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.
Highlights
Most commercial firms are motivated to some degree by profit; government providers and NGO’s, on the other hand, do not generally subscribe to a profit motive
We provide a method for optimally improving a service provider’s information regarding true client need through costly information gathering
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
Summary
Most commercial firms are motivated to some degree by profit; government providers and NGO’s, on the other hand, do not generally subscribe to a profit motive. The model presented in this paper explictly links the quality of information to the cost of obtaining that information, in a setting where the service provider can choose the quality of information (but at a cost) This formulation allows us to characterise the optimal level of costly information gathering, in, for instance, a health care setting. Our paper takes a different approach by modeling noise (or signal quality) via the correlation parameter between the true signal X and the observed signal Y.1. The solution obtained provides insights into the link between the quality of information obtained and signal extraction costs This is done by linking information cost to the correlation between the true distribution of client need and the observed distribution of client need.
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