Causal Inference Using Multiple Regressions

Richard J. Butler, Matthew J. Butler and Barbara L. Wilson

Chapter 5 in Advanced Statistics for Health Research, 2023, pp 83-109 from World Scientific Publishing Co. Pte. Ltd.

Abstract: In Chapter 3, we found that the OLS coefficients were ratios of particular covariances to variances. Variances are always positive. Hence, a coefficient, β^j generally has the same sign as the simple covariance between the associated regressor xj and y, and always has the same sign as the covariance between that part of xj unassociated with other xks and y. In Chapter 4, we found that OLS estimators could not reflect causal impacts unless E(μ|X) = 0 (assumption 3 held), which further implied that the error term was uncorrelated with the right-hand side regressors (or anything that should have been included in the model). We stress these two things in this chapter: first, a covariance (or correlation) does not indicate causality, and second, that causal estimates require that the treatment is either randomly assigned or can be treated “as if” it was randomly assigned.

Keywords: Nursing; Physician; Healthcare; Public Health; Regression; Orthogonal Projection; Geometric View of Causal Inference; 2SLS; Two-Stage Least Squares; Instrumental Variables; Probits; Logits; Proportional Hazards; Cox Regressions; Quantile Regression; Random Forest Regression; Randomization; Matching; Propensity-Score; Differences-in-Differences; Regression Discontinuity; Fixed Effects; R; SAS; STATA; Research Examples; Empirical Rule; Applied Statistics; Confidence Intervals; VIF; Standard Beta; Histograms; Scatterplots; Regression Gini Index; COVID-19; Gender Wage Differentials; LASSO; Area Under The Curve; AUC; ROC; Decision Trees; Maximum Likelihood; GMM; Data Generating Process; Split Sample Instrumental Variables; Local Average Treatment Effects (LATE); Data Visualization; Omitted Variable Bias; Simultaneous Equations; Measurement Error; Supervised Machine Learning; Panel Data; RGI; Health Professionals (search for similar items in EconPapers)
JEL-codes: C1 I11 I15 (search for similar items in EconPapers)
Date: 2023
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