【Job Talk】Nonlinear Synthetic Control and Unconfoundedness Approach
2025/01/14
研討會日期 : 2025-01-14
時間 : 10:30
主講人 : Mr. Chen Lin (林真)
地點 : Conference Room B110
主持人 : Professor Chu-An Liu
演講者簡介 : Mr. Lin is expected to receive his Ph.D. in Economics from the University of California, San Diego in 2025. His research fields are Econometrics and Applied Microeconomics. He is applying for a position of the Institute of Economics, Academia Sinica now.
演講摘要 : In this manuscript, we extend the synthetic control method to a nonlinear setting, where weights are chosen by matching both the outcome levels and their nonlinear transformations. We motivate the method by introducing a linear factor model in which the outcome level can directly depend nonlinearly on its lagged values, which we refer to as a dynamic linear factor model. In this context, we derive an error bound for estimating counterfactual potential outcomes and demonstrate that this bound can be significantly reduced by matching nonlinear transformations of the pre-treatment outcome variables. Additionally, we link the synthetic control method to the machine learning literature by reinterpreting the synthetic control method as a maximal mean discrepancy (MMD) minimization problem. The feature map therein serves as the nonlinear transformation in our proposed method. As part of our theoretical investigation, we establish a dual relationship between the synthetic control problem and an unconfoundedness problem. Specifically, we show that the asymptotic normality of synthetic control estimate, even when the number of features is increasing with respect to the sample size. We illustrate the performance of our proposed nonlinear synthetic control method in both simulation studies and an empirical example.
