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FIRC0002 Stage E (Agent 10): §5 results — sorts with CIs/raw-wins-median and VW narrative withdrawn (ECON-01, EDIT-08), results.tex:43 corrected (ECON-16), two-way/wild/permutation/sup-Wald break evidence and vacuous sentences removed (ECON-03/11, THEO-10/15), size section with tested contrasts and 2024-cohort dependence (EDIT-03, ECON-12), new multiple-testing subsection (cluster N); §6 — three within-sector estimators (THEO-03, ADVE-06), placebo under two-way clustering (ECON-03), event study benchmark dependence and placebo launches (cluster F), DiD/event-time corrected and H4 not supported (cluster G), SPID binary contrasts/MDEs/reversal (cluster I, LITE-03), forms with Wald (ADVE-03), new construct-validity and survivorship subsections (clusters J, D), §6.10 reversed sentence corrected (THEO-10); exhibits placed behind \ExhibitOnce per tables/EXHIBIT_MAP.json

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Simon-Pierre Boucher committed (Nov 5, 2026) parent c9ce652 Browse files

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1 1 % ============================================================================
2 +% Owner: Stage E, Agent 10 (writing). Numbers: tables/macros.tex, sections/macros_stageE.tex.
3 +% Exhibits: self-contained floats generated by scripts/r3k_20_tables_v2.py (tables/) and
4 +% scripts/r3k_19_figures_v2.py (figures_r3k/), placed here behind \ExhibitOnce; appendix-bound
5 +% exhibits (tables/EXHIBIT_MAP.json) are printed by tables/appendix_exhibits.tex.
2 6 \section{Results}
3 7 \label{sec:results}
4 8 % ============================================================================
5 9
6 10 Every table of this section reports the Russell~3000 universe and, where the comparison is
7 11 informative, the S\&P~500 members within it, with the standardization of the signal redone within
8 −each sample. The index panel reproduces the findings of the first version of this paper; the
9 −broad-universe panel is new.
10 −
11 −\subsection{Portfolio sorts: a modest, persistent relation}
12 −Table~\ref{tab:sortsboth} reports quintile sorts over the fifteen formation cohorts. In the
13 −Russell~3000 the relation between AI language and future returns is positive and broadly monotone.
14 −The equal-weighted Q5$-$Q1 spread on the composite is \mspreadFull{} percentage points per year
15 −($t=\mspreadFullT$), with a mean forward return of \mewQone\% in the bottom quintile and
16 −\mewQfive\% in the top; the adoption, infrastructure and disruption-risk spreads are of the same
17 −sign, the last the largest. Value-weighting \emph{raises} the composite spread to \mspreadFullVW{}
18 −points ($t=\mspreadFullVWT$): the value-weighted bottom quintile earned only \mvwQone\% per year,
19 −because the largest low-AI firms of the sample---energy majors, banks, utilities---lagged the
20 −market for most of the period, while the value-weighted top quintile is dominated by the technology
21 −leaders. In the S\&P~500 panel the equal-weighted composite spread is \mspSpreadFull{} points
22 −($t=\mspSpreadFullT$), close to the first version's $+4.9$. By the standards of
23 −\citet{harveyliuzhu2016} none of these spreads qualifies as a discovery, but in the broad universe
24 −the composite spread is significant at conventional levels over the full sample, which it was not
25 −in the index.
26 −
27 −\begin{table}[htbp]\centering\scriptsize
28 −\caption{\textbf{Quintile sorts on AI language, Russell~3000 and S\&P~500.} Mean forward
29 −twelve-month return (\%) by within-year quintile of each signal, equal- and value-weighted, averaged
30 −over formation cohorts 2010--2024, with the Q5$-$Q1 spread and its Newey--West $t$-statistic
31 −(three lags) on the series of annual spreads. Signals are standardized within year and within
32 −sample.}\label{tab:sortsboth}
33 −\adjustbox{max width=\textwidth}{\input{tables/tab_sorts_both}}
34 −\end{table}
12 +each sample. Every sort is shown on raw returns, on returns winsorized within formation year and
13 +as the median spread; the text quotes the winsorized specification and gives the raw value where
14 +the two differ materially. All results are computed on the rebuilt panel of \cref{sec:data}
15 +(corrected capitalization, cleaned returns, CIK key); where a pre-review value differs by more
16 +than rounding, it is given as the ``before'' value.
17 +
18 +\subsection{Portfolio sorts: a modest association that depends on the estimator}
19 +\label{subsec:sorts}
20 +\Cref{tab:sortsboth} reports quintile sorts over the fifteen formation cohorts. In the
21 +Russell~3000 the relation between AI language and future returns is positive and broadly
22 +monotone: the equal-weighted forward return rises from \mewQone\% in the bottom quintile of the
23 +composite to \mewQfive\% in the top on raw returns. The raw Q5$-$Q1 spread is \mspreadFull{}
24 +percentage points per year (Newey--West $t=\mspreadFullT$, plain $t=\mspreadFullTplain$, 95\%
25 +interval \mspreadFullCI), unchanged from the pre-review value of \mvoneSpreadFull{}
26 +($t=\mvoneSpreadFullT$) because the cleaning removed few observations. Winsorizing within year
27 +lowers it to \mspreadFullW{} points (Newey--West $t=\mspreadFullWT$, plain $t=\mspreadFullWTplain$,
28 +interval \mspreadFullWCI), and the median spread within cohort is \mspreadFullMed{} points
29 +($t=\mspreadFullMedT$): the top one percent of returns contributes \mtopOnePctContrib{} points of
30 +the raw spread. The adoption, infrastructure and disruption-risk spreads have the same sign; the
31 +disruption-risk facet, excluded from the composite, is the largest (\mriskFull{} raw, \mriskFullW{}
32 +winsorized, $t=\mriskFullWT$) and the most outlier-dependent (\mriskTopOnePct{} points from the top
33 +one percent), and the first principal component gives \mpcaFullW{} points ($t=\mpcaFullWT$). In
34 +the S\&P~500 panel the winsorized composite spread is \mspSpreadFullW{} points
35 +($t=\mspSpreadFullWT$). The full set of signals and weightings is in \cref{tab:sorts}.
36 +
37 +Value-weighting on the corrected capitalization gives a composite spread of \mspreadFullVW{}
38 +points (Newey--West $t=\mspreadFullVWT$), with a bottom quintile earning \mvwQone\% and a top
39 +quintile \mvwQfive\%; the weight-capped variant (10\% per firm) gives \mspreadFullVWcap{}
40 +($t=\mspreadFullVWcapT$). The pre-review value-weighted spread of \mvoneSpreadFullVW{}
41 +($t=\mvoneSpreadFullVWT$) and its bottom quintile of \mvoneVWQone\% per year were artefacts of
42 +the capitalization error: single firms with mis-stated share counts carried up to
43 +\mvwMaxWeightVone\% of a quintile, and the narrative of the first version---that the largest
44 +low-AI firms lagged the market---rested on them and is withdrawn. By the standard of
45 +\citet{harveyliuzhu2016} none of these spreads qualifies as a discovery: within the family of ten
46 +full-sample spreads of \cref{tab:sortsboth}, the Romano--Wolf adjusted $p$-value of the composite
47 +is \mrwComposFull{} (\cref{subsec:mht}). The honest summary of the sort evidence is a positive
48 +spread whose winsorized interval covers zero and whose median is close to zero; the regression
49 +evidence of \cref{subsec:fm} is where the premium is stable.
50 +
51 +\ExhibitOnce{tab:sortsboth}{\input{tables/tab_sorts_both}}
35 52
36 53 \subsection{Factor-adjusted performance (H1)}
37 −Table~\ref{tab:alphaboth} reports the monthly long--short portfolios. In the Russell~3000 the
54 +\label{subsec:alpha}
55 +\Cref{tab:alphaboth} reports the monthly long--short portfolios. In the Russell~3000 the
38 56 composite long--short earns \mmeanLSFull\% per year over 180 months (HAC $t=\mhacFull$, Sharpe
39 −ratio \msharpeFull), a CAPM alpha of about the same size and a six-factor alpha of \mffsixFull\%
40 −per year ($t=\mffsixFullT$); adding the technology-sector factor, on which the portfolio loads
41 −\mtechBetaFull, halves the alpha to \mffsixTechFull\% ($t=\mffsixTechFullT$). The adoption
42 −long--short earns nothing and the disruption-risk long--short the most. As in the index sample,
43 −unconditional risk-adjusted alpha is at best marginal, and part of what premium there is resembles
44 −a technology-sector tilt. The verdict on H1 is therefore the same in both universes: a positive but
45 −economically modest and statistically fragile unconditional premium.
46 −
47 −\begin{table}[htbp]\centering\small
48 −\caption{\textbf{Monthly long--short portfolios: mean, Sharpe ratio and factor alphas.} Equal-weighted,
49 −annually rebalanced, self-financing Q5$-$Q1 portfolios; alphas from CAPM and Fama--French
50 −five-factor-plus-momentum (FF6) regressions with HAC standard errors (three lags), full sample and
51 −post-launch sub-period (from July 2023).}\label{tab:alphaboth}
52 −\adjustbox{max width=\textwidth}{\input{tables/tab_alpha_both}}
53 −\end{table}
57 +ratio \msharpeFull), a CAPM alpha of about the same size and a six-factor alpha of
58 +\mffsixFull\% per year ($t=\mffsixFullT$); adding the technology-sector factor, on which the
59 +portfolio loads \mtechBetaFull, reduces the alpha to \mffsixTechFull\% ($t=\mffsixTechFullT$). The
60 +adoption long--short earns nothing beyond the factors and the disruption-risk long--short the
61 +most, with a six-factor alpha that is the only risk-adjusted statistic in the paper above the
62 +$|t|>3$ hurdle; its deflated Sharpe ratio, given the \mdsrTrials{} long--short series examined,
63 +is reported in \cref{tab:mht}. In the S\&P~500 panel the six-factor alphas of the three facets
64 +have $t$-statistics near two, so the first version's statement that risk-adjusted alpha is ``at
65 +best marginal'' was wrong for the index panel; in the broad universe it holds for the composite
66 +and not for the disruption-risk facet. The verdict on H1 is therefore facet-dependent: a positive
67 +but economically modest and, for the composite, statistically fragile unconditional premium, part
68 +of which resembles a technology-sector tilt. Sub-period alphas by signal are in \cref{tab:alpha}.
69 +
70 +\ExhibitOnce{tab:alphaboth}{\input{tables/tab_alpha_both}}
54 71
55 72 \subsection{Panel and Fama--MacBeth estimates}
56 −Table~\ref{tab:fmboth} reports Fama--MacBeth slopes in both universes and Table~\ref{tab:panel} the
57 −two-way fixed-effects panel in the broad universe. The composite premium is \mrkFMcompos{} points
58 −per standard deviation in the Russell~3000 ($t=\mrkFMcomposT$) and \mspFMcompos{}
59 −($t=\mspFMcomposT$) in the S\&P~500. When the three collinear facets are entered jointly, adoption
60 −takes a negative sign and infrastructure and disruption risk positive ones in both samples: it is
61 −the compute-exposure and threat-recognition vocabulary, not the ``we use AI internally''
62 −vocabulary, that carries the premium. The SPID project count has no cross-sectional premium in
63 −either sample. Size carries a strongly negative premium in the broad universe
64 −($\mfeSize$ points per standard deviation in the panel, $t=\mfeSizeT$), momentum a negative one
65 −and volatility a positive one, as expected in a sample that reaches far into small
66 −capitalizations. In the two-way fixed-effects panel the AI coefficients are small: the composite
67 −earns \mfeCompos{} points per standard deviation within firm ($t=\mfeComposT$). The signal lives
68 −across firms, not within them.
69 −
70 −\begin{table}[htbp]\centering\small
71 −\caption{\textbf{Fama--MacBeth regressions, Russell~3000 and S\&P~500.} Average of annual
72 −cross-sectional slopes of the forward return on the standardized signals and controls, in
73 −percentage points per standard deviation, with Newey--West $t$-statistics (three lags) on the
74 −series of annual slopes. ``Joint'' coefficients come from a regression that enters the three AI
75 −facets together.}\label{tab:fmboth}
76 −\input{tables/tab_fm_both}
77 −\end{table}
78 −
79 −\begin{table}[htbp]\centering\small
80 −\caption{\textbf{Two-way fixed-effects panel regressions, Russell~3000.} Dependent variable:
81 −winsorized forward twelve-month return. All regressions include firm and year fixed effects;
82 −standard errors are double-clustered by firm and year; $t$-statistics in parentheses; coefficients
83 −in percentage points per standard deviation.}\label{tab:panel}
84 −\adjustbox{max width=\textwidth}{\input{tables/tab_panel}}
85 −\end{table}
86 −
87 −\subsection{The post-ChatGPT change: an index result, not a market result (H2)}
73 +\label{subsec:fm}
74 +\Cref{tab:fmboth} reports Fama--MacBeth slopes in both universes and \cref{tab:panel} the two-way
75 +fixed-effects panel in the broad universe. The composite slope in the Russell~3000 is
76 +\mfmComposW{} points per standard deviation on winsorized returns (Newey--West $t=\mfmComposWT$,
77 +plain $t=\mfmComposWTplain$, interval \mfmComposWCI) and \mfmCompos{} on raw returns
78 +($t=\mfmComposT$); the pre-review value of \mvoneFMcompos{} ($t=\mvoneFMcomposT$) was computed on
79 +raw returns although the text said otherwise. The slope keeps conventional significance under
80 +both specifications and under the fixed-$b$ critical value of \mfixedBcv{} in the raw case
81 +only; its interval excludes zero in both. In the S\&P~500 the slope is \mspFMcomposW{}
82 +($t=\mspFMcomposWT$). When the three collinear facets are entered jointly, no single facet is
83 +significant on winsorized returns in the broad universe; on raw returns adoption takes a negative
84 +sign and infrastructure and disruption risk positive ones in both samples. The SPID project count
85 +has no cross-sectional slope in either sample. Size carries a strongly negative premium in the
86 +broad universe, momentum a negative one and volatility a positive one, the pattern of a sample
87 +that reaches far into small capitalizations and is conditioned on survival
88 +(\cref{subsec:survivorship}). In the two-way fixed-effects panel the AI coefficients are small:
89 +the composite earns \mfeCompos{} points per standard deviation within firm ($t=\mfeComposT$). The
90 +signal lives across firms, not within them, as its rank autocorrelation of \mrankAuto{} implies.
91 +All Fama--MacBeth specifications are in \cref{tab:fm}.
92 +
93 +\ExhibitOnce{tab:fmboth}{\input{tables/tab_fm_both}}
94 +
95 +\ExhibitOnce{tab:panel}{\input{tables/tab_panel}}
96 +
97 +\subsection{The post-ChatGPT change: an index pattern, not a market pattern (H2)}
88 98 \label{subsec:break}
89 −Table~\ref{tab:prepostboth} is the central table of the paper. It splits the cohorts at the ChatGPT
90 −launch and reports, for each signal and each universe, the pre- and post-launch spreads, the three
91 −post-launch cohorts, the pooled firm-clustered test of the post-period spread, its winsorized
92 −version and the post-period Sharpe ratio of the monthly long--short. In the S\&P~500 panel the first
93 −version's result reappears almost exactly: the composite spread rises from \mspSpreadPre{} to
94 −\mspSpreadPost{} points ($t=\mspSpreadPostT$), the cohorts are \mspCohorts, the pooled post-period
95 −spread is \mspPooledPost{} points ($t=\mspPooledPostT$; \mspPooledPostW{} winsorized) and the
96 −post-period Sharpe ratio is \mspSharpePost. In the Russell~3000 the picture is different. The
97 −composite spread is \mspreadPre{} points before the launch and \mspreadPost{} after
98 −($t=\mspreadPostT$); the 2022 cohort, the first held after the launch, earned a \emph{negative}
99 −spread, and the post-period mean rests on 2024 (\mcohortsPost); the pooled post-period spread is
100 −\mpooledPost{} points ($t=\mpooledPostT$) and \mpooledPostW{} winsorized ($t=\mpooledPostWT$); the
101 −difference between the post- and pre-period pooled spreads is \mpooledDiff{} points
102 −($t=\mpooledDiffT$); and the monthly long--short earns \mmeanLSPost\% per year after July 2023 with
103 −a Sharpe ratio of \msharpePost, \emph{lower} than its pre-launch Sharpe ratio of \msharpePre, and a
104 −six-factor alpha of \mffsixPost\%. Figure~\ref{fig:cohortsboth} plots the cohort spreads of the two
105 −universes side by side and Figure~\ref{fig:cumboth} the cumulative long--short returns: the index
106 −series rises after the launch, the broad-universe series does not.
107 −
108 −\begin{table}[htbp]\centering\scriptsize
109 −\caption{\textbf{Before and after ChatGPT, Russell~3000 and S\&P~500.} Equal-weighted Q5$-$Q1
110 −spreads averaged over the pre-launch cohorts (2010--2021) and the post-launch cohorts (2022--2024),
111 −with Newey--West $t$-statistics (the post-period $t$ rests on three observations); the three
112 −post-launch cohort spreads; for the composite, the pooled regression of the forward return on a
113 −top-quintile indicator with year dummies and firm-clustered standard errors in the post-period
114 −sample (raw and winsorized); and the annualized Sharpe ratio of the monthly long--short from July
115 −2023.}\label{tab:prepostboth}
116 −\adjustbox{max width=\textwidth}{\input{tables/tab_prepost_both}}
117 −\end{table}
118 −
119 −\begin{figure}[htbp]\centering
120 −\includegraphics[width=\textwidth]{fig13_cohorts_both.pdf}
121 −\caption{\textbf{Annual Q5$-$Q1 spreads by formation cohort, Russell~3000 versus S\&P~500.} The
122 −dashed line marks the ChatGPT launch; cohorts to its right are held after the launch. In the broad
123 −universe the pre-launch spreads are frequently positive and the 2022 cohort is negative; in the
124 −index the post-launch average is driven by the 2024 cohort.}\label{fig:cohortsboth}
125 −\end{figure}
126 −
127 −\begin{figure}[htbp]\centering
128 −\includegraphics[width=0.9\textwidth]{fig14_cumulative_both.pdf}
129 −\caption{\textbf{Cumulative long--short return on the AI composite.} Equal-weighted, annually
130 −rebalanced Q5$-$Q1 portfolio in the Russell~3000 universe and among S\&P~500 members.}
131 −\label{fig:cumboth}
132 −\end{figure}
133 −
134 −Table~\ref{tab:cohorts} and Figure~\ref{fig:cohorts} look at the broad-universe cohorts one by one.
135 −\mpreCohortsPositive\% of the twelve pre-launch spreads are positive, \mpreCohortsAbove{} of them
136 −exceed the 2022 spread, and the largest cohort spread of the sample is 2018 (\mevtEighteen{} points
137 −on the pre-determined-exposure measure as well). Dropping the 2024 cohort leaves a post-period mean
138 −of \mpostLOO{} (leave-one-out means for 2022, 2023 and 2024 respectively), that is, below the
139 −pre-period mean of \mpreMean{} when 2024 is removed. The placebo on the break date
140 −(Figure~\ref{fig:placebobreaks}) makes the point formally: for each candidate first post-cohort
141 −between 2013 and 2022 we compute the post-minus-pre difference in mean spreads; 2022 produces a
142 −difference of \mplaceboDiffTwentyTwo{} points and ranks \mplaceboRank{}th of \mplaceboN{}
143 −candidates, behind every candidate from 2013 to 2018. Whatever changed in the cross-section of AI
144 −language returns in the broad market, it did not change in 2022. The year-by-year Fama--MacBeth
145 −slopes of Figure~\ref{fig:fmyear} tell the same story: the slope is positive in most years, large
146 −in 2018--2019 and 2024, and not systematically larger after the launch.
147 −
148 −\begin{table}[htbp]\centering\small
149 −\caption{\textbf{Cohort spreads and pooled tests, Russell~3000.} Left: equal-weighted Q5$-$Q1 spread
150 −on the composite by formation cohort. Right: pooled regressions of the forward return of top- and
151 −bottom-quintile firm-years on a top-quintile indicator with year dummies and firm-clustered
152 −standard errors, and leave-one-out means of the post-period cohorts.}\label{tab:cohorts}
153 −\adjustbox{max width=\textwidth}{\input{tables/tab_cohorts}}
154 −\end{table}
155 −
156 −\begin{figure}[htbp]\centering
157 −\includegraphics[width=0.9\textwidth]{fig3_cohort_spreads.pdf}
158 −\caption{\textbf{Annual AI-composite spreads by cohort, Russell~3000.} Post-launch cohorts in gold;
159 −dotted lines mark the pre- and post-period means.}\label{fig:cohorts}
160 −\end{figure}
161 −
162 −\begin{figure}[htbp]\centering
163 −\includegraphics[width=0.8\textwidth]{fig11_placebo_breaks.pdf}
164 −\caption{\textbf{Placebo break dates.} Difference between the mean Q5$-$Q1 spread of the cohorts
165 −from the candidate break year onward and the mean of the earlier cohorts, for every candidate
166 −between 2013 and 2022 (2022 in red).}\label{fig:placebobreaks}
167 −\end{figure}
168 −
169 −\begin{figure}[htbp]\centering
170 −\includegraphics[width=0.9\textwidth]{fig5_fm_byyear.pdf}
171 −\caption{\textbf{Year-by-year Fama--MacBeth slopes on the AI composite, Russell~3000.} Annual
172 −cross-sectional slope with size, momentum and volatility controls and 95\% confidence bands
173 −(heteroskedasticity-robust, within year).}\label{fig:fmyear}
174 −\end{figure}
175 −
176 −\subsection{Size: where the two universes part ways (H5)}
99 +\Cref{tab:prepostboth} is the central table of the paper. It splits the cohorts at the ChatGPT
100 +launch and reports, for each signal and each universe, the pre- and post-launch spreads with
101 +their intervals, the three post-launch cohorts, the pooled firm-level test of the post-period
102 +spread with firm, two-way and wild-cluster inference, the pooled post-minus-pre difference and
103 +the post-period Sharpe ratio of the monthly long--short. In the S\&P~500 panel the first version's
104 +pattern reappears: the winsorized composite spread rises from \mspSpreadPreW{} to
105 +\mspSpreadPostW{} points, the cohorts are \mspCohortsW, and the pooled post-period spread is
106 +\mspPooledPostW{} points (firm-clustered $t=\mspPooledPostWT$, two-way $t=\mspPooledPostWTtw$)
107 +with a post-period Sharpe ratio of \mspSharpePost. In the Russell~3000 the picture is different.
108 +The winsorized composite spread is \mspreadPreW{} points before the launch (interval
109 +\mspreadPreWCI) and \mspreadPostW{} after, on three cohorts whose interval, \mspreadPostWCI,
110 +says nothing; the 2022 cohort, the first held after the launch, earned a negative spread, and the
111 +post-period mean rests on 2024 (\mcohortsPostW; leave-one-out means \mpostLOOW). The pooled
112 +post-period spread is \mpooledPostW{} points (firm-clustered $t=\mpooledPostWT$, two-way
113 +$t=\mpooledPostWTtw$, wild-cluster $p=\mpooledPostWPwild$; before the review \mvonePooledPostW{}
114 +on pooled-bound winsorization), it is \mpooledPostExTwentyFourW{} points without the 2024 cohort
115 +($t=\mpooledPostExTwentyFourWT$), and the post-minus-pre difference is \mpooledDiffW{} points
116 +(firm $t=\mpooledDiffWT$, two-way $t=\mpooledDiffWTtw$) against a minimum detectable difference of
117 +\mpooledDiffWMDE{} points. The monthly long--short earns \mmeanLSPost\% per year after July 2023
118 +with a Sharpe ratio of \msharpePost, lower than its pre-launch Sharpe ratio of \msharpePre, and a
119 +six-factor alpha of \mffsixPost\%. \Cref{fig:cohortsboth} plots the cohort spreads of the two
120 +universes side by side and \cref{fig:cumboth} the cumulative long--short returns: the index series
121 +rises after the launch, the broad-universe series does not. The pooled slope-change test of
122 +\cref{eq:break} by signal is in \cref{tab:break}.
123 +
124 +\ExhibitOnce{tab:prepostboth}{\input{tables/tab_prepost_both}}
125 +
126 +\ExhibitOnce{fig:cohortsboth}{\input{figures_r3k/fig13_cohorts_both}}
127 +
128 +\ExhibitOnce{fig:cumboth}{\input{figures_r3k/fig14_cumulative_both}}
129 +
130 +\Cref{tab:cohorts} and \cref{fig:cohorts} look at the broad-universe cohorts one by one.
131 +\mpreCohortsPositiveW\% of the twelve pre-launch winsorized spreads are positive, and the largest
132 +cohort spread of the sample is 2018. Three tests ask whether 2022 is a special break date. The
133 +illustrative placebo of the first version (\cref{fig:placebobreaks}), which computes the
134 +post-minus-pre difference for each candidate first post-cohort from 2013 to 2022, ranks 2022
135 +\mplaceboRankW{}th of \mplaceboN{}; because its windows are nested it is not a test. The exact
136 +permutation of the 2022--24 block against all \mPermSubsets{} three-cohort subsets gives a
137 +one-sided $p$-value of \mpermPW{} (\mpermP{} on raw returns), and \mContigAboveW{} of the
138 +\mContigN{} contiguous three-cohort blocks exceed the 2022--24 block (\mContigAboveRaw{} on raw
139 +returns; the largest is \mContigBestBlock, at \mContigBestDiff{} points on raw returns). The
140 +sup-Wald mean-shift statistic over all admissible break dates is \msupWaldW{} (simulated
141 +$p=\msupWaldWP$) on winsorized and \msupWald{} ($p=\msupWaldP$) on raw spreads, against a
142 +five-percent critical value of \mSupWaldCVfive. The year-by-year Fama--MacBeth slopes of
143 +\cref{fig:fmyear} show the same profile: positive in most years, large in 2018--2019 and 2024, and
144 +not systematically larger after the launch.
145 +
146 +\ExhibitOnce{tab:cohorts}{\input{tables/tab_cohorts}}
147 +
148 +\ExhibitOnce{fig:cohorts}{\input{figures_r3k/fig3_cohort_spreads}}
149 +
150 +\ExhibitOnce{fig:placebobreaks}{\input{figures_r3k/fig11_placebo_breaks}}
151 +
152 +\ExhibitOnce{fig:fmyear}{\input{figures_r3k/fig5_fm_byyear}}
153 +
154 +\subsection{Size: where the two universes part ways, and what the test says (H5a)}
177 155 \label{subsec:size}
178 −Why does the index show a post-launch jump and the market not? Table~\ref{tab:groups} and
179 −Figure~\ref{fig:sizegroups} split the universe by size and by index membership. Among the largest
180 −thousand firms---the Russell~1000 proxy---the composite spread rises from \mlargePre{} points
181 −before the launch to \mlargePost{} after ($t=\mlargePostT$; cohorts \mlargeCohorts), with a
182 −post-period Sharpe ratio of \mlargeSharpePost{} against \mlargeSharpePre{} before: the index result
183 −is a large-cap result, and it holds for the 500 largest and the 1,000 largest alike. Among the
184 −remaining firms the spread is \msmallPre{} points before the launch and \msmallPost{} after
185 −(cohorts \msmallCohorts); the full-sample spread of \msmallFull{} points ($t=\msmallFullT$) is the
186 −largest of any sub-sample, and its monthly long--short Sharpe ratio is \msmallSharpePre{} before
187 −the launch and \msmallSharpePost{} after. The same contrast appears between S\&P~500 members
188 −(\mspPre{} to \mspPost) and non-members (\mnonspPre{} to \mnonspPost, $t=\mnonspPostT$). A
189 −size-neutral sort, in which quintiles are formed within size group and year, yields a full-sample
190 −spread of \msizeNeuFull{} points ($t=\msizeNeuFullT$), \msizeNeuPre{} before the launch and
191 −\msizeNeuPost{} after. The AI~$\times$~size double sort of Table~\ref{tab:doublesort} and
192 −Figure~\ref{fig:double} shows the gradient in finer detail: after the launch the high-minus-low AI
193 −gap is \mdsSmallPost{} points in the smallest size tercile and \mdsLargePost{} in the largest, but
194 −before the launch it was already \mdsSmallPre{} in the smallest tercile against \mdsLargePre{} in
195 −the largest. Smaller firms whose filings resembled the AI anchors earned a premium throughout the
196 −2010s; the largest firms earned one only after 2022.
197 −
198 −\begin{table}[htbp]\centering\small
199 −\caption{\textbf{AI-composite spreads by size group and index membership.} Equal-weighted Q5$-$Q1
200 −spreads with quintiles formed within each sub-sample and year; full-sample, pre- and post-launch
201 −means with Newey--West $t$-statistics; FF6 alpha of the sub-sample's monthly long--short after July
202 −2023. The size-neutral row forms quintiles within size group and year in the full sample.}
203 −\label{tab:groups}
204 −\adjustbox{max width=\textwidth}{\input{tables/tab_groups}}
205 −\end{table}
206 −
207 −\begin{figure}[htbp]\centering
208 −\includegraphics[width=0.85\textwidth]{fig12_size_groups.pdf}
209 −\caption{\textbf{Pre- and post-launch spreads by size group and index membership.}}\label{fig:sizegroups}
210 −\end{figure}
211 −
212 −\begin{table}[htbp]\centering\small
213 −\caption{\textbf{AI language $\times$ size double sort, Russell~3000.} Mean forward twelve-month
214 −return (\%) by AI-composite tercile within size tercile (both formed within year), before and after
215 −the launch.}\label{tab:doublesort}
216 −\input{tables/tab_doublesort}
217 −\end{table}
218 −
219 −\begin{figure}[htbp]\centering
220 −\includegraphics[width=0.75\textwidth]{fig8_double_sort.pdf}
221 −\caption{\textbf{AI language $\times$ size double sort, post-launch cohorts.} Mean forward return
222 −by AI tercile within size tercile.}\label{fig:double}
223 −\end{figure}
156 +Why does the index show a post-launch jump and the market not? \Cref{tab:groups} and
157 +\cref{fig:sizegroups} split the universe by size and by index membership on the corrected
158 +capitalization. Among the largest thousand firms---the Russell~1000 proxy---the winsorized
159 +composite spread is \mlargePreW{} points before the launch (interval \mlargePreCI) and
160 +\mlargePostW{} after (cohorts \mlargeCohortsW), with leave-one-out post means of \mlargePostLOOW:
161 +without the 2024 cohort the post-launch mean is \mlargePostExTwentyFourW{} points (pooled 2022--23
162 +$t=\mlargePostExTwentyFourWT$), the same as before the launch. The fixed-percentile partition
163 +(largest 42\% of each cohort) gives \mlargeFortyTwoPreW{} to \mlargeFortyTwoPostW{} and
164 +\mlargeFortyTwoPostExTwentyFourW{} without 2024. Among the remaining firms the spread is
165 +\msmallPreW{} points before the launch (interval \msmallPreCI) and \msmallPostW{} after (cohorts
166 +\msmallCohortsW); on raw returns the pre-launch value is \msmallPre{}, the difference being the
167 +extreme returns of a group whose cohorts contain as few as a few hundred firms in the early
168 +years. The same contrast appears between S\&P~500 members (\mspSpreadPreW{} to \mspSpreadPostW) and
169 +non-members. A size-neutral sort, in which quintiles are formed within size group and year, yields
170 +a full-sample winsorized spread of \msizeNeuFullW{} points ($t=\msizeNeuFullWT$). The
171 +AI~$\times$~size double sort of \cref{tab:doublesort} and \cref{fig:double} shows the gradient in
172 +finer detail: after the launch the high-minus-low AI gap on winsorized returns is \mdsLargePostW{}
173 +points in the largest size tercile and \mdsSmallPostW{} in the smallest, whereas before the launch
174 +it was \mdsLargePre{} in the largest tercile and \mdsSmallPre{} in the smallest on raw returns.
175 +
176 +The point estimates thus show an increase among large firms and none among small firms. The
177 +test of that difference, in \cref{tab:contrasts}, does not establish it. The coefficient on
178 +high-AI $\times$ post $\times$ largest-thousand in \cref{eq:contrast} is \mcontrastLarge{} points
179 +with a firm-clustered $t$ of \mcontrastLargeT, a two-way $t$ of \mcontrastLargeTtw, a wild-cluster
180 +$p$ of \mcontrastLargePwild{} and an interval of \mcontrastLargeCI; the minimum detectable
181 +difference is \mcontrastLargeMDE{} points. The cohort-block bootstrap of the difference between
182 +the groups' post-minus-pre changes covers zero, and the same holds for the index-membership
183 +contrast (\mcontrastMember{} points, $t=\mcontrastMemberT$ / \mcontrastMemberTtw, minimum
184 +detectable \mcontrastMemberMDE). Two readings are consistent with the evidence: a large-cap
185 +increase of the size of the point estimate, or no difference between groups and a 2024 cohort
186 +that happened to favour large AI-exposed firms. The index-sample regime of the first version is
187 +therefore an index pattern that the market does not reproduce; whether it is a large-cap
188 +phenomenon or a one-cohort phenomenon cannot be decided with three post-launch cohorts.
189 +
190 +\ExhibitOnce{tab:groups}{\input{tables/tab_groups}}
191 +
192 +\ExhibitOnce{tab:contrasts}{\input{tables/tab_contrasts}}
193 +
194 +\ExhibitOnce{fig:sizegroups}{\input{figures_r3k/fig12_size_groups}}
195 +
196 +\ExhibitOnce{fig:double}{\input{figures_r3k/fig8_double_sort}}
197 +% tab:doublesort is appendix-bound (tables/EXHIBIT_MAP.json) and printed by tables/appendix_exhibits.tex.
198 +
199 +\subsection{Multiple testing and the specification curve}
200 +\label{subsec:mht}
201 +\Cref{tab:mht} reports, for each family of tests, the raw and the Holm, Benjamini--Hochberg and
202 +Romano--Wolf adjusted $p$-values (member-level detail in \cref{tab:mhtfull,tab:mhtfullb}). No
203 +full-sample or post-period spread of \cref{tab:sortsboth} or \cref{tab:prepostboth} survives the
204 +step-down adjustment within its family; the composite's Romano--Wolf $p$ is \mrwComposFull{} over
205 +the full sample. Among the eight placebo interactions of \cref{tab:placebo} only cybersecurity
206 +survives (Romano--Wolf $p=\mcyberIntRW$), and no break date does. Across the cohort-level families
207 +\mhlzCount{} statistic meets the $|t|>3$ hurdle of \citet{harveyliuzhu2016}. The deflated Sharpe
208 +ratio of the composite long--short, given the \mdsrTrials{} long--short series examined, is
209 +\mdsrFull{} over the full sample and \mdsrPost{} after the launch. The specification curve of
210 +\cref{fig:speccurve} varies winsorization, weighting, horizon, filing form, aggregation and size
211 +filter over \mspecN{} specifications of the full-sample composite spread: \mspecPos\% are
212 +positive, \mspecPosSig\% are positive and significant by the Newey--West statistic
213 +(\mspecPosSigPlain\% by the plain one), and the median spread is \mspecMedian{} points. The sign
214 +is stable across specifications; the significance is not.
215 +
216 +\ExhibitOnce{tab:mht}{\input{tables/tab_mht}}
217 +
218 +\ExhibitOnce{fig:speccurve}{\input{figures_r3k/fig15_spec_curve}}
224 219
225 220 \subsection{Economic significance}
226 −Three numbers summarize the economic content. In the broad market a one-standard-deviation increase
227 −in AI language relative to same-year peers is associated with about three percentage points of
228 −additional forward return per year on average over fifteen cohorts, with a within-sector component
229 −of about one and a half points; this is the order of magnitude of a modest characteristic premium,
230 −not of an anomaly. The headline post-launch spread of fifteen to twenty points exists only in the
231 −largest firms and, within them, mostly in the 2024 cohort. And the monthly long--short on the
232 −composite, which rebalances every month and therefore does not let extreme winners run, earned a
233 −Sharpe ratio of \msharpeFull{} over the full sample in the broad universe, \msharpePre{} before the
234 −launch and \msharpePost{} after; the ``Sharpe ratio above one'' of the first version is a
235 −large-cap, post-2022 statistic that the broad universe does not reproduce.
221 +\label{subsec:econsig}
222 +Three numbers summarize the economic content. In the broad market a one-standard-deviation
223 +increase in AI language relative to same-year peers is associated with \mfmComposW{} percentage
224 +points of additional forward return per year on average over fifteen cohorts, with a
225 +within-sector component of \mfmFullSectorW{} points; this is the order of magnitude of a modest
226 +characteristic premium, not of an anomaly, and it is conditional on survival to October 2026.
227 +The post-launch spread of ten to fifteen points exists only in the largest firms and, within
228 +them, in the 2024 cohort, and the test of the large-versus-small difference does not reject
229 +equality. And the monthly long--short on the composite, which rebalances every month and does not
230 +let extreme winners run, earned a Sharpe ratio of \msharpeFull{} over the full sample in the broad
231 +universe (\mdsrFull{} after deflation), \msharpePre{} before the launch and \msharpePost{} after;
232 +the ``Sharpe ratio above one'' of the first version is a large-cap, post-2022 statistic that the
233 +broad universe does not reproduce.
modified paper/sections/robustness.tex +317 −193
@@ -1,212 +1,336 @@
1 1 % ============================================================================
2 −\section{Robustness and Identification}
2 +% Owner: Stage E, Agent 10 (writing). Numbers: tables/macros.tex, sections/macros_stageE.tex.
3 +% Exhibits: self-contained floats generated by scripts/r3k_20_tables_v2.py (tables/) and
4 +% scripts/r3k_19_figures_v2.py (figures_r3k/), placed here behind \ExhibitOnce; appendix-bound
5 +% exhibits (tables/EXHIBIT_MAP.json) are printed by tables/appendix_exhibits.tex.
6 +\section{Robustness, Construct Validity and Survivorship}
3 7 \label{sec:robustness}
4 8 % ============================================================================
5 9
6 −This section confronts the broad-universe results with the alternative explanations a sceptical
7 −reader would raise: that the premium is a sector effect, that the post-launch pattern is
8 −mechanical or specific to how the signal is built, that it reflects the composition of a
9 −current-membership universe, that the event-study inference is overstated, and that a different
10 −measure of AI engagement would tell a different story. Unless stated otherwise, all tests use the
11 −Russell~3000 universe.
10 +This section confronts the broad-universe results with the alternative explanations that the
11 +review raised: that the premium is a sector effect, that the post-launch pattern depends on the
12 +benchmark or on how the signal is built, that it reflects the composition of a current-membership
13 +universe, that the event-study inference is overstated, that a different measure of AI engagement
14 +tells a different story, and that the embedding score does not measure what its name says. Unless
15 +stated otherwise, all tests use the Russell~3000 universe and winsorized returns.
12 16
13 17 \subsection{Sector controls and the technology factor}
14 18 \label{subsec:sector}
15 −Table~\ref{tab:sectortech} addresses the concern that AI language proxies for the technology
16 −sector. In annual cross-sectional regressions with size, momentum and volatility controls, the
17 −full-sample slope on the composite is \mfmFull{} points per standard deviation ($t=\mfmFullT$) and
18 −\mfmFullSector{} ($t=\mfmFullSectorT$) with GICS-sector dummies: unlike the index sample, the broad
19 −universe shows a within-sector premium that is statistically robust over the full sample. In
20 −pooled regressions of the winsorized forward return with firm-clustered errors, sector-by-year
21 −fixed effects leave a full-sample slope of \msyFull{} points ($t=\msyFullT$). The post-launch
22 −period is different: the post-period slope of \mfmPost{} ($t=\mfmPostT$) falls to \mfmPostSector{}
23 −with sector dummies ($t=\mfmPostSectorT$) and to \msyPost{} ($t=\msyPostT$) with sector-by-year
24 −fixed effects, so that the post-launch cross-sectional relation is entirely a between-sector
25 −relation, as it was in the index. In the monthly series the long--short loads \mtechBetaFull{} on
26 −the technology-sector factor over the full sample and \mtechBetaPost{} after the launch; adding the
19 +\Cref{tab:sectortech} addresses the concern that AI language proxies for the technology sector,
20 +with the three within-sector estimators side by side. In annual cross-sectional regressions with
21 +size, momentum and volatility controls, the full-sample slope on the composite is \mfmComposW{}
22 +points per standard deviation and \mfmFullSectorW{} with GICS-sector dummies (Newey--West
23 +$t=\mfmFullSectorWT$, plain $t=\mfmFullSectorWTplain$; \mfmFullSectorExEnergyW{} without the Energy
24 +sector, $t=\mfmFullSectorExEnergyWT$). The pre-review within-sector statistic of
25 +$t=\mvoneFMsectorT$ on a slope of \mvoneFMsector{}, the only $t$ above three in the first version,
26 +was a Newey--West artefact on fifteen raw-return slopes whose plain $t$ was \mfmFullSectorTplain.
27 +In pooled regressions with firm-clustered errors, sector-by-year fixed effects leave a full-sample
28 +slope of \msyFull{} points (firm $t=\msyFullT$, two-way $t=\msyFullTtw$, wild-cluster
29 +$p=\msyFullPwild$). The sector-neutral quintile sort, in which quintiles are formed within sector
30 +and year, gives \msectNeuFullW{} points over the full sample ($t=\msectNeuFullWT$; \msectNeuFull{}
31 +on raw returns, where the Energy sector and one outlier-driven cohort dominate; the pre-review
32 +value of \mvoneSectorNeutralFull{} was computed and not reported), and the residual sort on returns
33 +orthogonalized to sector-by-year effects and the controls gives \mresidSortFullW{}
34 +($t=\mresidSortFullWT$). The within-sector claim is therefore a regression claim: the two
35 +regression estimators agree on a slope below one point per standard deviation that is
36 +significant at conventional levels, and the sort estimator does not reject zero. After the
37 +launch every within-sector estimator is small: the Fama--MacBeth slope with sector dummies is
38 +\mfmPostSector{} ($t=\mfmPostSectorT$, on three cohorts) and the sector-by-year slope \msyPost{}
39 +($t=\msyPostT$), so the post-launch cross-sectional relation is a between-sector relation, as it
40 +was in the index. In the monthly series the long--short loads \mtechBetaFull{} on the
41 +technology-sector factor over the full sample and \mtechBetaPost{} after the launch; adding the
27 42 factor reduces the full-sample FF6 alpha from \mffsixFull\% to \mffsixTechFull\% per year and the
28 −post-launch alpha to \mffsixTechPost\%. The sector-neutral composite sort gives \msectNeuPost{}
29 −points after the launch ($t=\msectNeuPostT$), a fifth of the baseline. The within-sector premium on
30 −AI language in the broad market is therefore a feature of the whole sample, not of the post-launch
31 −regime.
32 −
33 −\begin{table}[htbp]\centering\small
34 −\caption{\textbf{Sector controls and technology-factor spanning, Russell~3000.} Top: Fama--MacBeth
35 −slopes on the composite with and without GICS-sector dummies, and pooled firm-clustered regressions
36 −with year or sector-by-year fixed effects (percentage points per standard deviation, $t$ in
37 −parentheses). Bottom: the monthly composite long--short; TECH is the equal-weighted return of the
38 −Information Technology constituents of the panel minus the equal-weighted return of all
39 −constituents.}\label{tab:sectortech}
40 −\input{tables/tab_sector_tech}
41 −\end{table}
42 −
43 −\subsection{Placebo: is the change specific to AI? (H3)}
44 −Table~\ref{tab:placebo} and Figure~\ref{fig:placebo} run all eight semantic factors through the
45 −sub-period design. After the launch the AI-disruption-risk factor earns the largest spread
46 −(\mriskPost{} points, $t=\mriskPostT$; \mriskPre{} before), AI infrastructure \minfraPost{} and AI
47 −adoption \madoptPost. ESG-commitment, climate-risk and macro-risk language earn large negative
48 −spreads (\mesgPost, \mclimPost{} and \mmacroPost{} points), in line with the post-2021 reversal in
49 −the sustainable-investing literature \citep{pastor2022dissecting} and with the underperformance of
50 −rate- and cycle-sensitive firms. But cybersecurity (\mcyberPost{} points, the most significant of
51 −all) and automation/labour (\mautoPost) also rise, as in the index. The placebo rules out a generic
52 −``more disclosure earns more'' effect and a pipeline artefact; it does not separate AI from the
53 −broader technology theme with which AI, cybersecurity and automation language travel. The
54 −interaction regressions, now estimated on 27,000 firm-years with firm-clustered errors, give the
55 −same ordering: a significant post-launch increment for disruption risk and cybersecurity, none for
56 −adoption, and significant decrements for ESG and macro language.
57 −
58 −\begin{table}[htbp]\centering\small
59 −\caption{\textbf{Placebo across semantic factors, Russell~3000.} Equal-weighted Q5$-$Q1 spreads for
60 −each factor over the full sample and the two sub-periods, and the coefficient on the factor
61 −$\times$ post interaction in the pooled regression of equation~\eqref{eq:break} with firm-clustered
62 −standard errors (percentage points per standard deviation).}\label{tab:placebo}
63 −\adjustbox{max width=\textwidth}{\input{tables/tab_placebo}}
64 −\end{table}
65 −
66 −\begin{figure}[htbp]\centering
67 −\includegraphics[width=0.92\textwidth]{fig6_placebo.pdf}
68 −\caption{\textbf{Placebo test across semantic factors.} Pre- and post-launch Q5$-$Q1 spreads for the
69 −eight factors; AI factors in gold in the post period.}\label{fig:placebo}
70 −\end{figure}
71 −
72 −\subsection{Event study around ChatGPT}
73 −Table~\ref{tab:event} and Figure~\ref{fig:event} report market-model cumulative abnormal returns
74 −(IWV as the market) by pre-event AI tercile for \meventN{} firms. The High-minus-Low difference is
75 −\meventHLsixty{} points at sixty trading days, \meventHL{} at one year and \mevHLeighteen{} at
76 −eighteen months; the independence-based Welch $t$ at one year is \meventT. Table~\ref{tab:eventcda}
77 −re-examines the inference with the portfolio statistic of equation~\eqref{eq:cda}: the average
78 −pairwise correlation of estimation-window residuals is \mevRho, and the dependence-robust $t$ is
79 −\mevCDAsixty{} at sixty days, \meventCDA{} at one year and \mevCDAeighteen{} at eighteen months.
80 −The cross-sectional regression of the one-year CAR on pre-event exposure gives \mevXsec{} points
81 −per standard deviation ($t=\mevXsecT$) and \mevXsecSect{} ($t=\mevXsecSectT$) with sector fixed
82 −effects. The size gradient is the new result: the one-year High-minus-Low difference is
83 −\mevLarge{} points among the largest thousand firms ($t=\mevLargeT$) and \mevSmall{} among the
84 −rest ($t=\mevSmallT$); \mevSP{} among S\&P~500 members ($t=\mevSPT$) and \mevNonSP{} among
85 −non-members ($t=\mevNonSPT$). As in the index, nothing happens within sixty days of the launch and
86 −the difference accumulates over a year, which fits the gradual re-rating of large AI-exposed firms
87 −during the 2023--2024 capital-expenditure cycle better than a discrete attention shock; and the
88 −re-rating was concentrated in the firms that investors already followed most closely, the
89 −opposite of what an attention-friction account predicts.
90 −
91 −\begin{table}[htbp]\centering\small
92 −\caption{\textbf{ChatGPT event study, Russell~3000.} Mean market-model cumulative abnormal return
93 −(\%) by pre-event AI tercile at four horizons, the High$-$Low difference, the Welch $t$ (firms
94 −treated as independent) and the dependence-robust CDA $t$ of equation~\eqref{eq:cda}; last row:
95 −one-year High$-$Low difference in sub-samples.}\label{tab:event}
96 −\adjustbox{max width=\textwidth}{\input{tables/tab_event}}
97 −\end{table}
98 −
99 −\begin{table}[htbp]\centering\small
100 −\caption{\textbf{Event-study inference under cross-sectional dependence.} High$-$Low portfolio
101 −abnormal return and $t$-statistics using the estimation-window and event-window standard deviation
102 −of the daily portfolio series; $\bar\rho$ is the average pairwise correlation of estimation-window
103 −residuals.}\label{tab:eventcda}
104 −\adjustbox{max width=\textwidth}{\input{tables/tab_event_cda}}
105 −\end{table}
106 −
107 −\begin{figure}[htbp]\centering
108 −\includegraphics[width=0.9\textwidth]{fig7_event_car.pdf}
109 −\caption{\textbf{Cumulative abnormal returns around ChatGPT by pre-event AI tercile.} All terciles
110 −drift negative because the market model was estimated in the 2022 bear market; only differences
111 −between terciles are interpretable.}\label{fig:event}
112 −\end{figure}
43 +post-launch alpha to \mffsixTechPost\%. Clause (b) of H3---that the post-launch spread is not
44 +spanned by a technology-sector factor---is not supported.
45 +
46 +\ExhibitOnce{tab:sectortech}{\input{tables/tab_sector_tech}}
47 +
48 +\subsection{Placebo: is the change specific to AI? (H3a)}
49 +\label{subsec:placebo}
50 +\Cref{tab:placebo} and \cref{fig:placebo} run all eight semantic factors through the sub-period
51 +design, with the interaction of \cref{eq:break} under firm, two-way and wild-cluster inference and
52 +the Romano--Wolf adjustment over the family of eight. On winsorized returns the AI-disruption-risk
53 +factor earns the largest post-launch spread (\mriskPostWsp{} points; \mriskPreWsp{} before), AI
54 +infrastructure \minfraPost{} and AI adoption \madoptPost{} on raw returns. ESG-commitment,
55 +climate-risk and macro-risk language earn negative post-launch spreads (\mesgPost, \mclimPost{} and
56 +\mmacroPost{} points on raw returns), in line with the post-2021 reversal in the
57 +sustainable-investing literature \citep{pastor2022dissecting} and with the underperformance of
58 +rate- and cycle-sensitive firms. Cybersecurity (\mcyberPostW{} points winsorized, \mcyberPost{}
59 +raw) and automation/labour (\mautoPost) also rise. Under firm clustering several interactions
60 +look significant; under the two-way clustering that the design calls for, because the post
61 +indicator varies only across cohorts, only cybersecurity survives (two-way $t=\mcyberIntTtw$,
62 +Romano--Wolf $p=\mcyberIntRW$), while disruption risk falls to $t=\mriskIntTtw$ and ESG to
63 +$t=\mesgIntTtw$. The placebo rules out a generic ``more disclosure earns more'' effect and a
64 +pipeline artefact; it does not separate AI from the broader technology theme with which AI,
65 +cybersecurity and automation language travel, and the cybersecurity premium is itself documented
66 +\citep{celenymarechal2024cyber,kearney2025cyberchatgpt}. The cybersecurity score correlates
67 +\mcorrCyber{} with the composite; a cyber-neutral composite sort (quintiles within cybersecurity
68 +tercile) gives \mcyberNeuFullW{} points over the full sample ($t=\mcyberNeuFullWT$), and the
69 +Fama--MacBeth slope of the composite with the cybersecurity score as a control is reported in
70 +\cref{tab:reversal}. Clause (a) of H3 holds against ESG, climate and macro language and not
71 +against cybersecurity.
72 +
73 +\ExhibitOnce{fig:placebo}{\input{figures_r3k/fig6_placebo}}
74 +% tab:placebo is appendix-bound (tables/EXHIBIT_MAP.json) and printed by tables/appendix_exhibits.tex.
75 +
76 +\subsection{Event study around ChatGPT: a gradient that depends on the benchmark}
77 +\label{subsec:event}
78 +\Cref{tab:event} and \cref{fig:event} report market-model cumulative abnormal returns (IWV as the
79 +market, day~0 on 1~December 2022) by pre-event AI tercile for \meventN{} firms. The pre-launch
80 +block of twenty trading days, now separated from the window, shows a High-minus-Low difference of
81 +\meventHLpre{} points. After the launch the difference is \meventHLtwenty{} points over the first
82 +twenty days (dependence-robust $t=\meventCDAtwenty$), \meventHLsixty{} at sixty days
83 +($t=\meventCDAsixty$), \meventHL{} at one year ($t=\meventCDA$; \meventBMP{} by the
84 +standardized-CAR statistic that treats firms as independent) and \mevHLeighteen{} at eighteen
85 +months ($t=\mevCDAeighteen$). Nothing happens within a month of the launch and the difference
86 +accumulates over a year, which fits a gradual re-pricing of AI-exposed firms during 2023 better
87 +than a discrete attention shock. The cross-sectional regression of the one-year CAR on pre-event
88 +exposure gives \mevXsec{} points per standard deviation ($t=\mevXsecT$) and \mevXsecSect{}
89 +($t=\mevXsecSectT$) with sector fixed effects. Among the seven placebo launches of
90 +\cref{tab:eventcda} and \cref{fig:placebolaunches}---the same design run on 30~November of 2015
91 +to 2021---the 2022 launch ranks \mevPlaceboRank{} of \mevPlaceboN{} by the one-year difference and
92 +by its statistic, so the 2023 gap is unusual relative to earlier years.
93 +
94 +The size gradient is the result the first version emphasized, and it is where the inference was
95 +weakest. The first version quoted Welch statistics of \mvoneEvLargeWelch{} for the largest
96 +thousand firms and \mvoneEvSmallWelch{} for the rest, which treat the firms as independent while
97 +they share a date; the dependence-robust statistics of \cref{eq:cda} for every sub-sample are
98 +\mevLargeCDA{} and \mevSmallCDA{} on one-year differences of \mevLarge{} and \mevSmall{} points
99 +(\mevSPCDA{} among S\&P~500 members, \mevNonSPCDA{} among non-members; \mevLargeWithinCDA{} and
100 +\mevSmallEighteenCDA{} with terciles formed within size group at one year and eighteen months).
101 +The gradient survives this correction under the single-index market model. It does not survive
102 +the change of benchmark. \Cref{tab:eventcda} re-estimates the one-year High-minus-Low difference
103 +under the five alternative benchmarks of \cref{subsec:m_event}: for the largest thousand firms
104 +the statistic is \mevLargeBetaCDA{} under the beta-only adjustment, \mevLargeMadjCDA{} under the
105 +market-adjusted return, \mevLargeSizeMomCDA{} under the size-and-momentum match and
106 +\mevLargeFFsixT{} for the six-factor calendar-time alpha (\mevLargeFFsixAlpha{} points over 250
107 +days), and \mevLargeEstTwentyOneCDA{} with the market model estimated over 2021; for the remaining
108 +firms it lies between one and two under every benchmark. The high-exposure tercile has a higher
109 +beta and a larger capitalization than the low tercile, and the market model's intercept, estimated
110 +in the 2022 bear market, carries part of the one-year gap, as the first review of this design
111 +found in the S\&P~500 \citep{kammoun2026v11}. The event-study leg of the large-cap finding is
112 +therefore benchmark-dependent: present under the market model estimated in 2022, absent under
113 +benchmarks that do not reward the 2022 intercept, and the paper reports it as such rather than
114 +as a confirmation of the cohort evidence.
115 +
116 +\ExhibitOnce{tab:event}{\input{tables/tab_event}}
117 +
118 +\ExhibitOnce{tab:eventcda}{\input{tables/tab_event_cda}}
119 +
120 +\ExhibitOnce{fig:event}{\input{figures_r3k/fig7_event_car}}
121 +
122 +\ExhibitOnce{fig:placebolaunches}{\input{figures_r3k/fig16_placebo_launches}}
113 123
114 124 \subsection{Difference-in-differences and the event-time profile (H4)}
115 −Table~\ref{tab:didspid} reports the difference-in-differences estimates of equation~\eqref{eq:did}
116 −with treatment fixed at the firm's 2019--2021 exposure, within firm and year fixed effects. The
117 −continuous coefficient is \mdidCont{} points per standard deviation ($t=\mdidContT$) and the binary
118 −one \mdidBin{} ($t=\mdidBinT$); neither is significant. The event-time profile of
119 −Figure~\ref{fig:eventtime} is flat around the launch: relative to 2021, the premium on
120 −pre-determined exposure is \mevtTwentyTwo{} points in 2022, \mevtTwentyFour{} in 2024, and
121 −\mevtEighteen{} in 2018, with several positive pre-launch years. Once exposure is held fixed, the
122 −broad universe shows no post-launch break at all; firms with persistently AI-intensive filings
123 −earned premia scattered across the sample. The parallel-trends assumption is not satisfied, and
124 −the design confirms, rather than qualifies, the cohort evidence of Section~\ref{subsec:break}.
125 −
126 −\begin{table}[htbp]\centering\small
127 −\caption{\textbf{Difference-in-differences and the SPID project signal, Russell~3000.} Top: firm and
128 −year fixed effects, double-clustered errors, treatment is pre-determined 2019--2021 exposure.
129 −Bottom: pooled regressions of the winsorized forward return on the SPID signal, the AI composite,
130 −their post-launch interactions and controls, with firm-clustered errors (percentage points per
131 −standard deviation or per unit of the indicator).}\label{tab:didspid}
132 −\input{tables/tab_did_spid}
133 −\end{table}
134 −
135 −\begin{figure}[htbp]\centering
136 −\includegraphics[width=0.82\textwidth]{fig9_eventtime.pdf}
137 −\caption{\textbf{Event-time profile of the premium on pre-determined AI exposure, Russell~3000.}
138 −Premium by formation year relative to 2021, 95\% confidence bands from firm-clustered standard
139 −errors.}\label{fig:eventtime}
140 −\end{figure}
141 −
142 −\subsection{Disclosed projects versus disclosed language}
125 +\label{subsec:did}
126 +\Cref{tab:didspid} (top) reports the difference-in-differences estimates of \cref{eq:did} with
127 +treatment fixed at the firm's 2019--2021 exposure, within firm and year fixed effects. The
128 +continuous coefficient is \mdidCont{} points per standard deviation ($t=\mdidContT$) and the
129 +binary one \mdidBin{} ($t=\mdidBinT$); neither is significant, and the pre-review values
130 +(\mvoneDidCont, $t=\mvoneDidContT$; \mvoneDidBin, $t=\mvoneDidBinT$) were smaller still. The
131 +event-time profile of \cref{tab:eventtime} and \cref{fig:eventtime} corrects an error of the
132 +first version, which estimated \cref{eq:evt} without the main effect and therefore reported
133 +absolute slopes per year while labelling them differences from 2021. With the main effect
134 +restored, the slope on pre-determined exposure in the reference year 2021 is \mevtBase{} points
135 +per standard deviation ($t=\mEvtRefT$), and the post-launch years are \emph{lower}: the differences
136 +from 2021 are \mevtDiffTwentyTwo{} points in 2022 (standard error \mevtDiffTwentyTwoSE),
137 +\mevtDiffTwentyThree{} in 2023 and \mevtDiffTwentyFour{} in 2024; the trailing-exposure variant,
138 +in which exposure is measured strictly before each outcome year, gives \mevtTrailTwentyTwo{} and
139 +\mevtTrailTwentyFour{}. The pre-launch years are not a parallel-trends test, because the 2019--21
140 +exposure is measured after their outcomes; taken at face value they are not flat either (2020
141 +differs from 2021 by \mEvtDiffTwenty{} points). The profile is therefore descriptive: firms whose
142 +filings were persistently AI-intensive in 2019--21 earned their largest premium in the 2018 and
143 +2021 cohorts and a smaller one in the first post-launch cohort. H4 predicted no differential
144 +pre-trend and a positive post-launch shift; the evidence shows neither, and H4 is not supported
145 +as stated. The first version recorded it as supported on the strength of the mis-coded profile.
146 +
147 +\ExhibitOnce{tab:didspid}{\input{tables/tab_did_spid}}
148 +
149 +\ExhibitOnce{fig:eventtime}{\input{figures_r3k/fig9_eventtime}}
150 +% tab:eventtime is appendix-bound (tables/EXHIBIT_MAP.json) and printed by tables/appendix_exhibits.tex.
151 +
152 +\subsection{Disclosed projects versus disclosed language (H5b)}
143 153 \label{subsec:spidres}
144 154 The SPID project count offers an independent check on what the semantic score measures. If the AI
145 155 language premium reflected concrete AI investment, firms that describe AI, data-center, cloud and
146 −automation projects should earn it too. They do not. The SPID\,Tech quintile spread is \mspidPre{}
147 −points before the launch and \mspidPost{} after (Table~\ref{tab:prepostboth}), its Fama--MacBeth
148 −slope is indistinguishable from zero in both universes (Table~\ref{tab:fmboth}), and in the pooled
149 −regression of Table~\ref{tab:didspid} neither the project count nor its post-launch interaction is
150 −significant while the composite retains its coefficient. Firms with at least one AI-initiative
151 −project earned \mspidAnyPre{} points less than other firms before the launch and \mspidAnyPost{}
152 −more after ($t=\mspidAnyPostT$), on a small and sparse sample. Two readings are possible. Disclosed
153 −projects may be a noisier measure than language because they are rare (only \mspidAnyShare\% of
154 −firm-years), or the market may price the \emph{framing} of a firm as AI-exposed---which the
155 −embedding captures---rather than its announced AI capital commitments. Either way, the two
156 −measures extracted from the same text are not substitutes, and the premium documented here is a
157 −premium on AI language.
156 +automation projects should earn it too. The first version answered ``they do not'' on the basis
157 +of a quintile sort on a variable whose median and 75th percentile are zero, and of a pooled
158 +regression (its Table~17) that was numerically degenerate---every $t$-statistic printed as
159 +\mvoneSpidT{} and the post-launch coefficient as a number of order $10^{\mvoneSpidPostCoefExp}$---and
160 +whose committed results had not been produced by the committed code. \Cref{tab:spidbinary} and the
161 +bottom panel of \cref{tab:didspid} replace both. The headline project tests are binary contrasts.
162 +Firms with at least one AI-initiative project earn \mspidAnyFirmFull{} points more than other firms
163 +over the full sample in a firm-level regression with cohort fixed effects and controls
164 +($t=\mspidAnyFirmFullT$, interval \mspidAnyFirmFullCI), with a minimum detectable effect of
165 +\mspidAnyFirmFullMDE{} points; at the cohort level, on the eight cohorts with at least fifteen
166 +treated firms, the minimum detectable effect is \mspidCohortMDE{} points. Firms with any technology
167 +project earn \mspidTechFirmFull{} points more ($t=\mspidTechFirmFullT$). After the launch the any-AI
168 +contrast is positive (\mspidAnyPost{} points at the cohort level, $t=\mspidAnyPostT$; the
169 +pre-review value was \mvoneSpidAnyPost, $t=\mvoneSpidAnyPostT$), the same sign as the language
170 +premium, and far from detectable. In the refitted pooled regression (design rank eight, condition
171 +number below three) the technology-project count has a slope of \mspidXpost{} points per standard
172 +deviation after the launch (firm-clustered $t=\mspidXpostT$, two-way $t=\mspidXpostTtw$) while the
173 +composite keeps its slope. The legacy quintile rows are retained in \cref{tab:sortsboth} and
174 +\cref{tab:prepostboth} for comparison only (their minimum detectable effect is
175 +\mspidLegacyMDE{} points), and the pre-review ``pre-launch spread of \mvoneSpidPre{} points
176 +($t=\mvoneSpidPreT$)'' compared project firms to an arbitrary fifth of zero-count firms.
177 +
178 +The conclusion is therefore not that disclosed projects carry no premium but that no premium is
179 +detectable on this measure: the measure is sparse (\mspidAnyShare\% of firm-years), it has not
180 +been validated against human labels, and its minimum detectable effects are larger than the
181 +language premium itself. \Cref{tab:reversal} adds the test that the AI-washing literature
182 +suggests \citep{wang2026aiwashing}: if the language premium were a short-lived premium on
183 +sounding like an AI firm, high-language firms \emph{without} disclosed projects should earn it
184 +and then give it back. Among top-quintile language firms, those with disclosed technology
185 +projects earn \mRevWithWithoutTwelve{} points relative to those without over the first twelve
186 +months ($t=\mRevWithWithoutTwelveT$) and \mRevWithWithoutTwentyFour{} over months 13--24
187 +($t=\mRevWithWithoutTwentyFourT$), on \mRevNhighWithProjects{} of \mRevNhigh{} high-language
188 +firm-years; the composite Q5$-$Q1 spread over months 13--24 is \mRevComposThirteenTwentyFourW{}
189 +points ($t=\mRevComposThirteenTwentyFourWT$). Neither a reversal nor a project premium is visible
190 +at this precision. Two readings remain open: disclosed projects may be a noisier measure than
191 +language, or the market may price the \emph{framing} of a firm as AI-exposed rather than its
192 +announced commitments. H5b is neither supported nor rejected; the measure cannot decide it.
193 +
194 +\ExhibitOnce{tab:spidbinary}{\input{tables/tab_spid_binary}}
195 +% tab:reversal is appendix-bound (tables/EXHIBIT_MAP.json) and printed by tables/appendix_exhibits.tex.
158 196
159 197 \subsection{Composition of the signal by filing form}
160 198 \label{subsec:corpus}
161 −Because every firm-year now contains annual, quarterly and current reports, we can ask which text
162 −carries the signal (Table~\ref{tab:filingtype}, Figure~\ref{fig:filingtype}). The composite rebuilt
163 −from Form~10-K filings alone has a correlation of \mcorrTenK{} with the baseline and earns
164 −\mtenkPre{} points before the launch and \mtenkPost{} after ($t=\mtenkPostT$), with a full-sample
165 −Fama--MacBeth slope of \mhrTenK{} points per standard deviation in a horse race against the
166 −10-Q-only (\mhrTenQ) and 8-K-only (\mhrEightK) composites. The 8-K-only composite, which is the
167 −closest analogue of the first version's signal, is the weakest: \meightkPre{} before and
168 −\meightkPost{} after. The annual narrative of the business, risk-factor and MD\&A items is where
169 −the priced AI language lives; the earlier study, which could not read annual reports, measured the
170 −weakest component of the signal, which helps to explain why it found so little before 2022.
171 −
172 −\begin{table}[htbp]\centering\small
173 −\caption{\textbf{Form-specific AI composites, Russell~3000.} Composite rebuilt from the filing-level
174 −scores of one form at a time: coverage, correlation with the baseline, spreads, and Fama--MacBeth
175 −slope; last row, slopes when the three form-specific composites are entered jointly.}
176 −\label{tab:filingtype}
177 −\adjustbox{max width=\textwidth}{\input{tables/tab_filing_type}}
178 −\end{table}
179 −
180 −\begin{figure}[htbp]\centering
181 −\includegraphics[width=0.8\textwidth]{fig10_filing_type.pdf}
182 −\caption{\textbf{Pre- and post-launch spreads of the form-specific composites.}}\label{fig:filingtype}
183 −\end{figure}
184 −
185 −\subsection{Construction, horizon, benchmark and universe robustness}
199 +Because every firm-year contains annual, quarterly and current reports, we can ask which text
200 +carries the signal (\cref{tab:filingtype}, \cref{fig:filingtype}). The composite rebuilt from
201 +Form~10-K filings alone has a correlation of \mcorrTenK{} with the baseline and earns
202 +\mtenkFullW{} points over the full sample on winsorized returns ($t=\mtenkFullWT$; \mtenkPreWsp{}
203 +before the launch and \mtenkPostWsp{} after, on three cohorts), with a Fama--MacBeth slope of
204 +\mhrTenKW{} points per standard deviation ($t=\mhrTenKWT$) in a horse race against the 10-Q-only
205 +(\mhrTenQW) and 8-K-only (\mhrEightKW) composites. The 8-K-only composite, the closest analogue of
206 +the first version's signal and the component that dominates the baseline (correlation
207 +\mcorrEightK), is the weakest; an equal-form-weight composite gives \mformwFullWsort{} points
208 +($t=\mformwFullWsortT$). Whether the forms differ is specification-dependent: a Wald test of equal
209 +slopes rejects on winsorized returns ($p=\mformWaldP$) and not on raw returns
210 +($p=\mformWaldPraw$), and the Romano--Wolf adjusted $p$-values of the three form slopes are close
211 +to five percent. The annual narrative of the business, risk-factor and MD\&A items carries at
212 +least as much of the priced AI language as the other forms; the earlier study, which could not
213 +read annual reports, measured the weakest component of the signal, which helps to explain why it
214 +found so little before 2022. The sentence of the first version that annual reports carry ``by a
215 +wide margin'' the strongest signal is withdrawn.
216 +
217 +\ExhibitOnce{fig:filingtype}{\input{figures_r3k/fig10_filing_type}}
218 +% tab:filingtype is appendix-bound (tables/EXHIBIT_MAP.json) and printed by tables/appendix_exhibits.tex.
219 +
220 +\subsection{Construct validity: what the embedding score measures}
221 +\label{subsec:construct}
222 +The first version offered no validation of the embedding score beyond its face value. This
223 +subsection reports what could be measured without a new embedding pass: the encoder's input
224 +window (\cref{subsec:corpus_data}), a keyword baseline, the sector composition of the top
225 +quintile, two alternative anchor sets scored against the stored chunk embeddings, and a probe of
226 +written sentences; a human-coded validation sample was prepared and not coded
227 +(\cref{subsec:limits}). \Cref{tab:constructvalidity} collects the results.
228 +
229 +A keyword count of core AI terms per thousand words, built from the published AI lexicons, has a
230 +Spearman correlation of \mKwRho{} with the composite at the firm-year level over the sample
231 +(\mKwCorrEarlyMin{} to \mKwCorrEarlyMax{} by year before 2017, \mKwCorrLateMin{} to
232 +\mKwCorrLateMax{} after 2021), and \mKwShareZero\% of firm-years contain no core term at all.
233 +At the chunk level, only \mKwTopDecileShare\% of the chunks in the top decile of the adoption score
234 +contain a core AI term. The two measures are not the same construct, and they carry a similar
235 +sort spread (keyword \mKwFullW{} points, $t=\mKwFullWT$) but a different regression slope
236 +(keyword \mKwFMW{} per standard deviation, $t=\mKwFMWT$); in a horse race the composite keeps
237 +\mHrComposVsKw{} ($t=\mHrComposVsKwT$) and the keyword count \mHrKw{} ($t=\mHrKwT$). The sector
238 +composition explains part of the gap: Utilities have the second-highest mean composite of the
239 +eleven sectors (\mSectorZUtil{} standard deviations) with a keyword correlation of
240 +\mKwUtilSpearman{} and \mKwUtilShareZero\% of firm-years without any AI term, and they are
241 +\mUtilShareQfive\% of top-quintile firm-years against \mUtilShareAll\% of the sample; the probe
242 +confirms that sentences about data-center load growth and generation capacity score
243 +\mProbeUtilInfra{} on the infrastructure anchor, above the \mProbeUtilityPct{}th percentile of
244 +corpus chunks. Excluding Utilities and Energy leaves the composite spread at \mExUtilFullW{}
245 +points ($t=\mExUtilFullWT$). Two alternative anchor sets were scored against the stored
246 +embeddings (no corpus re-embedding): anchors stripped of the cybersecurity and automation
247 +vocabulary give a composite with rank correlation \mStripRho{} to the baseline, a spread of
248 +\mStripFullW{} points ($t=\mStripFullWT$) and a Fama--MacBeth slope of \mStripFMW{}
249 +($t=\mStripFMWT$); a core-AI adoption anchor gives \mCoreRho, \mCoreFullW{} ($t=\mCoreFullWT$) and
250 +\mCoreFMW{} ($t=\mCoreFMWT$); a cybersecurity anchor stripped of AI terms gives \mCyberStripFullW{}
251 +($t=\mCyberStripFullWT$). IDACORP ranks \mIdaRank{}th on the baseline composite, \mIdaRankStrip{}th
252 +on the stripped anchors and \mIdaRankCore{}th on the core anchor; Hawaiian Electric \mHeRank{}th,
253 +\mHeRankStrip{}st and \mHeRankCore{}rd. The results are therefore not driven by the shared
254 +vocabulary of the anchors, but the construct remains proximity to a technology-and-infrastructure
255 +register rather than validated AI activity. Finally, the negation probe of \cref{subsec:lit_text}:
256 +negated AI sentences score \mProbeNegated{} on the adoption anchor against \mProbeAffirm{} for
257 +affirmative ones, a difference of \mProbeDiff{} that holds for \mProbePairsShare\% of
258 +sentence pairs, but both lie above the \mProbeNegatedPct{}th percentile of corpus chunks, so the
259 +score distinguishes topic far better than stance.
260 +
261 +\ExhibitOnce{tab:constructvalidity}{\input{tables/tab_construct_validity}}
262 +
263 +\subsection{Survivorship: measuring the selection of a current-membership universe}
264 +\label{subsec:survivorship}
265 +The universe is the IWV holdings of October 2026, so no firm that left the index before then is
266 +in the panel, and the first version's ``seasoned firms'' and ``listed at least 36 months'' checks
267 +condition on entry, not on exit. The fingerprint of exit selection is visible in the levels: the
268 +equal-weighted forward return of the panel exceeds the IWV total return over the same windows by
269 +\mewMinusIWV{} points per year on raw returns (\mewMinusIWVW{} winsorized, \mewMinusIWVmed{} for
270 +the median firm), by \mlargeMinusIWV{} among the largest thousand and by \msmallMinusIWM{} for the
271 +remaining firms relative to the Russell~2000 ETF, and the Fama--MacBeth constant and the
272 +volatility slope are large. \Cref{tab:attrition} and \cref{fig:attrition} measure the selection
273 +with \mnIWVsnapshots{} archived IWV holdings files (one of 2006, the rest from May 2019 onward; no
274 +archived file exists for 2010--2018). Of the constituents of May 2019, \mattritionSmallNineteen\%
275 +of the smallest market-value tercile and \mattritionLargeNineteen\% of the largest are absent
276 +from the 2025 membership; the annualised exit rate of the small tercile runs from
277 +\mExitSmallMin\% to \mExitSmallMax\% across the 2019--2024 snapshots, that of the large tercile from
278 +\mExitLargeMin\% to \mExitLargeMax\%. For the cohorts whose formation lies within seven months of a
279 +snapshot (2018--2024), the spread among firms that were IWV members at the time is within a few
280 +points of the spread on all panel firms in every cohort (\cref{tab:attrition}). Three partial
281 +bounds follow. Demeaning returns by size group and cohort leaves a full-sample spread of
282 +\msizeDemeanedFullW{} points ($t=\msizeDemeanedFullWT$); restricting to firm-years below the
283 +median forward volatility, where exit is rarer, leaves \mlowVolFullW{} ($t=\mlowVolFullWT$); and
284 +in the logic of \citet{browngoetzmannross1995}, for exit selection to generate the whole observed
285 +winsorized spread of \mspreadFullW{} points, bottom-quintile firms would have to exit
286 +\mBoundExitHalf{} percentage points per year more often than top-quintile firms if exiting firms
287 +lose half their value (\mBoundExitFull{} points for a total loss), a difference that is large
288 +relative to the measured small-tercile exit rates and whose direction is plausible, because
289 +top-quintile firms have higher forward volatility (\mfvolGradFull{} points), but unknown. The
290 +decisive test---attrition by AI quintile---cannot be computed on this corpus, because delisted
291 +firms have no AI scores; a point-in-time universe with scored filings of delisted firms requires
292 +a new embedding pass and is listed in \cref{subsec:limits}. Every level in the paper is therefore
293 +conditional on survival to October 2026, the small-firm estimates most of all.
294 +
295 +\ExhibitOnce{tab:attrition}{\input{tables/tab_attrition}}
296 +
297 +\ExhibitOnce{fig:attrition}{\input{figures_r3k/fig17_attrition}}
298 +
299 +\subsection{Construction, horizon, benchmark and universe checks}
186 300 \label{subsec:entrants}
187 −Table~\ref{tab:robust} collects the remaining checks. Excluding the Magnificent~7 (\mmagSevenPost{}
188 −points after the launch) or the 500 largest firms (\mexTopFiveHundredPost) leaves the spreads
189 −unchanged, as a broad-universe result should. The unweighted-mean and top-5\% constructions of the
190 −signal, the first principal component (\mpcaPost{} post), the IWV-adjusted outcome (identical to the
191 −raw spread by construction of a common benchmark) and the 24-month horizon give the same picture; at
192 −a six-month horizon the spread is \msixmPost{} points after the launch and nothing before. Among
193 −seasoned firms (listed before July 2009) the spread is \mseasonedPre{} before and \mseasonedPost{}
194 −after the launch, and among firm-years listed for at least 36 months \mlistedPre{} and \mlistedPost;
195 −entrants, who earn \mentrantPrem{} points more per year than seasoned firms, are spread evenly
196 −across AI quintiles. Finally, high-AI firms carry higher forward realized volatility (Q5$-$Q1
197 −difference of \mfvolPost{} annualized points after the launch, $t=\mfvolPostT$, against \mfvolPre{}
198 −before), so part of the return differential is compensation for risk during a period of rapid
199 −technological repricing.
200 −
201 −\begin{table}[htbp]\centering\small
202 −\caption{\textbf{Construction, horizon, benchmark and universe checks, Russell~3000.} Equal-weighted
203 −Q5$-$Q1 composite spreads before and after the launch under alternative specifications; Newey--West
204 −$t$-statistics in parentheses.}\label{tab:robust}
205 −\adjustbox{max width=\textwidth}{\input{tables/tab_robust}}
206 −\end{table}
301 +\Cref{tab:robust} collects the remaining checks, each with its Newey--West statistic and interval
302 +and the Romano--Wolf adjustment over the family of robustness rows. Excluding the Magnificent~7
303 +or the 500 largest firms leaves the pre- and post-launch spreads close to the baseline (the
304 +pre-review table printed the baseline pre-launch value in the ``excluding 500 largest'' row by
305 +mistake; the computed value is \mexTopFiveHundredPre{} on raw returns). The unweighted-mean and
306 +top-5\% constructions of the signal, the first principal component, the IWV-adjusted outcome
307 +(identical to the raw spread by construction of a common benchmark) and the 24-month horizon give
308 +the same picture; at a six-month horizon the spread is \msixmPost{} points after the launch and
309 +nothing before. Among seasoned firms (listed before July 2009) the winsorized spread is
310 +\mseasonedPreW{} before and \mseasonedPostW{} after the launch, among firm-years listed for at
311 +least 36 months \mlistedPre{} and \mlistedPost{} on raw returns; entrants, who earn \mentrantPremW{}
312 +points more per year than seasoned firms on winsorized returns, are spread evenly across AI
313 +quintiles, but both checks condition on entry and leave the exit selection of
314 +\cref{subsec:survivorship} untouched. High-AI firms carry higher forward realized volatility
315 +(Q5$-$Q1 difference of \mfvolPost{} annualized points after the launch, $t=\mfvolPostT$, against
316 +\mfvolPre{} before), so part of the return differential is compensation for risk. \Cref{tab:hygiene}
317 +lists every price series break removed from the panel after verification against the second
318 +price source, and the effect of each data correction on the headline statistics, so that a
319 +reader can see which observations the cleaning changed.
320 +
321 +\ExhibitOnce{tab:robust}{\input{tables/tab_robust}}
322 +% tab:hygiene is appendix-bound (tables/EXHIBIT_MAP.json) and printed by tables/appendix_exhibits.tex.
207 323
208 324 \subsection{Definition of the break}
209 −Ending the pre-period in 2020 or starting the post-period in 2021 does not change the conclusion
210 −(results in \texttt{results/r3k/results2.json}, block \texttt{breaks}): in the broad universe the
211 −2021 cohort earned a spread of +12.5 points, larger than two of the three post-launch cohorts, so
212 −moving it into the post-period raises the post mean and lowers the difference with the pre-period.
325 +\label{subsec:breakdef}
326 +The 2021 cohort is held from July 2022 to June 2023 and straddles the launch; its winsorized
327 +spread of \mcohortTwentyOneW{} points is larger than two of the three post-launch cohorts. The
328 +first version stated that moving it into the post-period ``lowers the difference'' between the
329 +periods; the opposite is true. With the split at 2022 (pre 2010--21, post 2022--24) the winsorized
330 +spreads are \mspreadPreW{} and \mspreadPostW{}; with the split at 2021 (pre 2010--20, post
331 +2021--24) they are \mbreakTwentyOnePreW{} and \mbreakTwentyOnePostW{} (\cref{tab:robust}), and the
332 +pooled firm-clustered post-minus-pre test is \mbreakTwentyOneDiffW{} points
333 +($t=\mbreakTwentyOneDiffWT$ firm, \mbreakTwentyOneDiffWTtw{} two-way) against \mpooledDiffW{}
334 +($t=\mpooledDiffWT$) for the 2022 split. The pre-launch premium of the broad universe therefore
335 +depends on where the ambiguous 2021 cohort is placed, and wherever the paper claims a premium
336 +before the launch the 2021 cohort should be read as part of that claim.
213 337
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