TY  - JOUR
AU  - Angrist,Joshua D.
AU  - Imbens,Guido W.
TI  - Average Causal Response with Variable Treatment Intensity
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 127
PY  - 1995
Y2  - June 1995
UR  - http://www.nber.org/papers/t0127
L1  - http://www.nber.org/papers/t0127.pdf
N1  - Author contact info:
Joshua Angrist
Department of Economics
MIT, E52-353
50 Memorial Drive
Cambridge, MA  02142-1347
Tel: 617/253-8909
Fax: 617/253-1330
E-Mail: angrist@mit.edu

Guido Imbens
Department of Economics
Littauer Center
Harvard University
1805 Cambridge Street
Cambridge, MA 02138
Tel: 617/384-7485
Fax: 617/495-7730
E-Mail: imbens@fas.harvard.edu
AB  - 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.
ER  -