统计与数据科学学院知识库

合成控制法通过构建一个合成控制模型来估计干预组在未干预状态下的潜 在结果，比较干预组与控制组之间的干预效应差异，从而评估干预措施或政策变 化的因果效应。该方法通过对控制组样本单元进行加权平均或适当地线性组合产 生一个合成的控制组，解决了基于反事实结果因果效应分析中的大样本限制条 件。但合成控制组的过程中，常见加权方法不同时期采用权重不变，而由于研究 时期的拉长，各单元在不同时期的影响程度发生变化，单元的合成权重也应相应 改变才更符合实践情况。

首先，本文将控制组样本单元合成权重看作随时间变化的函数，根据预干预 期间干预单元潜在结果观测值与合成控制组潜在结果加权值均方误差最小确认 预干预期的时变合成权重矩阵。该方法可以不受时间期数的限制，在研究期每一 个时间节点上都能找到最接近干预单元的合成控制单元，极大地降低了干预单元 潜在反事实结果的估计误差，提高了因果效应分析结果的准确性。

其次，考虑到合成控制法一般应用于面板数据，政策干预存在时间上的滞后 效应，本文提出一种组合的灰色预测模型，组合全信息 GM (1,1) 、新信息 GM (1,1) 和新陈代谢 GM (1,1) 模型，将预干预期时序数据按照 3:1 分为训练集和验证集， 根据验证集模型误差最小自动选择最优方法来预测合成控制单元在干预期的时 变权重，经验证本文所提出的方法更加稳健有效。

最后，应用该方法对我国碳排放权交易试点政策的效果评价进行实证分析。 基于 2005 年至 2019 年的各省级行政区年度面板数据，根据时变合成组和试点地 区碳排放强度差值，判断碳排放权交易是否有效抑制了该地区二氧化碳排放。

结果表明，本文提出的方法更适合处理面板数据的时间趋势，拥有更小的合 成误差及更宽泛的应用场景，并且保持了防外推优势。应用该方法找到的合成控 制组与干预单元在未被干预时潜在结果基本重合，模型预测结果通过安慰剂检验 证明其更加精确。

Synthetic control method approach evaluates the causal effect of the intervention or policy change by constructing a synthetic control model to estimate the potential outcome of the intervention group in the non-intervention state and comparing the difference in the intervention effect between the intervention group and the control group. This method solves the large sample constraints in the causal effect analysis based on counterfactual results by weighted average or appropriate linear combination of control group sample units to produce a composite control group. However, in the process of synthesizing the control group, the weight of the common weighting method remains unchanged in different periods. Due to the extension of the research period, the influence degree of each unit changes in different periods, and the synthetic weight of the unit should also change accordingly to be more in line with the practice.

First of all, the synthetic weight of sample units in the control group is regarded as a function of time change, and the time-varying synthetic weight matrix of the pre-intervention period is confirmed according to the minimum mean square error of the observed value of the potential outcome of the intervention unit during the pre-intervention period and the weighted value of the potential outcome of the synthetic control group. This method is not limited by the number of time periods, and can find the synthesis control unit closest to the intervention unit at every time node in the study period, which greatly reduces the estimation error of the potential counterfactual results of the intervention unit and improves the accuracy of the causal effect analysis results.

Secondly, considering that synthetic control method is generally applied to panel data and policy intervention has time lag effect, this paper proposes a combined gray prediction model, which combines full information, new information and metabolic model, and divides the time series data of pre-intervention period into training set and validation set according to 3:1. According to the minimum model error of the verification set, the optimal method is automatically selected to predict the time-varying weight of the synthetic control unit in the intervention period, and the proposed method is more robust and effective.

Finally, appling this method to analyze and evaluate the effect of China's carbon emission trading pilot policy. Based on the annual panel data of each provincial administrative region from 2005 to 2019, the difference between the time-varying composite group and the carbon emission intensity of the pilot region is used to determine whether carbon emission trading has effectively suppressed the carbon dioxide emissions of the region.

The results show that the time-varying weight synthesis control method is more suitable for processing the time trend of panel data, has smaller synthesis error and wider application scenarios, and maintains the advantage of anti-extrapolation. The potential results of the synthetic control group found by this method were basically identical with those of the intervention unit without intervention, and the prediction results of the model were proved to be more accurate by placebo test.