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 identifying power of supply-side assumptions in the estimation of models of supply and demand. Pairing supply with demand expands the set of restrictions that identify a general class of models. As is well known, the problem of price endogeneity is resolved with an instrument that shifts supply. We show that, even with imperfect competition, an instrument that shifts demand also obtains identification. Our analysis establishes a fundamental link between the (endogenous) price coefficient and the covariance of unobservable cost and demand shocks. Thus, a covariance restriction on unobserved shocks can achieve identification, even in the absence of instruments. Further, it can be possible to bound the structural parameters using the supply and demand assumptions alone. We develop an estimator based on the covariance restriction that is efficiently estimated by 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;

Language: English

Format: Print

59 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 May 2019.)

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Estimating Models of Supply and Demand: Instruments and Covariance Restrictions

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