NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Average Causal Response with Variable Treatment Intensity

Joshua D. Angrist, Guido W. Imbens

NBER Technical Working Paper No. 127
Issued in June 1995
NBER Program(s):   LS

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.

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Document Object Identifier (DOI): 10.3386/t0127

Published: Journal of the American Statistical Association, vol. 90, no. 430, pp. 431-442, (June 1995).

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