The schooling model is based on the idea that education increases a worker’s productiv- ity and that this increase in productivity raises wages. An alternative argument is that education need not increase the worker’s productivity at all, but that “sheepskin” levels of educational attainment (such as a high school or college diploma) signal a worker’s quali- fications to potential employers.29 In this view, education increases earnings not because it increases productivity, but because it certifies that the worker is cut out for “smart” work. Education can play this signaling role only when it is difficult for potential employers to observe the worker’s ability directly. If the employer could determine cheaply whether the worker is qualified for the job, the firm would not have to rely on third-party certifications.
To illustrate how workers decide how much schooling to get when education plays only a signaling role, let’s work through a simple numerical example. Suppose there are two types of workers in the labor market, low-productivity workers and high-productivity work- ers, and that the distribution of productivity in the population is given by