Temporal Aggregation for the Synthetic Control Method

The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit with panel data. Two challenges arise with higher frequency data (e.g., monthly versus yearly): (1) achieving excellent pre-treatment fit is typically more challenging; and (2) overfitting to noise is more likely. Aggregating data over time can mitigate these problems but can also destroy important signal. In this paper, we bound the bias for SCM with disaggregated and aggregated outcomes and give conditions under which aggregating tightens the bounds. We then propose finding weights that balance both disaggregated and aggregated series.