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The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish

Posted: 8 Nov 2000  

Joshua D. Angrist

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER); IZA Institute of Labor Economics

Kathryn Graddy

Brandeis University - Department of Economics

Guido W. Imbens

Stanford Graduate School of Business

Abstract

In markets where prices are determined by the intersection of supply and demand curves, standard identification results require the presence of instruments that shift one curve but not the other. These results are typically presented in the context of linear models with fixed coefficients and additive residuals. The first contribution of this paper is an investigation of the consequences of relaxing both the linearity and the additivity assumption for the interpretation of linear instrumental variables estimators. Without these assumptions, the standard linear instrumental variables estimator identifies a weighted average of the derivative of the behavioural relationship of interest. A second contribution is the formulation of critical identifying assumptions in terms of demand and supply at different prices and instruments, rather than in terms of functional-form specific residuals. Our approach to the simultaneous equations problem and the average-derivative interpretation of instrumental variables estimates is illustrated by estimating the demand for fresh whiting at the Fulton fish market. Strong and credible instruments for identification of this demand function are available in the form of weather conditions at sea.

Suggested Citation

Angrist, Joshua D. and Graddy, Kathryn and Imbens, Guido W., The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish. The Review of Economic Studies, Vol. 67, Issue 3, July 2000. Available at SSRN: https://ssrn.com/abstract=239294

Joshua Angrist (Contact Author)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
E52-353
Cambridge, MA 02142
United States
617-253-8909 (Phone)
617-253-1330 (Fax)

Kathryn Graddy

Brandeis University - Department of Economics ( email )

415 South Street MS 021
Waltham, MA 02453-2728
United States
781-736-8616 (Phone)
781-736-2269 (Fax)

HOME PAGE: http://people.brandeis.edu/~kgraddy/

Guido W. Imbens

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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