Treatment effects without multicollinearity? Temporal order and the Gram-Schmidt process in causal inference

Abstract

This paper incorporates information about the temporal order of regressors to estimate orthogonal and economically interpretable regression coefficients. We establish new finite sample properties for the Gram-Schmidt orthogonalization process. Coefficients are unbiased and stable with lower standard errors than those from Ordinary Least Squares. We provide conditions under which coefficients represent average total treatment effects on the treated and extend the model to groups of ordered and simultaneous regressors. Finally, we reanalyze two studies that controlled for temporally ordered and collinear characteristics, including race, education, and income. The new approach expands Bohren et al.'s decomposition of systemic discrimination into channel-specific effects and improves significance levels.