Wages as Sorting Mechanisms in Competitive Markets with Asymmetric Information: A Theory of Testing

Abstract

In most exchanges of labour services, there is substantial ignorance about the ability of individual workers. As long as a firm is not paying wholly on the basis of piece work, it has an incentive to learn the ability of its applicants, and the more able workers have an incentive to sort themselves from the less able. The most common means of sorting workers is through an examination, i.e. a questionnaire or an apprenticeship programme during which performance is monitored. The cost of an examination increases with its accuracy and precision and one would seldom expect a perfectly accurate and precise test to be used by firms. One way of increasing the effectiveness of a test is to impose penalties upon workers who receive low examination scores and rewards for those who receive high scores. Those who think it is likely that they will receive a high score are most likely to apply for the examination. Thus, the firm has converted a single examination into a two-part test; those who pass receive high scores not only on the firm examination, but also on their own self-appraisal. We show that when tests (apprenticeships) are used as self-selection devices, so that in effect workers are charged an application fee, a Nash equilibrium with free entry may not exist. When an equilibrium does exist, it is characterized by a wage distribution and workers who fail the test receive a net wage below their net marginal product, while those who pass the test receive a net wage above their net marginal product. The failures subsidize the successes. The application fee paid by a job applicant is an increasing function of his perceived productivity and is greater than the real testing costs incurred by the firm. These results do not depend upon any monopoly power of workers or firms nor upon the test being costly. However, they do depend upon the test being an imprecise measure of productivity. If the test score is a sufficient statistic of productivity, a Nash equilibrium always exists; workers who pass and who fail the test receive wages equal to their respective marginal product and the fee charged for taking the test is equal to the actual cost of administering the test. By introducing informational considerations and viewing low-wage training programmes as tests, we provide a new explanation for the positive correlation between wages and seniority. This increase in wages has been attributed to on-the-job training (see