatively independent over time. If firm characteristics are highly persistent (e.g. firm size barely changes month-to-month), FM may underperform double-clustered SE approaches
• Balanced panel preference: FM works best when each cross-section has a similar set of firms. If the firm universe changes dramatically over time, the \(\hat{\gamma}_{1,t}\) estimates may not be comparable
• Modern alternatives: Double-clustered standard errors (Petersen 2008) address the same problem and are easier to implement in standard software

Fama–MacBeth Regression

Summary

Synthesis

The complete methods toolkit

Each method trades off different assumptions. The art of empirical finance is choosing the method whose assumptions are most credible for your specific research question and data.

Synthesis

Standard errors: A unifying thread

The standard error story has been building across the course:

• L3: Heteroskedasticity-robust SE → solves non-constant variance
• L4: Cluster-robust SE → handles within-group correlation (Moulton problem)
• L5: Fama–MacBeth SE → handles cross-sectional correlation of residuals

All three address the same fundamental issue: when residuals are not independent, naive standard errors are too small. The solution is always to match the inference method to the correlation structure of the data.

Synthesis

Connection to A5

Assignment 5 asks you to:

1. Load daily stock return data for auto firms
2. Drop VW subsidiaries to avoid mechanical linkages
3. Define estimation [−120, −30] and event [0, +5] windows
4. Estimate Market Model and Fama–French 3-Factor expected returns
5. Calculate abnormal returns (AR) and cumulative abnormal returns (CAR)
6. Create the classic event study visualization
7. Conduct cross-sectional tests on CARs

This is the full event study pipeline from raw data to publishable results. Everything from today’s lecture maps directly onto specific assignment tasks.

Synthesis

Connection to your thesis

Both methods from today are staples of finance research:

• Event studies appear in papers on M&A announcements, earnings surprises, regulatory changes, CEO turnovers, patent issuances, and many more corporate events
• Fama–MacBeth is the standard approach for testing asset pricing models and cross-sectional return predictability

Synthesis

Looking ahead — L6: Replication Workshop

In the final lecture, we bring everything together:

• How to read and replicate a published paper, seagway through Huck (2024) before next lecture
• Connecting methods (OLS, DiD, event studies, FM) to research designs
• Common pitfalls in replication work
• How to extend a replication for your thesis

Appendix

MacKinlay (1997) — The classic event study reference

MacKinlay (1997) established the modern event study framework:

• Formalized the estimation window / event window structure
• Showed that the Market Model dominates simpler approaches (mean-adjusted, market-adjusted)
• Provided test statistics for single-firm and multi-firm event studies
• Discussed parametric and non-parametric tests

This paper remains the default citation for event study methodology. Nearly every event study paper begins with a sentence like: “We follow the standard event study methodology of MacKinlay (1997).”

Appendix

Fama & French (1993) — Factor construction

How SMB and HML are constructed

• SMB: Sort all stocks by market capitalization into two groups (small, big). SMB = return of small portfolio − return of big portfolio
• HML: Sort all stocks by book-to-market ratio into three groups (low, medium, high). HML = return of high B/M portfolio − return of low B/M portfolio
• Both factors are rebalanced annually and returns are computed daily or monthly

Why these factors?

Fama and French (1993) documented that size and value explain a large share of cross-sectional return variation that CAPM beta alone cannot. Whether these reflect risk or mispricing remains debated — but the empirical regularity is well-established.

Appendix

Petersen (2008) — Choosing the right standard errors

Petersen (2008) provides a decision framework:

Key finding: Fama–MacBeth and clustering by time produce similar standard errors when the number of time periods is large. Double-clustering is more general and handles both dimensions simultaneously.

Appendix

Event study cross-sectional correlation

Kolari and Pynnönen (2010) address a subtle issue: even in short-window event studies, abnormal returns may be cross-sectionally correlated when the event affects multiple firms simultaneously (as in Dieselgate).

Standard event study tests assume independence across firms. When this fails:

• Aggregate test statistics are inflated
• The adjusted BMP test accounts for cross-sectional correlation in ARs
• Alternative: bootstrap methods that resample clusters of firms

This matters for Dieselgate because all German automakers are hit by the same event on the same day — their ARs are not independent draws.

Appendix

Goldsmith-Pinkham & Lyu (2024) — Key results summary

Three empirical examples

1. Geithner connections (single event, non-random timing): Standard methods overstate effects; synthetic control finds near-zero effects
2. S&P 500 index inclusion (many events, random timing): All methods agree in the short run — model choice does not matter
3. M&A acquirer returns (many events, quasi-random): Short-run effects similar across methods; long-run effects diverge substantially

Key takeaways

• Short-run + random timing → classical methods work well
• Single event OR long horizon → factor model misspecification can seriously bias results
• Synthetic control and GSynth are robust alternatives, especially for long-horizon studies
• The bias compounds over time: a daily misspecification of 0.02% becomes 5% over a year