Causal inference using regression on the treatment variable

CHAPTER 9 Causal inference using regression on thetreatment Causal inference and predictive comparisonsSo far, we have been interpreting regressionspredictively: given the values of severalinputs, the fitted model allows us to predicty, considering thendata points as asimple random sample from a hypothetical infinite superpopulation or probabilitydistribution. Then we can make comparisons across differentcombinations of valuesfor these chapter and the next considercausal inference , which concerns whatwouldhappento an outcomeyas a result of a hypothesized treatment or a regression framework, the treatment can be written as a variableT:1Ti={1 if unitireceives the treatment 0 if unitireceives the control, or, for a continuous treatment ,Ti= level of the treatment assigned to the usual regression context, predictive inference relates to comparisonsbetweenunits, whereas Causal inference addresses comparisons of different treatments ifapplied to thesameunits.}

Formula for omitted variable bias We can quantify the bias incurred by excluding a confounding covariate in the context where a simple linear regression model is appropriate and there is only one confounding covariate. First define the “correct” specification as yi = β0 +β1Ti +β2xi + i (9.1)

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  Variable, Bias, Omitted, Omitted variable bias

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