Same Book, Different Fills: Partial Identification of FIFO Execution from Aggregate Order Books

Price-level limit order book (L2) data reveal aggregate liquidity but not the ordered queue required by price--time priority. Passive-execution backtests can therefore depend on an unobserved cancellation-allocation rule even when observed prices, quantities, and trades are held fixed. We frame recovery of market-by-order histories from aggregate snapshots as a conditional partial identification problem: multiple histories can reproduce the same aggregate path. Holding that path, reconciled market removals, latent order partitions, and additions fixed, our path-preserving compiler varies only cancellation allocation among front, quantity-weighted-random, and back rules. Within this compiler class, we establish front--back fill ordering for a virtual tagged order during one touch-price spell. We study seven months of synchronized 2025 Tokyo Stock Exchange data for two instruments with different trading activity: RIC 1301.T and RIC 7911.T. Ten-level L2 snapshots provide book states, while L1 trades permit inference of market removals and resting side through reconciliation. Each instrument contributes 1,080 matched five-minute episodes over the same 18 held-out trading days. The aggressive benchmark is invariant across FIFO realizations, but passive execution is sensitive to the cancellation rule. For 1301.T, front rather than back cancellation raises preterminal completion by 8.01 percentage points and reduces implementation shortfall by 1.010 bps. For 7911.T, the corresponding differences are 7.39 percentage points and 0.384 bps. Thus, observationally equivalent aggregate-book paths can imply economically different passive-execution outcomes. Execution policies evaluated from aggregate data should be accompanied by FIFO sensitivity analysis rather than reported as single-point estimates based on an unobservable queue assumption.