spb/uqo-research-db

1% ============================================================================2\section{Methodology}3\label{sec:methodology}4% ============================================================================56We bring six complementary research designs to bear, ranging from simple portfolio sorts to a7market-model event study. Using multiple designs with different identifying assumptions guards8against any single method's weaknesses and lets us triangulate the economic interpretation.910\subsection{Portfolio sorts}11Each formation year we sort firms into quintiles on a given (within-year standardized) AI signal and12compute the equal-weighted (EW) and value-weighted (VW) forward return of each quintile, plus the13high-minus-low (Q5$-$Q1) spread. We report the time-series average of the annual spreads and test its14significance with Newey--West \citep{neweywest1987} standard errors (three lags) to account for any15serial correlation in the overlapping return windows. Sorts are model-free and transparent, and the16EW--VW comparison reveals whether an effect is concentrated in larger or smaller firms.1718\subsection{Factor-model spanning of a long--short portfolio}19To ask whether the AI spread survives risk adjustment, we build an annually rebalanced, equal-weighted,20self-financing long--short portfolio (top minus bottom quintile), record its monthly return, and21regress it on (i)~the CAPM market factor and (ii)~the Fama--French five factors plus momentum (FF6).22The intercept (alpha) measures the average return unexplained by known risk factors; we use23heteroskedasticity- and autocorrelation-consistent (HAC) standard errors. A significant alpha would24indicate pricing beyond standard exposures.2526\subsection{Two-way fixed-effects panel regressions}27We estimate28\begin{equation}29  r_{i,t\to t+12} = \beta\, \text{AI}_{i,t} + \gamma' X_{i,t} + \alpha_i + \delta_t + \varepsilon_{i,t},30  \label{eq:panel}31\end{equation}32where $r$ is the winsorized forward return, $\text{AI}_{i,t}$ the standardized signal, $X$ the33controls, and $\alpha_i,\delta_t$ firm and year fixed effects. Standard errors are double-clustered by34firm and year \citep{petersen2009,cameron2011}. Firm fixed effects absorb all time-invariant35cross-firm differences, so $\beta$ identifies whether \emph{within-firm} changes in AI language36predict returns; year fixed effects absorb common shocks. Contrasting this estimate with the37cross-sectional ones isolates whether the signal lives across or within firms (H4).3839\subsection{Fama--MacBeth regressions}40We also run annual cross-sectional regressions of the forward return on the AI signal and controls and41average the slopes following \citet{famamacbeth1973}, with Newey--West errors on the time series of42coefficients. This estimator weights each year equally and yields an interpretable43per-standard-deviation premium; plotting the annual slopes reveals the time profile of the premium44directly.4546\subsection{Structural-break and difference-in-differences designs}47To test regime dependence (H2) we split the sample at the 30~November 2022 ChatGPT launch and compare48sub-period spreads, and we estimate pooled interaction models of the form49$r = \beta_1 \text{AI} + \beta_2 (\text{AI}\times \text{Post}) + \gamma' X + \varepsilon$, where50$\text{Post}=\mathbb{1}[\text{formation year}\ge 2022]$ and $\beta_2$ captures the change in the51premium. We complement this with a difference-in-differences design in which treatment is the firm's52\emph{pre-determined} AI exposure---fixed at its 2019--2021 average so it cannot respond to the53event---interacted with Post, within firm and year fixed effects. An event-time version interacts54pre-determined exposure with each year dummy (relative to 2021) to trace the dynamic response.5556\subsection{Market-model event study}57Finally, we run a classic event study \citep{mackinlay1997} around the ChatGPT launch. For each stock58we estimate a market model ($r_{i,d}=a_i+b_i r^{m}_{d}+e_{i,d}$) over the estimation window59January--October 2022 and compute daily abnormal returns $\text{AR}_{i,d}=r_{i,d}-(\hat a_i+\hat b_i60r^m_d)$ over the event window November 2022--June 2024. Cumulative abnormal returns (CAR) are compared61across terciles of \emph{pre-event} AI disclosure (from the FY2021 10-K), and we regress firm-level62CAR on pre-event exposure with size, beta, and sector controls. Because abnormal returns net out63market-beta exposure, the event study isolates the cross-sectional response to the AI-narrative shock64from the contemporaneous (and initially negative) market drift of 2022--2023.65