使用無效工具進行工具變數回歸時的雙重機器學習方法：封城是否有效？

透過考慮封城的內生性，本研究了封城對COVID-19在中國傳播的影響。我們發現封城顯著降低了中國城市每日新增確診病例的增長率。更重要的是，如此顯著的影響考慮到了無效工具的控制。現有關於COVID-19傳播的文獻研究使用兩週之前的天氣變量作為工具變數。但是，無症狀感染者可能會導致以天氣做為工具變數無效。我們利用Chernozhukov等人(2018)提出的雙重機器學習方法(Double machine learning)來進行估計。具體來說，本文將Kolesár(2015)等人提出的條件改寫為Neyman 正交條件，透過 Lasso 和 post-Lasso 估計干擾參數，並通過交叉驗證的兩階段最小平方法估計關注的參數。結果發現，封城使每日新增確診病例的成長率顯著降低了14%，而如果不考慮內生性，效果會被低估，約6%。

關鍵字

COVID-19 ；雙重機器學習方法；無效工具變數； Lasso

並列摘要

By taking into account the endogeneity of lockdowns, we examine the effect of lockdowns on the spread of COVID-19 in China. We find that lockdowns significantly reduce the rate of the increase in daily new confirmed cases of China cities. More importantly, such a significant effect takes into account the control of invalid instruments. The existing literature study of the spread of COVID-19 used weather variables earlier than two weeks as instruments. However, countless asymptomatic COVID-19 infections could lead to weather instruments being invalid. These instruments are not only correlated with the lockdowns, but also have a direct impact on the spread of the COVID-19. We use the double machine learning approach of Chernozhukov et al. (2018) to achieve exact estimation. Specifically, we rewrite the condition proposed by Koles´ar et al. (2015) to a Neyman-orthogonal moment, estimate the nuisance parameters by post-Lasso and Lasso, and identify the parameter of interest by 2SLS with cross-fitting. The results show that lockdowns significantly reduced the spreading rate in daily new confirmed cases at least by 12%, while if we do not take into account the endogeneity, it will underestimate the effect as 6%.