Optimal Costly Information Gathering in Public Service Provision

Abstract

Imperfect information regarding the true needs of recipients is a common problem for governmental or not-for-profit service providers. This can lead to potentially dangerous under-provision or wasteful over-provision of services. We provide a method for optimally improving a service provider’s information regarding true client need through costly information gathering. Our contribution is to allow providers to endogenously and optimally choose the intensity of information gathering. Providers do so by specifying the level of correlation between observed and true recipient need, subject to an arbitrary cost function over the specified correlation. We derive the conditions that characterize the choice of optimal correlation for providers with quadratic utility. Using a realistic exponential correlation cost function, we show that there exists a critical value of true client need variance below which it is never optimal to engage in information gathering. Further, for true client variance above this critical level the optimal correlation will always exceed 0.5. Our findings have a wide range of policy implications in areas such as health care, social wellfare and even counter-terroism.