Productivity Beliefs and Efficiency in Science

We develop a method to estimate producers’ productivity beliefs in settings where output quantities and input prices are unobservable, and we use it to evaluate allocative efficiency in the market for science. Our model of researchers’ labor supply shows that their willingness to pay for their two key inputs, funding and time, reveals their underlying productivity beliefs. We estimate the model’s parameters using data from a nationally representative survey of research-active professors from all major fields of science. We find that the distribution of research productivity is highly skewed. Using these estimates, we assess the market’s allocative efficiency by comparing actual input allocations to optimal allocations given various objectives. Overall, the market for science is moderately efficient at maximizing output and researchers’ utility: actual input levels are positively correlated with the optimal levels implied by the model. However, the wedge between researchers’ actual and optimal input levels is often significant and difficult to predict. Our estimates imply that total budgets would need to increase by roughly 40% under actual allocations in order to achieve the same growth in scientific output that we predict under alternative allocations of the current budget. Scaling to the population level, this equates to billions of dollars in funding — there are substantial gains from developing new ways of identifying and supporting productive scientists.