Bounds on a Slope from Size Restrictions on Economic Shocks

We study the problem of learning about the slope of a linear relationship between an outcome (e.g., quantity) and an input (e.g., price) when the outcome is subject to time-varying, unobserved economic shocks. We show that restrictions on the absolute magnitude of the economic shocks are informative for the value of the slope. We argue that such restrictions are reasonable in some economic situations. We illustrate with an application to the demand and supply of food grains. We consider extensions including to the case of a nonlinear relationship.