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.
Kevin Murphy's lectures in price theory inspired this work. We acknowledge funding from the Population Studies and Training Center, the Eastman Professorship, and the JP Morgan Chase Research Assistant Program at Brown University, and the Jan Wallander and Tom Hedelius Foundation (Grant P2015-0095:1). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding sources. We thank Isaiah Andrews, Steve Berry, Ray Fair, Ed Glaeser, Phil Haile, Alex MacKay, Serena Ng, Emily Oster, Sharon Oster, Michael Roberts, Chris Snyder, Elie Tamer, and seminar participants at Brown University for helpful comments. We thank our dedicated research assistants for their contributions to this project. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Jesse M. Shapiro
Shapiro has, in the past, been a paid visitor at Microsoft Research New England and a paid consultant for FutureOfCapitalism, LLC. Shapiro has been paid for writing by the New York Times.
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