There has been a debate in macroeconomics over whether sticky prices -- the key feature of New Keynesian models -- are actually as sticky as assumed, and how large the costs associated with price stickiness actually are. This paper finds "evidence that sticky prices are indeed costly":
Are Sticky Prices Costly? Evidence From The Stock Market, by Yuriy Gorodnichenko and Michael Weber, NBER Working Paper No. 18860, February 2013 [open link]: We propose a simple framework to assess the costs of nominal price adjustment using stock market returns. We document that, after monetary policy announcements, the conditional volatility rises more for firms with stickier prices than for firms with more flexible prices. This differential reaction is economically large as well as strikingly robust to a broad array of checks. These results suggest that menu costs---broadly defined to include physical costs of price adjustment, informational frictions, etc.---are an important factor for nominal price rigidity. We also show that our empirical results qualitatively and, under plausible calibrations, quantitatively consistent with New Keynesian macroeconomic models where firms have heterogeneous price stickiness. Since our approach is valid for a wide variety of theoretical models and frictions preventing firms from price adjustment, we provide "model-free" evidence that sticky prices are indeed costly.