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\section{Robustness and Identification}
\label{sec:robustness}
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The structural break is economically large; this section asks how much we should believe it. We
subject it to a placebo across non-AI factors, an event study, a difference-in-differences design, and
a battery of construction and universe robustness checks.

\subsection{Placebo: is the effect specific to AI? (H3)}
If the post-2022 spread were a mechanical artifact of our pipeline---or a generic ``high-disclosure
firms did well'' phenomenon---it should appear for any semantic factor. Table~\ref{tab:placebo} and
Figure~\ref{fig:placebo} re-run the entire sub-period and interaction design on all eight factors. The
result strongly supports AI-specificity. The three AI factors show large positive post-2022 spreads
($+13.6$ to $+14.3$ points). Macro-risk language shows essentially no spread ($-0.5$, $t=-0.1$). And,
strikingly, ESG-commitment and climate-risk disclosure earn \emph{negative} post-2022 spreads
($-8.8$ and $-5.0$ points, both significant)---high-ESG firms \emph{underperformed} after 2022, in
line with the post-2021 reversal in the sustainable-investing literature \citep{pastor2022dissecting}.
The one non-AI factor that does show a large positive post-2022 spread is cybersecurity ($+13.5$); we
read this not as a violation but as confirmation, since cybersecurity disclosure is tightly bundled
with technology exposure and is itself increasingly AI-related. The cleanest contrast---AI rewarded,
ESG and climate penalized---makes a powerful case that the post-ChatGPT re-rating reflects a thematic
rotation \emph{toward AI}, not a generic disclosure effect.

\input{tables/tab_placebo}

\begin{figure}[htbp]\centering
\includegraphics[width=0.92\textwidth]{fig7_placebo.png}
\caption{Placebo test: post-ChatGPT high-minus-low return spread for each of the eight semantic
factors. AI-related factors (red) cluster at the top; ESG and climate disclosure earn negative
spreads.}\label{fig:placebo}
\end{figure}

\subsection{Event study around ChatGPT}
The portfolio results use annual formation and forward returns; the event study provides a
higher-frequency, cleanly identified complement. Table~\ref{tab:event} and Figure~\ref{fig:event}
report market-model cumulative abnormal returns by pre-event AI tercile. The ordering is monotone at
every horizon and widens steadily over time. The High-minus-Low CAR difference is $+2.9$ points at 60
trading days \tstat{1.77}, $+10.1$ points at one year \tstat{1.97}, and $+14.6$ points at eighteen
months \tstat{1.89}. Because these are abnormal returns---purged of each firm's market beta---the
spread cannot be attributed to high-AI firms simply being higher-beta in a recovering market. A
cross-sectional regression of one-year CAR on pre-event AI exposure yields $+3.1$ points per standard
deviation \tstat{1.39}; adding sector fixed effects halves it to $+2.1$ points \tstat{0.99}, again
locating much---but not all---of the effect in a sector channel. Figure~\ref{fig:eventbin} shows the
relation is smooth across the exposure distribution, not driven by a few outliers.

\input{tables/tab_event}

\begin{figure}[htbp]\centering
\includegraphics[width=\textwidth]{fig8_event_car.png}
\caption{ChatGPT event study. Left: mean cumulative abnormal return (market model) by pre-event AI
tercile. Right: the High$-$Low CAR spread.}\label{fig:event}
\end{figure}

\begin{figure}[htbp]\centering
\includegraphics[width=0.66\textwidth]{fig13_event_binscatter.png}
\caption{One-year cumulative abnormal return after ChatGPT versus pre-event AI exposure (binned
scatter with fitted line).}\label{fig:eventbin}
\end{figure}

\subsection{Difference-in-differences and the cross-sectional nature of the effect (H4)}
Table~\ref{tab:did} reports difference-in-differences estimates in which treatment is the firm's
pre-determined (2019--2021) AI exposure interacted with the post-2022 indicator, within firm and year
fixed effects. The continuous-exposure DiD coefficient is $+2.7$ percentage points per standard
deviation \tstat{1.51}; the binary version is $+1.7$ points \tstat{0.78}. These are positive and
economically meaningful but weaker than the cross-sectional estimates---exactly the pattern predicted
by H4. Once firm fixed effects absorb the permanent component of AI exposure, only the residual
within-firm variation identifies the effect, and that variation is small. The event-time profile in
Figure~\ref{fig:eventtime} reinforces this reading: the return premium on a firm's \emph{fixed}
pre-event AI exposure is flat and near zero through 2021 and jumps after 2022, peaking in 2024. The
market did not reward firms for adding AI sentences to their filings; it repriced the firms whose
pre-existing, persistent exposure made them AI winners once the narrative turned.

\input{tables/tab_did}

\begin{figure}[htbp]\centering
\includegraphics[width=0.82\textwidth]{fig11_eventtime.png}
\caption{Event-study coefficients: the return premium on pre-determined (2019--2021) AI exposure by
year (95\% confidence intervals), relative to 2021. The premium activates after ChatGPT.}
\label{fig:eventtime}
\end{figure}

\subsection{Construction, horizon, and universe robustness}
Table~\ref{tab:robust} collects the remaining checks. The post-2022 spread is essentially unchanged
whether the signal is the section-weighted mean (base, $+14.6$), the simple mean ($+13.4$), or the
top-5\% tail ($+14.9$). It holds at six-, twelve-, and twenty-four-month horizons (growing with the
horizon, as a persistent premium should). It survives replacing the three AI signals with their first
principal component---which alone explains 86.8\% of their common variance, confirming the ``single
latent AI construct'' interpretation---yielding a post-2022 PC1 spread of $+13.4$ points \tstat{1.97}.
Most importantly for the mega-cap concern, the spread is $+14.1$ points \tstat{1.92} when the
Magnificent~7 are excluded and $+14.5$ points \tstat{1.93} when the ten largest firms are dropped
(Figure~\ref{fig:mag7}). The AI re-rating is a broad-based feature of the index, not the mechanical
footprint of a handful of trillion-dollar winners. Finally, the sector-neutral composite---which
compares firms only to others \emph{within} their GICS sector---produces a much smaller and
insignificant post-2022 spread ($+3.8$ points, $t=0.84$). This is not a failure of the result but a
sharpening of it: a large share of the AI premium operates through a \emph{between-sector} channel, as
the market re-rated AI-exposed sectors (technology above all) relative to others, with a smaller
within-sector residual.

\input{tables/tab_robust}

\begin{figure}[htbp]\centering
\includegraphics[width=0.78\textwidth]{fig10_mag7.png}
\caption{Robustness of the AI return spread to excluding mega-cap winners. The post-2022 composite
spread is stable when the Magnificent~7 or the ten largest firms are removed.}\label{fig:mag7}
\end{figure}

\subsection{An alternative performance outcome: risk}
Performance is not only about mean returns. We also relate AI disclosure to subsequent realized
volatility. High-AI firms exhibit modestly higher forward volatility, and the gap widens after 2022 (a
Q5$-$Q1 difference of about 2.9 annualized volatility points, $t=3.1$). The post-2022 AI premium
therefore came bundled with somewhat higher risk---part, though by no means all, of the elevated
returns is compensation for the greater volatility of AI-exposed firms during a period of rapid
technological repricing.