My research topic is: The impact of remittances on household welfare in Kyrgyzstan. I have two panel datasets for the years 2013 and 2016, (the data on migration and remittance receiving is included). The welfare of families is measured through consumer and productive asset indices.
I face the problem of choosing an appropriate method for empirical analysis. According to my adviser, the best solution is propensity score matching (PSM). Moreover, he suggested to consider more than one year to see a dynamics in how much families are better off from receiving remittances or vice a versa.
However, according to what I have already read about the PSM, most researches apply it only to one year, not two or more. I am confused how to use them for the purpose of my research and this specific method of analysis.
Most studies use PSM before and after an intervention. Treatment and control are matched based on PSM score computed out of observable indicators that show similarities between the case and control. PSM can be used for projects older than 2 years (see Impact evaluation in Practice by World Bank pdf, however, its application should be done at the inception of a project. In your case, if remittance to families was the intervention, PSM should be calculated based on 2013 data, then the treatment and finally an evaluation/comparison between 2013 and 2016. In this case, was PSM in part of the impact evaluation design, if not I would be sceptical not to use it because; you make a big assumption of assuming there was no contamination of the control which in this case you don't know. An alternative would be mixing PSM with DiD (difference-in-difference) but be sure to read the study design of how data was collected and overall experiment designed
PSM is a preparation step for outcome analysis. It matches groups on covariates. So after matching, you can then use whichever outcome model is suitable to answer your research question. If you are using panel data, then use a method that is suitable. You need to distinguish PSM from whatever outcome model you (or your mentor) wants to use.