Macroeconomists increasingly use external sources of exogenous variation for causal inference. However, unless such external instruments (proxies) capture the underlying shock without measurement error, existing methods are silent on the importance of that shock for macroeconomic fluctuations....

In a textbook New Keynesian model extended to allow for uninsurable household income risk, any path of inflation and output implementable via interest rate policy is similarly implementable through uniform lump-sum transfers ("stimulus checks"). A dual-mandate policymaker can thus use checks to...