Real rigidities can help to generate persistent effects of monetary policy shocks. We analyse an industry equilibrium model with two types of real rigidities: a ‘micro’ real rigidity from a kinked demand curve, and a ‘macro’ real rigidity due to sticky intermediate prices. We estimate key model parameters using micro data from the US CPI, which features big movements in relative prices within and across sectors. The micro real rigidity necessitates large idiosyncratic shocks to productivity. The macro real rigidity does not entail such large idiosyncratic shocks, and is consistent with the volatility of sectoral TFP growth.