其二,希望诸位能建立起 Stata 的基本架构,熟知 Stata 能做什么、如何做?以便为后续学习打下宽厚扎实的基础。
翻阅 Top 期刊上的论文,文中的方法我们似乎都会。细细想来,原因在于这些论文的想法或视角通常都比较独特,并使用了恰当的方法来论证。这里的关键在于研究设计,而这在目前的计量教科书中却鲜有涉及。为此,本次研讨班突出两个特点:一方面,我会努力把基础知识讲解透彻,进度上不求快;另一方面,我在每个专题中都会提供了 2-3 篇比较经典的论文,展示这些方法的合理应用。
在内容安排上,基本上遵循了由浅入深,循序渐进的原则。
A0-A1 讲 依序介绍 Stata 的基本用法、数据处理、程序编写和可视化分析,学习这些内容无需太多的计量经济学基础,但对于提高实证分析能力和分析效率,大有裨益。本讲中,我会以一篇文章为实例,说明 Stata 的基本语法结构,并对数据处理过程中的关键问题进行介绍,如离群值的处理、文字变量的处理等。就我个人的经验而言,数据处理能力的高低直接决定实证分析的效率,而对于离群值等问题的处理是否妥善会直接影响全文结果的稳健性,是多数人不够重视但却至关重要的问题。此前有不少学完了高级班的同学又回炉初级班,便是感悟到了这一点。
Cameron, C. A., D. L. Miller, 2015, A practitioner’s guide to cluster-robust inference, Journal of Human Resources, 50 (2): 317-372. -Link-, -PDF-
Correia, S. 2016. reghdfe, Linear Models with High-Dimensional Fixed Effects: An Efficient and Feasible Estimator. Working Paper. -PDF-, Examples
A6. 一篇 Top 期刊论文重现
Akcigit, U., J. Grigsby, T. Nicholas, S. Stantcheva, 2022, Taxation and innovation in the twentieth century, The Quarterly Journal of Economics, 137 (1): 329-385. -Link-, -PDF-, -Appendix-, -cited-, -Replication-
Sherman M G, Tookes H E. Female representation in the academic finance profession. Journal of Finance, 2022, 77(1): 317-365. -Link-, -cited-, -PDF-, -Replication-
近期的 Top 期刊越来越强调模型不确定性,比如:控制变量也有好坏之分、是否存在非线性特征、不同模型的优劣对比等。这就需要进行各类检验,以便排除各种「混杂因素」和「似是而非」的论述,让论文的研究结论具有排他性,经济含义也更为清晰明确。本专题包括假设检验的基本原理、模型筛选和对比检验,以及「不容易做好」的稳健性检验等内容。在介绍检验方法和命令的同时,重点在于如何解释它们的经济含义,如何选择合适的检验方法并采用合适的方式加以呈现和分析。在后续的专题中,会结合具体模型设定来讲解这些检验方法的变种的灵活运用。
系数的联合检验:Wald,LR,LM 检验
test, testparm, lincom, nlcom, testnl
结果的汇集与呈现
模型比较:嵌套模型比较、非嵌套模型比较
R2 分解和贡献度分析
系数差异检验:Chow 检验,SUR,Bootstrap,排序检验
内生性检验、稳健性检验、安慰剂检验
参考文献:
Hansen B E . 2021. Econometrics. Princeton University Press. Data and Contents, PDF. Chap 9.
Yan, G., & Chen, Q. (2023). synth2: Synthetic control method with placebo tests, robustness test, and visualization. The Stata Journal, 23(3), 597–624. Link, PDF, Google.
复现论文
Ye, D., Y. K. Ng, Y. Lian, 2015, Culture and happiness, Social Indicators Research, 123 (2): 519-547. -Link-, -PDF-, -cited-,-Replication-
Akcigit, U., J. Grigsby, T. Nicholas, S. Stantcheva, 2022, Taxation and innovation in the twentieth century, The Quarterly Journal of Economics, 137 (1): 329-385. -Link-, -PDF-, -Appendix-, -cited-, -Replication-
Lee, C.-C., Feng, Y., & Peng, D. (2022). A green path towards sustainable development: The impact of low-carbon city pilot on energy transition. Energy Economics, 115, 106343. Link (rep), PDF, Google. -Replication-
B2. IV 和 GMM (3 小时)
IV 的思想并不复杂,但想找到一个能说服审稿人的 IV 却往往是可遇不可求的事情。在横截面分析中确实如此。随着面板数据模型的快速发展,IV 的构造思路已经发生了很大的变化,「就地取材」、「差别反应」都是非常有用的构造思路。GMM 是估计动态面板的标准方法,它在投资方程、DSGE 等领域也是重要的估计方法。本讲以因果图为基础,介绍 IV,2SLS 和 GMM 的基本思想,辅以几篇经典论文的 Stata 实操。
IV 和 2SLS 估计的原理
GMM 估计的原理
假设检验:内生性、排他性
应用 1:动态面板数据模型
应用 2:Lasso-IV
参考文献:
Hansen B E . 2021. Econometrics. Princeton University Press. Data and Contents, PDF. Chap 12-13.
Lal, A., Lockhart, M., Xu, Y., & Zu, Z. (2024). How Much Should We Trust Instrumental Variable Estimates in Political Science? Practical Advice Based on 67 Replicated Studies. Political Analysis, 1–20. Link, PDF, -Appendix-, -Replication-, PDF+附录-260页,
复现文档
Akcigit, U., J. Grigsby, T. Nicholas, S. Stantcheva, 2022, Taxation and innovation in the twentieth century, The Quarterly Journal of Economics, 137 (1): 329-385. -Link-, -PDF-, -Appendix-, -cited-, -Replication-
Acemoglu, D., & Restrepo, P. (2017). Secular Stagnation? The Effect of Aging on Economic Growth in the Age of Automation. American Economic Review, 107(5), 174–179. Link, PDF, -PDF2-, Google.
Bai, J. 2009. Panel Data Models With Interactive Fixed Effects. (2009). Econometrica, 77(4), 1229–1279. Link (rep), PDF, Google.
Bai, J., Liao, Y., & Yang, J. (2015). Unbalanced Panel Data Models with Interactive Effects. In The Oxford Handbook of Panel Data, ed. B. H. Baltagi, 149–170. Oxford:Oxford University Press, 149–170. Link, PDF, Google.
Norkutė, M., Sarafidis, V., Yamagata, T., & Cui, G. (2021). Instrumental variable estimation of dynamic linear panel data models with defactored regressors and a multifactor error structure. Journal of Econometrics, 220(2), 416–446. Link, PDF, Google.
Cui, G., Norkutė, M., Sarafidis, V., & Yamagata, T. (2021). Two-stage instrumental variable estimation of linear panel data models with interactive effects. The Econometrics Journal, 25(2), 340–361. Link, PDF, Google. -Replication-
Kripfganz, S., & Sarafidis, V. (2021). Instrumental-variable estimation of large-T panel-data models with common factors. The Stata Journal, 21(3), 659–686. Link, PDF, Google. -cited-
Arkhangelsky D, Athey S, Hirshberg D A, et al. Synthetic difference-in-differences[J]. American Economic Review, 2021, 111(12): 4088-4118. Link, -PDF- -Replicate- -Github-
Ditzen, J., & Reese, S. (2023). xtnumfac: A battery of estimators for the number of common factors in time series and panel-data models. The Stata Journal , 23(2), 438–454. Link, PDF, Google. github
Sul, D. Panel data econometrics: Common factor analysis for empirical researchers[M]. 2019. -Link-, -PDF-, Book-review, Codes-Stata/Gauss/Matlab, R-codes-readme
Huang, W., Wang, Y., & Zhou, L. (2024). Identify latent group structures in panel data: The classifylasso command. The Stata Journal, 24(1), 46–71. Link, PDF, Google.
Yan, G., & Chen, Q. (2022). rcm: A command for the regression control method. The Stata Journal, 22(4), 842–883. Link, PDF, Google.
Cattaneo, M. D., Crump, R. K., Farrell, M. H., & Feng, Y. (2024). On Binscatter. American Economic Review, 114(5), 1488–1514. Link, PDF, Appendix, Google, -Replication-, github, Slides
Cattaneo, Crump, Farrell and Feng (2024): Binscatter Regressions. Stata Journal, Forthcoming.
Du, K., Zhang, Y., & Zhou, Q. (2020). Fitting partially linear functional-coefficient panel-data models with Stata. The Stata Journal, 20(4), 976–998. Link, PDF, Google. -cited-, -Github-
复现文档
Akcigit, U., J. Grigsby, T. Nicholas, S. Stantcheva, 2022, Taxation and innovation in the twentieth century, The Quarterly Journal of Economics, 137 (1): 329-385. -Link-, -PDF-, -Appendix-, -cited-, -Replication-
Chen Yu, S. Shi, Y. Tang. 2019, Valuing the urban hukou in China: Evidence from a regression discontinuity design for housing prices. The Journal of Development Economics, 141 (2019) 102381. -Link-,-PDF-
Du, K., Cheng, Y., & Yao, X. (2021). Environmental regulation, green technology innovation, and industrial structure upgrading: The road to the green transformation of Chinese cities. Energy Economics, 98, 105247. Link (rep), PDF, -Replication-, Google.
Du, C., Cao, Y., Ling, Y., Jin, Z., Wang, S., & Wang, D. (2024). Does manufacturing agglomeration promote green productivity growth in China? Fresh evidence from partially linear functional-coefficient models. Energy Economics, 131, 107352. Link (rep), PDF, Google. -Replication-
Chernozhukov, Victor, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, and Whitney Newey. 2017. "Double/Debiased/Neyman Machine Learning of Treatment Effects." American Economic Review, 107 (5): 261-265. -Link-, -PDF-, -Replication-R, -2-
Chernozhukov, V., D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W. Newey,J. Robins, 2018, Double/debiased machine learning for treatment and structural parameters, The Econometrics Journal, 21 (1): C1-C68. -Link-, -PDF-, Replication
Ahrens, A., Hansen, C. B., Schaffer, M. E., & Wiemann, T. (2024). ddml: Double/debiased machine learning in Stata. The Stata Journal, 24(1), 3–45. Link, PDF, Google.
Ahrens, A., Hansen, C. B., & Schaffer, M. E. (2023). pystacked: Stacking generalization and machine learning in Stata. The Stata Journal, 23(4), 909–931. Link, PDF, Google.
Ahrens, A., Hansen, C. B., & Schaffer, M. E. (2020). lassopack: Model selection and prediction with regularized regression in Stata. The Stata Journal, 20(1), 176–235. Link, PDF, Google. -PDF-, 程序更新到了 2024.2, ssc des lassopack
Ahrens, A., Hansen, C. B., Schaffer, M. E., & Wiemann, T. (2024). Model averaging and double machine learning. arXiv Working Paper. Link, PDF
Dallakyan, A. (2022). graphiclasso: Graphical lasso for learning sparse inverse-covariance matrices. The Stata Journal, 22(3), 625–642. Link, PDF, Google.
Chiang, H. D., Kato, K., Ma, Y., & Sasaki, Y. (2022). Multiway Cluster Robust Double/Debiased Machine Learning. Journal of Business & Economic Statistics, 40(3), 1046–1056. Link, PDF, Google. 推文
Dhar, D., Jain, T., & Jayachandran, S. (2022). Reshaping Adolescents’ Gender Attitudes: Evidence from a School-Based Experiment in India. American Economic Review, 112(3), 899–927. Link (rep), PDF, Appendix, Google. -Replication-Stata, -cited-
在政策评估中,尤其是「多期政策干预」或「多个处理变量并存」的场景中,我们经常面临遗漏关键变量问题。例如,多期 DID 模型中,不同阶段的政策可能相互影响,而遗漏关键变量会导致政策效果估计存在严重偏误。此时,借助「遗漏变量检验」,我们可以识别那些未被观察到但可能对结果产生重要影响的因素;而「排他性检验」则能够有效避免多个处理变量之间的“污染效应”(如补贴和税收政策的交叉影响),确保每个变量的独立影响被准确估计,如在多阶段政策干预时分离各阶段的政策效应。
Q2. 平行趋势检验与安慰剂检验到底有多关键?如果忽视这些检验,会带来哪些隐患?
平行趋势和安慰剂检验是确保 DID 估计有效的核心。然而,现有的平行趋势检验在应对复杂场景时存在诸多局限,尤其是在面对时间趋势变化(如经济周期)、引入控制变量(如个体特征和环境因素)以及多期政策干预(如分阶段实施的政策)时,容易失效。原因在于,现有方法多以只能事后验证,无法在事前判断是否满足平性趋势假设,这可能导致政策效果估计出现偏误。本课程将引入一些新进提出的平行趋势和安慰剂检验方法,以便在复杂样本(如多群体异质性)和多维数据场景(如多个调节变量和交互效应)中,更精准地识别政策效应,实现更稳健的政策评估。
不变因果预测(Invariant causal prediction)(Kook et al., 2024)
双重有效/双重尖锐(Doubly-Valid/Doubly-Sharp)、敏感性分析(Dorn et al.,2024)
基于模型辅助的敏感性分析(Tan,2024)
排他性检验(Goldsmith et al.,2022)
平行趋势检验
传统平行趋势检验
Event Study(Freyaldenhoven et al.,2021;Roth,2022)
Treeffuser(Beltran-Velezet al.,2024)
安慰剂检验
DID的新范式
TWFE与标准DID(Wooldridge, 2021)
纽曼正交框架下的DID(包括TWFE,DRDID,DML,GRF, Npcausal)(Sant & Zhao,2020;Kennedy et al.,2023)
匹配框架下的DID(包括:PSM-DID,SDID,WGAN)(Athey et al.,2021)
多期DID(包括:CSDID,动态IPW,RIPW)(Arkhangelsky et al.,2021;Callaway & Sant,2021;Goodman-Bacon,2021;van den Berg & Gerard,2022)
参考文献:
以下是处理后的完整引文信息:
Boileau, P., Leng, N., Hejazi, N. S., Van Der Laan, M., & Dudoit, S. (2024). A nonparametric framework for treatment effect modifier discovery in high dimensions. Journal of the Royal Statistical Society Series B: Statistical Methodology. Link, PDF, Google.
Beltran-Velez, N., Grande, A. A., Nazaret, A., Kucukelbir, A., & Blei, D. (2024). Treeffuser: Probabilistic Predictions via Conditional Diffusions with Gradient-Boosted Trees (Version 2). arXiv. Link (rep), PDF, Google.
Chang, H., Middleton, J. A., & Aronow, P. M. (2024). Exact Bias Correction for Linear Adjustment of Randomized Controlled Trials. Econometrica, 92(5), 1503–1519. Link (rep), PDF, Google.
Di Giuli, A., & Laux, P. A. (2022). The effect of media-linked directors on financing and external governance. Journal of Financial Economics, 145(2), 103–131. Link (rep), PDF, Google.
Dorn, J., Guo, K., & Kallus, N. (2024). Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding. Journal of the American Statistical Association, 1–12. Link, PDF, Google.
Guo, X., Li, R., Liu, J., & Zeng, M., 2022. High-Dimensional Mediation Analysis for Selecting DNA Methylation Loci Mediating Childhood Trauma and Cortisol Stress Reactivity. Journal of the American Statistical Association, 117(539), 1110-1121. Link, PDF, Google.
Guo, Z., Ćevid, D., & Bühlmann, P.,2022. Doubly debiased lasso: High-dimensional inference under hidden confounding. Annals of Statistics, 50(3), 1320.Link, PDF, Google.
Imai, K., Keele, L., & Yamamoto, T. (2010). Identification, inference and sensitivity analysis for causal mediation effects. Statistical Science, 25(1), 51-71. Link, PDF, Google.
Kook, L., Saengkyongam, S., Lundborg, A. R., Hothorn, T., & Peters, J. (2024). Model-Based Causal Feature Selection for General Response Types. Journal of the American Statistical Association, 1–12. Link, PDF, -PDF2-, Google.
Lin, Y., Windmeijer, F., Song, X., & Fan, Q. (2024). On the instrumental variable estimation with many weak and invalid instruments. Journal of the Royal Statistical Society Series B: Statistical Methodology, qkae025. Link, PDF, Google.
Ouyang, J., Tan, K. M., & Xu, G. (2023). High-dimensional inference for generalized linear models with hidden confounding. The Journal of Machine Learning Research, 24(1), 14030-14090. Link, PDF, Google.
Zhou, X. (2022). Semiparametric Estimation for Causal Mediation Analysis with Multiple Causally Ordered Mediators. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(3), 794–821. Link, PDF, Google.
Zhou, X., & Yamamoto, T., 2023. Tracing causal paths from experimental and observational data. The Journal of Politics, 85(1), 250-265.Link (rep), PDF, Appendix, Google.
首先,我们将讨论传统遗漏变量检验(Oyster, 2019)以及它在处理因果关系复杂场景中的局限性。Q1.在复杂的政策环境中,如何识别未观测的关键变量?(如教育政策在不同社会经济背景下的差异)。为应对这一挑战,不变因果预测(Invariant Causal Prediction)(Kook et al., 2024)通过在多个环境下寻找因果关系的稳定性,帮助识别可能被忽略的关键变量,特别适用于跨区域政策分析(如跨城市的住房政策)。接着,双重有效/双重尖锐(Doubly-Valid/Doubly-Sharp)敏感性分析模型(Dorn et al., 2024)通过构建双重稳健估计,即使部分模型假设失效,依然能准确估计政策效果。Q2.在模型设定偏差或高维数据中,如何确保估计结果的稳健性?(如公共卫生政策在多个变量干扰下的效果评估)。同时,基于模型辅助的敏感性分析(Tan, 2024)结合了倾向评分和结果均值回归模型,解决了未观测混杂因素带来的偏差问题,适合高维数据和复杂模型的因果推断
此外,针对处理多个政策干预的情境,本专题还将介绍排他性检验(Goldsmith et al., 2022),Q3.在存在多个政策干预时,如何避免变量间的相互污染?(如同时进行的经济刺激政策和税收政策对经济增长的影响)。排他性检验确保多个处理变量独立,从而防止政策效果估计中的交叉干扰,特别适用于多期、多政策场景下的政策分析。
首先,平行趋势假设要求处理组和对照组在政策实施前必须有相同的趋势。Q1.如何做「事后的」平行趋势检验,并确保政策实施前的平行趋势假定成立? 在传统的平行趋势检验中,这一假设通常只做事前检验,但在现实场景中,政策实施前的时间趋势可能具有复杂的动态结构。事件研究法(Event Study)(Freyaldenhoven et al., 2021;Roth, 2022)通过多个时间窗口捕捉政策前后的动态趋势,能够灵活处理多期数据和复杂时间趋势问题。Q2.在存在时间趋势的情况下,平行趋势检验满足时是否就能得到ATT? 事件研究法不仅可以检测不同时间窗口中的政策影响,还可以避免因非线性趋势或数据异质性导致的偏差,提供更精细的政策效果估计。
进一步提升平行趋势检验能力的工具是Treeffuser模型(Beltran-Velez et al., 2024),它通过决策树框架对政策前后的非线性趋势进行建模,特别适用于多维数据和复杂因果关系的场景。Treeffuser在处理多个政策变量时,能够捕捉到变量之间的交互效应并提供更灵活的检验方式,适用于复杂环境下的平行趋势检验。
传统检验方法的可行性分析:逐步检验法、敏感性分析(Imai et al.,2010)、两阶段工具变量法(Di Giuli & Laux,2022)
双重纠偏拉索估计:线性模型(Guo et al.,2022AoS),广义线性模型(Ouyang et al.,2023)
多重中介检验
有效中介识别检验(Guo et al.,2022JASA)
因果路径分析(Zhou,2022;Zhou & Yamamoto,2023)
连续型处理变量下的中介效应分析(Lin et al.,2024)
参考文献:
Boileau, P., Leng, N., Hejazi,N. S., van der Laan, M., & Dudoit, S. 2024. A nonparametric framework fortreatment effect modifier discovery in high dimensions. Journal of the RoyalStatistical Society Series B: Statistical Methodology, qkae084.
Chang, H., Middleton, J. A.,& Aronow, P. M. 2024. Exact bias correction for linear adjustment ofrandomized controlled trials. Econometrica, 92(5), 1503-1519.
Di Giuli, A., & Laux, P. A., 2022. The effect of media-linked directors on financing and external governance. Journal of Financial Economics, 145(2), 103-131.Link (rep), PDF, Google
Guo, X., Li, R., Liu, J., & Zeng, M., 2022. High-Dimensional Mediation Analysis for Selecting DNA Methylation Loci Mediating Childhood Trauma and Cortisol Stress Reactivity. Journal of the American Statistical Association, 117(539), 1110-1121. Link, PDF, Google.
Guo, Z., Ćevid, D., & Bühlmann, P.,2022. Doubly debiased lasso: High-dimensional inference under hidden confounding. Annals of Statistics, 50(3), 1320.Link, PDF, Google.
Imai, K., Keele, L., & Yamamoto, T. (2010). Identification, inference and sensitivity analysis for causal mediation effects. Statistical Science, 25(1), 51-71. Link, PDF, Google.
Lin, Y., Windmeijer, F., Song, X., & Fan, Q. (2024). On the instrumental variable estimation with many weak and invalid instruments. Journal of the Royal Statistical Society Series B: Statistical Methodology, qkae025. Link, PDF, Google.
Ouyang, J., Tan, K. M., & Xu, G. (2023). High-dimensional inference for generalized linear models with hidden confounding. The Journal of Machine Learning Research, 24(1), 14030-14090. Link, PDF, Google.
Zhou, X. (2022). Semiparametric Estimation for Causal Mediation Analysis with Multiple Causally Ordered Mediators. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(3), 794–821. Link, PDF, Google.
Zhou, X., & Yamamoto, T., 2023. Tracing causal paths from experimental and observational data. The Journal of Politics, 85(1), 250-265.Link (rep), PDF, Appendix, Google.
首先,我们将聚焦于调节效应检验。政策效果往往受到不同群体或环境的调节,理解这些调节因素对于准确评估政策效应至关重要。Q1.如何在复杂的高维数据中自动识别出关键的调节变量? 如借鉴Boileau et al.(2024),筛选合适调节变量,进而评估环境政策在不同污染水平下的效果。Q2.在不同调节因素存在时,如何估计其对政策效果的相对重要性? (Chang et al., 2024)比如用于衡量教育政策在不同收入群体中的影响。这些工具将帮助学员在多期政策或多群体异质性背景下,精准评估政策效果的差异性与敏感性。
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接下来,Bian et al. (2024)的强化学习方法是本专题的核心内容之一。强化学习通过不断的反馈和数据更新,帮助研究者在复杂的政策环境中做出动态优化决策Q2.如何通过实时数据反馈动态优化政策? (例如,医保政策随着病人健康状况变化而进行的自动调整)。与传统方法不同,强化学习不仅能够适应政策环境中的复杂性(如个体异质性和时间波动),还能够通过学习过程逐步改善政策效果,最大化长期收益。特别是在面对长期实施的政策(如养老金政策)时,强化学习能够根据历史数据实时优化决策,确保政策效果的持续改善。
市场均衡状态下的政策效应评估(Munro et al., 2021)将探讨在存在溢出效应的复杂市场环境中,如何评估政策对个体和整体市场的影响。传统因果推断依赖SUTVA假设,但在现实场景中(如企业投资或地方政府政策)个体之间存在相互影响,无法满足这一假设。Q4.如何在政策影响下估计市场中的直接和间接效应? (如环保政策对企业生产和市场价格的双重影响)。Munro et al. (2023) 提出的模型通过区分直接处理效应(ADE)和间接处理效应(AIE),评估政策对个体自身和其他个体的传导效应,并提出了最优政策目标规则,帮助研究者在保持市场均衡的前提下实现政策优化。本专题将通过实例展示如何在R中实现这一模型。
同时,政策的公平是优化中的另一关键问题。Viviano & Bradic (2023)提出的政策公平性评价模型,帮助研究者在优化政策效果的同时兼顾公平性。Q5.如何确保政策在不同群体间的公平分配? (如税收政策在不同收入群体中的公平性问题)。此外,本专题还将介绍多臂Qini曲线(Sverdrup et al., 2023),为评估和比较不同政策措施的边际效益提供了一种直观有效的工具。通过多臂Qini曲线,研究者可以识别出在特定时间节点或周期内表现最优的政策措施,最大化资源分配效益。
最后,针对连续处理变量(Kennedy et al., 2017;Colangelo & Lee, 2023;Xu & Tan, 2024)的政策优化,本专题将展示如何通过非参数因果推断方法,细化政策效果评估,尤其是在处理变量为连续变量的场景下(如碳税税率或补贴金额)。这些方法将帮助学者在更复杂的政策情境下实现灵活、精准的政策决策。