Estimating Models of Supply and Demand: Instruments and Covariance Restrictions

55 Pages Posted: 28 Aug 2017 Last revised: 22 Apr 2021

See all articles by Alexander MacKay

Alexander MacKay

Harvard University - Business School (HBS)

Nathan Miller

Georgetown University - Robert Emmett McDonough School of Business

Date Written: April 21, 2021

Abstract

We consider the identification of empirical models of supply and demand. As is well known, a supply-side instrument can resolve price endogeneity in demand estimation. We show that, under common assumptions, two other approaches also yield consistent estimates of the joint model: (i) a demand-side instrument, or (ii) a covariance restriction between unobserved demand and cost shocks. The covariance restriction approach can obtain identification even the absence of instruments. Further, supply and demand assumptions alone may bound the structural parameters. We develop an estimator for the covariance restriction approach that is constructed from the output of ordinary least squares regression and performs well in small samples. We illustrate the methodology 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 (April 21, 2021). 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 - Robert Emmett McDonough School of Business ( email )

3700 O Street, NW
Washington, DC 20057
United States

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