01835cam a22002417 4500001000600000003000500006005001700011008004100028100002300069245012400092260006600216490005100282500001500333520085400348530006101202538007201263538003601335700002101371710004201392830008601434856003701520856003601557t0127NBER20180527074528.0180527s1995 mau||||fs|||| 000 0 eng d1 aAngrist, Joshua D.10aAverage Causal Response with Variable Treatment Intensityh[electronic resource] /cJoshua D. Angrist, Guido W. Imbens. aCambridge, Mass.bNational Bureau of Economic Researchc1995.1 aNBER technical working paper seriesvno. t0127 aJune 1995.3 aIn 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.1 aImbens, Guido W.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0127.4 uhttp://www.nber.org/papers/t012741uhttp://dx.doi.org/10.3386/t0127