I recently came across this paper by Sibley et al. in which propensity score matching (PSM) was applied to examine the effects of COVID-19 lockdowns on well-being and government attitudes in New Zealand. Specifically, they treat COVID lockdown as the treatment and use PSM "to match the 1,003 post-lockdown (March 26 to April 12, 2020) respondents with 1,003 from the pool of 23,351 pre-lockdown 'controls'".
Is this a justified use of propensity score matching? I've am perplexed by this specific application. I have not been able to determine exactly why this may (or may not) be an inappropriate application.
The primary issue I see with the approach is that everyone in the 'control' eventually received the treatment, with the treatment being not just "non-random" but entirely deterministic. The best predictor of being in the treatment (i.e., COVID lockdowns) group is simply being in the dataset at all. In other words, because COVID lockdown is exogenous, none of the individual differences captured in the study should be related in any way to the treatment. In turn, I struggle to see how the resulting propensity scores would comprise a valid matching criteria. Is this the only issue?
My assumption is that other matching methods may be far more appropriate here, but I am not entirely sure what these would be or mathematically why. In this example, I would have assumed a fixed-effects regression approach would have likely led to similar conclusions (albeit with likely increased model complexity).
Sibley, C. G., Greaves, L. M., Satherley, N., Wilson, M. S., Overall, N. C., Lee, C. H. J., Milojev, P., Bulbulia, J., Osborne, D., Milfont, T. L., Houkamau, C. A., Duck, I. M., Vickers-Jones, R., & Barlow, F. K. (2020). Effects of the COVID-19 pandemic and nationwide lockdown on trust, attitudes toward government, and well-being. The American Psychologist, 75(5), 618–630. https://doi.org/10.1037/amp0000662