Another interesting paper that supports the New Keynesian sticky price assumption:
Are Sticky Prices Costly? Evidence From The Stock Market, by Yuriy Gorodnichenko and and Michael Weber, NBER: Abstract We show that after monetary policy announcements, the conditional volatility of stock market returns rises more for rms 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 are qualitatively and, under plausible calibrations, quantitatively consistent with New Keynesian macroeconomic models where firms have heterogeneous price stickiness. Since our framework 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.