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Do You Know that I Know that You Know…? Higher-Order Beliefs in Survey Data*
The Quarterly Journal of Economics  (IF11.375),  Pub Date : 2021-01-30, DOI: 10.1093/qje/qjab005
Coibion O, Gorodnichenko Y, Kumar S, et al.

Abstract
We implement a new survey of firms, focusing on their higher-order macroeconomic expectations. The survey provides a novel set of stylized facts regarding the relationship between first-order and higher-order expectations of economic agents, including how they adjust their beliefs in response to a variety of information treatments. We show how these facts can be used to calibrate key parameters of noisy-information models with infinite regress as well as to test predictions made by this class of models. We also consider a range of extensions to the basic noisy-information model that can potentially better reconcile theory and empirics. Although some extensions like level-k thinking are unsuccessful, incorporating heterogeneous long-run priors can address the empirical shortcomings of the basic noisy-information model.