We develop methods for estimating how infinitesimal policy changes affect long-term outcomes in dynamic systems. We show that dynamic marginal policy effects (MPEs) can be identified via tractable reduced-form expressions, and can be estimated under a general sequential unconfoundedness assumption. We also propose a doubly robust estimator for dynamic MPEs. Our approach does not require observing full dynamic state information (as is typically assumed for off-policy evaluation in Markov decision processes), and does not incur an exponential curse of horizon (as is typical in non-Markovian off-policy evaluation). We demonstrate practicality and robustness of our approach in a number of simulations, including one motivated by a dynamic pricing application where people use past prices to form a reference level for current prices. Joint work with I-han Lai.