Price Adjustment When Updating Requires Execution: Evidence from Automated Market Makers

Abstract When price updating requires an execution, aggregate correction toward a reference can conceal offsetting movement in the margins that generate it: which discrepancy states a market visits, how often execution occurs in those states, and how much correction follows conditional on execution. We formalize this as an exact decomposition – state composition, execution incidence, and conditional correction magnitude – estimated nonparametrically from sample analogs within fixed discrepancy bins. Passive Uniswap v3 pools make the decomposition unusually transparent: absent a focal-pool execution, native pool price does not change, so the non-execution correction branch is mechanically zero. We implement the decomposition in two matched 5 basis-point (bp) ETH–USDC pools on Ethereum and Base, drawing on a high-frequency analytic panel of 2.52 million block-level observations after reference and finiteness screening, a strict-prior two-venue external reference, and same-block measurement. A pre-specified fixed-hinge diagnostic shows that a simple fee-normalized discrepancy-response shape is not stable across the two non-overlapping windows. More importantly, raw aggregate correction is higher in Confirmation in both pools, while standardizing the two windows to a common discrepancy-state distribution reverses the comparison: positive state-composition and negative conditional-magnitude changes offset, with a smaller execution-incidence contribution, so that raw aggregate correction rises only modestly while these underlying margins move substantially. The offsetting pattern survives removal of the open-ended tail, while its magnitude is support-dependent and amplified on full support. The estimates are specific to the studied pools and windows; the transport analysis is descriptive and post-confirmatory.