Business cycles when consumers learn by shopping

Empirical evidence suggests consumers rely on their shopping experiences to form beliefs about inflation. In other words, they "learn by shopping". I introduce this empirical observation as an informational friction in the New Keynesian model and use it to study its consequences for the transmission of aggregate shocks and the design of monetary policy. Learning by shopping anchors households' beliefs about inflation to its past, causing disagreement with firms over the value of the real wage. The discrepancy allows nominal shocks to have real effects and makes the slope of the Phillips curve a function of the monetary policy stance. As a result, a more hawkish monetary policy reduces the volatility and persistence of inflation, increases the degree of anchoring of households' inflation expectations, and flattens the slope of the Phillips curve of the economy.