spb/wp15_uqo

1\section{Robustness}2\label{sec:robustness}34Table~\ref{tab:robustness} re-estimates the market-wide5difference-in-differences at $h\in\{5,30\}$ and the network differential at6$h=5$ under eleven designs; Tables~\ref{tab:design_checks}7and~\ref{tab:network_components} report the design diagnostics discussed8above. We describe only checks that were executed; analyses that the9replication package does not contain are listed as such in the Online10Appendix and in the concluding section.1112\emph{Tick regime.} Pre-2001 minute returns embed eighth- and sixteenth-tick13bid--ask bounce. Restricting events to 2002 onward leaves the market-wide14estimates unchanged ($-1.03$ and $-3.04\times10^{-4}$) and the network15differential at $65.8\times10^{-4}$. \emph{Time of day.} Restricting events16to 10:00--15:30 ET, which removes the opening and closing periods where17seasonal scaling is most demanding, and separately excluding the 10:00 and1814:00--14:30 ET windows that host most scheduled macroeconomic releases,19changes no estimate by more than one standard error. \emph{Market state.}20Excluding 2008--2009 and 2020 leaves both objects unchanged; within the21crisis years alone the market-wide estimate is imprecise22($2.7\pm5.1\times10^{-4}$) and the network differential is, if anything,23larger ($68\times10^{-4}$). \emph{Source magnitude.} Raising the source24threshold to $|z|\ge8$ and $|z|\ge12$ moves the market-wide point estimates25toward zero or slightly positive, consistent with the co-arrival pattern of26Table~\ref{tab:design_checks}, and lowers the network differential from27$64$ to $50$ and $34\times10^{-4}$. The decline with magnitude is the one28systematic pattern in the table; it is consistent with the largest moves29being firm-specific news that peers correctly do not price, and also with30the largest moves being the ones most often accompanied by halts or31erroneous prints that bars cannot flag. \emph{Universe composition.}32Excluding source securities flagged as likely non-common by the33ticker-shape heuristic leaves every estimate within rounding of the34baseline; ETFs cannot be identified and are not excluded. \emph{Inference.}35Month-cluster resampling raises the standard error of the network36differential from $1.8$ to $3.4\times10^{-4}$ and ticker-cluster resampling37to \NetDiffFiveTickerSE$\times10^{-4}$, leaving a $t$-statistic above38fourteen in every case; the market-wide standard errors are insensitive to39the clustering unit. \emph{Placebo network.} The neighbor-minus-other40contrast computed on placebo events alone is $-2.7\pm2.8\times10^{-4}$ over41the full sample. As Table~\ref{tab:network_components} shows, this average42conceals decade-level offsets of opposite signs, which is why every network43statistic in the paper is a real-minus-placebo difference and never a44real-arm contrast on its own.4546\input{tables/table8_robustness}4748Several checks that a complete treatment would include were not executed49and are not claimed. The pipeline stores events at the $|z|\ge6$ threshold50and the receiver threshold $|z|>2$ only, so lower source thresholds51($|z|\ge4,5$), a higher receiver threshold ($|z|>3$), and the top-1000 and52top-3000 universes would require re-running the detection stage on the raw53panel. Neighbor sets built on 5- or 30-minute residual correlations, or on a54transaction-time covariance estimator, and the pre-event ($t-5$) network55contrast, are the two extensions most needed to settle the interpretation of56the secular increase in the network differential. Permuted-network placebos57that preserve industry and liquidity composition, a separate estimate of58propagation inside announcement windows, and a Hawkes-type model of the59co-jump minute series are natural further steps.60