“Kernel balancing: a weighting approach for causal inference and sample adjustment”
Abstract: When making causal inferences from observational data under the assumption of no unobserved confounders, matching and weighting estimators are used to adjust the joint distribution of observed covariates for treated and control units to be the same. Similarly, investigators often have data from an observed sample, which they wish to adjust to make more similar to a target sample or known population. However, existing weighting and matching approaches for both problems have important limitations: matches are generally not exact, and standard weighting approaches ensure that the observed sample is similar to the target sample/population only on a finite set of pre-specified moments. I introduce kernel balancing, first in the context of causal inference and then as a solution to the general sample-adjustment problem. The method works by taking a high-dimensional expansion of the observed covariates, and choosing weights on the control group (or observed sample) such that it has equal means to the treated group (or target sample) on this high-order expansion of the covariates. By using kernels, it is possible to choose an expansion such that all continuous functions of the covariates are linear in that expansion. This proves very desirable, as the weighting then ensures that any unspecified but plausibly important continuous function of the covariates (such as a ratio of two variables) will automatically have the same means for the two groups as well. I provide empirical examples, and show that this method also implies that a particular estimator of the entire multivariate density of covariates is the same for the two samples at every observed location in the covariate space. An R package implementing the procedure is available from the author.
If you are interested in meeting with or joining the speaker for lunch, please send email to Seminars@ccpr.ucla.edu
12:00 pm – 1:30 pm: Seminar
1:30 pm – 2:30 pm: Proseminar Lunch: