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\section{Robustness and Identification}
\label{sec:robustness}
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The structural break is economically large---and large effects invite scrutiny, since they are also
the ones most likely to be artifacts. This section therefore asks how much we should believe it,
confronting the result with the alternative explanations a skeptical reader would raise: that the
break is mechanical, that it is a mega-cap rally in disguise, that it is sensitive to how the signal
is built, or that it merely tracks the technology sector. We subject it in turn to a placebo across
non-AI factors, an event study, a difference-in-differences design, and a battery of construction and
universe robustness checks. The result withstands each.

\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{\textbf{Placebo test across semantic factors.} The figure plots the post-ChatGPT
high-minus-low (Q5$-$Q1) return spread for each of the eight semantic factors. The AI-related factors
(in red) cluster at the top with large positive spreads, while ESG-commitment and climate-risk
disclosure earn \emph{negative} spreads and macro-risk disclosure earns essentially none. The contrast
shows the post-2022 re-rating is a thematic rotation toward AI, not a generic disclosure
effect.}\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{\textbf{Cumulative abnormal returns around ChatGPT.} The left panel plots the mean
market-model cumulative abnormal return (CAR) by pre-event AI-disclosure tercile over the event window;
the right panel plots the High$-$Low CAR spread. The tercile ordering is monotone at every horizon and
widens steadily, reaching roughly $+10$ percentage points one year after the launch. Because abnormal
returns are purged of market beta, the spread reflects a cross-sectional response to the AI-narrative
shock.}\label{fig:event}
\end{figure}

\begin{figure}[htbp]\centering
\includegraphics[width=0.66\textwidth]{fig13_event_binscatter.png}
\caption{\textbf{One-year abnormal return versus pre-event AI exposure.} The figure plots a binned
scatter, with fitted line, of each firm's one-year cumulative abnormal return after ChatGPT against its
pre-event AI exposure (measured from the FY2021 10-K). The relation is positive and smooth across the
exposure distribution, confirming that the event-study spread is not driven by a handful of
outliers.}\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{\textbf{Event-time profile of the AI premium.} The figure plots the estimated return premium
on firms' pre-determined (2019--2021) AI exposure by year, with 95\% confidence intervals, measured
relative to the 2021 base year and within firm and year fixed effects. The premium is flat and near
zero through 2021 and activates after ChatGPT, peaking in 2024---evidence that the market repriced
persistent pre-existing exposure rather than rewarding incremental wording.}
\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{\textbf{The AI spread is not a mega-cap artifact.} The figure compares the post-2022
composite Q5$-$Q1 return spread for the full index against the spread computed after excluding the
Magnificent~7 and after excluding the ten largest firms by market capitalization. The spread is
essentially unchanged in both cases, showing that the AI re-rating is a broad-based feature of the
index rather than the footprint of a handful of trillion-dollar winners.}\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.