The Synthetic Control Method for Estimating Effects of Aggregate Interventions

The Synthetic Control Method for Estimating Effects of Aggregate Interventions

Introduction:
When it comes to estimating the effects of aggregate interventions on aggregate outcomes, such as policy interventions implemented at a city, regional, or country level, researchers face various challenges. One of the main complications arises from the presence of shocks to the outcome of interest, aside from the effect of the intervention. In this article, we will explore the synthetic control method, which aims to address these challenges by creating a weighted average of units in a donor pool to approximate the characteristics of the affected unit.

The Synthetic Control Method:
The synthetic control method is based on the observation that a combination of units in the donor pool may better approximate the characteristics of the affected unit compared to any unaffected unit alone. To construct a synthetic control, we define it as a weighted average of the units in the donor pool. These weights are nonnegative and sum up to one, allowing for regression and extrapolation.

Predictors and Rescaling:
To ensure accurate estimation, we consider a set of k predictors of the outcome. These predictors can include variables such as per capita GDP, which are rescaled to correct for differences in size between units. By minimizing the weighted root mean squared error (RMSE) of the k predictors, we can select the appropriate weights for constructing the synthetic control.

Minimizing Prediction Error:
The goal of the synthetic control method is to minimize the mean squared prediction error (MSPE) of the synthetic control with respect to the potential response under the intervention. This is achieved by finding the weights that minimize the MSPE for a set of pre-intervention periods. By dividing the pre-intervention periods into an initial training period and a subsequent validation period, we can evaluate the accuracy of the synthetic control.

Actionable Advice:

1. Carefully select the predictors: When using the synthetic control method, it is crucial to choose the appropriate predictors that capture the characteristics of the affected unit. Consider variables that are relevant to the outcome of interest and can be rescaled to account for differences in size between units.

2. Validate the synthetic control: After constructing the synthetic control, it is essential to validate its accuracy. Divide the pre-intervention periods into training and validation periods and assess the performance of the synthetic control in predicting the potential response under the intervention. Adjust the weights if necessary to improve the accuracy of the synthetic control.

3. Consider the sparsity of weights: Synthetic control estimators often result in sparse weights, meaning that only a small number of units in the donor pool have significant influence on the synthetic control. Take this into account when interpreting the results and consider the geometric characteristics of the optimization problem that generates the synthetic controls.

Conclusion:
The synthetic control method provides a valuable approach for estimating the effects of aggregate interventions on aggregate outcomes. By constructing a synthetic control as a weighted average of units in a donor pool, researchers can approximate the characteristics of the affected unit and account for the presence of shocks to the outcome of interest. By carefully selecting predictors, validating the synthetic control, and considering the sparsity of weights, researchers can improve the accuracy and reliability of the estimates.