How to Choose Donors for Individual Synthetic Control

• In Event: 20858 - Reimagining How We Measure and Model the Social World: Causation, Flows, and Artificial Intelligence

Abstract

Methods for causal inference often apply to a common panel data structure: units are observed over time periods, and some of those units experience an irreversible event at various periods. For example, some women experience a first birth while others do not. Those who give birth do so at various ages. We might ask: how does the event affect future outcomes, such as hourly wages? We show that a good answer requires careful attention to a key question of research design: who should be included in the comparison group? While the most obvious choice might seem to be those who never experience the event, we show that the comparison group should also include those who have not yet experienced the event. The reason for structuring the comparison group this way is that whether a unit is treated in the future is a post-treatment variable that should not be adjusted. With a simulation, we illustrate the bias that can arise from using the wrong comparison group. With analysis of real data on motherhood and hourly wages, we show that the choice can change estimates. Our result has implications beyond this particular example. Whenever methods such as matching or synthetic control are used to estimate the causal effects in settings with staggered treatment adoption, valid estimates require use of the correct comparison group.

Authors

• Ian Lundberg, University of California, Los Angeles

• Yaling Xu, Cornell University