\section{Data}
\label{ch3:sec:data}

\subsection{FOMC Statement Collection}

We collect 451 FOMC communications from the Federal Reserve Board website, spanning 2000--2025. After filtering to policy statements only, our textual corpus contains $N = 217$ FOMC statements, each averaging 3,840 characters. We use the broader 2000--2025 textual sample to train the embedding models and construct the semantic axes, which requires examples spanning multiple policy regimes. For the high-frequency event study, we focus on 148 FOMC events from 2008 to 2025. The 2008 start date reflects two considerations. First, reliable 1-minute futures data became consistently available following the shift to predominantly electronic trading on CME Globex in 2006--2007; pre-2008 high-frequency data for several of our contracts contains gaps and timing errors that would compromise our minute-level identification. Second, the 2008--2025 window encompasses sufficient variation in monetary policy regimes---the zero lower bound (2008--2015), quantitative easing programs, post-crisis normalization (2016--2019), the pandemic response (2020--2021), and the inflation-driven tightening cycle (2022--2025)---across three Fed Chairs (Bernanke, Yellen, Powell) to identify communication effects without sacrificing data quality \citep{swanson2014,gurtler2010,blinder2008}. The broader 2000--2025 textual sample used for model fine-tuning starts in 2000 because the FOMC adopted its current practice of issuing post-meeting statements with substantive policy language beginning in 1999--2000; earlier statements were shorter and formulaic, providing too little variation for our NLP models to learn from.

All statements are obtained directly from Federal Reserve official releases archived on the Board of Governors website. We focus exclusively on post-meeting statements rather than meeting minutes, transcripts, or other Fed communications because these statements represent the information that is immediately available to market participants at precise announcement times \citep{gurkaynak2005}. This temporal precision is necessary for high-frequency identification \citep{andersen2003micro,rosa2013}.

We preprocess statements following \citet{gentzkow2019}: we remove headers, footers, voting records, and administrative content, keeping only policy-relevant text. We account for structural breaks in statement format (e.g., the lengthening of statements post-2008) to avoid introducing spurious variation in our semantic measures \citep{hansen2017}. We cross-reference all statements with the Fed's public archives to verify completeness.

\subsection{Dual-Model Embedding Generation}

We convert each FOMC statement into a numerical vector using two sentence transformer models, adapted to the FOMC corpus through the training procedure described in Section~\ref{ch3:sec:nlp_framework}.

\subsubsection{Model Architectures}

\begin{enumerate}
\item \textbf{MiniLM} (\texttt{all-MiniLM-L6-v2}): 33M parameters, 384-dimensional embeddings.
\item \textbf{BERT} (\texttt{bert-base-uncased} with mean pooling): 110M parameters, 768-dimensional embeddings. A larger model that captures finer contextual distinctions in policy language \citep{kenton2019}.
\end{enumerate}

We train both models on the FOMC corpus using the two-stage procedure (TSDAE domain adaptation, then MNRL contrastive learning) described in Section~\ref{ch3:sec:nlp_framework}. The training hyperparameters are: batch size 32 (MiniLM) / 16 (BERT), learning rate $1 \times 10^{-5}$, 5 (MiniLM) / 4 (BERT) supervised epochs with cosine warmup schedule (10\% warmup ratio), and approximately 4,000 training examples per model from six pairing strategies.

\subsubsection{Construction of Training Pairs}

We construct training pairs using six strategies: (1) overlapping text segments from the same document; (2) consecutive sentence pairs within a document; (3) hawk--dove contrastive pairs classified through keyword banks; (4) temporal proximity pairs from consecutive FOMC meetings; (5) topic-based pairs sharing the same Fed topic (monetary policy, inflation, employment, etc.); and (6) key phrase paraphrases containing identical policy phrases (\textit{``maintain the target range''}, \textit{``decided to raise''}, etc.). The diversity of pairing strategies prevents the trained models from learning only a single sentiment dimension.

\subsubsection{Data-Driven Reference Selection}

Previous studies select reference dates manually or construct counterfactual statements by hand. We instead use the hybrid PCA--percentile approach described in Definition~\ref{ch3:def:pca_axes} to identify semantically extreme statements algorithmically. This procedure eliminates researcher degrees of freedom and produces more stable centroids (5 reference statements per pole versus 2 in typical manual selection). All semantic axes exceed the 0.04 minimum separation threshold. Ensemble separations are: total policy stance (0.302), risk assessment (0.274), policy communication (0.248), and economic priority (0.252).

We validate the embeddings in three ways. First, we compare embedding-based tone rankings with expert classifications and verify that known dovish and hawkish statements sort correctly. Second, we measure inter-model agreement: mean ensemble confidence is 0.837 for novelty and 0.562--0.806 for tone across axes. Third, we verify that the PCA axis assignments produce intuitive orderings.

\subsection{High-Frequency Financial Data Construction}

We use 1-minute OHLCV data for seven futures contracts spanning the major asset classes relevant to monetary policy transmission:

\begin{itemize}
\item \textbf{ES}: E-mini S\&P 500 (equity benchmark)---responds to policy communications through discount rate effects, growth expectations, and risk premium adjustments.
\item \textbf{VX}: VIX Futures (volatility)---captures implied volatility and uncertainty resolution, providing the most direct measure of information processing effects.
\item \textbf{ZN}: 10-Year Treasury Note---reflects the interaction between policy expectations and term premium effects.
\item \textbf{ZF}: 5-Year Treasury Note---primarily captures expectations about near-term policy rate changes.
\item \textbf{DX}: Dollar Index---reflects relative monetary policy stances and international spillover effects.
\item \textbf{CL}: Crude Oil WTI---reflects both inflation expectations and growth concerns influenced by monetary policy.
\item \textbf{GC}: Gold---a safe-haven asset whose demand falls when accommodative communication triggers a rotation toward risk assets, and rises with policy-induced uncertainty.
\end{itemize}

The data span 148 FOMC events (approximately 8 per year from 2008 to 2025). For each event, we extract a $\pm 120$ minute window around the 14:00~ET announcement time. We interpolate the raw data to a regular 1-minute grid with forward-filling of short gaps ($\leq 5$ minutes) and returns recomputed on the regularized grid. We require at least 80\% valid observations per rolling window.

For each instrument, we construct minute-by-minute log returns as:
\begin{equation}
r_{i,m}^{(j)} = \log\left(P_{i,m}^{(j)}\right) - \log\left(P_{i,m-1}^{(j)}\right)
\end{equation}
where $P_{i,m}^{(j)}$ is the price of asset $i$ at minute $m$ relative to FOMC event $j$. We align timestamps across instruments and exchanges, handle market closures and trading halts, and filter outliers following standard microstructure procedures.

\subsection{Event Window Specification and Temporal Alignment}

Our primary analysis employs a 45-minute event window following each FOMC announcement, spanning from the announcement time ($t=0$) to 45 minutes after ($t=+45$). We choose this window length for two reasons.

First, most of the announcement effect occurs within 15 minutes of the release, but equity responses to tone continue to develop through 45 minutes post-announcement. Second, press conferences typically begin 30 minutes after the statement, so a 45-minute window includes only the first 15 minutes of the press conference, limiting contamination.

We also implement several alternative window specifications as robustness checks. A narrow 15-minute post-announcement window provides very clean identification but with reduced statistical power. An extended 60-minute post-announcement window captures longer adjustment dynamics but with increased contamination risk, particularly from press conferences that typically begin 30 minutes after the statement release.

FOMC statements are typically released at 2:00 PM Eastern Time. We verify actual release times using Federal Reserve timestamps, news services, and market data providers, and correct any timing discrepancies before aligning with price data.

