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 $\Delta Y_{i,t}(h) = Y_{i,t}(h) - Y_{i,t}(-5)$, where $Y_{i,t}(-5)$8denotes the same outcome evaluated five minutes before the event. The9baseline estimand is the difference-in-differences10\begin{equation}11\Delta\Delta Y(h) \;=\;12\mathbb{E}\big[\Delta Y(h)\,\big|\,\text{real event}\big]13\;-\;14\mathbb{E}\big[\Delta Y(h)\,\big|\,\text{matched placebo}\big],15\label{eq:dd}16\end{equation}17estimated as the difference between the two arms' sample means. In18potential-outcomes language, the placebo arm estimates the path of19cross-sectional activity that the event window would have followed had the20source stock not moved, holding fixed the stock, the minute of day, the21month, and the calm-market state. Three biases that a naive event study would22absorb are differenced out explicitly. \emph{Volatility clustering}: shocks23arrive in already-active minutes, so post-event activity is elevated even24absent transmission; the inner difference removes the level.25\emph{Deterministic intraday drift}: breadth trends over the trading day; the26placebo, matched on minute of day, follows the same drift.27\emph{Filter-induced selection}: conditioning on a calm market at $t$ selects28minutes followed by reversion toward normal activity; the placebo is drawn29under the identical filters and inherits the identical reversion.3031The inner difference has a cost that we quantify rather than assume away. If32real events select minutes whose ambient activity is elevated for transient33reasons, part of that elevation reverts over the following minutes, and34$\Delta\Delta$ is biased downward by the reversion. We therefore report,35alongside~\eqref{eq:dd}, the post-event level difference without36pre-differencing and a stratified estimator that compares real and placebo37post-event levels within deciles of the pre-event level,38\begin{equation}39\widehat{\theta}^{\,S}(h) \;=\; \sum_{b=1}^{10} w_b\,40\Big(\bar Y^{\,\mathrm{real}}_{b}(h) - \bar Y^{\,\mathrm{placebo}}_{b}(h)\Big),41\qquad w_b = \frac{n^{\mathrm{real}}_b}{\sum_{b'} n^{\mathrm{real}}_{b'}},42\label{eq:strat}43\end{equation}44where $b$ indexes deciles of $Y_{i,t}(-5)$ over the pooled sample. Because the45placebo arm has a lower latent activity level than the real arm within any46stratum defined on a noisy pre-event measurement, regression to the mean47pushes~\eqref{eq:strat} upward; the two estimators therefore bracket the48market-wide response from below and from above.4950\subsection{Placebo construction}5152For each real event $(i,t)$ the matched placebo is drawn as follows, with a53fixed seed recorded in the replication package. The candidate set collects all54minutes of the same month with the same minute of day $\tau(t)$ on a different55trading day at which security $i$ has an observable return with56$|z_{i,\cdot}|<2$, the market-calm filter holds, and the simultaneity filter57holds. One candidate is drawn uniformly at random, and every outcome of58Section~\ref{sec:outcomes} is computed at the placebo minute by the identical59code path. The placebo is labelled with the real event's magnitude and sign so60that all conditional cuts---by $|z|$ bin, by sign, by number of co-arriving61events---compare real and placebo events within the same cell. Events with an62empty candidate set contribute to the real arm only; the match rate is63\MatchRate\% over the full sample, \MatchRateNineties\% in the 1990s, when64calm candidate minutes with an observable return are scarcer, and at least65\MatchRateMinPost\% in each later decade. The placebo is not66matched on the pre-event level of the outcome, which is why the pre-event67levels of the two arms can differ and are reported.6869\subsection{Inference}7071Outcomes are correlated across events within a trading day---mechanically so,72because events of the same minute share receivers and \MeanCoArrival{} source73events on average share each event minute---and within a source security74across days. All inference therefore resamples clusters: for75$b=1,\dots,500$, draw event dates with replacement, recompute date-level sums76and counts for both arms, and form the bootstrap distribution of the full77statistic. Standard errors are bootstrap standard deviations. Two78alternatives are reported: a month-cluster variant (resampling year-months),79which roughly doubles the standard error of the network differential without80changing any conclusion, and a ticker-cluster variant (resampling source81securities), which more than doubles it. With \EventDays{} event days and82\NEventsRealMM{} million events, the minimum detectable effect for83market-wide breadth at $h=5$ at the 5\% level with 80\% power is about84\MDEFive$\times10^{-4}$, or one additional responding security per85\MDEEventsPer{} events given \NEligMean{} observable receivers on average.86Null results below are powered nulls in this sense.8788\subsection{Identification: what is and is not claimed}8990The design identifies the predictive association between an isolated91idiosyncratic extreme and subsequent cross-sectional tail activity, purged of92intraday seasonality, calm-market selection, and the stock's own base rates,93and bounded with respect to ambient-activity selection as described above. It94does not identify the structural channel behind the network differential:95lagged-correlation neighbors are typically industry peers, ETF co-members, and96factor-exposure twins, and the differential aggregates fundamental97information transmission (investors repricing linked firms on the same news)98with trading-channel transmission (basket flows, hedging, liquidity99withdrawal). Separating those requires timestamped news and order-flow data100and is beyond OHLCV bars; the paper's claims are phrased as predictive101propagation, not causal transmission. Likewise, the systemic co-jump series102conflates common news arrivals with endogenous synchronization; we document103its evolution and severity without attributing minutes to either source.104105\subsection{Falsification and diagnostic battery}106107Five checks are reported. (1) \emph{Pre-event levels}: the levels of every108outcome at $t-5$ in the two arms, with their difference; a non-zero109difference is not a failure of the design but a measured quantity that the110estimators above handle in different ways. (2) \emph{Placebo network111contrast}: the neighbor-minus-other contrast computed on placebo events112alone, over the full sample and by decade. (3) \emph{Announcement windows}:113excluding the 10:00 and 14:00--14:30 ET windows that host most scheduled114releases. (4) \emph{Coverage}: fixed-rule lagged universes make the 2020115source-coverage expansion irrelevant to any comparison. (5)116\emph{Tick regime}: the post-decimalization subsample is reported for every117headline estimate. Tables~\ref{tab:design_checks},118\ref{tab:network_components}, and~\ref{tab:robustness} quantify each.119