Can you provide a reference regarding a revealed preference test(s) of rational inattention models, as proposed by Sims, ergo, using a mutual information measure as the cost of putting attention. And if possible can you briefly explained it. A link that explains the model is given here http://sims.princeton.edu/yftp/Gerzensee/info.pdf
Empirical Evidence on rational inattention:
-Title: Attention Discrimination: Theory and Field Experiments with Monitoring Information Acquisition, Authors: Vojtěch Bartoš, Michal Bauer, Julie Chytilová, and Filip Matějka. Source: IZA Discussion Paper No. 8058.
-Title: What Can Survey Forecasts Tell Us about Information Rigidities? Authors: Olivier Coibion and Yuriy Gorodnichenko. Source: Journal of Political Economy, Vol. 120, No. 1 (February 2012), pp. 116-159
-Title: A Rational Theory of Mutual Funds’ Attention Allocation, Authors: Marcin Kacperczyk, Stijn Van Nieuwerburgh, Laura Veldkamp. Source: NYU Working Paper No. 2451/28347 June 5, 2014
The following two papers by Andrew Caplin and Mark Dean focus on tests of rational inattention in a lab setting (i.e. with data one could in principle find the field). As BB King said, I won't do it any justice summarizing myself. The second is about Shannon entropy specifically.