Regulators and academics are increasingly interested in the causal effect that algorithmic actions of a digital platform have on consumption. We introduce a general causal inference problem we call the steerability of consumption that abstracts many settings of interest. Focusing on observational designs, we exhibit a set of assumptions for identifiability that significantly weakens the often unrealistic coverage assumptions of standard designs. They key insight behind our assumptions is to model the dynamics of consumption, viewing the platform as a controller acting on a dynamical system. From this dynamical systems perspective, we are able to show that exogenous variation in consumption and appropriately responsive control actions are sufficient for indentifying steerability of consumption. Our results illustrate the fruitful interplay of control theory and causal inference, which we illustrate with examples from econometrics, macroeconomics, and machine learning.