We show that the concurrent relation between quarterly stock returns and inflation shocks is economically and robustly significant only over weaker economic times, strongly negative prior to the late 1990s and strongly positive afterwards. Conversely, in the stronger economic times over our 1981 to 2017 sample, this stock-inflation relation is relatively much smaller and usually marginally negative. Our evidence suggests a role for two complementary channels. First, we find consistent state-dependent patterns in how inflation shocks are related to expected economic growth and the equity risk premium, indicating that inflation non-neutrality is stronger over weaker economic times. Second, our findings imply that the inflation signal about the underlying economic state intensifies during weaker economic times, due to the elevated economic-state uncertainty then. We also contribute by contrasting subjective (survey-based) vs. objective inflation shocks and by evaluating the relation between inflation shocks and forward equity yields.