This article identifies previously unknown, fundamental constraints on the effectiveness of economic policy instruments. The constraints arise from unstable zero dynamics , which occur commonly in macroeconomic models, and require (in the linear, time-invariant case) that infinite sums of discounted future values of certain endogenous variables necessarily equal zero, irrespective of policy. Unstable zero dynamics potentially explain the “price puzzle,” and are exemplified by classic explanations of the effect of changes in the rate of money creation on interest rates. They furnish a mathematical formulation of elements of Minsky’s financial instability hypothesis. In the multivariable case, they give rise to constraints involving multiple endogenous variables, which relate to the Phillips curve and Okun’s Law, and provide a system-theoretic paradigm for phenomena such as stagflation and stagnation.