Synthetic Control Method, Stationarity and Pointwise Statistical Inference

This article shows that, under some common assumptions, the pointwise synthetic control estimator would be unbiased if the outcome variable follows an autoregressive process. However, if such autoregressive process is nonstationary, then the variance of the pointwise estimator would be sensitive to the choice of the cutoff date (i.e. the last date of the chosen pre-treatment period if the exact start date of the treatment is uncertain), and the variance would increase over time unboundedly after the cutoff date. These two consequences of nonstationarity would create enormous challenges to the feasibility of pointwise statistical inference. Hence, I advise to take the first difference of the outcome variable to remove the unit root before using the synthetic control method when the panels are nonstationary. I apply the synthetic control method to a panel data set of housing price indexes of 33 small cities in China both before and after taking first difference to examine whether the inter-Korean rapprochement in early 2018 has increased the housing price in the Chinese border city Dandong. I show that the synthetic control estimation results after taking first difference are more robust in my empirical context. Numerically, the d'etente on the Korean Peninsula increased Dandong's housing price by around 9% in the second quarter of 2018, but there has been no significant appreciation afterwards