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.