  This paper discusses the problem of estimation and inference on time-varying
treatments. We propose a method for inference on treatment histories, by
introducing a \textit{dynamic} covariate balancing method. Our approach allows
for (i) treatments to propagate arbitrarily over time; (ii) non-stationarity
and heterogeneity of treatment effects; (iii) high-dimensional covariates, and
(iv) unknown propensity score functions. We study the asymptotic properties of
the estimator, and we showcase the parametric convergence rate of the proposed
procedure. We illustrate in simulations and an empirical application the
advantage of the method over state-of-the-art competitors.
