spb/wp15_uqo

1\section{Empirical design}2\label{sec:design}34\subsection{The estimand}56For an outcome $Y$ from Section~\ref{sec:outcomes}, define the within-event7change $\Delta Y_{i,t}(h) = Y_{i,t}(t{+}h) - Y_{i,t}(t{-}5)$. The estimand is8the difference-in-differences9\begin{equation}10\Delta\Delta Y(h) \;=\;11\mathbb{E}\big[\Delta Y(h)\,\big|\,\text{real event}\big]12\;-\;13\mathbb{E}\big[\Delta Y(h)\,\big|\,\text{matched placebo}\big].14\label{eq:dd}15\end{equation}16In potential-outcomes language, the placebo arm estimates the counterfactual17path of cross-sectional activity that the event window would have followed had18the source stock not jumped, holding fixed the stock, the minute of day, the19month, and the calm-market state. Three biases that a naive event study would20absorb are differenced out explicitly. \emph{Volatility clustering}: shocks21arrive in already-active minutes, so post-event activity is elevated even22absent transmission; the inner difference removes the level.23\emph{Deterministic intraday drift}: breadth trends over the trading day; the24placebo, matched on minute of day, follows the same drift.25\emph{Filter-induced selection}: conditioning on a calm market at $t$ selects26minutes followed by reversion toward normal activity; the placebo is drawn27under the identical filters and inherits the identical reversion.2829\subsection{Placebo construction}3031For each real event $(i,t)$ the matched placebo is drawn by the following32algorithm, with a fixed seed recorded in the replication package:33\begin{enumerate}34\item collect all minutes of the same month with the same minute of day35$\tau(t)$, on a different trading day, at which (a) security $i$ has an36observable return with $|z_{i,\cdot}|<2$, (b) the market-calm filter holds,37and (c) the simultaneity filter holds;38\item draw one candidate uniformly at random; compute every outcome of39Section~\ref{sec:outcomes} at the placebo minute by the identical code path;40\item label the placebo with the real event's magnitude and sign so that all41conditional cuts (by $|z|$ bin, by sign, by state) compare real and placebo42events within the same cell.43\end{enumerate}44Events with an empty candidate set (rare) contribute to the real arm only and45are dropped from difference-in-differences estimation by the pairing on46dates within cells. The match rate exceeds 95\% throughout.4748\subsection{Inference}4950Outcomes are correlated across events within a trading day---mechanically so,51because events of the same minute share receivers. All inference therefore52resamples \emph{days}: for $b=1,\dots,500$, draw event dates with replacement,53recompute date-level sums and counts for both arms, and form the bootstrap54distribution of the full statistic~\eqref{eq:dd}. Standard errors are55bootstrap standard deviations; the month-cluster variant (resampling56year-months) appears in the robustness table and roughly doubles the standard57error of the network differential without changing any conclusion. With58roughly 8,500 event days, the effective sample is large, and the design's59minimum detectable effect for market-wide breadth at $h=5$ is approximately60$2\times10^{-4}$ at the 5\% level with 80\% power---one additional responding61security per twenty-five events. Null results below are powered nulls.6263\subsection{Identification: what is and is not claimed}6465The design identifies the \emph{association} between an isolated idiosyncratic66jump and subsequent cross-sectional tail activity, purged of ambient levels,67intraday seasonality, calm-market selection, and the stock's own base rates.68It does not identify the structural channel behind the network differential:69lagged-correlation neighbors are typically industry peers, ETF co-members, and70factor-exposure twins, and the differential aggregates fundamental71information transmission (investors rationally repricing linked firms) with72trading-channel transmission (basket flows, hedging, liquidity withdrawal).73Separating those requires timestamped news and order-flow data and is beyond74OHLCV bars; the paper's claims are correspondingly phrased as predictive75propagation, not causal transmission. Likewise, the systemic co-jump series76conflates common news arrivals with endogenous synchronization; we document77its evolution and severity without attributing minutes to either source.7879\subsection{Falsification battery}8081Five falsifiable predictions are tested and reported. (1) \emph{No82pre-event response}: real-event outcomes at $t-5$ equal placebo levels.83(2) \emph{No placebo network structure}: the neighbor--non-neighbor84differential computed on placebo events alone is zero85($-2.7\pm2.8\times10^{-4}$). (3) \emph{No announcement artifact}: excluding86the 10:00 and 14:00--14:30 ET windows that host most scheduled releases87leaves all estimates unchanged. (4) \emph{No coverage artifact}: fixed-rule88lagged universes make the 2020 source-coverage expansion irrelevant to any89comparison. (5) \emph{No tick-regime artifact}: the post-decimalization90subsample reproduces the market-wide null and the network differential. All91five pass; Table~\ref{tab:robustness} quantifies each.92