Estimating Models of Supply and Demand: Instruments and Covariance Restrictions

Alexander  MacKay; Nathan H. Miller

Working Paper | HBS Working Paper Series | 2019

Estimating Models of Supply and Demand: Instruments and Covariance Restrictions

by Alexander MacKay and Nathan H. Miller

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: demand estimation; identification; endogeneity bias; covariance restrictions; ordinary least squares; instrumental variables;

Language: English

Format: Print

58 pages

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Citation:

MacKay, Alexander, and Nathan H. Miller. "Estimating Models of Supply and Demand: Instruments and Covariance Restrictions." Harvard Business School Working Paper, No. 19-051, October 2018. (Revised October 2019. Direct download.)

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Estimating Models of Supply and Demand: Instruments and Covariance Restrictions

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