Estimating Models of Supply and Demand: Instruments and Covariance Restrictions

55 Pages Posted: 28 Aug 2017 Last revised: 10 Feb 2023

See all articles by Alexander MacKay

Alexander MacKay

Harvard University - Business School (HBS)

Nathan Miller

Georgetown University - McDonough School of Business

Date Written: February 1, 2023

Abstract

We consider the identification of empirical models of supply and demand with imperfect competition. We show that a covariance restriction on unobserved demand and cost shocks resolves endogeneity and identifies the price parameter. We demonstrate how to employ this approach in estimation, and we provide a comparison to instrumental variables approaches. Our formal results also indicate how weaker assumptions about the covariance term can be used to construct bounds on the price parameter. We illustrate the covariance restriction approach with applications to ready-to-eat cereal, cement, and airlines.

Keywords: Identification, Demand Estimation, Covariance Restrictions, Instrumental Variables

JEL Classification: C13, C36, D12, D22, D40, L10

Suggested Citation

MacKay, Alexander and Miller, Nathan, Estimating Models of Supply and Demand: Instruments and Covariance Restrictions (February 1, 2023). Harvard Business School Strategy Unit Working Paper No. 19-051, Available at SSRN: https://ssrn.com/abstract=3025845 or http://dx.doi.org/10.2139/ssrn.3025845

Alexander MacKay

Harvard University - Business School (HBS) ( email )

Soldiers Field Road
Boston, MA 02163
United States

HOME PAGE: http://alexandermackay.org/

Nathan Miller (Contact Author)

Georgetown University - McDonough School of Business ( email )

3700 O Street, NW
Washington, DC 20057
United States

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