For causal inferences, matching methods have become more and more attracting aiming to reduce the imbalance of the treated and control groups. The basic idea in matching methods is to look for one or more observations in the control group for treated observations, based on a set of controls variables. While controlling for the changing factors, we can estimate the average treatment effects (ATE) and ATE on treated (ATT) directly. Generally speaking, the most widely used matching method is the propensity score matching, which is proposed by Paul Rosenbaum and Donald Rubin in 1983. To improve the accuracy of matching process, a variety of methods were developed from basic one to one match based on the propensity score, to matching with the nearest neighbor, radius and kernel, to the most recent machine learning matching methods like lasso, support vector machine. Each method has its pros and cons.
Details: Matching Methods.