Average Causal Response with Variable Treatment Intensity

40 Pages Posted: 29 Dec 2006

See all articles by Joshua D. Angrist

Joshua D. Angrist

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

Guido W. Imbens

Stanford Graduate School of Business

Date Written: June 1995

Abstract

In evaluation research, an average causal effect is usually defined as the expected difference between the outcomes of the treated, and what these outcomes would have been in the absence of treatment. This definition of causal effects makes sense for binary treatments only. In this paper, we extend the definition of average causal effects to the case of variable treatments such as drug dosage, hours of exam preparation, cigarette smoking, and years of schooling. We show that given mild regularity assumptions, instrumental variables independence assumptions identify a weighted average of per-unit causal effects along the length of an appropriately defined causal response function. Conventional instrumental variables and Two-Stage Least Squares procedures can be interpreted as estimating the average causal response to a variable treatment.

Suggested Citation

Angrist, Joshua and Imbens, Guido W., Average Causal Response with Variable Treatment Intensity (June 1995). NBER Working Paper No. t0127. Available at SSRN: https://ssrn.com/abstract=573119

Joshua Angrist (Contact Author)

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

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National Bureau of Economic Research (NBER)

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Guido W. Imbens

Stanford Graduate School of Business ( email )

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