We study how monetary policy impacts stock market returns, and vice versa under different communication regimes employed by the Fed. We cast this problem in a method of moments framework, where the moment conditions are derived from a simple structural vector autoregression model. Based on this representation, we can apply the generalised-S test of Magnusson and Mavroeidis (2014}, which exploit the exogenous variation in the variance of the structural shocks to perform inference of the structural stable parameters. By inverting this test, we simultaneously construct a confidence region for both impacts, without the need for restrictive identification assumptions. For the USA economy, we find a statistically insignificant stock market response to changes in monetary policy and a time-dependant monetary policy response to changes in stock prices.