Topics in Causal Inference
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CitationKolokotrones, Thomas. 2020. Topics in Causal Inference. Doctoral dissertation, Harvard T.H. Chan School of Public Health.
AbstractMethods for drawing causal inferences from observational data play a central role in fields such as the social sciences and epidemiology, in which performing experiments may be difficult or impossible for technical, practical, or ethical reasons. Though regression methods remain the most popular, many other techniques are also widely used. We focus on two of them, matching and instrumental variables.
The matching literature is fiercely divided over the optimal method for matching, with the majority of investigators advocating for either direct covariate or propensity score matching. We compare the performance of these two techniques in estimating the average effect of treatment on the treated using a variety of metrics including bias, variance, and model dependence, a measure of a bias corrected matching estimator's sensitivity to the regression model used. We find that neither method dominates the other and that which one is preferred will depend on the distribution of the covariates, the structure of the true and regression models, and the numbers of treated and untreated subjects, as well upon how many covariates are actually matched.
We also explore the use of instrumental variables when the exclusion restriction is violated, focusing particularly on the use of Egger Regression to analyze Mendelian Randomization studies. Though this estimator is widely used, it has not been rigorously analyzed. We do so here, giving conditions under which it is consistent and providing its limit under other circumstances. We also show that, when only finitely many instruments are used, it is biased, but asymptotically normal, and compute its properties in the setting in which all quantities except the causal effect are known, which provides a bound on the rate of convergence of the standard estimator, in which these quantities are estimated by linear regression.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:42676021