Uncertainty Shocks, Information Acquisition and Endogenous Productivity Dispersion

This paper provides a simple model of information acquisition when individuals observe endogenous public signals that reveal when low-probability events occur and can acquire private information about the state-of-the-world. Private signals about a given event are more costly to obtain as the likelihood of that event decreases. The endogenous public signal is such that signals of low-probability events also result in higher uncertainty for those who do not acquire private information. As an application, the paper models the problem of firms that much choose a production method that is appropriate for the state-of-the-world along with a capital stock. Poor choices of production methods result in low realized productivity. An outcome is that in states of high uncertainty, fewer firms acquire information causing high variance in the choice of production methods but similar choice of capital stocks. Ex post, firms with similar capital stocks have very different realized productivity. When firms interact with each other, this variance in realized productivity reduces the incentive for firms to acquire information. In contrast, in low uncertainty states, there is a unique, optimal production method that is chosen by the uninformed and few firms acquire information because the value of reducing uncertainty is low. The result is low ex post dispersion in productivity across firms.