Any alternative method to PSM as “dimension reduction” in empirical economic study?

Question

Applied microeconomics often choose propensity score matching (PSM) to "preprocess" their dataset, making two groups (treatment and control) looking more similar. But sometimes, PSM did not so well. For example, some character has a natural trend, like urbanization in many developing countries bring new-build flat further away from city center.Naive PSM cannot improve the similarities of this variable (d2center) across different years.

More generally, if we just want to select the pair which shares the most similarity, why must we use profit or logit? We cannot even decide which dimension is the most important and should be put more weight on (can we?) In most case, it does not have any particular economic meaning. It's just a method of projection from many dimensions of character to one dimension, on which we can compare and decide the similarity.

Is there something alternative we can pick up to substitute PSM? not necessary constraint to econometric tools. Thank you.

Answer 1

There are several advanced methods built on the PS logic that might be of interest to you. One is "covariate balancing propensity scores," which use logistic regression but instead of maximum likelihood, they use GMM with covariate balance as the moment condition. In this way balance is included in the estimation procedure itself. This yields propensity scores which almost always achieve very good balance. Another is entropy balancing, which generates weights that satisfy moment conditions, where the moment conditions are user-specified statements of balance. For example, you can say you want balance on average age and after entropy balancing the groups will be nearly identical on average age. Another that you might find particularly appealing is genetic matching, which allows you to specify a matrix that contains balancing criteria and preferences of some variables over others. These three methods are the cutting edge in preprocessing and may alleviate your distaste for traditional propensity scores. All of these can be implemented in R.