Intertemporal Statistical Matching for Causal Inference in the Context of Multivariate Time-Series Data

This paper develops an intertemporal statistical matching (SM) approach for causal inference in the context of multivariate time-series data. While SM models have been developed and implemented exclusively for the matching of cross-sectional units (or observations from different cross-sectional time series, holding constant a same temporal unit), this paper shows that, under specific impact identification conditions, SM can be also applied for estimating causal inference by means of matching across different temporal units, holding constant a same cross-sectional time series. We apply our inter-temporal SM model, with propensity score (PS) and Mahalanobis-distance (MAHD) specifications, to the data collected from a large number of air-pollution-measurement stations in Northern Italy in a period before and during the stringent national covid-19 lockdown of March–May 2020. The estimated causal effects from the PS and MAHD matching are then compared to the results from a random forest regression model, with a discussion on the advantages of our intertemporal SM approach. The findings from our empirical application are significant for informing on the air-quality improvements that can be expected from future measures aimed at drastically reducing fossil-fuel emission in areas with high concentration of air pollutants.