Optimal Sequential Search with Recall

Abstract

We introduce a simple new general model of nonstationary sequential search with recall. It fits realistic economic setting with partially informed search, like web search. Payoffs are the sum of a random known factor and a hidden factor, learned after inspection. Ours is the ex ante version of Weitzman (1979) Pandora’s box problem, suitable for estimation, with known factors unseen by the modeler.

1. We resolve a long open important question in search: which distributional changes increase search duration? The general answer is more dispersed payoffs.

2. We generally prove that the modeler thinks search intensifies over time: the chance one exercises a current option, recalls a prior one, or quits rises. In a first, we fully characterize recall, finding that earlier options are recalled more often.

3. We prove that stationary search can terribly approximate search with finitely many options: If the known factor distribution lacks a thin tail (like the exponential), the recall chance is boundedly positive in the infinite option limit!

4. We find that search lasts longer with more options: If worker applicant pools of firms increase, vacancy duration increases, as search grows more ambitious.

Keywords: sequential and nonstationary search, duration, logconcavity, dispersion

JEL Classification: D81, D83