Directed Search, Nominal Rigidities and Markup Cyclicality

New Keynesian models with sticky prices built on the Dixit-Stiglitz framework must have countercyclical mark-ups conditional on monetary shocks, which is inconsistent with empirical evidence based on labor share data. We pose a directed search style shopping friction in goods market to model firms' price setting, on top of Dixit-Stiglitz. Our theory allows for procyclical mark-ups conditional on monetary shocks, without sacrificing the performance of the model along other dimensions. We prove this in a static model, and test it in an estimated medium scale DSGE model. Unlike the literature that criticizes the use of labor share, we provide a complementary view that New Keynesian models can actually be compatible with procyclical mark-ups conditional on monetary shocks, if there is goods market shopping friction.