Information-Gathering and Producing: Complements or Substitutes?
68 Pages Posted: 30 Oct 2014
Date Written: October 28, 2014
We aim at some simple theoretical underpinnings for a complex empirical question studied by labor economists and others: does Information-technology improvement lead to occupational shifts -- toward "information workers" and away from other occupations -- and to changes in the productivity of non-information workers? In our simple model there is a Producer, whose payoff depends on a production quantity and an unknown state of the world, and an Information-gatherer (IG) who expends effort to learn more about the unknown state. The IG's effort yields a signal which is conveyed to the Producer. The Producer uses the signal to revise prior beliefs about the state and uses the posterior to make an expected-payoff-maximizing quantity choice. Our central aim is to find conditions on the IG and the Producer under which more IG effort leads to a larger average production quantity (Complements) and conditions under which it leads to a smaller average quantity (Substitutes). For each of the IG's possible efforts there is an information structure, which specifies a signal distribution for every state and (for a given prior) a posterior state distribution for every signal. We start by considering various Blackwell IGs. For such an IG, we can define an effort measure on the possible structures so that more effort is more useful to every Producer, no matter what the prior and the payoff function may be. The Blackwell theorems state that one structure has more effort than another if and only if the expected value (over the possible signals) of any convex function on the posteriors is not less for the higher-effort structure. So we have Complements (Substitutes) if the Producer's best quantity is indeed a convex (concave) function of the posteriors. That gives us Complements/Substitutes results for a variety of Producers who use Blackwell IGs. We then turn to non-Blackwell IGs, where the Blackwell theorems cannot be used and special techniques are needed to obtain Complements/Substitutes results.
Keywords: Information technology and productivity; Blackwell Theorem; Garbling
JEL Classification: C44; D24; L11
Suggested Citation: Suggested Citation