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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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Alpha 策略全流程","\u002Fzh\u002Fquant\u002F09-case-study","zh\u002Fquant\u002F09-case-study",{"title":1779,"path":1780,"stem":1781},"量化投资文献与软件图谱","\u002Fzh\u002Fquant\u002F10-reading-software-map","zh\u002Fquant\u002F10-reading-software-map",null,{"id":1784,"title":1362,"body":1785,"description":6932,"extension":6933,"features":1782,"hero":1782,"layout":1782,"locale":1782,"meta":6934,"navigation":1782,"path":1363,"published":6937,"seo":6938,"stem":1364,"__hash__":6939},"docs\u002Fzh\u002Feconometrics\u002F09-frontier-literature-2026.md",{"type":1786,"value":1787,"toc":6905},"minimark",[1788,1792,1796,1804,1808,1811,1833,1837,1842,1982,2194,2426,2835,2945,2949,2952,3327,3359,3362,3366,3369,3826,3829,4132,4139,4142,4146,4149,4323,4326,4329,4347,4350,4382,4862,4951,4955,4959,4962,4965,4969,4972,5304,5688,6005,6134,6528,6531,6535,6664,6667,6684,6688,6691,6698,6703,6706,6720,6725,6728,6732,6735,6739,6742,6823,6826,6829,6887],[1789,1790,1362],"h1",{"id":1791},"第九章前沿文献与现代计量案例20232026",[1793,1794,1795],"p",{},"现代计量经济学的进步，往往不是发明一个更复杂的回归，而是发现一个常用回归在什么条件下不再估计研究者以为的对象。本章选择三组近期文献，集中训练三个能力：先定义 estimand，再识别“谁在充当谁的对照组”，最后检查灵活预测工具有没有破坏有效推断。",[1793,1797,1798,1799,1803],{},"本章基于截至 ",[1800,1801,1802],"strong",{},"2026 年 7 月 31 日"," 的一手文献定向检索，不是系统综述。示例使用合成数据，仅复现方法的逻辑，不复现论文的经验结果。",[1805,1806,1807],"h2",{"id":1807},"学习目标",[1793,1809,1810],{},"完成本章后，你应能够：",[1812,1813,1814,1818,1821,1824,1827,1830],"ol",{},[1815,1816,1817],"li",{},"解释交错实施政策下传统双向固定效应回归为何可能混合不合适的比较；",[1815,1819,1820],{},"写出组别—时间处理效应与动态事件时间效应；",[1815,1822,1823],{},"用“只在未处理观测上拟合反事实”的插补逻辑估计 ATT；",[1815,1825,1826],{},"说明平行趋势检验为什么不能把“未拒绝”误写成“已证明”；",[1815,1828,1829],{},"解释双重机器学习中的正交化、交叉拟合和高维混淆控制；",[1815,1831,1832],{},"区分预测准确率、参数识别和置信区间覆盖率。",[1805,1834,1836],{"id":1835},"案例一交错实施下传统事件研究到底在平均什么","案例一：交错实施下，传统事件研究到底在平均什么",[1838,1839,1841],"h3",{"id":1840},"_1-基本设定","1. 基本设定",[1793,1843,1844,1845,1891,1892,1981],{},"令单位 ",[1846,1847,1850,1872],"span",{"className":1848},[1849],"katex",[1846,1851,1854],{"className":1852},[1853],"katex-mathml",[1855,1856,1858],"math",{"xmlns":1857},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1859,1860,1861,1868],"semantics",{},[1862,1863,1864],"mrow",{},[1865,1866,1867],"mi",{},"i",[1869,1870,1867],"annotation",{"encoding":1871},"application\u002Fx-tex",[1846,1873,1877],{"className":1874,"ariaHidden":1876},[1875],"katex-html","true",[1846,1878,1881,1886],{"className":1879},[1880],"base",[1846,1882],{"className":1883,"style":1885},[1884],"strut","height:0.6595em;",[1846,1887,1867],{"className":1888},[1889,1890],"mord","mathnormal"," 在时期 ",[1846,1893,1895,1915],{"className":1894},[1849],[1846,1896,1898],{"className":1897},[1853],[1855,1899,1900],{"xmlns":1857},[1859,1901,1902,1912],{},[1862,1903,1904],{},[1905,1906,1907,1910],"msub",{},[1865,1908,1909],{},"G",[1865,1911,1867],{},[1869,1913,1914],{"encoding":1871},"G_i",[1846,1916,1918],{"className":1917,"ariaHidden":1876},[1875],[1846,1919,1921,1925],{"className":1920},[1880],[1846,1922],{"className":1923,"style":1924},[1884],"height:0.8333em;vertical-align:-0.15em;",[1846,1926,1928,1931],{"className":1927},[1889],[1846,1929,1909],{"className":1930},[1889,1890],[1846,1932,1935],{"className":1933},[1934],"msupsub",[1846,1936,1940,1972],{"className":1937},[1938,1939],"vlist-t","vlist-t2",[1846,1941,1944,1967],{"className":1942},[1943],"vlist-r",[1846,1945,1949],{"className":1946,"style":1948},[1947],"vlist","height:0.3117em;",[1846,1950,1952,1957],{"style":1951},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1846,1953],{"className":1954,"style":1956},[1955],"pstrut","height:2.7em;",[1846,1958,1964],{"className":1959},[1960,1961,1962,1963],"sizing","reset-size6","size3","mtight",[1846,1965,1867],{"className":1966},[1889,1890,1963],[1846,1968,1971],{"className":1969},[1970],"vlist-s","​",[1846,1973,1975],{"className":1974},[1943],[1846,1976,1979],{"className":1977,"style":1978},[1947],"height:0.15em;",[1846,1980],{}," 首次接受处理，此后持续处于处理状态：",[1846,1983,1986],{"className":1984},[1985],"katex-display",[1846,1987,1989,2045],{"className":1988},[1849],[1846,1990,1992],{"className":1991},[1853],[1855,1993,1995],{"xmlns":1857,"display":1994},"block",[1859,1996,1997,2042],{},[1862,1998,1999,2011,2015,2020,2024,2026,2029,2035,2038],{},[1905,2000,2001,2004],{},[1865,2002,2003],{},"D",[1862,2005,2006,2008],{},[1865,2007,1867],{},[1865,2009,2010],{},"t",[2012,2013,2014],"mo",{},"=",[2016,2017,2019],"mn",{"mathvariant":2018},"bold","1",[2012,2021,2023],{"stretchy":2022},"false","(",[1865,2025,2010],{},[2012,2027,2028],{},"≥",[1905,2030,2031,2033],{},[1865,2032,1909],{},[1865,2034,1867],{},[2012,2036,2037],{"stretchy":2022},")",[1865,2039,2041],{"mathvariant":2040},"normal",".",[1869,2043,2044],{"encoding":1871},"D_{it}=\\mathbf 1(t\\ge G_i).",[1846,2046,2048,2114,2141],{"className":2047,"ariaHidden":1876},[1875],[1846,2049,2051,2054,2102,2107,2111],{"className":2050},[1880],[1846,2052],{"className":2053,"style":1924},[1884],[1846,2055,2057,2061],{"className":2056},[1889],[1846,2058,2003],{"className":2059,"style":2060},[1889,1890],"margin-right:0.0278em;",[1846,2062,2064],{"className":2063},[1934],[1846,2065,2067,2094],{"className":2066},[1938,1939],[1846,2068,2070,2091],{"className":2069},[1943],[1846,2071,2073],{"className":2072,"style":1948},[1947],[1846,2074,2076,2079],{"style":2075},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1846,2077],{"className":2078,"style":1956},[1955],[1846,2080,2082],{"className":2081},[1960,1961,1962,1963],[1846,2083,2085,2088],{"className":2084},[1889,1963],[1846,2086,1867],{"className":2087},[1889,1890,1963],[1846,2089,2010],{"className":2090},[1889,1890,1963],[1846,2092,1971],{"className":2093},[1970],[1846,2095,2097],{"className":2096},[1943],[1846,2098,2100],{"className":2099,"style":1978},[1947],[1846,2101],{},[1846,2103],{"className":2104,"style":2106},[2105],"mspace","margin-right:0.2778em;",[1846,2108,2014],{"className":2109},[2110],"mrel",[1846,2112],{"className":2113,"style":2106},[2105],[1846,2115,2117,2121,2125,2129,2132,2135,2138],{"className":2116},[1880],[1846,2118],{"className":2119,"style":2120},[1884],"height:1em;vertical-align:-0.25em;",[1846,2122,2019],{"className":2123},[1889,2124],"mathbf",[1846,2126,2023],{"className":2127},[2128],"mopen",[1846,2130,2010],{"className":2131},[1889,1890],[1846,2133],{"className":2134,"style":2106},[2105],[1846,2136,2028],{"className":2137},[2110],[1846,2139],{"className":2140,"style":2106},[2105],[1846,2142,2144,2147,2187,2191],{"className":2143},[1880],[1846,2145],{"className":2146,"style":2120},[1884],[1846,2148,2150,2153],{"className":2149},[1889],[1846,2151,1909],{"className":2152},[1889,1890],[1846,2154,2156],{"className":2155},[1934],[1846,2157,2159,2179],{"className":2158},[1938,1939],[1846,2160,2162,2176],{"className":2161},[1943],[1846,2163,2165],{"className":2164,"style":1948},[1947],[1846,2166,2167,2170],{"style":1951},[1846,2168],{"className":2169,"style":1956},[1955],[1846,2171,2173],{"className":2172},[1960,1961,1962,1963],[1846,2174,1867],{"className":2175},[1889,1890,1963],[1846,2177,1971],{"className":2178},[1970],[1846,2180,2182],{"className":2181},[1943],[1846,2183,2185],{"className":2184,"style":1978},[1947],[1846,2186],{},[1846,2188,2037],{"className":2189},[2190],"mclose",[1846,2192,2041],{"className":2193},[1889],[1793,2195,2196,2197,2296,2297,2392,2393,2425],{},"潜在结果写为 ",[1846,2198,2200,2230],{"className":2199},[1849],[1846,2201,2203],{"className":2202},[1853],[1855,2204,2205],{"xmlns":1857},[1859,2206,2207,2227],{},[1862,2208,2209,2220,2222,2225],{},[1905,2210,2211,2214],{},[1865,2212,2213],{},"Y",[1862,2215,2216,2218],{},[1865,2217,1867],{},[1865,2219,2010],{},[2012,2221,2023],{"stretchy":2022},[2016,2223,2224],{},"0",[2012,2226,2037],{"stretchy":2022},[1869,2228,2229],{"encoding":1871},"Y_{it}(0)",[1846,2231,2233],{"className":2232,"ariaHidden":1876},[1875],[1846,2234,2236,2239,2287,2290,2293],{"className":2235},[1880],[1846,2237],{"className":2238,"style":2120},[1884],[1846,2240,2242,2246],{"className":2241},[1889],[1846,2243,2213],{"className":2244,"style":2245},[1889,1890],"margin-right:0.2222em;",[1846,2247,2249],{"className":2248},[1934],[1846,2250,2252,2279],{"className":2251},[1938,1939],[1846,2253,2255,2276],{"className":2254},[1943],[1846,2256,2258],{"className":2257,"style":1948},[1947],[1846,2259,2261,2264],{"style":2260},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[1846,2262],{"className":2263,"style":1956},[1955],[1846,2265,2267],{"className":2266},[1960,1961,1962,1963],[1846,2268,2270,2273],{"className":2269},[1889,1963],[1846,2271,1867],{"className":2272},[1889,1890,1963],[1846,2274,2010],{"className":2275},[1889,1890,1963],[1846,2277,1971],{"className":2278},[1970],[1846,2280,2282],{"className":2281},[1943],[1846,2283,2285],{"className":2284,"style":1978},[1947],[1846,2286],{},[1846,2288,2023],{"className":2289},[2128],[1846,2291,2224],{"className":2292},[1889],[1846,2294,2037],{"className":2295},[2190]," 与 ",[1846,2298,2300,2328],{"className":2299},[1849],[1846,2301,2303],{"className":2302},[1853],[1855,2304,2305],{"xmlns":1857},[1859,2306,2307,2325],{},[1862,2308,2309,2319,2321,2323],{},[1905,2310,2311,2313],{},[1865,2312,2213],{},[1862,2314,2315,2317],{},[1865,2316,1867],{},[1865,2318,2010],{},[2012,2320,2023],{"stretchy":2022},[2016,2322,2019],{},[2012,2324,2037],{"stretchy":2022},[1869,2326,2327],{"encoding":1871},"Y_{it}(1)",[1846,2329,2331],{"className":2330,"ariaHidden":1876},[1875],[1846,2332,2334,2337,2383,2386,2389],{"className":2333},[1880],[1846,2335],{"className":2336,"style":2120},[1884],[1846,2338,2340,2343],{"className":2339},[1889],[1846,2341,2213],{"className":2342,"style":2245},[1889,1890],[1846,2344,2346],{"className":2345},[1934],[1846,2347,2349,2375],{"className":2348},[1938,1939],[1846,2350,2352,2372],{"className":2351},[1943],[1846,2353,2355],{"className":2354,"style":1948},[1947],[1846,2356,2357,2360],{"style":2260},[1846,2358],{"className":2359,"style":1956},[1955],[1846,2361,2363],{"className":2362},[1960,1961,1962,1963],[1846,2364,2366,2369],{"className":2365},[1889,1963],[1846,2367,1867],{"className":2368},[1889,1890,1963],[1846,2370,2010],{"className":2371},[1889,1890,1963],[1846,2373,1971],{"className":2374},[1970],[1846,2376,2378],{"className":2377},[1943],[1846,2379,2381],{"className":2380,"style":1978},[1947],[1846,2382],{},[1846,2384,2023],{"className":2385},[2128],[1846,2387,2019],{"className":2388},[1889],[1846,2390,2037],{"className":2391},[2190],"。研究者真正关心的通常不是一个永恒不变的 ",[1846,2394,2396,2411],{"className":2395},[1849],[1846,2397,2399],{"className":2398},[1853],[1855,2400,2401],{"xmlns":1857},[1859,2402,2403,2408],{},[1862,2404,2405],{},[1865,2406,2407],{},"β",[1869,2409,2410],{"encoding":1871},"\\beta",[1846,2412,2414],{"className":2413,"ariaHidden":1876},[1875],[1846,2415,2417,2421],{"className":2416},[1880],[1846,2418],{"className":2419,"style":2420},[1884],"height:0.8889em;vertical-align:-0.1944em;",[1846,2422,2407],{"className":2423,"style":2424},[1889,1890],"margin-right:0.0528em;","，而是组别—时间效应：",[1846,2427,2429],{"className":2428},[1985],[1846,2430,2432,2536],{"className":2431},[1849],[1846,2433,2435],{"className":2434},[1853],[1855,2436,2437],{"xmlns":1857,"display":1994},[1859,2438,2439,2533],{},[1862,2440,2441,2444,2447,2449,2451,2454,2457,2459,2461,2463,2466,2469,2479,2481,2483,2485,2488,2498,2500,2502,2504,2507,2513,2515,2517,2520,2522,2525,2527,2529,2531],{},[1865,2442,2443],{},"A",[1865,2445,2446],{},"T",[1865,2448,2446],{},[2012,2450,2023],{"stretchy":2022},[1865,2452,2453],{},"g",[2012,2455,2456],{"separator":1876},",",[1865,2458,2010],{},[2012,2460,2037],{"stretchy":2022},[2012,2462,2014],{},[1865,2464,2465],{},"E",[2012,2467,2468],{"stretchy":2022},"[",[1905,2470,2471,2473],{},[1865,2472,2213],{},[1862,2474,2475,2477],{},[1865,2476,1867],{},[1865,2478,2010],{},[2012,2480,2023],{"stretchy":2022},[2016,2482,2019],{},[2012,2484,2037],{"stretchy":2022},[2012,2486,2487],{},"−",[1905,2489,2490,2492],{},[1865,2491,2213],{},[1862,2493,2494,2496],{},[1865,2495,1867],{},[1865,2497,2010],{},[2012,2499,2023],{"stretchy":2022},[2016,2501,2224],{},[2012,2503,2037],{"stretchy":2022},[2012,2505,2506],{},"∣",[1905,2508,2509,2511],{},[1865,2510,1909],{},[1865,2512,1867],{},[2012,2514,2014],{},[1865,2516,2453],{},[2012,2518,2519],{"stretchy":2022},"]",[2012,2521,2456],{"separator":1876},[2105,2523],{"width":2524},"2em",[1865,2526,2010],{},[2012,2528,2028],{},[1865,2530,2453],{},[1865,2532,2041],{"mathvariant":2040},[1869,2534,2535],{"encoding":1871},"ATT(g,t)=E[Y_{it}(1)-Y_{it}(0)\\mid G_i=g],\\qquad t\\ge g.",[1846,2537,2539,2585,2663,2733,2788,2822],{"className":2538,"ariaHidden":1876},[1875],[1846,2540,2542,2545,2548,2552,2555,2558,2562,2566,2570,2573,2576,2579,2582],{"className":2541},[1880],[1846,2543],{"className":2544,"style":2120},[1884],[1846,2546,2443],{"className":2547},[1889,1890],[1846,2549,2446],{"className":2550,"style":2551},[1889,1890],"margin-right:0.1389em;",[1846,2553,2446],{"className":2554,"style":2551},[1889,1890],[1846,2556,2023],{"className":2557},[2128],[1846,2559,2453],{"className":2560,"style":2561},[1889,1890],"margin-right:0.0359em;",[1846,2563,2456],{"className":2564},[2565],"mpunct",[1846,2567],{"className":2568,"style":2569},[2105],"margin-right:0.1667em;",[1846,2571,2010],{"className":2572},[1889,1890],[1846,2574,2037],{"className":2575},[2190],[1846,2577],{"className":2578,"style":2106},[2105],[1846,2580,2014],{"className":2581},[2110],[1846,2583],{"className":2584,"style":2106},[2105],[1846,2586,2588,2591,2595,2598,2644,2647,2650,2653,2656,2660],{"className":2587},[1880],[1846,2589],{"className":2590,"style":2120},[1884],[1846,2592,2465],{"className":2593,"style":2594},[1889,1890],"margin-right:0.0576em;",[1846,2596,2468],{"className":2597},[2128],[1846,2599,2601,2604],{"className":2600},[1889],[1846,2602,2213],{"className":2603,"style":2245},[1889,1890],[1846,2605,2607],{"className":2606},[1934],[1846,2608,2610,2636],{"className":2609},[1938,1939],[1846,2611,2613,2633],{"className":2612},[1943],[1846,2614,2616],{"className":2615,"style":1948},[1947],[1846,2617,2618,2621],{"style":2260},[1846,2619],{"className":2620,"style":1956},[1955],[1846,2622,2624],{"className":2623},[1960,1961,1962,1963],[1846,2625,2627,2630],{"className":2626},[1889,1963],[1846,2628,1867],{"className":2629},[1889,1890,1963],[1846,2631,2010],{"className":2632},[1889,1890,1963],[1846,2634,1971],{"className":2635},[1970],[1846,2637,2639],{"className":2638},[1943],[1846,2640,2642],{"className":2641,"style":1978},[1947],[1846,2643],{},[1846,2645,2023],{"className":2646},[2128],[1846,2648,2019],{"className":2649},[1889],[1846,2651,2037],{"className":2652},[2190],[1846,2654],{"className":2655,"style":2245},[2105],[1846,2657,2487],{"className":2658},[2659],"mbin",[1846,2661],{"className":2662,"style":2245},[2105],[1846,2664,2666,2669,2715,2718,2721,2724,2727,2730],{"className":2665},[1880],[1846,2667],{"className":2668,"style":2120},[1884],[1846,2670,2672,2675],{"className":2671},[1889],[1846,2673,2213],{"className":2674,"style":2245},[1889,1890],[1846,2676,2678],{"className":2677},[1934],[1846,2679,2681,2707],{"className":2680},[1938,1939],[1846,2682,2684,2704],{"className":2683},[1943],[1846,2685,2687],{"className":2686,"style":1948},[1947],[1846,2688,2689,2692],{"style":2260},[1846,2690],{"className":2691,"style":1956},[1955],[1846,2693,2695],{"className":2694},[1960,1961,1962,1963],[1846,2696,2698,2701],{"className":2697},[1889,1963],[1846,2699,1867],{"className":2700},[1889,1890,1963],[1846,2702,2010],{"className":2703},[1889,1890,1963],[1846,2705,1971],{"className":2706},[1970],[1846,2708,2710],{"className":2709},[1943],[1846,2711,2713],{"className":2712,"style":1978},[1947],[1846,2714],{},[1846,2716,2023],{"className":2717},[2128],[1846,2719,2224],{"className":2720},[1889],[1846,2722,2037],{"className":2723},[2190],[1846,2725],{"className":2726,"style":2106},[2105],[1846,2728,2506],{"className":2729},[2110],[1846,2731],{"className":2732,"style":2106},[2105],[1846,2734,2736,2739,2779,2782,2785],{"className":2735},[1880],[1846,2737],{"className":2738,"style":1924},[1884],[1846,2740,2742,2745],{"className":2741},[1889],[1846,2743,1909],{"className":2744},[1889,1890],[1846,2746,2748],{"className":2747},[1934],[1846,2749,2751,2771],{"className":2750},[1938,1939],[1846,2752,2754,2768],{"className":2753},[1943],[1846,2755,2757],{"className":2756,"style":1948},[1947],[1846,2758,2759,2762],{"style":1951},[1846,2760],{"className":2761,"style":1956},[1955],[1846,2763,2765],{"className":2764},[1960,1961,1962,1963],[1846,2766,1867],{"className":2767},[1889,1890,1963],[1846,2769,1971],{"className":2770},[1970],[1846,2772,2774],{"className":2773},[1943],[1846,2775,2777],{"className":2776,"style":1978},[1947],[1846,2778],{},[1846,2780],{"className":2781,"style":2106},[2105],[1846,2783,2014],{"className":2784},[2110],[1846,2786],{"className":2787,"style":2106},[2105],[1846,2789,2791,2794,2797,2800,2803,2807,2810,2813,2816,2819],{"className":2790},[1880],[1846,2792],{"className":2793,"style":2120},[1884],[1846,2795,2453],{"className":2796,"style":2561},[1889,1890],[1846,2798,2519],{"className":2799},[2190],[1846,2801,2456],{"className":2802},[2565],[1846,2804],{"className":2805,"style":2806},[2105],"margin-right:2em;",[1846,2808],{"className":2809,"style":2569},[2105],[1846,2811,2010],{"className":2812},[1889,1890],[1846,2814],{"className":2815,"style":2106},[2105],[1846,2817,2028],{"className":2818},[2110],[1846,2820],{"className":2821,"style":2106},[2105],[1846,2823,2825,2829,2832],{"className":2824},[1880],[1846,2826],{"className":2827,"style":2828},[1884],"height:0.625em;vertical-align:-0.1944em;",[1846,2830,2453],{"className":2831,"style":2561},[1889,1890],[1846,2833,2041],{"className":2834},[1889],[1793,2836,2837,2838,2915,2916,2944],{},"若再按事件时间 ",[1846,2839,2841,2864],{"className":2840},[1849],[1846,2842,2844],{"className":2843},[1853],[1855,2845,2846],{"xmlns":1857},[1859,2847,2848,2861],{},[1862,2849,2850,2853,2855,2857,2859],{},[1865,2851,2852],{},"k",[2012,2854,2014],{},[1865,2856,2010],{},[2012,2858,2487],{},[1865,2860,2453],{},[1869,2862,2863],{"encoding":1871},"k=t-g",[1846,2865,2867,2887,2906],{"className":2866,"ariaHidden":1876},[1875],[1846,2868,2870,2874,2878,2881,2884],{"className":2869},[1880],[1846,2871],{"className":2872,"style":2873},[1884],"height:0.6944em;",[1846,2875,2852],{"className":2876,"style":2877},[1889,1890],"margin-right:0.0315em;",[1846,2879],{"className":2880,"style":2106},[2105],[1846,2882,2014],{"className":2883},[2110],[1846,2885],{"className":2886,"style":2106},[2105],[1846,2888,2890,2894,2897,2900,2903],{"className":2889},[1880],[1846,2891],{"className":2892,"style":2893},[1884],"height:0.6984em;vertical-align:-0.0833em;",[1846,2895,2010],{"className":2896},[1889,1890],[1846,2898],{"className":2899,"style":2245},[2105],[1846,2901,2487],{"className":2902},[2659],[1846,2904],{"className":2905,"style":2245},[2105],[1846,2907,2909,2912],{"className":2908},[1880],[1846,2910],{"className":2911,"style":2828},[1884],[1846,2913,2453],{"className":2914,"style":2561},[1889,1890]," 聚合，得到政策实施后第 ",[1846,2917,2919,2932],{"className":2918},[1849],[1846,2920,2922],{"className":2921},[1853],[1855,2923,2924],{"xmlns":1857},[1859,2925,2926,2930],{},[1862,2927,2928],{},[1865,2929,2852],{},[1869,2931,2852],{"encoding":1871},[1846,2933,2935],{"className":2934,"ariaHidden":1876},[1875],[1846,2936,2938,2941],{"className":2937},[1880],[1846,2939],{"className":2940,"style":2873},[1884],[1846,2942,2852],{"className":2943,"style":2877},[1889,1890]," 期的平均动态效应。到这里，目标参数已经告诉我们：不同批次和不同处理时长可以有不同效果。",[1838,2946,2948],{"id":2947},"_2-为什么双向固定效应可能失败","2. 为什么双向固定效应可能失败",[1793,2950,2951],{},"传统回归常写成：",[1846,2953,2955],{"className":2954},[1985],[1846,2956,2958,3028],{"className":2957},[1849],[1846,2959,2961],{"className":2960},[1853],[1855,2962,2963],{"xmlns":1857,"display":1994},[1859,2964,2965,3025],{},[1862,2966,2967,2977,2979,2986,2989,2996,2998,3000,3010,3012,3023],{},[1905,2968,2969,2971],{},[1865,2970,2213],{},[1862,2972,2973,2975],{},[1865,2974,1867],{},[1865,2976,2010],{},[2012,2978,2014],{},[1905,2980,2981,2984],{},[1865,2982,2983],{},"α",[1865,2985,1867],{},[2012,2987,2988],{},"+",[1905,2990,2991,2994],{},[1865,2992,2993],{},"λ",[1865,2995,2010],{},[2012,2997,2988],{},[1865,2999,2407],{},[1905,3001,3002,3004],{},[1865,3003,2003],{},[1862,3005,3006,3008],{},[1865,3007,1867],{},[1865,3009,2010],{},[2012,3011,2988],{},[1905,3013,3014,3017],{},[1865,3015,3016],{},"u",[1862,3018,3019,3021],{},[1865,3020,1867],{},[1865,3022,2010],{},[1865,3024,2041],{"mathvariant":2040},[1869,3026,3027],{"encoding":1871},"Y_{it}=\\alpha_i+\\lambda_t+\\beta D_{it}+u_{it}.",[1846,3029,3031,3092,3150,3207,3271],{"className":3030,"ariaHidden":1876},[1875],[1846,3032,3034,3037,3083,3086,3089],{"className":3033},[1880],[1846,3035],{"className":3036,"style":1924},[1884],[1846,3038,3040,3043],{"className":3039},[1889],[1846,3041,2213],{"className":3042,"style":2245},[1889,1890],[1846,3044,3046],{"className":3045},[1934],[1846,3047,3049,3075],{"className":3048},[1938,1939],[1846,3050,3052,3072],{"className":3051},[1943],[1846,3053,3055],{"className":3054,"style":1948},[1947],[1846,3056,3057,3060],{"style":2260},[1846,3058],{"className":3059,"style":1956},[1955],[1846,3061,3063],{"className":3062},[1960,1961,1962,1963],[1846,3064,3066,3069],{"className":3065},[1889,1963],[1846,3067,1867],{"className":3068},[1889,1890,1963],[1846,3070,2010],{"className":3071},[1889,1890,1963],[1846,3073,1971],{"className":3074},[1970],[1846,3076,3078],{"className":3077},[1943],[1846,3079,3081],{"className":3080,"style":1978},[1947],[1846,3082],{},[1846,3084],{"className":3085,"style":2106},[2105],[1846,3087,2014],{"className":3088},[2110],[1846,3090],{"className":3091,"style":2106},[2105],[1846,3093,3095,3099,3141,3144,3147],{"className":3094},[1880],[1846,3096],{"className":3097,"style":3098},[1884],"height:0.7333em;vertical-align:-0.15em;",[1846,3100,3102,3106],{"className":3101},[1889],[1846,3103,2983],{"className":3104,"style":3105},[1889,1890],"margin-right:0.0037em;",[1846,3107,3109],{"className":3108},[1934],[1846,3110,3112,3133],{"className":3111},[1938,1939],[1846,3113,3115,3130],{"className":3114},[1943],[1846,3116,3118],{"className":3117,"style":1948},[1947],[1846,3119,3121,3124],{"style":3120},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1846,3122],{"className":3123,"style":1956},[1955],[1846,3125,3127],{"className":3126},[1960,1961,1962,1963],[1846,3128,1867],{"className":3129},[1889,1890,1963],[1846,3131,1971],{"className":3132},[1970],[1846,3134,3136],{"className":3135},[1943],[1846,3137,3139],{"className":3138,"style":1978},[1947],[1846,3140],{},[1846,3142],{"className":3143,"style":2245},[2105],[1846,3145,2988],{"className":3146},[2659],[1846,3148],{"className":3149,"style":2245},[2105],[1846,3151,3153,3157,3198,3201,3204],{"className":3152},[1880],[1846,3154],{"className":3155,"style":3156},[1884],"height:0.8444em;vertical-align:-0.15em;",[1846,3158,3160,3163],{"className":3159},[1889],[1846,3161,2993],{"className":3162},[1889,1890],[1846,3164,3166],{"className":3165},[1934],[1846,3167,3169,3190],{"className":3168},[1938,1939],[1846,3170,3172,3187],{"className":3171},[1943],[1846,3173,3176],{"className":3174,"style":3175},[1947],"height:0.2806em;",[1846,3177,3178,3181],{"style":1951},[1846,3179],{"className":3180,"style":1956},[1955],[1846,3182,3184],{"className":3183},[1960,1961,1962,1963],[1846,3185,2010],{"className":3186},[1889,1890,1963],[1846,3188,1971],{"className":3189},[1970],[1846,3191,3193],{"className":3192},[1943],[1846,3194,3196],{"className":3195,"style":1978},[1947],[1846,3197],{},[1846,3199],{"className":3200,"style":2245},[2105],[1846,3202,2988],{"className":3203},[2659],[1846,3205],{"className":3206,"style":2245},[2105],[1846,3208,3210,3213,3216,3262,3265,3268],{"className":3209},[1880],[1846,3211],{"className":3212,"style":2420},[1884],[1846,3214,2407],{"className":3215,"style":2424},[1889,1890],[1846,3217,3219,3222],{"className":3218},[1889],[1846,3220,2003],{"className":3221,"style":2060},[1889,1890],[1846,3223,3225],{"className":3224},[1934],[1846,3226,3228,3254],{"className":3227},[1938,1939],[1846,3229,3231,3251],{"className":3230},[1943],[1846,3232,3234],{"className":3233,"style":1948},[1947],[1846,3235,3236,3239],{"style":2075},[1846,3237],{"className":3238,"style":1956},[1955],[1846,3240,3242],{"className":3241},[1960,1961,1962,1963],[1846,3243,3245,3248],{"className":3244},[1889,1963],[1846,3246,1867],{"className":3247},[1889,1890,1963],[1846,3249,2010],{"className":3250},[1889,1890,1963],[1846,3252,1971],{"className":3253},[1970],[1846,3255,3257],{"className":3256},[1943],[1846,3258,3260],{"className":3259,"style":1978},[1947],[1846,3261],{},[1846,3263],{"className":3264,"style":2245},[2105],[1846,3266,2988],{"className":3267},[2659],[1846,3269],{"className":3270,"style":2245},[2105],[1846,3272,3274,3278,3324],{"className":3273},[1880],[1846,3275],{"className":3276,"style":3277},[1884],"height:0.5806em;vertical-align:-0.15em;",[1846,3279,3281,3284],{"className":3280},[1889],[1846,3282,3016],{"className":3283},[1889,1890],[1846,3285,3287],{"className":3286},[1934],[1846,3288,3290,3316],{"className":3289},[1938,1939],[1846,3291,3293,3313],{"className":3292},[1943],[1846,3294,3296],{"className":3295,"style":1948},[1947],[1846,3297,3298,3301],{"style":1951},[1846,3299],{"className":3300,"style":1956},[1955],[1846,3302,3304],{"className":3303},[1960,1961,1962,1963],[1846,3305,3307,3310],{"className":3306},[1889,1963],[1846,3308,1867],{"className":3309},[1889,1890,1963],[1846,3311,2010],{"className":3312},[1889,1890,1963],[1846,3314,1971],{"className":3315},[1970],[1846,3317,3319],{"className":3318},[1943],[1846,3320,3322],{"className":3321,"style":1978},[1947],[1846,3323],{},[1846,3325,2041],{"className":3326},[1889],[1793,3328,3329,3330,3358],{},"当所有单位同时处理且效应恒定时，",[1846,3331,3333,3346],{"className":3332},[1849],[1846,3334,3336],{"className":3335},[1853],[1855,3337,3338],{"xmlns":1857},[1859,3339,3340,3344],{},[1862,3341,3342],{},[1865,3343,2407],{},[1869,3345,2410],{"encoding":1871},[1846,3347,3349],{"className":3348,"ariaHidden":1876},[1875],[1846,3350,3352,3355],{"className":3351},[1880],[1846,3353],{"className":3354,"style":2420},[1884],[1846,3356,2407],{"className":3357,"style":2424},[1889,1890]," 的解释相对清楚。交错实施时，回归会利用多类比较：尚未处理与已处理、较早处理与较晚处理，甚至较晚处理单位实施后与已经处理很久的单位比较。若效应随处理时长增长，后者已经受到处理，便不是干净的反事实。",[1793,3360,3361],{},"问题不只是“标准误算错”，而是回归系数可能成为许多组别—时间效应的非透明加权平均；某些隐含权重还可能为负。此时提高样本量不能修复 estimand 错位。",[1838,3363,3365],{"id":3364},"_3-borusyakjaravel-与-spiess-的插补思路","3. Borusyak、Jaravel 与 Spiess 的插补思路",[1793,3367,3368],{},"Borusyak、Jaravel 与 Spiess（2024）针对交错处理和异质处理效应建立统一框架，并推导了在其条件下有效的估计量。无限制异质性下，估计量具有直观的插补形式：",[1812,3370,3371,3469,3619,3823],{},[1815,3372,3373,3374,3468],{},"只用未处理观测估计 ",[1846,3375,3377,3404],{"className":3376},[1849],[1846,3378,3380],{"className":3379},[1853],[1855,3381,3382],{"xmlns":1857},[1859,3383,3384,3402],{},[1862,3385,3386,3396,3398,3400],{},[1905,3387,3388,3390],{},[1865,3389,2213],{},[1862,3391,3392,3394],{},[1865,3393,1867],{},[1865,3395,2010],{},[2012,3397,2023],{"stretchy":2022},[2016,3399,2224],{},[2012,3401,2037],{"stretchy":2022},[1869,3403,2229],{"encoding":1871},[1846,3405,3407],{"className":3406,"ariaHidden":1876},[1875],[1846,3408,3410,3413,3459,3462,3465],{"className":3409},[1880],[1846,3411],{"className":3412,"style":2120},[1884],[1846,3414,3416,3419],{"className":3415},[1889],[1846,3417,2213],{"className":3418,"style":2245},[1889,1890],[1846,3420,3422],{"className":3421},[1934],[1846,3423,3425,3451],{"className":3424},[1938,1939],[1846,3426,3428,3448],{"className":3427},[1943],[1846,3429,3431],{"className":3430,"style":1948},[1947],[1846,3432,3433,3436],{"style":2260},[1846,3434],{"className":3435,"style":1956},[1955],[1846,3437,3439],{"className":3438},[1960,1961,1962,1963],[1846,3440,3442,3445],{"className":3441},[1889,1963],[1846,3443,1867],{"className":3444},[1889,1890,1963],[1846,3446,2010],{"className":3447},[1889,1890,1963],[1846,3449,1971],{"className":3450},[1970],[1846,3452,3454],{"className":3453},[1943],[1846,3455,3457],{"className":3456,"style":1978},[1947],[1846,3458],{},[1846,3460,2023],{"className":3461},[2128],[1846,3463,2224],{"className":3464},[1889],[1846,3466,2037],{"className":3467},[2190]," 的模型；",[1815,3470,3471,3472,3618],{},"为已经处理的观测预测反事实 ",[1846,3473,3475,3509],{"className":3474},[1849],[1846,3476,3478],{"className":3477},[1853],[1855,3479,3480],{"xmlns":1857},[1859,3481,3482,3506],{},[1862,3483,3484,3500,3502,3504],{},[1905,3485,3486,3494],{},[3487,3488,3489,3491],"mover",{"accent":1876},[1865,3490,2213],{},[2012,3492,3493],{"stretchy":1876},"^",[1862,3495,3496,3498],{},[1865,3497,1867],{},[1865,3499,2010],{},[2012,3501,2023],{"stretchy":2022},[2016,3503,2224],{},[2012,3505,2037],{"stretchy":2022},[1869,3507,3508],{"encoding":1871},"\\widehat Y_{it}(0)",[1846,3510,3512],{"className":3511,"ariaHidden":1876},[1875],[1846,3513,3515,3519,3609,3612,3615],{"className":3514},[1880],[1846,3516],{"className":3517,"style":3518},[1884],"height:1.1733em;vertical-align:-0.25em;",[1846,3520,3522,3569],{"className":3521},[1889],[1846,3523,3526],{"className":3524},[1889,3525],"accent",[1846,3527,3529],{"className":3528},[1938],[1846,3530,3532],{"className":3531},[1943],[1846,3533,3536,3546],{"className":3534,"style":3535},[1947],"height:0.9233em;",[1846,3537,3539,3543],{"style":3538},"top:-3em;",[1846,3540],{"className":3541,"style":3542},[1955],"height:3em;",[1846,3544,2213],{"className":3545,"style":2245},[1889,1890],[1846,3547,3551,3554],{"className":3548,"style":3550},[3549],"svg-align","top:-3.6833em;",[1846,3552],{"className":3553,"style":3542},[1955],[1846,3555,3557],{"style":3556},"height:0.24em;",[3558,3559,3565],"svg",{"xmlns":3560,"width":3561,"height":3562,"viewBox":3563,"preserveAspectRatio":3564},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","100%","0.24em","0 0 1062 239","none",[3566,3567],"path",{"d":3568},"M529 0h5l519 115c5 1 9 5 9 10 0 1-1 2-1 3l-4 22\nc-1 5-5 9-11 9h-2L532 67 19 159h-2c-5 0-9-4-11-9l-5-22c-1-6 2-12 8-13z",[1846,3570,3572],{"className":3571},[1934],[1846,3573,3575,3601],{"className":3574},[1938,1939],[1846,3576,3578,3598],{"className":3577},[1943],[1846,3579,3581],{"className":3580,"style":1948},[1947],[1846,3582,3583,3586],{"style":2260},[1846,3584],{"className":3585,"style":1956},[1955],[1846,3587,3589],{"className":3588},[1960,1961,1962,1963],[1846,3590,3592,3595],{"className":3591},[1889,1963],[1846,3593,1867],{"className":3594},[1889,1890,1963],[1846,3596,2010],{"className":3597},[1889,1890,1963],[1846,3599,1971],{"className":3600},[1970],[1846,3602,3604],{"className":3603},[1943],[1846,3605,3607],{"className":3606,"style":1978},[1947],[1846,3608],{},[1846,3610,2023],{"className":3611},[2128],[1846,3613,2224],{"className":3614},[1889],[1846,3616,2037],{"className":3617},[2190],"；",[1815,3620,3621,3622,3618],{},"计算处理观测的残差 ",[1846,3623,3625,3669],{"className":3624},[1849],[1846,3626,3628],{"className":3627},[1853],[1855,3629,3630],{"xmlns":1857},[1859,3631,3632,3666],{},[1862,3633,3634,3644,3646,3660,3662,3664],{},[1905,3635,3636,3638],{},[1865,3637,2213],{},[1862,3639,3640,3642],{},[1865,3641,1867],{},[1865,3643,2010],{},[2012,3645,2487],{},[1905,3647,3648,3654],{},[3487,3649,3650,3652],{"accent":1876},[1865,3651,2213],{},[2012,3653,3493],{"stretchy":1876},[1862,3655,3656,3658],{},[1865,3657,1867],{},[1865,3659,2010],{},[2012,3661,2023],{"stretchy":2022},[2016,3663,2224],{},[2012,3665,2037],{"stretchy":2022},[1869,3667,3668],{"encoding":1871},"Y_{it}-\\widehat Y_{it}(0)",[1846,3670,3672,3733],{"className":3671,"ariaHidden":1876},[1875],[1846,3673,3675,3678,3724,3727,3730],{"className":3674},[1880],[1846,3676],{"className":3677,"style":1924},[1884],[1846,3679,3681,3684],{"className":3680},[1889],[1846,3682,2213],{"className":3683,"style":2245},[1889,1890],[1846,3685,3687],{"className":3686},[1934],[1846,3688,3690,3716],{"className":3689},[1938,1939],[1846,3691,3693,3713],{"className":3692},[1943],[1846,3694,3696],{"className":3695,"style":1948},[1947],[1846,3697,3698,3701],{"style":2260},[1846,3699],{"className":3700,"style":1956},[1955],[1846,3702,3704],{"className":3703},[1960,1961,1962,1963],[1846,3705,3707,3710],{"className":3706},[1889,1963],[1846,3708,1867],{"className":3709},[1889,1890,1963],[1846,3711,2010],{"className":3712},[1889,1890,1963],[1846,3714,1971],{"className":3715},[1970],[1846,3717,3719],{"className":3718},[1943],[1846,3720,3722],{"className":3721,"style":1978},[1947],[1846,3723],{},[1846,3725],{"className":3726,"style":2245},[2105],[1846,3728,2487],{"className":3729},[2659],[1846,3731],{"className":3732,"style":2245},[2105],[1846,3734,3736,3739,3814,3817,3820],{"className":3735},[1880],[1846,3737],{"className":3738,"style":3518},[1884],[1846,3740,3742,3774],{"className":3741},[1889],[1846,3743,3745],{"className":3744},[1889,3525],[1846,3746,3748],{"className":3747},[1938],[1846,3749,3751],{"className":3750},[1943],[1846,3752,3754,3762],{"className":3753,"style":3535},[1947],[1846,3755,3756,3759],{"style":3538},[1846,3757],{"className":3758,"style":3542},[1955],[1846,3760,2213],{"className":3761,"style":2245},[1889,1890],[1846,3763,3765,3768],{"className":3764,"style":3550},[3549],[1846,3766],{"className":3767,"style":3542},[1955],[1846,3769,3770],{"style":3556},[3558,3771,3772],{"xmlns":3560,"width":3561,"height":3562,"viewBox":3563,"preserveAspectRatio":3564},[3566,3773],{"d":3568},[1846,3775,3777],{"className":3776},[1934],[1846,3778,3780,3806],{"className":3779},[1938,1939],[1846,3781,3783,3803],{"className":3782},[1943],[1846,3784,3786],{"className":3785,"style":1948},[1947],[1846,3787,3788,3791],{"style":2260},[1846,3789],{"className":3790,"style":1956},[1955],[1846,3792,3794],{"className":3793},[1960,1961,1962,1963],[1846,3795,3797,3800],{"className":3796},[1889,1963],[1846,3798,1867],{"className":3799},[1889,1890,1963],[1846,3801,2010],{"className":3802},[1889,1890,1963],[1846,3804,1971],{"className":3805},[1970],[1846,3807,3809],{"className":3808},[1943],[1846,3810,3812],{"className":3811,"style":1978},[1947],[1846,3813],{},[1846,3815,2023],{"className":3816},[2128],[1846,3818,2224],{"className":3819},[1889],[1846,3821,2037],{"className":3822},[2190],[1815,3824,3825],{},"按预先声明的组别、时期或事件时间权重聚合。",[1793,3827,3828],{},"在最简单的平行趋势模型中：",[1846,3830,3832],{"className":3831},[1985],[1846,3833,3835,3894],{"className":3834},[1849],[1846,3836,3838],{"className":3837},[1853],[1855,3839,3840],{"xmlns":1857,"display":1994},[1859,3841,3842,3891],{},[1862,3843,3844,3854,3856,3858,3860,3862,3868,3870,3876,3878,3889],{},[1905,3845,3846,3848],{},[1865,3847,2213],{},[1862,3849,3850,3852],{},[1865,3851,1867],{},[1865,3853,2010],{},[2012,3855,2023],{"stretchy":2022},[2016,3857,2224],{},[2012,3859,2037],{"stretchy":2022},[2012,3861,2014],{},[1905,3863,3864,3866],{},[1865,3865,2983],{},[1865,3867,1867],{},[2012,3869,2988],{},[1905,3871,3872,3874],{},[1865,3873,2993],{},[1865,3875,2010],{},[2012,3877,2988],{},[1905,3879,3880,3883],{},[1865,3881,3882],{},"ε",[1862,3884,3885,3887],{},[1865,3886,1867],{},[1865,3888,2010],{},[1865,3890,2041],{"mathvariant":2040},[1869,3892,3893],{"encoding":1871},"Y_{it}(0)=\\alpha_i+\\lambda_t+\\varepsilon_{it}.",[1846,3895,3897,3967,4022,4077],{"className":3896,"ariaHidden":1876},[1875],[1846,3898,3900,3903,3949,3952,3955,3958,3961,3964],{"className":3899},[1880],[1846,3901],{"className":3902,"style":2120},[1884],[1846,3904,3906,3909],{"className":3905},[1889],[1846,3907,2213],{"className":3908,"style":2245},[1889,1890],[1846,3910,3912],{"className":3911},[1934],[1846,3913,3915,3941],{"className":3914},[1938,1939],[1846,3916,3918,3938],{"className":3917},[1943],[1846,3919,3921],{"className":3920,"style":1948},[1947],[1846,3922,3923,3926],{"style":2260},[1846,3924],{"className":3925,"style":1956},[1955],[1846,3927,3929],{"className":3928},[1960,1961,1962,1963],[1846,3930,3932,3935],{"className":3931},[1889,1963],[1846,3933,1867],{"className":3934},[1889,1890,1963],[1846,3936,2010],{"className":3937},[1889,1890,1963],[1846,3939,1971],{"className":3940},[1970],[1846,3942,3944],{"className":3943},[1943],[1846,3945,3947],{"className":3946,"style":1978},[1947],[1846,3948],{},[1846,3950,2023],{"className":3951},[2128],[1846,3953,2224],{"className":3954},[1889],[1846,3956,2037],{"className":3957},[2190],[1846,3959],{"className":3960,"style":2106},[2105],[1846,3962,2014],{"className":3963},[2110],[1846,3965],{"className":3966,"style":2106},[2105],[1846,3968,3970,3973,4013,4016,4019],{"className":3969},[1880],[1846,3971],{"className":3972,"style":3098},[1884],[1846,3974,3976,3979],{"className":3975},[1889],[1846,3977,2983],{"className":3978,"style":3105},[1889,1890],[1846,3980,3982],{"className":3981},[1934],[1846,3983,3985,4005],{"className":3984},[1938,1939],[1846,3986,3988,4002],{"className":3987},[1943],[1846,3989,3991],{"className":3990,"style":1948},[1947],[1846,3992,3993,3996],{"style":3120},[1846,3994],{"className":3995,"style":1956},[1955],[1846,3997,3999],{"className":3998},[1960,1961,1962,1963],[1846,4000,1867],{"className":4001},[1889,1890,1963],[1846,4003,1971],{"className":4004},[1970],[1846,4006,4008],{"className":4007},[1943],[1846,4009,4011],{"className":4010,"style":1978},[1947],[1846,4012],{},[1846,4014],{"className":4015,"style":2245},[2105],[1846,4017,2988],{"className":4018},[2659],[1846,4020],{"className":4021,"style":2245},[2105],[1846,4023,4025,4028,4068,4071,4074],{"className":4024},[1880],[1846,4026],{"className":4027,"style":3156},[1884],[1846,4029,4031,4034],{"className":4030},[1889],[1846,4032,2993],{"className":4033},[1889,1890],[1846,4035,4037],{"className":4036},[1934],[1846,4038,4040,4060],{"className":4039},[1938,1939],[1846,4041,4043,4057],{"className":4042},[1943],[1846,4044,4046],{"className":4045,"style":3175},[1947],[1846,4047,4048,4051],{"style":1951},[1846,4049],{"className":4050,"style":1956},[1955],[1846,4052,4054],{"className":4053},[1960,1961,1962,1963],[1846,4055,2010],{"className":4056},[1889,1890,1963],[1846,4058,1971],{"className":4059},[1970],[1846,4061,4063],{"className":4062},[1943],[1846,4064,4066],{"className":4065,"style":1978},[1947],[1846,4067],{},[1846,4069],{"className":4070,"style":2245},[2105],[1846,4072,2988],{"className":4073},[2659],[1846,4075],{"className":4076,"style":2245},[2105],[1846,4078,4080,4083,4129],{"className":4079},[1880],[1846,4081],{"className":4082,"style":3277},[1884],[1846,4084,4086,4089],{"className":4085},[1889],[1846,4087,3882],{"className":4088},[1889,1890],[1846,4090,4092],{"className":4091},[1934],[1846,4093,4095,4121],{"className":4094},[1938,1939],[1846,4096,4098,4118],{"className":4097},[1943],[1846,4099,4101],{"className":4100,"style":1948},[1947],[1846,4102,4103,4106],{"style":1951},[1846,4104],{"className":4105,"style":1956},[1955],[1846,4107,4109],{"className":4108},[1960,1961,1962,1963],[1846,4110,4112,4115],{"className":4111},[1889,1963],[1846,4113,1867],{"className":4114},[1889,1890,1963],[1846,4116,2010],{"className":4117},[1889,1890,1963],[1846,4119,1971],{"className":4120},[1970],[1846,4122,4124],{"className":4123},[1943],[1846,4125,4127],{"className":4126,"style":1978},[1947],[1846,4128],{},[1846,4130,2041],{"className":4131},[1889],[1793,4133,4134,4135,4138],{},"关键纪律是：",[1800,4136,4137],{},"处理后的结果不能用来拟合未处理路径。"," 这不意味着插补自动可信；它仍依赖未处理结果模型、无预期效应、可用对照组和误差结构。",[1793,4140,4141],{},"论文将方法用于美国退税后的消费反应，报告第一季度名义边际消费倾向约为 8%—11%，大约是用于校准宏观模型的一些基准估计的一半，而且支出反应主要集中在第一个月。这个数字属于论文特定数据和定义，不能直接当作其他财政转移的乘数。",[1805,4143,4145],{"id":4144},"案例二现代-did-不是换一个软件包","案例二：现代 DID 不是“换一个软件包”",[1793,4147,4148],{},"Roth、Sant’Anna、Bilinski 与 Poe（2023）的综述把近年来 DID 的进展组织为三类：多期与处理时点变化、平行趋势可能偏离、以及替代推断框架。教学上可把它转成下面的决策表。",[4150,4151,4152,4168],"table",{},[4153,4154,4155],"thead",{},[4156,4157,4158,4162,4165],"tr",{},[4159,4160,4161],"th",{},"研究情形",[4159,4163,4164],{},"首先要问",[4159,4166,4167],{},"不能只做什么",[4169,4170,4171,4183,4194,4301,4312],"tbody",{},[4156,4172,4173,4177,4180],{},[4174,4175,4176],"td",{},"所有单位同一时点处理",[4174,4178,4179],{},"对照组是否给出可信趋势",[4174,4181,4182],{},"只看一条处理后系数",[4156,4184,4185,4188,4191],{},[4174,4186,4187],{},"分批处理",[4174,4189,4190],{},"每个时期谁仍未处理",[4174,4192,4193],{},"机械使用 TWFE 事件研究",[4156,4195,4196,4199,4269],{},[4174,4197,4198],{},"处理效应动态变化",[4174,4200,4201,4202],{},"想聚合哪一组 ",[1846,4203,4205,4233],{"className":4204},[1849],[1846,4206,4208],{"className":4207},[1853],[1855,4209,4210],{"xmlns":1857},[1859,4211,4212,4230],{},[1862,4213,4214,4216,4218,4220,4222,4224,4226,4228],{},[1865,4215,2443],{},[1865,4217,2446],{},[1865,4219,2446],{},[2012,4221,2023],{"stretchy":2022},[1865,4223,2453],{},[2012,4225,2456],{"separator":1876},[1865,4227,2010],{},[2012,4229,2037],{"stretchy":2022},[1869,4231,4232],{"encoding":1871},"ATT(g,t)",[1846,4234,4236],{"className":4235,"ariaHidden":1876},[1875],[1846,4237,4239,4242,4245,4248,4251,4254,4257,4260,4263,4266],{"className":4238},[1880],[1846,4240],{"className":4241,"style":2120},[1884],[1846,4243,2443],{"className":4244},[1889,1890],[1846,4246,2446],{"className":4247,"style":2551},[1889,1890],[1846,4249,2446],{"className":4250,"style":2551},[1889,1890],[1846,4252,2023],{"className":4253},[2128],[1846,4255,2453],{"className":4256,"style":2561},[1889,1890],[1846,4258,2456],{"className":4259},[2565],[1846,4261],{"className":4262,"style":2569},[2105],[1846,4264,2010],{"className":4265},[1889,1890],[1846,4267,2037],{"className":4268},[2190],[4174,4270,4271,4272,4300],{},"把一个 ",[1846,4273,4275,4288],{"className":4274},[1849],[1846,4276,4278],{"className":4277},[1853],[1855,4279,4280],{"xmlns":1857},[1859,4281,4282,4286],{},[1862,4283,4284],{},[1865,4285,2407],{},[1869,4287,2410],{"encoding":1871},[1846,4289,4291],{"className":4290,"ariaHidden":1876},[1875],[1846,4292,4294,4297],{"className":4293},[1880],[1846,4295],{"className":4296,"style":2420},[1884],[1846,4298,2407],{"className":4299,"style":2424},[1889,1890]," 当成普遍效应",[4156,4302,4303,4306,4309],{},[4174,4304,4305],{},"处理前趋势不完全平行",[4174,4307,4308],{},"多大偏离会改变结论",[4174,4310,4311],{},"把 lead 不显著当作证明",[4156,4313,4314,4317,4320],{},[4174,4315,4316],{},"少量处理组或组内相关",[4174,4318,4319],{},"有多少独立分配单元",[4174,4321,4322],{},"仅使用个体级普通标准误",[1838,4324,4325],{"id":4325},"预趋势检验的正确读法",[1793,4327,4328],{},"事件研究中处理前系数没有显著偏离零，可能是因为趋势确实接近平行，也可能是检验功效太低。反过来，某个 lead 显著也可能来自随机波动、多重检验、提前反应或模型设定。一个强分析至少要报告：",[4330,4331,4332,4335,4338,4341,4344],"ul",{},[1815,4333,4334],{},"处理前系数及联合置信区间；",[1815,4336,4337],{},"处理组和对照组的原始或残差化趋势；",[1815,4339,4340],{},"对不同幅度非平行趋势的敏感性；",[1815,4342,4343],{},"处理时点、预期效应和样本构成变化；",[1815,4345,4346],{},"推断在哪个层级聚类，以及处理组数量是否足够。",[1838,4348,4349],{"id":4349},"研究生应写出的聚合式",[1793,4351,4352,4353,4381],{},"如果目标是事件时间 ",[1846,4354,4356,4369],{"className":4355},[1849],[1846,4357,4359],{"className":4358},[1853],[1855,4360,4361],{"xmlns":1857},[1859,4362,4363,4367],{},[1862,4364,4365],{},[1865,4366,2852],{},[1869,4368,2852],{"encoding":1871},[1846,4370,4372],{"className":4371,"ariaHidden":1876},[1875],[1846,4373,4375,4378],{"className":4374},[1880],[1846,4376],{"className":4377,"style":2873},[1884],[1846,4379,2852],{"className":4380,"style":2877},[1889,1890]," 的平均效应，应明确权重：",[1846,4383,4385],{"className":4384},[1985],[1846,4386,4388,4493],{"className":4387},[1849],[1846,4389,4391],{"className":4390},[1853],[1855,4392,4393],{"xmlns":1857,"display":1994},[1859,4394,4395,4490],{},[1862,4396,4397,4404,4406,4430,4443,4445,4447,4449,4451,4453,4455,4457,4459,4461,4463,4465,4467,4473,4485,4487],{},[1905,4398,4399,4402],{},[1865,4400,4401],{},"τ",[1865,4403,2852],{},[2012,4405,2014],{},[4407,4408,4409,4412],"munder",{},[2012,4410,4411],{},"∑",[1862,4413,4414,4416,4419,4421,4423,4425,4428],{},[1865,4415,2453],{},[2012,4417,4418],{},":",[1865,4420,2453],{},[2012,4422,2988],{},[1865,4424,2852],{},[2012,4426,4427],{},"≤",[1865,4429,2446],{},[1905,4431,4432,4435],{},[1865,4433,4434],{},"w",[1862,4436,4437,4439,4441],{},[1865,4438,2453],{},[2012,4440,2456],{"separator":1876},[1865,4442,2852],{},[1865,4444,2443],{},[1865,4446,2446],{},[1865,4448,2446],{},[2012,4450,2023],{"stretchy":2022},[1865,4452,2453],{},[2012,4454,2456],{"separator":1876},[1865,4456,2453],{},[2012,4458,2988],{},[1865,4460,2852],{},[2012,4462,2037],{"stretchy":2022},[2012,4464,2456],{"separator":1876},[2105,4466],{"width":2524},[4407,4468,4469,4471],{},[2012,4470,4411],{},[1865,4472,2453],{},[1905,4474,4475,4477],{},[1865,4476,4434],{},[1862,4478,4479,4481,4483],{},[1865,4480,2453],{},[2012,4482,2456],{"separator":1876},[1865,4484,2852],{},[2012,4486,2014],{},[2016,4488,4489],{},"1.",[1869,4491,4492],{"encoding":1871},"\\tau_k=\\sum_{g:g+k\\le T}w_{g,k}ATT(g,g+k),\n\\qquad \\sum_g w_{g,k}=1.",[1846,4494,4496,4554,4723,4852],{"className":4495,"ariaHidden":1876},[1875],[1846,4497,4499,4502,4545,4548,4551],{"className":4498},[1880],[1846,4500],{"className":4501,"style":3277},[1884],[1846,4503,4505,4509],{"className":4504},[1889],[1846,4506,4401],{"className":4507,"style":4508},[1889,1890],"margin-right:0.1132em;",[1846,4510,4512],{"className":4511},[1934],[1846,4513,4515,4537],{"className":4514},[1938,1939],[1846,4516,4518,4534],{"className":4517},[1943],[1846,4519,4522],{"className":4520,"style":4521},[1947],"height:0.3361em;",[1846,4523,4525,4528],{"style":4524},"top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;",[1846,4526],{"className":4527,"style":1956},[1955],[1846,4529,4531],{"className":4530},[1960,1961,1962,1963],[1846,4532,2852],{"className":4533,"style":2877},[1889,1890,1963],[1846,4535,1971],{"className":4536},[1970],[1846,4538,4540],{"className":4539},[1943],[1846,4541,4543],{"className":4542,"style":1978},[1947],[1846,4544],{},[1846,4546],{"className":4547,"style":2106},[2105],[1846,4549,2014],{"className":4550},[2110],[1846,4552],{"className":4553,"style":2106},[2105],[1846,4555,4557,4561,4635,4638,4690,4693,4696,4699,4702,4705,4708,4711,4714,4717,4720],{"className":4556},[1880],[1846,4558],{"className":4559,"style":4560},[1884],"height:2.4882em;vertical-align:-1.4382em;",[1846,4562,4566],{"className":4563},[4564,4565],"mop","op-limits",[1846,4567,4569,4626],{"className":4568},[1938,1939],[1846,4570,4572,4623],{"className":4571},[1943],[1846,4573,4576,4610],{"className":4574,"style":4575},[1947],"height:1.05em;",[1846,4577,4579,4583],{"style":4578},"top:-1.8479em;margin-left:0em;",[1846,4580],{"className":4581,"style":4582},[1955],"height:3.05em;",[1846,4584,4586],{"className":4585},[1960,1961,1962,1963],[1846,4587,4589,4592,4595,4598,4601,4604,4607],{"className":4588},[1889,1963],[1846,4590,2453],{"className":4591,"style":2561},[1889,1890,1963],[1846,4593,4418],{"className":4594},[2110,1963],[1846,4596,2453],{"className":4597,"style":2561},[1889,1890,1963],[1846,4599,2988],{"className":4600},[2659,1963],[1846,4602,2852],{"className":4603,"style":2877},[1889,1890,1963],[1846,4605,4427],{"className":4606},[2110,1963],[1846,4608,2446],{"className":4609,"style":2551},[1889,1890,1963],[1846,4611,4613,4616],{"style":4612},"top:-3.05em;",[1846,4614],{"className":4615,"style":4582},[1955],[1846,4617,4618],{},[1846,4619,4411],{"className":4620},[4564,4621,4622],"op-symbol","large-op",[1846,4624,1971],{"className":4625},[1970],[1846,4627,4629],{"className":4628},[1943],[1846,4630,4633],{"className":4631,"style":4632},[1947],"height:1.4382em;",[1846,4634],{},[1846,4636],{"className":4637,"style":2569},[2105],[1846,4639,4641,4645],{"className":4640},[1889],[1846,4642,4434],{"className":4643,"style":4644},[1889,1890],"margin-right:0.0269em;",[1846,4646,4648],{"className":4647},[1934],[1846,4649,4651,4681],{"className":4650},[1938,1939],[1846,4652,4654,4678],{"className":4653},[1943],[1846,4655,4657],{"className":4656,"style":4521},[1947],[1846,4658,4660,4663],{"style":4659},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1846,4661],{"className":4662,"style":1956},[1955],[1846,4664,4666],{"className":4665},[1960,1961,1962,1963],[1846,4667,4669,4672,4675],{"className":4668},[1889,1963],[1846,4670,2453],{"className":4671,"style":2561},[1889,1890,1963],[1846,4673,2456],{"className":4674},[2565,1963],[1846,4676,2852],{"className":4677,"style":2877},[1889,1890,1963],[1846,4679,1971],{"className":4680},[1970],[1846,4682,4684],{"className":4683},[1943],[1846,4685,4688],{"className":4686,"style":4687},[1947],"height:0.2861em;",[1846,4689],{},[1846,4691,2443],{"className":4692},[1889,1890],[1846,4694,2446],{"className":4695,"style":2551},[1889,1890],[1846,4697,2446],{"className":4698,"style":2551},[1889,1890],[1846,4700,2023],{"className":4701},[2128],[1846,4703,2453],{"className":4704,"style":2561},[1889,1890],[1846,4706,2456],{"className":4707},[2565],[1846,4709],{"className":4710,"style":2569},[2105],[1846,4712,2453],{"className":4713,"style":2561},[1889,1890],[1846,4715],{"className":4716,"style":2245},[2105],[1846,4718,2988],{"className":4719},[2659],[1846,4721],{"className":4722,"style":2245},[2105],[1846,4724,4726,4730,4733,4736,4739,4742,4745,4791,4794,4843,4846,4849],{"className":4725},[1880],[1846,4727],{"className":4728,"style":4729},[1884],"height:2.4361em;vertical-align:-1.3861em;",[1846,4731,2852],{"className":4732,"style":2877},[1889,1890],[1846,4734,2037],{"className":4735},[2190],[1846,4737,2456],{"className":4738},[2565],[1846,4740],{"className":4741,"style":2806},[2105],[1846,4743],{"className":4744,"style":2569},[2105],[1846,4746,4748],{"className":4747},[4564,4565],[1846,4749,4751,4782],{"className":4750},[1938,1939],[1846,4752,4754,4779],{"className":4753},[1943],[1846,4755,4757,4769],{"className":4756,"style":4575},[1947],[1846,4758,4760,4763],{"style":4759},"top:-1.9em;margin-left:0em;",[1846,4761],{"className":4762,"style":4582},[1955],[1846,4764,4766],{"className":4765},[1960,1961,1962,1963],[1846,4767,2453],{"className":4768,"style":2561},[1889,1890,1963],[1846,4770,4771,4774],{"style":4612},[1846,4772],{"className":4773,"style":4582},[1955],[1846,4775,4776],{},[1846,4777,4411],{"className":4778},[4564,4621,4622],[1846,4780,1971],{"className":4781},[1970],[1846,4783,4785],{"className":4784},[1943],[1846,4786,4789],{"className":4787,"style":4788},[1947],"height:1.3861em;",[1846,4790],{},[1846,4792],{"className":4793,"style":2569},[2105],[1846,4795,4797,4800],{"className":4796},[1889],[1846,4798,4434],{"className":4799,"style":4644},[1889,1890],[1846,4801,4803],{"className":4802},[1934],[1846,4804,4806,4835],{"className":4805},[1938,1939],[1846,4807,4809,4832],{"className":4808},[1943],[1846,4810,4812],{"className":4811,"style":4521},[1947],[1846,4813,4814,4817],{"style":4659},[1846,4815],{"className":4816,"style":1956},[1955],[1846,4818,4820],{"className":4819},[1960,1961,1962,1963],[1846,4821,4823,4826,4829],{"className":4822},[1889,1963],[1846,4824,2453],{"className":4825,"style":2561},[1889,1890,1963],[1846,4827,2456],{"className":4828},[2565,1963],[1846,4830,2852],{"className":4831,"style":2877},[1889,1890,1963],[1846,4833,1971],{"className":4834},[1970],[1846,4836,4838],{"className":4837},[1943],[1846,4839,4841],{"className":4840,"style":4687},[1947],[1846,4842],{},[1846,4844],{"className":4845,"style":2106},[2105],[1846,4847,2014],{"className":4848},[2110],[1846,4850],{"className":4851,"style":2106},[2105],[1846,4853,4855,4859],{"className":4854},[1880],[1846,4856],{"className":4857,"style":4858},[1884],"height:0.6444em;",[1846,4860,4489],{"className":4861},[1889],[1793,4863,4864,4950],{},[1846,4865,4867,4891],{"className":4866},[1849],[1846,4868,4870],{"className":4869},[1853],[1855,4871,4872],{"xmlns":1857},[1859,4873,4874,4888],{},[1862,4875,4876],{},[1905,4877,4878,4880],{},[1865,4879,4434],{},[1862,4881,4882,4884,4886],{},[1865,4883,2453],{},[2012,4885,2456],{"separator":1876},[1865,4887,2852],{},[1869,4889,4890],{"encoding":1871},"w_{g,k}",[1846,4892,4894],{"className":4893,"ariaHidden":1876},[1875],[1846,4895,4897,4901],{"className":4896},[1880],[1846,4898],{"className":4899,"style":4900},[1884],"height:0.7167em;vertical-align:-0.2861em;",[1846,4902,4904,4907],{"className":4903},[1889],[1846,4905,4434],{"className":4906,"style":4644},[1889,1890],[1846,4908,4910],{"className":4909},[1934],[1846,4911,4913,4942],{"className":4912},[1938,1939],[1846,4914,4916,4939],{"className":4915},[1943],[1846,4917,4919],{"className":4918,"style":4521},[1947],[1846,4920,4921,4924],{"style":4659},[1846,4922],{"className":4923,"style":1956},[1955],[1846,4925,4927],{"className":4926},[1960,1961,1962,1963],[1846,4928,4930,4933,4936],{"className":4929},[1889,1963],[1846,4931,2453],{"className":4932,"style":2561},[1889,1890,1963],[1846,4934,2456],{"className":4935},[2565,1963],[1846,4937,2852],{"className":4938,"style":2877},[1889,1890,1963],[1846,4940,1971],{"className":4941},[1970],[1846,4943,4945],{"className":4944},[1943],[1846,4946,4948],{"className":4947,"style":4687},[1947],[1846,4949],{}," 可以按组规模、目标人群或政策相关性设定。没有“自然唯一”的聚合；不同权重回答不同问题。",[1805,4952,4954],{"id":4953},"案例三文本和图像成为混淆变量以后","案例三：文本和图像成为混淆变量以后",[1838,4956,4958],{"id":4957},"_1-从低维控制到多模态混淆","1. 从低维控制到多模态混淆",[1793,4960,4961],{},"在很多现代研究中，处理选择可能受病历文本、卫星图像、简历或产品图片影响。把这些信息压缩成几个手工指标，可能遗漏重要混淆；直接把高维表示塞进结果回归，又可能产生正则化偏误和过拟合。",[1793,4963,4964],{},"Spindler 等（2026）在双重机器学习框架中为文本与图像混淆设计神经网络结构，并通过半合成数据评估覆盖率。论文的贡献是方法与评估，不是声称任何神经网络都能解决未观测混淆。",[1838,4966,4968],{"id":4967},"_2-部分线性模型与正交化","2. 部分线性模型与正交化",[1793,4970,4971],{},"考虑：",[1846,4973,4975],{"className":4974},[1985],[1846,4976,4978,5050],{"className":4977},[1849],[1846,4979,4981],{"className":4980},[1853],[1855,4982,4983],{"xmlns":1857,"display":1994},[1859,4984,4985,5047],{},[1862,4986,4987,4989,4991,4998,5000,5002,5008,5010,5013,5015,5017,5019,5021,5023,5025,5027,5034,5036,5038,5040,5042,5045],{},[1865,4988,2213],{},[2012,4990,2014],{},[1905,4992,4993,4996],{},[1865,4994,4995],{},"θ",[2016,4997,2224],{},[1865,4999,2003],{},[2012,5001,2988],{},[1905,5003,5004,5006],{},[1865,5005,2453],{},[2016,5007,2224],{},[2012,5009,2023],{"stretchy":2022},[1865,5011,5012],{},"X",[2012,5014,2037],{"stretchy":2022},[2012,5016,2988],{},[1865,5018,3882],{},[2012,5020,2456],{"separator":1876},[2105,5022],{"width":2524},[1865,5024,2003],{},[2012,5026,2014],{},[1905,5028,5029,5032],{},[1865,5030,5031],{},"m",[2016,5033,2224],{},[2012,5035,2023],{"stretchy":2022},[1865,5037,5012],{},[2012,5039,2037],{"stretchy":2022},[2012,5041,2988],{},[1865,5043,5044],{},"v",[2012,5046,2456],{"separator":1876},[1869,5048,5049],{"encoding":1871},"Y=\\theta_0D+g_0(X)+\\varepsilon,\n\\qquad\nD=m_0(X)+v,",[1846,5051,5053,5072,5131,5197,5228,5292],{"className":5052,"ariaHidden":1876},[1875],[1846,5054,5056,5060,5063,5066,5069],{"className":5055},[1880],[1846,5057],{"className":5058,"style":5059},[1884],"height:0.6833em;",[1846,5061,2213],{"className":5062,"style":2245},[1889,1890],[1846,5064],{"className":5065,"style":2106},[2105],[1846,5067,2014],{"className":5068},[2110],[1846,5070],{"className":5071,"style":2106},[2105],[1846,5073,5075,5078,5119,5122,5125,5128],{"className":5074},[1880],[1846,5076],{"className":5077,"style":3156},[1884],[1846,5079,5081,5084],{"className":5080},[1889],[1846,5082,4995],{"className":5083,"style":2060},[1889,1890],[1846,5085,5087],{"className":5086},[1934],[1846,5088,5090,5111],{"className":5089},[1938,1939],[1846,5091,5093,5108],{"className":5092},[1943],[1846,5094,5097],{"className":5095,"style":5096},[1947],"height:0.3011em;",[1846,5098,5099,5102],{"style":2075},[1846,5100],{"className":5101,"style":1956},[1955],[1846,5103,5105],{"className":5104},[1960,1961,1962,1963],[1846,5106,2224],{"className":5107},[1889,1963],[1846,5109,1971],{"className":5110},[1970],[1846,5112,5114],{"className":5113},[1943],[1846,5115,5117],{"className":5116,"style":1978},[1947],[1846,5118],{},[1846,5120,2003],{"className":5121,"style":2060},[1889,1890],[1846,5123],{"className":5124,"style":2245},[2105],[1846,5126,2988],{"className":5127},[2659],[1846,5129],{"className":5130,"style":2245},[2105],[1846,5132,5134,5137,5178,5181,5185,5188,5191,5194],{"className":5133},[1880],[1846,5135],{"className":5136,"style":2120},[1884],[1846,5138,5140,5143],{"className":5139},[1889],[1846,5141,2453],{"className":5142,"style":2561},[1889,1890],[1846,5144,5146],{"className":5145},[1934],[1846,5147,5149,5170],{"className":5148},[1938,1939],[1846,5150,5152,5167],{"className":5151},[1943],[1846,5153,5155],{"className":5154,"style":5096},[1947],[1846,5156,5158,5161],{"style":5157},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1846,5159],{"className":5160,"style":1956},[1955],[1846,5162,5164],{"className":5163},[1960,1961,1962,1963],[1846,5165,2224],{"className":5166},[1889,1963],[1846,5168,1971],{"className":5169},[1970],[1846,5171,5173],{"className":5172},[1943],[1846,5174,5176],{"className":5175,"style":1978},[1947],[1846,5177],{},[1846,5179,2023],{"className":5180},[2128],[1846,5182,5012],{"className":5183,"style":5184},[1889,1890],"margin-right:0.0785em;",[1846,5186,2037],{"className":5187},[2190],[1846,5189],{"className":5190,"style":2245},[2105],[1846,5192,2988],{"className":5193},[2659],[1846,5195],{"className":5196,"style":2245},[2105],[1846,5198,5200,5204,5207,5210,5213,5216,5219,5222,5225],{"className":5199},[1880],[1846,5201],{"className":5202,"style":5203},[1884],"height:0.8778em;vertical-align:-0.1944em;",[1846,5205,3882],{"className":5206},[1889,1890],[1846,5208,2456],{"className":5209},[2565],[1846,5211],{"className":5212,"style":2806},[2105],[1846,5214],{"className":5215,"style":2569},[2105],[1846,5217,2003],{"className":5218,"style":2060},[1889,1890],[1846,5220],{"className":5221,"style":2106},[2105],[1846,5223,2014],{"className":5224},[2110],[1846,5226],{"className":5227,"style":2106},[2105],[1846,5229,5231,5234,5274,5277,5280,5283,5286,5289],{"className":5230},[1880],[1846,5232],{"className":5233,"style":2120},[1884],[1846,5235,5237,5240],{"className":5236},[1889],[1846,5238,5031],{"className":5239},[1889,1890],[1846,5241,5243],{"className":5242},[1934],[1846,5244,5246,5266],{"className":5245},[1938,1939],[1846,5247,5249,5263],{"className":5248},[1943],[1846,5250,5252],{"className":5251,"style":5096},[1947],[1846,5253,5254,5257],{"style":1951},[1846,5255],{"className":5256,"style":1956},[1955],[1846,5258,5260],{"className":5259},[1960,1961,1962,1963],[1846,5261,2224],{"className":5262},[1889,1963],[1846,5264,1971],{"className":5265},[1970],[1846,5267,5269],{"className":5268},[1943],[1846,5270,5272],{"className":5271,"style":1978},[1947],[1846,5273],{},[1846,5275,2023],{"className":5276},[2128],[1846,5278,5012],{"className":5279,"style":5184},[1889,1890],[1846,5281,2037],{"className":5282},[2190],[1846,5284],{"className":5285,"style":2245},[2105],[1846,5287,2988],{"className":5288},[2659],[1846,5290],{"className":5291,"style":2245},[2105],[1846,5293,5295,5298,5301],{"className":5294},[1880],[1846,5296],{"className":5297,"style":2828},[1884],[1846,5299,5044],{"className":5300,"style":2561},[1889,1890],[1846,5302,2456],{"className":5303},[2565],[1793,5305,5306,5307,5335,5336,5481,5482,5546,5547,2296,5617,5687],{},"其中 ",[1846,5308,5310,5323],{"className":5309},[1849],[1846,5311,5313],{"className":5312},[1853],[1855,5314,5315],{"xmlns":1857},[1859,5316,5317,5321],{},[1862,5318,5319],{},[1865,5320,5012],{},[1869,5322,5012],{"encoding":1871},[1846,5324,5326],{"className":5325,"ariaHidden":1876},[1875],[1846,5327,5329,5332],{"className":5328},[1880],[1846,5330],{"className":5331,"style":5059},[1884],[1846,5333,5012],{"className":5334,"style":5184},[1889,1890]," 可以同时含表格、文本和图像。再定义结果条件均值 ",[1846,5337,5339,5378],{"className":5338},[1849],[1846,5340,5342],{"className":5341},[1853],[1855,5343,5344],{"xmlns":1857},[1859,5345,5346,5375],{},[1862,5347,5348,5355,5357,5359,5361,5363,5365,5367,5369,5371,5373],{},[1905,5349,5350,5353],{},[1865,5351,5352],{"mathvariant":2040},"ℓ",[2016,5354,2224],{},[2012,5356,2023],{"stretchy":2022},[1865,5358,5012],{},[2012,5360,2037],{"stretchy":2022},[2012,5362,2014],{},[1865,5364,2465],{},[2012,5366,2468],{"stretchy":2022},[1865,5368,2213],{},[2012,5370,2506],{},[1865,5372,5012],{},[2012,5374,2519],{"stretchy":2022},[1869,5376,5377],{"encoding":1871},"\\ell_0(X)=E[Y\\mid X]",[1846,5379,5381,5445,5469],{"className":5380,"ariaHidden":1876},[1875],[1846,5382,5384,5387,5427,5430,5433,5436,5439,5442],{"className":5383},[1880],[1846,5385],{"className":5386,"style":2120},[1884],[1846,5388,5390,5393],{"className":5389},[1889],[1846,5391,5352],{"className":5392},[1889],[1846,5394,5396],{"className":5395},[1934],[1846,5397,5399,5419],{"className":5398},[1938,1939],[1846,5400,5402,5416],{"className":5401},[1943],[1846,5403,5405],{"className":5404,"style":5096},[1947],[1846,5406,5407,5410],{"style":1951},[1846,5408],{"className":5409,"style":1956},[1955],[1846,5411,5413],{"className":5412},[1960,1961,1962,1963],[1846,5414,2224],{"className":5415},[1889,1963],[1846,5417,1971],{"className":5418},[1970],[1846,5420,5422],{"className":5421},[1943],[1846,5423,5425],{"className":5424,"style":1978},[1947],[1846,5426],{},[1846,5428,2023],{"className":5429},[2128],[1846,5431,5012],{"className":5432,"style":5184},[1889,1890],[1846,5434,2037],{"className":5435},[2190],[1846,5437],{"className":5438,"style":2106},[2105],[1846,5440,2014],{"className":5441},[2110],[1846,5443],{"className":5444,"style":2106},[2105],[1846,5446,5448,5451,5454,5457,5460,5463,5466],{"className":5447},[1880],[1846,5449],{"className":5450,"style":2120},[1884],[1846,5452,2465],{"className":5453,"style":2594},[1889,1890],[1846,5455,2468],{"className":5456},[2128],[1846,5458,2213],{"className":5459,"style":2245},[1889,1890],[1846,5461],{"className":5462,"style":2106},[2105],[1846,5464,2506],{"className":5465},[2110],[1846,5467],{"className":5468,"style":2106},[2105],[1846,5470,5472,5475,5478],{"className":5471},[1880],[1846,5473],{"className":5474,"style":2120},[1884],[1846,5476,5012],{"className":5477,"style":5184},[1889,1890],[1846,5479,2519],{"className":5480},[2190],"。若直接把机器学习估计的高维控制函数代入结果回归，正则化误差可能传入 ",[1846,5483,5485,5503],{"className":5484},[1849],[1846,5486,5488],{"className":5487},[1853],[1855,5489,5490],{"xmlns":1857},[1859,5491,5492,5500],{},[1862,5493,5494],{},[3487,5495,5496,5498],{"accent":1876},[1865,5497,4995],{},[2012,5499,3493],{"stretchy":1876},[1869,5501,5502],{"encoding":1871},"\\widehat\\theta",[1846,5504,5506],{"className":5505,"ariaHidden":1876},[1875],[1846,5507,5509,5513],{"className":5508},[1880],[1846,5510],{"className":5511,"style":5512},[1884],"height:0.9344em;",[1846,5514,5516],{"className":5515},[1889,3525],[1846,5517,5519],{"className":5518},[1938],[1846,5520,5522],{"className":5521},[1943],[1846,5523,5525,5533],{"className":5524,"style":5512},[1947],[1846,5526,5527,5530],{"style":3538},[1846,5528],{"className":5529,"style":3542},[1955],[1846,5531,4995],{"className":5532,"style":2060},[1889,1890],[1846,5534,5537,5540],{"className":5535,"style":5536},[3549],"width:calc(100% - 0.1667em);margin-left:0.1667em;top:-3.6944em;",[1846,5538],{"className":5539,"style":3542},[1955],[1846,5541,5542],{"style":3556},[3558,5543,5544],{"xmlns":3560,"width":3561,"height":3562,"viewBox":3563,"preserveAspectRatio":3564},[3566,5545],{"d":3568},"。DML 先估计 ",[1846,5548,5550,5568],{"className":5549},[1849],[1846,5551,5553],{"className":5552},[1853],[1855,5554,5555],{"xmlns":1857},[1859,5556,5557,5565],{},[1862,5558,5559],{},[1905,5560,5561,5563],{},[1865,5562,5352],{"mathvariant":2040},[2016,5564,2224],{},[1869,5566,5567],{"encoding":1871},"\\ell_0",[1846,5569,5571],{"className":5570,"ariaHidden":1876},[1875],[1846,5572,5574,5577],{"className":5573},[1880],[1846,5575],{"className":5576,"style":3156},[1884],[1846,5578,5580,5583],{"className":5579},[1889],[1846,5581,5352],{"className":5582},[1889],[1846,5584,5586],{"className":5585},[1934],[1846,5587,5589,5609],{"className":5588},[1938,1939],[1846,5590,5592,5606],{"className":5591},[1943],[1846,5593,5595],{"className":5594,"style":5096},[1947],[1846,5596,5597,5600],{"style":1951},[1846,5598],{"className":5599,"style":1956},[1955],[1846,5601,5603],{"className":5602},[1960,1961,1962,1963],[1846,5604,2224],{"className":5605},[1889,1963],[1846,5607,1971],{"className":5608},[1970],[1846,5610,5612],{"className":5611},[1943],[1846,5613,5615],{"className":5614,"style":1978},[1947],[1846,5616],{},[1846,5618,5620,5638],{"className":5619},[1849],[1846,5621,5623],{"className":5622},[1853],[1855,5624,5625],{"xmlns":1857},[1859,5626,5627,5635],{},[1862,5628,5629],{},[1905,5630,5631,5633],{},[1865,5632,5031],{},[2016,5634,2224],{},[1869,5636,5637],{"encoding":1871},"m_0",[1846,5639,5641],{"className":5640,"ariaHidden":1876},[1875],[1846,5642,5644,5647],{"className":5643},[1880],[1846,5645],{"className":5646,"style":3277},[1884],[1846,5648,5650,5653],{"className":5649},[1889],[1846,5651,5031],{"className":5652},[1889,1890],[1846,5654,5656],{"className":5655},[1934],[1846,5657,5659,5679],{"className":5658},[1938,1939],[1846,5660,5662,5676],{"className":5661},[1943],[1846,5663,5665],{"className":5664,"style":5096},[1947],[1846,5666,5667,5670],{"style":1951},[1846,5668],{"className":5669,"style":1956},[1955],[1846,5671,5673],{"className":5672},[1960,1961,1962,1963],[1846,5674,2224],{"className":5675},[1889,1963],[1846,5677,1971],{"className":5678},[1970],[1846,5680,5682],{"className":5681},[1943],[1846,5683,5685],{"className":5684,"style":1978},[1947],[1846,5686],{}," 两个干扰函数，再构造残差：",[1846,5689,5691],{"className":5690},[1985],[1846,5692,5694,5761],{"className":5693},[1849],[1846,5695,5697],{"className":5696},[1853],[1855,5698,5699],{"xmlns":1857,"display":1994},[1859,5700,5701,5758],{},[1862,5702,5703,5710,5712,5714,5716,5722,5724,5726,5728,5730,5732,5738,5740,5742,5744,5750,5752,5754,5756],{},[3487,5704,5705,5707],{"accent":1876},[1865,5706,2213],{},[2012,5708,5709],{"stretchy":1876},"~",[2012,5711,2014],{},[1865,5713,2213],{},[2012,5715,2487],{},[3487,5717,5718,5720],{"accent":1876},[1865,5719,5352],{"mathvariant":2040},[2012,5721,3493],{"stretchy":1876},[2012,5723,2023],{"stretchy":2022},[1865,5725,5012],{},[2012,5727,2037],{"stretchy":2022},[2012,5729,2456],{"separator":1876},[2105,5731],{"width":2524},[3487,5733,5734,5736],{"accent":1876},[1865,5735,2003],{},[2012,5737,5709],{"stretchy":1876},[2012,5739,2014],{},[1865,5741,2003],{},[2012,5743,2487],{},[3487,5745,5746,5748],{"accent":1876},[1865,5747,5031],{},[2012,5749,3493],{"stretchy":1876},[2012,5751,2023],{"stretchy":2022},[1865,5753,5012],{},[2012,5755,2037],{"stretchy":2022},[2012,5757,2456],{"separator":1876},[1869,5759,5760],{"encoding":1871},"\\widetilde Y=Y-\\widehat \\ell(X),\n\\qquad\n\\widetilde D=D-\\widehat m(X),",[1846,5762,5764,5816,5835,5935,5953],{"className":5763,"ariaHidden":1876},[1875],[1846,5765,5767,5771,5807,5810,5813],{"className":5766},[1880],[1846,5768],{"className":5769,"style":5770},[1884],"height:0.9433em;",[1846,5772,5774],{"className":5773},[1889,3525],[1846,5775,5777],{"className":5776},[1938],[1846,5778,5780],{"className":5779},[1943],[1846,5781,5783,5791],{"className":5782,"style":5770},[1947],[1846,5784,5785,5788],{"style":3538},[1846,5786],{"className":5787,"style":3542},[1955],[1846,5789,2213],{"className":5790,"style":2245},[1889,1890],[1846,5792,5794,5797],{"className":5793,"style":3550},[3549],[1846,5795],{"className":5796,"style":3542},[1955],[1846,5798,5800],{"style":5799},"height:0.26em;",[3558,5801,5804],{"xmlns":3560,"width":3561,"height":5802,"viewBox":5803,"preserveAspectRatio":3564},"0.26em","0 0 600 260",[3566,5805],{"d":5806},"M200 55.538c-77 0-168 73.953-177 73.953-3 0-7\n-2.175-9-5.437L2 97c-1-2-2-4-2-6 0-4 2-7 5-9l20-12C116 12 171 0 207 0c86 0\n 114 68 191 68 78 0 168-68 177-68 4 0 7 2 9 5l12 19c1 2.175 2 4.35 2 6.525 0\n 4.35-2 7.613-5 9.788l-19 13.05c-92 63.077-116.937 75.308-183 76.128\n-68.267.847-113-73.952-191-73.952z",[1846,5808],{"className":5809,"style":2106},[2105],[1846,5811,2014],{"className":5812},[2110],[1846,5814],{"className":5815,"style":2106},[2105],[1846,5817,5819,5823,5826,5829,5832],{"className":5818},[1880],[1846,5820],{"className":5821,"style":5822},[1884],"height:0.7667em;vertical-align:-0.0833em;",[1846,5824,2213],{"className":5825,"style":2245},[1889,1890],[1846,5827],{"className":5828,"style":2245},[2105],[1846,5830,2487],{"className":5831},[2659],[1846,5833],{"className":5834,"style":2245},[2105],[1846,5836,5838,5842,5875,5878,5881,5884,5887,5890,5893,5926,5929,5932],{"className":5837},[1880],[1846,5839],{"className":5840,"style":5841},[1884],"height:1.1933em;vertical-align:-0.25em;",[1846,5843,5845],{"className":5844},[1889,3525],[1846,5846,5848],{"className":5847},[1938],[1846,5849,5851],{"className":5850},[1943],[1846,5852,5854,5862],{"className":5853,"style":5512},[1947],[1846,5855,5856,5859],{"style":3538},[1846,5857],{"className":5858,"style":3542},[1955],[1846,5860,5352],{"className":5861},[1889],[1846,5863,5866,5869],{"className":5864,"style":5865},[3549],"width:calc(100% - 0.2222em);margin-left:0.2222em;top:-3.6944em;",[1846,5867],{"className":5868,"style":3542},[1955],[1846,5870,5871],{"style":3556},[3558,5872,5873],{"xmlns":3560,"width":3561,"height":3562,"viewBox":3563,"preserveAspectRatio":3564},[3566,5874],{"d":3568},[1846,5876,2023],{"className":5877},[2128],[1846,5879,5012],{"className":5880,"style":5184},[1889,1890],[1846,5882,2037],{"className":5883},[2190],[1846,5885,2456],{"className":5886},[2565],[1846,5888],{"className":5889,"style":2806},[2105],[1846,5891],{"className":5892,"style":2569},[2105],[1846,5894,5896],{"className":5895},[1889,3525],[1846,5897,5899],{"className":5898},[1938],[1846,5900,5902],{"className":5901},[1943],[1846,5903,5905,5913],{"className":5904,"style":5770},[1947],[1846,5906,5907,5910],{"style":3538},[1846,5908],{"className":5909,"style":3542},[1955],[1846,5911,2003],{"className":5912,"style":2060},[1889,1890],[1846,5914,5917,5920],{"className":5915,"style":5916},[3549],"width:calc(100% - 0.1111em);margin-left:0.1111em;top:-3.6833em;",[1846,5918],{"className":5919,"style":3542},[1955],[1846,5921,5922],{"style":5799},[3558,5923,5924],{"xmlns":3560,"width":3561,"height":5802,"viewBox":5803,"preserveAspectRatio":3564},[3566,5925],{"d":5806},[1846,5927],{"className":5928,"style":2106},[2105],[1846,5930,2014],{"className":5931},[2110],[1846,5933],{"className":5934,"style":2106},[2105],[1846,5936,5938,5941,5944,5947,5950],{"className":5937},[1880],[1846,5939],{"className":5940,"style":5822},[1884],[1846,5942,2003],{"className":5943,"style":2060},[1889,1890],[1846,5945],{"className":5946,"style":2245},[2105],[1846,5948,2487],{"className":5949},[2659],[1846,5951],{"className":5952,"style":2245},[2105],[1846,5954,5956,5959,5993,5996,5999,6002],{"className":5955},[1880],[1846,5957],{"className":5958,"style":2120},[1884],[1846,5960,5962],{"className":5961},[1889,3525],[1846,5963,5965],{"className":5964},[1938],[1846,5966,5968],{"className":5967},[1943],[1846,5969,5972,5980],{"className":5970,"style":5971},[1947],"height:0.6706em;",[1846,5973,5974,5977],{"style":3538},[1846,5975],{"className":5976,"style":3542},[1955],[1846,5978,5031],{"className":5979},[1889,1890],[1846,5981,5984,5987],{"className":5982,"style":5983},[3549],"top:-3.4306em;",[1846,5985],{"className":5986,"style":3542},[1955],[1846,5988,5989],{"style":3556},[3558,5990,5991],{"xmlns":3560,"width":3561,"height":3562,"viewBox":3563,"preserveAspectRatio":3564},[3566,5992],{"d":3568},[1846,5994,2023],{"className":5995},[2128],[1846,5997,5012],{"className":5998,"style":5184},[1889,1890],[1846,6000,2037],{"className":6001},[2190],[1846,6003,2456],{"className":6004},[2565],[1793,6006,6007,6008,6070,6071,6133],{},"最后用 ",[1846,6009,6011,6029],{"className":6010},[1849],[1846,6012,6014],{"className":6013},[1853],[1855,6015,6016],{"xmlns":1857},[1859,6017,6018,6026],{},[1862,6019,6020],{},[3487,6021,6022,6024],{"accent":1876},[1865,6023,2213],{},[2012,6025,5709],{"stretchy":1876},[1869,6027,6028],{"encoding":1871},"\\widetilde Y",[1846,6030,6032],{"className":6031,"ariaHidden":1876},[1875],[1846,6033,6035,6038],{"className":6034},[1880],[1846,6036],{"className":6037,"style":5770},[1884],[1846,6039,6041],{"className":6040},[1889,3525],[1846,6042,6044],{"className":6043},[1938],[1846,6045,6047],{"className":6046},[1943],[1846,6048,6050,6058],{"className":6049,"style":5770},[1947],[1846,6051,6052,6055],{"style":3538},[1846,6053],{"className":6054,"style":3542},[1955],[1846,6056,2213],{"className":6057,"style":2245},[1889,1890],[1846,6059,6061,6064],{"className":6060,"style":3550},[3549],[1846,6062],{"className":6063,"style":3542},[1955],[1846,6065,6066],{"style":5799},[3558,6067,6068],{"xmlns":3560,"width":3561,"height":5802,"viewBox":5803,"preserveAspectRatio":3564},[3566,6069],{"d":5806}," 对 ",[1846,6072,6074,6092],{"className":6073},[1849],[1846,6075,6077],{"className":6076},[1853],[1855,6078,6079],{"xmlns":1857},[1859,6080,6081,6089],{},[1862,6082,6083],{},[3487,6084,6085,6087],{"accent":1876},[1865,6086,2003],{},[2012,6088,5709],{"stretchy":1876},[1869,6090,6091],{"encoding":1871},"\\widetilde D",[1846,6093,6095],{"className":6094,"ariaHidden":1876},[1875],[1846,6096,6098,6101],{"className":6097},[1880],[1846,6099],{"className":6100,"style":5770},[1884],[1846,6102,6104],{"className":6103},[1889,3525],[1846,6105,6107],{"className":6106},[1938],[1846,6108,6110],{"className":6109},[1943],[1846,6111,6113,6121],{"className":6112,"style":5770},[1947],[1846,6114,6115,6118],{"style":3538},[1846,6116],{"className":6117,"style":3542},[1955],[1846,6119,2003],{"className":6120,"style":2060},[1889,1890],[1846,6122,6124,6127],{"className":6123,"style":5916},[3549],[1846,6125],{"className":6126,"style":3542},[1955],[1846,6128,6129],{"style":5799},[3558,6130,6131],{"xmlns":3560,"width":3561,"height":5802,"viewBox":5803,"preserveAspectRatio":3564},[3566,6132],{"d":5806}," 回归。相应矩条件",[1846,6135,6137],{"className":6136},[1985],[1846,6138,6140,6230],{"className":6139},[1849],[1846,6141,6143],{"className":6142},[1853],[1855,6144,6145],{"xmlns":1857,"display":1994},[1859,6146,6147,6227],{},[1862,6148,6149,6151,6153,6155,6157,6159,6165,6167,6169,6171,6173,6175,6177,6179,6185,6187,6189,6191,6193,6199,6201,6203,6205,6211,6213,6215,6217,6219,6221,6223,6225],{},[1865,6150,2465],{},[2012,6152,2468],{"stretchy":2022},[2012,6154,2023],{"stretchy":2022},[1865,6156,2003],{},[2012,6158,2487],{},[1905,6160,6161,6163],{},[1865,6162,5031],{},[2016,6164,2224],{},[2012,6166,2023],{"stretchy":2022},[1865,6168,5012],{},[2012,6170,2037],{"stretchy":2022},[2012,6172,2037],{"stretchy":2022},[2012,6174,2023],{"stretchy":2022},[1865,6176,2213],{},[2012,6178,2487],{},[1905,6180,6181,6183],{},[1865,6182,5352],{"mathvariant":2040},[2016,6184,2224],{},[2012,6186,2023],{"stretchy":2022},[1865,6188,5012],{},[2012,6190,2037],{"stretchy":2022},[2012,6192,2487],{},[1905,6194,6195,6197],{},[1865,6196,4995],{},[2016,6198,2224],{},[2012,6200,2023],{"stretchy":2022},[1865,6202,2003],{},[2012,6204,2487],{},[1905,6206,6207,6209],{},[1865,6208,5031],{},[2016,6210,2224],{},[2012,6212,2023],{"stretchy":2022},[1865,6214,5012],{},[2012,6216,2037],{"stretchy":2022},[2012,6218,2037],{"stretchy":2022},[2012,6220,2037],{"stretchy":2022},[2012,6222,2519],{"stretchy":2022},[2012,6224,2014],{},[2016,6226,2224],{},[1869,6228,6229],{"encoding":1871},"E[(D-m_0(X))(Y-\\ell_0(X)-\\theta_0(D-m_0(X)))]=0",[1846,6231,6233,6258,6329,6393,6454,6519],{"className":6232,"ariaHidden":1876},[1875],[1846,6234,6236,6239,6242,6246,6249,6252,6255],{"className":6235},[1880],[1846,6237],{"className":6238,"style":2120},[1884],[1846,6240,2465],{"className":6241,"style":2594},[1889,1890],[1846,6243,6245],{"className":6244},[2128],"[(",[1846,6247,2003],{"className":6248,"style":2060},[1889,1890],[1846,6250],{"className":6251,"style":2245},[2105],[1846,6253,2487],{"className":6254},[2659],[1846,6256],{"className":6257,"style":2245},[2105],[1846,6259,6261,6264,6304,6307,6310,6314,6317,6320,6323,6326],{"className":6260},[1880],[1846,6262],{"className":6263,"style":2120},[1884],[1846,6265,6267,6270],{"className":6266},[1889],[1846,6268,5031],{"className":6269},[1889,1890],[1846,6271,6273],{"className":6272},[1934],[1846,6274,6276,6296],{"className":6275},[1938,1939],[1846,6277,6279,6293],{"className":6278},[1943],[1846,6280,6282],{"className":6281,"style":5096},[1947],[1846,6283,6284,6287],{"style":1951},[1846,6285],{"className":6286,"style":1956},[1955],[1846,6288,6290],{"className":6289},[1960,1961,1962,1963],[1846,6291,2224],{"className":6292},[1889,1963],[1846,6294,1971],{"className":6295},[1970],[1846,6297,6299],{"className":6298},[1943],[1846,6300,6302],{"className":6301,"style":1978},[1947],[1846,6303],{},[1846,6305,2023],{"className":6306},[2128],[1846,6308,5012],{"className":6309,"style":5184},[1889,1890],[1846,6311,6313],{"className":6312},[2190],"))",[1846,6315,2023],{"className":6316},[2128],[1846,6318,2213],{"className":6319,"style":2245},[1889,1890],[1846,6321],{"className":6322,"style":2245},[2105],[1846,6324,2487],{"className":6325},[2659],[1846,6327],{"className":6328,"style":2245},[2105],[1846,6330,6332,6335,6375,6378,6381,6384,6387,6390],{"className":6331},[1880],[1846,6333],{"className":6334,"style":2120},[1884],[1846,6336,6338,6341],{"className":6337},[1889],[1846,6339,5352],{"className":6340},[1889],[1846,6342,6344],{"className":6343},[1934],[1846,6345,6347,6367],{"className":6346},[1938,1939],[1846,6348,6350,6364],{"className":6349},[1943],[1846,6351,6353],{"className":6352,"style":5096},[1947],[1846,6354,6355,6358],{"style":1951},[1846,6356],{"className":6357,"style":1956},[1955],[1846,6359,6361],{"className":6360},[1960,1961,1962,1963],[1846,6362,2224],{"className":6363},[1889,1963],[1846,6365,1971],{"className":6366},[1970],[1846,6368,6370],{"className":6369},[1943],[1846,6371,6373],{"className":6372,"style":1978},[1947],[1846,6374],{},[1846,6376,2023],{"className":6377},[2128],[1846,6379,5012],{"className":6380,"style":5184},[1889,1890],[1846,6382,2037],{"className":6383},[2190],[1846,6385],{"className":6386,"style":2245},[2105],[1846,6388,2487],{"className":6389},[2659],[1846,6391],{"className":6392,"style":2245},[2105],[1846,6394,6396,6399,6439,6442,6445,6448,6451],{"className":6395},[1880],[1846,6397],{"className":6398,"style":2120},[1884],[1846,6400,6402,6405],{"className":6401},[1889],[1846,6403,4995],{"className":6404,"style":2060},[1889,1890],[1846,6406,6408],{"className":6407},[1934],[1846,6409,6411,6431],{"className":6410},[1938,1939],[1846,6412,6414,6428],{"className":6413},[1943],[1846,6415,6417],{"className":6416,"style":5096},[1947],[1846,6418,6419,6422],{"style":2075},[1846,6420],{"className":6421,"style":1956},[1955],[1846,6423,6425],{"className":6424},[1960,1961,1962,1963],[1846,6426,2224],{"className":6427},[1889,1963],[1846,6429,1971],{"className":6430},[1970],[1846,6432,6434],{"className":6433},[1943],[1846,6435,6437],{"className":6436,"style":1978},[1947],[1846,6438],{},[1846,6440,2023],{"className":6441},[2128],[1846,6443,2003],{"className":6444,"style":2060},[1889,1890],[1846,6446],{"className":6447,"style":2245},[2105],[1846,6449,2487],{"className":6450},[2659],[1846,6452],{"className":6453,"style":2245},[2105],[1846,6455,6457,6460,6500,6503,6506,6510,6513,6516],{"className":6456},[1880],[1846,6458],{"className":6459,"style":2120},[1884],[1846,6461,6463,6466],{"className":6462},[1889],[1846,6464,5031],{"className":6465},[1889,1890],[1846,6467,6469],{"className":6468},[1934],[1846,6470,6472,6492],{"className":6471},[1938,1939],[1846,6473,6475,6489],{"className":6474},[1943],[1846,6476,6478],{"className":6477,"style":5096},[1947],[1846,6479,6480,6483],{"style":1951},[1846,6481],{"className":6482,"style":1956},[1955],[1846,6484,6486],{"className":6485},[1960,1961,1962,1963],[1846,6487,2224],{"className":6488},[1889,1963],[1846,6490,1971],{"className":6491},[1970],[1846,6493,6495],{"className":6494},[1943],[1846,6496,6498],{"className":6497,"style":1978},[1947],[1846,6499],{},[1846,6501,2023],{"className":6502},[2128],[1846,6504,5012],{"className":6505,"style":5184},[1889,1890],[1846,6507,6509],{"className":6508},[2190],")))]",[1846,6511],{"className":6512,"style":2106},[2105],[1846,6514,2014],{"className":6515},[2110],[1846,6517],{"className":6518,"style":2106},[2105],[1846,6520,6522,6525],{"className":6521},[1880],[1846,6523],{"className":6524,"style":4858},[1884],[1846,6526,2224],{"className":6527},[1889],[1793,6529,6530],{},"对干扰函数的小误差具有局部不敏感性，这就是 Neyman 正交性的直觉。",[1838,6532,6534],{"id":6533},"_3-为什么还要交叉拟合","3. 为什么还要交叉拟合",[1793,6536,6537,6538,6663],{},"若同一观测既训练复杂模型又计算残差，模型可能记住噪声。交叉拟合将样本分折：在其他折上训练 ",[1846,6539,6541,6581],{"className":6540},[1849],[1846,6542,6544],{"className":6543},[1853],[1855,6545,6546],{"xmlns":1857},[1859,6547,6548,6578],{},[1862,6549,6550,6556,6558,6560,6562,6565,6568,6571,6574,6576],{},[3487,6551,6552,6554],{"accent":1876},[1865,6553,2453],{},[2012,6555,3493],{"stretchy":1876},[2012,6557,2456],{"separator":1876},[1865,6559,4434],{},[1865,6561,1867],{},[1865,6563,6564],{},"d",[1865,6566,6567],{},"e",[1865,6569,6570],{},"h",[1865,6572,6573],{},"a",[1865,6575,2010],{},[1865,6577,5031],{},[1869,6579,6580],{"encoding":1871},"\\widehat g,widehat m",[1846,6582,6584],{"className":6583,"ariaHidden":1876},[1875],[1846,6585,6587,6590,6635,6638,6641,6644,6647,6650,6653,6657,6660],{"className":6586},[1880],[1846,6588],{"className":6589,"style":2420},[1884],[1846,6591,6593],{"className":6592},[1889,3525],[1846,6594,6596,6626],{"className":6595},[1938,1939],[1846,6597,6599,6623],{"className":6598},[1943],[1846,6600,6602,6610],{"className":6601,"style":5971},[1947],[1846,6603,6604,6607],{"style":3538},[1846,6605],{"className":6606,"style":3542},[1955],[1846,6608,2453],{"className":6609,"style":2561},[1889,1890],[1846,6611,6614,6617],{"className":6612,"style":6613},[3549],"width:calc(100% - 0.0556em);margin-left:0.0556em;top:-3.4306em;",[1846,6615],{"className":6616,"style":3542},[1955],[1846,6618,6619],{"style":3556},[3558,6620,6621],{"xmlns":3560,"width":3561,"height":3562,"viewBox":3563,"preserveAspectRatio":3564},[3566,6622],{"d":3568},[1846,6624,1971],{"className":6625},[1970],[1846,6627,6629],{"className":6628},[1943],[1846,6630,6633],{"className":6631,"style":6632},[1947],"height:0.1944em;",[1846,6634],{},[1846,6636,2456],{"className":6637},[2565],[1846,6639],{"className":6640,"style":2569},[2105],[1846,6642,4434],{"className":6643,"style":4644},[1889,1890],[1846,6645,1867],{"className":6646},[1889,1890],[1846,6648,6564],{"className":6649},[1889,1890],[1846,6651,6567],{"className":6652},[1889,1890],[1846,6654,6656],{"className":6655},[1889,1890],"ha",[1846,6658,2010],{"className":6659},[1889,1890],[1846,6661,5031],{"className":6662},[1889,1890],"，再为当前折生成样本外预测。每个观测最终都获得“未见过自己”的干扰函数预测。",[1793,6665,6666],{},"这解决的是过拟合传入矩条件的问题，不解决以下风险：",[4330,6668,6669,6672,6675,6678,6681],{},[1815,6670,6671],{},"关键混淆变量根本没有被记录；",[1815,6673,6674],{},"处理概率接近 0 或 1，缺乏重叠；",[1815,6676,6677],{},"文本或图像在处理后生成，成为坏控制；",[1815,6679,6680],{},"表示学习目标泄漏了结果；",[1815,6682,6683],{},"模型在新人群或新设备上分布漂移。",[1805,6685,6687],{"id":6686},"浏览器实验twfe-与未处理观测插补","浏览器实验：TWFE 与未处理观测插补",[1793,6689,6690],{},"下面生成 60 个单位、8 个时期。三分之一在第 4 期处理，三分之一在第 6 期处理，其余从不处理。处理效应随暴露时长增加，因此“已经处理的单位”不是稳定对照。代码比较真实处理观测平均效应、传统 TWFE 系数与一个简化插补估计。",[6692,6693],"pyodide",{"code64":6694,"layout":6695,"locale":7,"packages":6696,"title":6697},"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","vertical","numpy","Python：交错处理下的 TWFE 与插补",[6699,6700],"web-r",{"code64":6701,"layout":6695,"locale":7,"title":6702},"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","R：交错处理下的 TWFE 与插补",[1838,6704,6705],{"id":6705},"实验审计",[4330,6707,6708,6711,6714,6717],{},[1815,6709,6710],{},"将真实效应改成恒定的 1，观察 TWFE 与插补差距如何变化。",[1815,6712,6713],{},"删除从不处理组，检查最后几个时期是否还有足够的未处理观测识别时间效应。",[1815,6715,6716],{},"给早处理组加入一条不同的处理前趋势，说明插补方法也依赖平行趋势。",[1815,6718,6719],{},"把噪声标准差增大到 1.5，区分估计偏误与抽样不确定性。",[6721,6722,6724],"warning",{"title":6723},"教学简化","这里的插补模型只含单位和时期固定效应，没有构造正式标准误、有效权重或识别检验。真实应用应使用经过验证的实现，并按处理分配层级处理聚类、少量组和重复抽样问题。",[1805,6726,6727],{"id":6727},"分层作业",[1838,6729,6731],{"id":6730},"本科生审计一张事件研究图","本科生：审计一张事件研究图",[1793,6733,6734],{},"找一篇 2023 年后的政策论文，只根据正文和附录回答：处理何时开始、谁从未处理、谁尚未处理、处理是否可逆、图中每个事件时间系数平均了哪些批次、标准误聚类在哪里。不要先评价系数显著性。",[1838,6736,6738],{"id":6737},"研究生比较两个-estimand","研究生：比较两个 estimand",[1793,6740,6741],{},"在同一合成数据上估计：",[1812,6743,6744,6747,6820],{},[1815,6745,6746],{},"所有处理观测的总体 ATT；",[1815,6748,6749,6750,3618],{},"实施后第一期的 ",[1846,6751,6753,6771],{"className":6752},[1849],[1846,6754,6756],{"className":6755},[1853],[1855,6757,6758],{"xmlns":1857},[1859,6759,6760,6768],{},[1862,6761,6762],{},[1905,6763,6764,6766],{},[1865,6765,4401],{},[2016,6767,2224],{},[1869,6769,6770],{"encoding":1871},"\\tau_0",[1846,6772,6774],{"className":6773,"ariaHidden":1876},[1875],[1846,6775,6777,6780],{"className":6776},[1880],[1846,6778],{"className":6779,"style":3277},[1884],[1846,6781,6783,6786],{"className":6782},[1889],[1846,6784,4401],{"className":6785,"style":4508},[1889,1890],[1846,6787,6789],{"className":6788},[1934],[1846,6790,6792,6812],{"className":6791},[1938,1939],[1846,6793,6795,6809],{"className":6794},[1943],[1846,6796,6798],{"className":6797,"style":5096},[1947],[1846,6799,6800,6803],{"style":4524},[1846,6801],{"className":6802,"style":1956},[1955],[1846,6804,6806],{"className":6805},[1960,1961,1962,1963],[1846,6807,2224],{"className":6808},[1889,1963],[1846,6810,1971],{"className":6811},[1970],[1846,6813,6815],{"className":6814},[1943],[1846,6816,6818],{"className":6817,"style":1978},[1947],[1846,6819],{},[1815,6821,6822],{},"每个批次等权与每个个体等权的聚合。",[1793,6824,6825],{},"解释为什么它们都可以“估计正确”却数值不同。再加入一个处理后才产生的文本变量，讨论将其作为 DML 控制为什么可能造成后处理偏误。",[1805,6827,6828],{"id":6828},"一手文献与延伸阅读",[1812,6830,6831,6851,6863,6875],{},[1815,6832,6833,6834,6840,6841,6845,6846,2041],{},"Borusyak, K., Jaravel, X., & Spiess, J. (2024). ",[6573,6835,6839],{"href":6836,"rel":6837},"https:\u002F\u002Fwww.restud.com\u002Frevisiting-event-study-designs-robust-and-efficient-estimation\u002F",[6838],"nofollow","Revisiting Event Study Designs: Robust and Efficient Estimation",". ",[6842,6843,6844],"em",{},"Review of Economic Studies",". DOI: ",[6573,6847,6850],{"href":6848,"rel":6849},"https:\u002F\u002Fdoi.org\u002F10.1093\u002Frestud\u002Frdae007",[6838],"10.1093\u002Frestud\u002Frdae007",[1815,6852,6853,6854,6840,6859,6862],{},"Roth, J., Sant’Anna, P. H. C., Bilinski, A., & Poe, J. (2023). ",[6573,6855,6858],{"href":6856,"rel":6857},"https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.jeconom.2023.03.008",[6838],"What’s Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature",[6842,6860,6861],{},"Journal of Econometrics",", 235(2), 2218–2244.",[1815,6864,6865,6866,6840,6871,6874],{},"Spindler, M., Bach, P., Chernozhukov, V., Klaassen, S., Teichert-Kluge, J., & Vijaykumar, S. (2026). ",[6573,6867,6870],{"href":6868,"rel":6869},"https:\u002F\u002Fproceedings.mlr.press\u002Fv323\u002Fspindler26a.html",[6838],"Valid Inference for Treatment Effects under Multimodal Confounding",[6842,6872,6873],{},"Proceedings of Machine Learning Research",", 323, 222–247.",[1815,6876,6877,6878,6840,6883,6886],{},"Chernozhukov, V. et al. (2018). ",[6573,6879,6882],{"href":6880,"rel":6881},"https:\u002F\u002Facademic.oup.com\u002Fectj\u002Farticle\u002F21\u002F1\u002FC1\u002F5056401",[6838],"Double\u002Fdebiased machine learning for treatment and structural parameters",[6842,6884,6885],{},"The Econometrics Journal",", 21(1), C1–C68. 这是理解第三个案例正交矩条件的基础文献。",[1793,6888,6889,6890,6894,6895,6899,6900,6904],{},"建议与",[6573,6891,6893],{"href":6892},".\u002F05-panel-and-time-series","面板和时间序列","、",[6573,6896,6898],{"href":6897},".\u002F06-estimation-and-causal-design","估计与因果设计","以及",[6573,6901,6903],{"href":6902},".\u002F08-interactive-regression-labs","浏览器回归实验","配套学习。",{"title":10,"searchDepth":6906,"depth":6906,"links":6907},2,[6908,6909,6915,6919,6924,6927,6931],{"id":1807,"depth":6906,"text":1807},{"id":1835,"depth":6906,"text":1836,"children":6910},[6911,6913,6914],{"id":1840,"depth":6912,"text":1841},3,{"id":2947,"depth":6912,"text":2948},{"id":3364,"depth":6912,"text":3365},{"id":4144,"depth":6906,"text":4145,"children":6916},[6917,6918],{"id":4325,"depth":6912,"text":4325},{"id":4349,"depth":6912,"text":4349},{"id":4953,"depth":6906,"text":4954,"children":6920},[6921,6922,6923],{"id":4957,"depth":6912,"text":4958},{"id":4967,"depth":6912,"text":4968},{"id":6533,"depth":6912,"text":6534},{"id":6686,"depth":6906,"text":6687,"children":6925},[6926],{"id":6705,"depth":6912,"text":6705},{"id":6727,"depth":6906,"text":6727,"children":6928},[6929,6930],{"id":6730,"depth":6912,"text":6731},{"id":6737,"depth":6912,"text":6738},{"id":6828,"depth":6906,"text":6828},"通过交错处理事件研究、现代双重差分与多模态双重机器学习理解当代计量经济学的识别和推断。","md",{"sidebar":6935},{"order":6936},9,true,{"title":1362,"description":6932},"t_D0DLkQDMHuMx1-b9w7mTsC_pHjEZi4jUcIHAXZh6E",[6941,6943],{"title":1358,"path":1359,"stem":1360,"description":6942,"children":-1},"用可点击运行的 Python 与 R 单元学习 OLS、遗漏变量偏误、稳健推断、IV、固定效应、聚类标准误与 Bootstrap。",{"title":1370,"path":1371,"stem":1372,"description":6944,"children":-1},"经济学基础入门课程，涵盖微观经济学与宏观经济学的核心原理与应用",1785754748102]