2-STAGE LEAST-SQUARES ESTIMATION OF AVERAGE CAUSAL EFFECTS IN MODELS WITH VARIABLE TREATMENT INTENSITY

Two-stage least squares (TSLS) is widely used in econometrics to estim ate parameters in systems of linear simultaneous equations and to solv e problems of omitted-variables bias in single-equation estimation. We show here that TSLS can also be used to estimate the average causal e ffect of variable treatments such as drug dosage, hours of exam prepar ation, cigarette smoking, and years of schooling. The average causal e ffect in which we are interested is a conditional expectation of the d ifference between the outcomes of the treated and what these outcomes would have been in the absence of treatment. Given mild regularity ass umptions, the probability limit of TSLS is a weighted average of per-u nit average causal effects along the length of an appropriately define d causal response function. The weighting function is illustrated in a n empirical example based on the relationship between schooling and ea rnings.