What do We Gain? Combining Propensity Score Methods and Multilevel Modeling

The fundamental problem of causal inference is that an individual cannot be simultaneously observed in both the treatment and control states (Holland 1986). Propensity score methods that compare the treatment and control groups by discarding the unmatched units are now widely used to deal with this problem. Propensity score matching works well when using individual level data (persons, countries, counties, etc.); however, when using data that have a multilevel structure, such as time-series-cross-sectional (TSCS) data we need to combine propensity score matching procedures with multilevel modeling in order to take into account the unique structure of the data. In this paper we conduct Monte Carlo simulations with 36 different scenarios to test the performance of the two combined methods. The result shows that combining propensity score methods with multilevel modeling yields less biased and more efficient estimates. Two empirical case studies that reexamine the relationship between democratization and development and democracy and militarized interstate disputes also show the advantage of combining these two methods