Identification and Inference with Many Invalid Instruments

44 Pages Posted: 22 Oct 2011 Last revised: 24 Oct 2011

See all articles by Michal Kolesár

Michal Kolesár

Princeton University

Raj Chetty

Harvard University

John Friedman

Brown University

John N. Friedman

Harvard University - Harvard Kennedy School (HKS); National Bureau of Economic Research (NBER)

Edward L. Glaeser

Harvard University - Department of Economics; Brookings Institution; National Bureau of Economic Research (NBER)

Guido W. Imbens

Stanford Graduate School of Business

Date Written: October 2011

Abstract

We analyze linear models with a single endogenous regressor in the presence of many instrumental variables. We weaken a key assumption typically made in this literature by allowing all the instruments to have direct effects on the outcome. We consider restrictions on these direct effects that allow for point identification of the effect of interest. The setup leads to new insights concerning the properties of conventional estimators, novel identification strategies, and new estimators to exploit those strategies. A key assumption underlying the main identification strategy is that the product of the direct effects of the instruments on the outcome and the effects of the instruments on the endogenous regressor has expectation zero. We argue in the context of two specific examples with a group structure that this assumption has substantive content.

Suggested Citation

Kolesar, Michal and Chetty, Raj and Friedman, John and Friedman, John Norton and Glaeser, Edward L. and Imbens, Guido W., Identification and Inference with Many Invalid Instruments (October 2011). NBER Working Paper No. w17519. Available at SSRN: https://ssrn.com/abstract=1947176

Michal Kolesar (Contact Author)

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

Raj Chetty

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

John Friedman

Brown University ( email )

Box 1860
Providence, RI 02912
United States

John Norton Friedman

Harvard University - Harvard Kennedy School (HKS) ( email )

79 John F. Kennedy Street
Cambridge, MA 02138
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Edward L. Glaeser

Harvard University - Department of Economics ( email )

Littauer Center
Room 315A
Cambridge, MA 02138
United States
617-496-2150 (Phone)
617-496-1722 (Fax)

Brookings Institution

1775 Massachusetts Ave. NW
Washington, DC 20036-2188
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Guido W. Imbens

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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