Optimal Monetary Policy with Confounding Information

We develop a model of optimal monetary policy in an economy where firms' price-setting decisions are distorted by a signal-extraction problem: they cannot perfectly distinguish aggregate from idiosyncratic shocks based on noisy local information. This systematic misattribution of aggregate nominal disturbances to firm-specific factors generates an additional indirect price response, implying that strict price stability is no longer optimal. Instead, the optimal policy fully stabilizes the output gap, which necessarily requires accommodating fluctuations in the price level. The cyclicality of the optimal price level depends critically on the source of firms' incomplete information: learning from local demand signals implies a procyclical price level, whereas learning from local productivity signals yields a countercyclical one. We show that these results are robust to extensions featuring elastic attention and sentiment shocks.