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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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provides:",[2584,2585,2586,2590,2593,2596],"ul",{},[2587,2588,2589],"li",{},"conditional forecasts;",[2587,2591,2592],{},"forecast-error covariance;",[2587,2594,2595],{},"Granger-predictive relations;",[2587,2597,2598],{},"a compact representation of dynamic propagation.",[1798,2600,2601,2602,2606,2607,2678],{},"It does ",[2603,2604,2605],"strong",{},"not"," label ",[1802,2608,2610,2628],{"className":2609},[1805],[1802,2611,2613],{"className":2612},[1809],[1811,2614,2615],{"xmlns":1813},[1815,2616,2617,2625],{},[1818,2618,2619],{},[1897,2620,2621,2623],{},[1821,2622,1969],{"mathvariant":1901},[1821,2624,1905],{},[1825,2626,2627],{"encoding":1827},"\\mathbf u_t",[1802,2629,2631],{"className":2630,"ariaHidden":1832},[1831],[1802,2632,2634,2638],{"className":2633},[1836],[1802,2635],{"className":2636,"style":2637},[1840],"height:0.5944em;vertical-align:-0.15em;",[1802,2639,2641,2644],{"className":2640},[1845],[1802,2642,1969],{"className":2643},[1845,2037],[1802,2645,2647],{"className":2646},[2042],[1802,2648,2650,2670],{"className":2649},[2046,2047],[1802,2651,2653,2667],{"className":2652},[2051],[1802,2654,2656],{"className":2655,"style":2056},[2055],[1802,2657,2658,2661],{"style":2149},[1802,2659],{"className":2660,"style":2064},[2063],[1802,2662,2664],{"className":2663},[2068,2069,2070,2071],[1802,2665,1905],{"className":2666},[1845,1846,2071],[1802,2668,2079],{"className":2669},[2078],[1802,2671,2673],{"className":2672},[2051],[1802,2674,2676],{"className":2675,"style":2086},[2055],[1802,2677],{}," as an economic shock. Reduced-form innovations can be contemporaneously correlated and can combine several underlying disturbances.",[1793,2680,2682],{"id":2681},"companion-matrix","Companion matrix",[1798,2684,2685],{},"Stack the state",[1802,2687,2689],{"className":2688},[1882],[1802,2690,2692,2773],{"className":2691},[1805],[1802,2693,2695],{"className":2694},[1809],[1811,2696,2697],{"xmlns":1813,"display":1891},[1815,2698,2699,2770],{},[1818,2700,2701,2708,2710,2712,2720,2722,2736,2738,2741,2743,2761,2768],{},[1897,2702,2703,2706],{},[1821,2704,2705],{"mathvariant":1901},"s",[1821,2707,1905],{},[1907,2709,1909],{},[1907,2711,1985],{"stretchy":1984},[1993,2713,2714,2716,2718],{},[1821,2715,1902],{"mathvariant":1901},[1821,2717,1905],{},[1821,2719,2002],{"mathvariant":2001},[1907,2721,1974],{"separator":1832},[1993,2723,2724,2726,2734],{},[1821,2725,1902],{"mathvariant":1901},[1818,2727,2728,2730,2732],{},[1821,2729,1905],{},[1907,2731,1935],{},[1922,2733,1924],{},[1821,2735,2002],{"mathvariant":2001},[1907,2737,1974],{"separator":1832},[1907,2739,2740],{},"…",[1907,2742,1974],{"separator":1832},[1993,2744,2745,2747,2759],{},[1821,2746,1902],{"mathvariant":1901},[1818,2748,2749,2751,2753,2755,2757],{},[1821,2750,1905],{},[1907,2752,1935],{},[1821,2754,1798],{},[1907,2756,1915],{},[1922,2758,1924],{},[1821,2760,2002],{"mathvariant":2001},[2762,2763,2764,2766],"msup",{},[1907,2765,2005],{"stretchy":1984},[1821,2767,2002],{"mathvariant":2001},[1821,2769,2017],{"mathvariant":2001},[1825,2771,2772],{"encoding":1827},"\\mathbf s_t=\n(\\mathbf y_t^\\top,\\mathbf y_{t-1}^\\top,\\ldots,\n\\mathbf y_{t-p+1}^\\top)^\\top.",[1802,2774,2776,2831],{"className":2775,"ariaHidden":1832},[1831],[1802,2777,2779,2782,2822,2825,2828],{"className":2778},[1836],[1802,2780],{"className":2781,"style":2637},[1840],[1802,2783,2785,2788],{"className":2784},[1845],[1802,2786,2705],{"className":2787},[1845,2037],[1802,2789,2791],{"className":2790},[2042],[1802,2792,2794,2814],{"className":2793},[2046,2047],[1802,2795,2797,2811],{"className":2796},[2051],[1802,2798,2800],{"className":2799,"style":2056},[2055],[1802,2801,2802,2805],{"style":2149},[1802,2803],{"className":2804,"style":2064},[2063],[1802,2806,2808],{"className":2807},[2068,2069,2070,2071],[1802,2809,1905],{"className":2810},[1845,1846,2071],[1802,2812,2079],{"className":2813},[2078],[1802,2815,2817],{"className":2816},[2051],[1802,2818,2820],{"className":2819,"style":2086},[2055],[1802,2821],{},[1802,2823],{"className":2824,"style":2092},[1976],[1802,2826,1909],{"className":2827},[2096],[1802,2829],{"className":2830,"style":2092},[1976],[1802,2832,2834,2838,2841,2893,2896,2899,2960,2963,2966,2969,2972,2975,2978,3045,3074],{"className":2833},[1836],[1802,2835],{"className":2836,"style":2837},[1840],"height:1.2822em;vertical-align:-0.3831em;",[1802,2839,1985],{"className":2840},[2421],[1802,2842,2844,2847],{"className":2843},[1845],[1802,2845,1902],{"className":2846,"style":2038},[1845,2037],[1802,2848,2850],{"className":2849},[2042],[1802,2851,2853,2885],{"className":2852},[2046,2047],[1802,2854,2856,2882],{"className":2855},[2051],[1802,2857,2859,2871],{"className":2858,"style":2480},[2055],[1802,2860,2862,2865],{"style":2861},"top:-2.453em;margin-left:-0.016em;margin-right:0.05em;",[1802,2863],{"className":2864,"style":2064},[2063],[1802,2866,2868],{"className":2867},[2068,2069,2070,2071],[1802,2869,1905],{"className":2870},[1845,1846,2071],[1802,2872,2873,2876],{"style":2495},[1802,2874],{"className":2875,"style":2064},[2063],[1802,2877,2879],{"className":2878},[2068,2069,2070,2071],[1802,2880,2002],{"className":2881},[1845,2071],[1802,2883,2079],{"className":2884},[2078],[1802,2886,2888],{"className":2887},[2051],[1802,2889,2891],{"className":2890,"style":2514},[2055],[1802,2892],{},[1802,2894,1974],{"className":2895},[2405],[1802,2897],{"className":2898,"style":2413},[1976],[1802,2900,2902,2905],{"className":2901},[1845],[1802,2903,1902],{"className":2904,"style":2038},[1845,2037],[1802,2906,2908],{"className":2907},[2042],[1802,2909,2911,2951],{"className":2910},[2046,2047],[1802,2912,2914,2948],{"className":2913},[2051],[1802,2915,2917,2937],{"className":2916,"style":2480},[2055],[1802,2918,2919,2922],{"style":2861},[1802,2920],{"className":2921,"style":2064},[2063],[1802,2923,2925],{"className":2924},[2068,2069,2070,2071],[1802,2926,2928,2931,2934],{"className":2927},[1845,2071],[1802,2929,1905],{"className":2930},[1845,1846,2071],[1802,2932,1935],{"className":2933},[2117,2071],[1802,2935,1924],{"className":2936},[1845,2071],[1802,2938,2939,2942],{"style":2495},[1802,2940],{"className":2941,"style":2064},[2063],[1802,2943,2945],{"className":2944},[2068,2069,2070,2071],[1802,2946,2002],{"className":2947},[1845,2071],[1802,2949,2079],{"className":2950},[2078],[1802,2952,2954],{"className":2953},[2051],[1802,2955,2958],{"className":2956,"style":2957},[2055],"height:0.3053em;",[1802,2959],{},[1802,2961,1974],{"className":2962},[2405],[1802,2964],{"className":2965,"style":2413},[1976],[1802,2967,2740],{"className":2968},[2238],[1802,2970],{"className":2971,"style":2413},[1976],[1802,2973,1974],{"className":2974},[2405],[1802,2976],{"className":2977,"style":2413},[1976],[1802,2979,2981,2984],{"className":2980},[1845],[1802,2982,1902],{"className":2983,"style":2038},[1845,2037],[1802,2985,2987],{"className":2986},[2042],[1802,2988,2990,3036],{"className":2989},[2046,2047],[1802,2991,2993,3033],{"className":2992},[2051],[1802,2994,2996,3022],{"className":2995,"style":2480},[2055],[1802,2997,2998,3001],{"style":2861},[1802,2999],{"className":3000,"style":2064},[2063],[1802,3002,3004],{"className":3003},[2068,2069,2070,2071],[1802,3005,3007,3010,3013,3016,3019],{"className":3006},[1845,2071],[1802,3008,1905],{"className":3009},[1845,1846,2071],[1802,3011,1935],{"className":3012},[2117,2071],[1802,3014,1798],{"className":3015},[1845,1846,2071],[1802,3017,1915],{"className":3018},[2117,2071],[1802,3020,1924],{"className":3021},[1845,2071],[1802,3023,3024,3027],{"style":2495},[1802,3025],{"className":3026,"style":2064},[2063],[1802,3028,3030],{"className":3029},[2068,2069,2070,2071],[1802,3031,2002],{"className":3032},[1845,2071],[1802,3034,2079],{"className":3035},[2078],[1802,3037,3039],{"className":3038},[2051],[1802,3040,3043],{"className":3041,"style":3042},[2055],"height:0.3831em;",[1802,3044],{},[1802,3046,3048,3051],{"className":3047},[2520],[1802,3049,2005],{"className":3050},[2520],[1802,3052,3054],{"className":3053},[2042],[1802,3055,3057],{"className":3056},[2046],[1802,3058,3060],{"className":3059},[2051],[1802,3061,3063],{"className":3062,"style":2480},[2055],[1802,3064,3065,3068],{"style":2495},[1802,3066],{"className":3067,"style":2064},[2063],[1802,3069,3071],{"className":3070},[2068,2069,2070,2071],[1802,3072,2002],{"className":3073},[1845,2071],[1802,3075,2017],{"className":3076},[1845],[1798,3078,3079],{},"Then",[1802,3081,3083],{"className":3082},[1882],[1802,3084,3086,3134],{"className":3085},[1805],[1802,3087,3089],{"className":3088},[1809],[1811,3090,3091],{"xmlns":1813,"display":1891},[1815,3092,3093,3131],{},[1818,3094,3095,3101,3103,3106,3118,3120,3123,3129],{},[1897,3096,3097,3099],{},[1821,3098,2705],{"mathvariant":1901},[1821,3100,1905],{},[1907,3102,1909],{},[1821,3104,3105],{},"F",[1897,3107,3108,3110],{},[1821,3109,2705],{"mathvariant":1901},[1818,3111,3112,3114,3116],{},[1821,3113,1905],{},[1907,3115,1935],{},[1922,3117,1924],{},[1907,3119,1915],{},[1821,3121,3122],{},"G",[1897,3124,3125,3127],{},[1821,3126,1969],{"mathvariant":1901},[1821,3128,1905],{},[1907,3130,1974],{"separator":1832},[1825,3132,3133],{"encoding":1827},"\\mathbf s_t=F\\mathbf s_{t-1}+G\\mathbf u_t,",[1802,3135,3137,3192,3260],{"className":3136,"ariaHidden":1832},[1831],[1802,3138,3140,3143,3183,3186,3189],{"className":3139},[1836],[1802,3141],{"className":3142,"style":2637},[1840],[1802,3144,3146,3149],{"className":3145},[1845],[1802,3147,2705],{"className":3148},[1845,2037],[1802,3150,3152],{"className":3151},[2042],[1802,3153,3155,3175],{"className":3154},[2046,2047],[1802,3156,3158,3172],{"className":3157},[2051],[1802,3159,3161],{"className":3160,"style":2056},[2055],[1802,3162,3163,3166],{"style":2149},[1802,3164],{"className":3165,"style":2064},[2063],[1802,3167,3169],{"className":3168},[2068,2069,2070,2071],[1802,3170,1905],{"className":3171},[1845,1846,2071],[1802,3173,2079],{"className":3174},[2078],[1802,3176,3178],{"className":3177},[2051],[1802,3179,3181],{"className":3180,"style":2086},[2055],[1802,3182],{},[1802,3184],{"className":3185,"style":2092},[1976],[1802,3187,1909],{"className":3188},[2096],[1802,3190],{"className":3191,"style":2092},[1976],[1802,3193,3195,3198,3202,3251,3254,3257],{"className":3194},[1836],[1802,3196],{"className":3197,"style":2127},[1840],[1802,3199,3105],{"className":3200,"style":3201},[1845,1846],"margin-right:0.1389em;",[1802,3203,3205,3208],{"className":3204},[1845],[1802,3206,2705],{"className":3207},[1845,2037],[1802,3209,3211],{"className":3210},[2042],[1802,3212,3214,3243],{"className":3213},[2046,2047],[1802,3215,3217,3240],{"className":3216},[2051],[1802,3218,3220],{"className":3219,"style":2146},[2055],[1802,3221,3222,3225],{"style":2149},[1802,3223],{"className":3224,"style":2064},[2063],[1802,3226,3228],{"className":3227},[2068,2069,2070,2071],[1802,3229,3231,3234,3237],{"className":3230},[1845,2071],[1802,3232,1905],{"className":3233},[1845,1846,2071],[1802,3235,1935],{"className":3236},[2117,2071],[1802,3238,1924],{"className":3239},[1845,2071],[1802,3241,2079],{"className":3242},[2078],[1802,3244,3246],{"className":3245},[2051],[1802,3247,3249],{"className":3248,"style":2217},[2055],[1802,3250],{},[1802,3252],{"className":3253,"style":2113},[1976],[1802,3255,1915],{"className":3256},[2117],[1802,3258],{"className":3259,"style":2113},[1976],[1802,3261,3263,3267,3270,3310],{"className":3262},[1836],[1802,3264],{"className":3265,"style":3266},[1840],"height:0.8778em;vertical-align:-0.1944em;",[1802,3268,3122],{"className":3269},[1845,1846],[1802,3271,3273,3276],{"className":3272},[1845],[1802,3274,1969],{"className":3275},[1845,2037],[1802,3277,3279],{"className":3278},[2042],[1802,3280,3282,3302],{"className":3281},[2046,2047],[1802,3283,3285,3299],{"className":3284},[2051],[1802,3286,3288],{"className":3287,"style":2056},[2055],[1802,3289,3290,3293],{"style":2149},[1802,3291],{"className":3292,"style":2064},[2063],[1802,3294,3296],{"className":3295},[2068,2069,2070,2071],[1802,3297,1905],{"className":3298},[1845,1846,2071],[1802,3300,2079],{"className":3301},[2078],[1802,3303,3305],{"className":3304},[2051],[1802,3306,3308],{"className":3307,"style":2086},[2055],[1802,3309],{},[1802,3311,1974],{"className":3312},[2405],[1798,3314,3315,3316,3344,3345,3485,3486,3514,3515,3545,3546,2017],{},"where the first block row of ",[1802,3317,3319,3332],{"className":3318},[1805],[1802,3320,3322],{"className":3321},[1809],[1811,3323,3324],{"xmlns":1813},[1815,3325,3326,3330],{},[1818,3327,3328],{},[1821,3329,3105],{},[1825,3331,3105],{"encoding":1827},[1802,3333,3335],{"className":3334,"ariaHidden":1832},[1831],[1802,3336,3338,3341],{"className":3337},[1836],[1802,3339],{"className":3340,"style":1841},[1840],[1802,3342,3105],{"className":3343,"style":3201},[1845,1846]," contains ",[1802,3346,3348,3378],{"className":3347},[1805],[1802,3349,3351],{"className":3350},[1809],[1811,3352,3353],{"xmlns":1813},[1815,3354,3355,3375],{},[1818,3356,3357,3363,3365,3367,3369],{},[1897,3358,3359,3361],{},[1821,3360,1920],{},[1922,3362,1924],{},[1907,3364,1974],{"separator":1832},[1907,3366,2740],{},[1907,3368,1974],{"separator":1832},[1897,3370,3371,3373],{},[1821,3372,1920],{},[1821,3374,1798],{},[1825,3376,3377],{"encoding":1827},"A_1,\\ldots,A_p",[1802,3379,3381],{"className":3380,"ariaHidden":1832},[1831],[1802,3382,3384,3387,3427,3430,3433,3436,3439,3442,3445],{"className":3383},[1836],[1802,3385],{"className":3386,"style":2254},[1840],[1802,3388,3390,3393],{"className":3389},[1845],[1802,3391,1920],{"className":3392},[1845,1846],[1802,3394,3396],{"className":3395},[2042],[1802,3397,3399,3419],{"className":3398},[2046,2047],[1802,3400,3402,3416],{"className":3401},[2051],[1802,3403,3405],{"className":3404,"style":2146},[2055],[1802,3406,3407,3410],{"style":2149},[1802,3408],{"className":3409,"style":2064},[2063],[1802,3411,3413],{"className":3412},[2068,2069,2070,2071],[1802,3414,1924],{"className":3415},[1845,2071],[1802,3417,2079],{"className":3418},[2078],[1802,3420,3422],{"className":3421},[2051],[1802,3423,3425],{"className":3424,"style":2086},[2055],[1802,3426],{},[1802,3428,1974],{"className":3429},[2405],[1802,3431],{"className":3432,"style":2413},[1976],[1802,3434,2740],{"className":3435},[2238],[1802,3437],{"className":3438,"style":2413},[1976],[1802,3440,1974],{"className":3441},[2405],[1802,3443],{"className":3444,"style":2413},[1976],[1802,3446,3448,3451],{"className":3447},[1845],[1802,3449,1920],{"className":3450},[1845,1846],[1802,3452,3454],{"className":3453},[2042],[1802,3455,3457,3477],{"className":3456},[2046,2047],[1802,3458,3460,3474],{"className":3459},[2051],[1802,3461,3463],{"className":3462,"style":2273},[2055],[1802,3464,3465,3468],{"style":2149},[1802,3466],{"className":3467,"style":2064},[2063],[1802,3469,3471],{"className":3470},[2068,2069,2070,2071],[1802,3472,1798],{"className":3473},[1845,1846,2071],[1802,3475,2079],{"className":3476},[2078],[1802,3478,3480],{"className":3479},[2051],[1802,3481,3483],{"className":3482,"style":2294},[2055],[1802,3484],{}," and lower blocks shift lags. Stability requires every eigenvalue of ",[1802,3487,3489,3502],{"className":3488},[1805],[1802,3490,3492],{"className":3491},[1809],[1811,3493,3494],{"xmlns":1813},[1815,3495,3496,3500],{},[1818,3497,3498],{},[1821,3499,3105],{},[1825,3501,3105],{"encoding":1827},[1802,3503,3505],{"className":3504,"ariaHidden":1832},[1831],[1802,3506,3508,3511],{"className":3507},[1836],[1802,3509],{"className":3510,"style":1841},[1840],[1802,3512,3105],{"className":3513,"style":3201},[1845,1846]," to lie inside the unit circle. The ",[1802,3516,3518,3532],{"className":3517},[1805],[1802,3519,3521],{"className":3520},[1809],[1811,3522,3523],{"xmlns":1813},[1815,3524,3525,3530],{},[1818,3526,3527],{},[1821,3528,3529],{},"h",[1825,3531,3529],{"encoding":1827},[1802,3533,3535],{"className":3534,"ariaHidden":1832},[1831],[1802,3536,3538,3542],{"className":3537},[1836],[1802,3539],{"className":3540,"style":3541},[1840],"height:0.6944em;",[1802,3543,3529],{"className":3544},[1845,1846],"-step propagation is ",[1802,3547,3549,3567],{"className":3548},[1805],[1802,3550,3552],{"className":3551},[1809],[1811,3553,3554],{"xmlns":1813},[1815,3555,3556,3564],{},[1818,3557,3558],{},[2762,3559,3560,3562],{},[1821,3561,3105],{},[1821,3563,3529],{},[1825,3565,3566],{"encoding":1827},"F^h",[1802,3568,3570],{"className":3569,"ariaHidden":1832},[1831],[1802,3571,3573,3577],{"className":3572},[1836],[1802,3574],{"className":3575,"style":3576},[1840],"height:0.8491em;",[1802,3578,3580,3583],{"className":3579},[1845],[1802,3581,3105],{"className":3582,"style":3201},[1845,1846],[1802,3584,3586],{"className":3585},[2042],[1802,3587,3589],{"className":3588},[2046],[1802,3590,3592],{"className":3591},[2051],[1802,3593,3595],{"className":3594,"style":3576},[2055],[1802,3596,3598,3601],{"style":3597},"top:-3.063em;margin-right:0.05em;",[1802,3599],{"className":3600,"style":2064},[2063],[1802,3602,3604],{"className":3603},[2068,2069,2070,2071],[1802,3605,3529],{"className":3606},[1845,1846,2071],[1798,3608,3609],{},"This is the direct bridge from the classical companion matrix to multivariate finance and macroeconomics.",[1793,3611,3613],{"id":3612},"structural-impact-matrix","Structural impact matrix",[1798,3615,3616],{},"Suppose",[1802,3618,3620],{"className":3619},[1882],[1802,3621,3623,3685],{"className":3622},[1805],[1802,3624,3626],{"className":3625},[1809],[1811,3627,3628],{"xmlns":1813,"display":1891},[1815,3629,3630,3682],{},[1818,3631,3632,3638,3640,3643,3651,3653,3655,3657,3659,3665,3673,3675,3677,3680],{},[1897,3633,3634,3636],{},[1821,3635,1969],{"mathvariant":1901},[1821,3637,1905],{},[1907,3639,1909],{},[1821,3641,3642],{},"B",[1897,3644,3645,3649],{},[1821,3646,3648],{"mathvariant":3647},"bold-italic","ε",[1821,3650,1905],{},[1907,3652,1974],{"separator":1832},[1976,3654],{"width":1978},[1821,3656,1981],{},[1907,3658,1985],{"stretchy":1984},[1897,3660,3661,3663],{},[1821,3662,3648],{"mathvariant":3647},[1821,3664,1905],{},[1993,3666,3667,3669,3671],{},[1821,3668,3648],{"mathvariant":3647},[1821,3670,1905],{},[1821,3672,2002],{"mathvariant":2001},[1907,3674,2005],{"stretchy":1984},[1907,3676,1909],{},[1821,3678,3679],{},"I",[1821,3681,2017],{"mathvariant":2001},[1825,3683,3684],{"encoding":1827},"\\mathbf u_t=B\\boldsymbol\\varepsilon_t,\\qquad\nE(\\boldsymbol\\varepsilon_t\\boldsymbol\\varepsilon_t^\\top)=I.",[1802,3686,3688,3743,3932],{"className":3687,"ariaHidden":1832},[1831],[1802,3689,3691,3694,3734,3737,3740],{"className":3690},[1836],[1802,3692],{"className":3693,"style":2637},[1840],[1802,3695,3697,3700],{"className":3696},[1845],[1802,3698,1969],{"className":3699},[1845,2037],[1802,3701,3703],{"className":3702},[2042],[1802,3704,3706,3726],{"className":3705},[2046,2047],[1802,3707,3709,3723],{"className":3708},[2051],[1802,3710,3712],{"className":3711,"style":2056},[2055],[1802,3713,3714,3717],{"style":2149},[1802,3715],{"className":3716,"style":2064},[2063],[1802,3718,3720],{"className":3719},[2068,2069,2070,2071],[1802,3721,1905],{"className":3722},[1845,1846,2071],[1802,3724,2079],{"className":3725},[2078],[1802,3727,3729],{"className":3728},[2051],[1802,3730,3732],{"className":3731,"style":2086},[2055],[1802,3733],{},[1802,3735],{"className":3736,"style":2092},[1976],[1802,3738,1909],{"className":3739},[2096],[1802,3741],{"className":3742,"style":2092},[1976],[1802,3744,3746,3749,3753,3801,3804,3807,3810,3813,3816,3862,3920,3923,3926,3929],{"className":3745},[1836],[1802,3747],{"className":3748,"style":2361},[1840],[1802,3750,3642],{"className":3751,"style":3752},[1845,1846],"margin-right:0.0502em;",[1802,3754,3756,3766],{"className":3755},[1845],[1802,3757,3759],{"className":3758},[1845],[1802,3760,3762],{"className":3761},[1845],[1802,3763,3648],{"className":3764},[1845,3765],"boldsymbol",[1802,3767,3769],{"className":3768},[2042],[1802,3770,3772,3793],{"className":3771},[2046,2047],[1802,3773,3775,3790],{"className":3774},[2051],[1802,3776,3778],{"className":3777,"style":2056},[2055],[1802,3779,3781,3784],{"style":3780},"top:-2.55em;margin-right:0.05em;",[1802,3782],{"className":3783,"style":2064},[2063],[1802,3785,3787],{"className":3786},[2068,2069,2070,2071],[1802,3788,1905],{"className":3789},[1845,1846,2071],[1802,3791,2079],{"className":3792},[2078],[1802,3794,3796],{"className":3795},[2051],[1802,3797,3799],{"className":3798,"style":2086},[2055],[1802,3800],{},[1802,3802,1974],{"className":3803},[2405],[1802,3805],{"className":3806,"style":2409},[1976],[1802,3808],{"className":3809,"style":2413},[1976],[1802,3811,1981],{"className":3812,"style":2417},[1845,1846],[1802,3814,1985],{"className":3815},[2421],[1802,3817,3819,3828],{"className":3818},[1845],[1802,3820,3822],{"className":3821},[1845],[1802,3823,3825],{"className":3824},[1845],[1802,3826,3648],{"className":3827},[1845,3765],[1802,3829,3831],{"className":3830},[2042],[1802,3832,3834,3854],{"className":3833},[2046,2047],[1802,3835,3837,3851],{"className":3836},[2051],[1802,3838,3840],{"className":3839,"style":2056},[2055],[1802,3841,3842,3845],{"style":3780},[1802,3843],{"className":3844,"style":2064},[2063],[1802,3846,3848],{"className":3847},[2068,2069,2070,2071],[1802,3849,1905],{"className":3850},[1845,1846,2071],[1802,3852,2079],{"className":3853},[2078],[1802,3855,3857],{"className":3856},[2051],[1802,3858,3860],{"className":3859,"style":2086},[2055],[1802,3861],{},[1802,3863,3865,3874],{"className":3864},[1845],[1802,3866,3868],{"className":3867},[1845],[1802,3869,3871],{"className":3870},[1845],[1802,3872,3648],{"className":3873},[1845,3765],[1802,3875,3877],{"className":3876},[2042],[1802,3878,3880,3912],{"className":3879},[2046,2047],[1802,3881,3883,3909],{"className":3882},[2051],[1802,3884,3886,3898],{"className":3885,"style":2480},[2055],[1802,3887,3889,3892],{"style":3888},"top:-2.453em;margin-right:0.05em;",[1802,3890],{"className":3891,"style":2064},[2063],[1802,3893,3895],{"className":3894},[2068,2069,2070,2071],[1802,3896,1905],{"className":3897},[1845,1846,2071],[1802,3899,3900,3903],{"style":2495},[1802,3901],{"className":3902,"style":2064},[2063],[1802,3904,3906],{"className":3905},[2068,2069,2070,2071],[1802,3907,2002],{"className":3908},[1845,2071],[1802,3910,2079],{"className":3911},[2078],[1802,3913,3915],{"className":3914},[2051],[1802,3916,3918],{"className":3917,"style":2514},[2055],[1802,3919],{},[1802,3921,2005],{"className":3922},[2520],[1802,3924],{"className":3925,"style":2092},[1976],[1802,3927,1909],{"className":3928},[2096],[1802,3930],{"className":3931,"style":2092},[1976],[1802,3933,3935,3938,3942],{"className":3934},[1836],[1802,3936],{"className":3937,"style":1841},[1840],[1802,3939,3679],{"className":3940,"style":3941},[1845,1846],"margin-right:0.0785em;",[1802,3943,2017],{"className":3944},[1845],[1798,3946,3079],{},[1802,3948,3950],{"className":3949},[1882],[1802,3951,3953,3983],{"className":3952},[1805],[1802,3954,3956],{"className":3955},[1809],[1811,3957,3958],{"xmlns":1813,"display":1891},[1815,3959,3960,3980],{},[1818,3961,3962,3968,3970,3972,3978],{},[1897,3963,3964,3966],{},[1821,3965,2012],{"mathvariant":2001},[1821,3967,1969],{},[1907,3969,1909],{},[1821,3971,3642],{},[2762,3973,3974,3976],{},[1821,3975,3642],{},[1821,3977,2002],{"mathvariant":2001},[1821,3979,2017],{"mathvariant":2001},[1825,3981,3982],{"encoding":1827},"\\Sigma_u=BB^\\top.",[1802,3984,3986,4041],{"className":3985,"ariaHidden":1832},[1831],[1802,3987,3989,3992,4032,4035,4038],{"className":3988},[1836],[1802,3990],{"className":3991,"style":2536},[1840],[1802,3993,3995,3998],{"className":3994},[1845],[1802,3996,2012],{"className":3997},[1845],[1802,3999,4001],{"className":4000},[2042],[1802,4002,4004,4024],{"className":4003},[2046,2047],[1802,4005,4007,4021],{"className":4006},[2051],[1802,4008,4010],{"className":4009,"style":2273},[2055],[1802,4011,4012,4015],{"style":2149},[1802,4013],{"className":4014,"style":2064},[2063],[1802,4016,4018],{"className":4017},[2068,2069,2070,2071],[1802,4019,1969],{"className":4020},[1845,1846,2071],[1802,4022,2079],{"className":4023},[2078],[1802,4025,4027],{"className":4026},[2051],[1802,4028,4030],{"className":4029,"style":2086},[2055],[1802,4031],{},[1802,4033],{"className":4034,"style":2092},[1976],[1802,4036,1909],{"className":4037},[2096],[1802,4039],{"className":4040,"style":2092},[1976],[1802,4042,4044,4047,4050,4079],{"className":4043},[1836],[1802,4045],{"className":4046,"style":2480},[1840],[1802,4048,3642],{"className":4049,"style":3752},[1845,1846],[1802,4051,4053,4056],{"className":4052},[1845],[1802,4054,3642],{"className":4055,"style":3752},[1845,1846],[1802,4057,4059],{"className":4058},[2042],[1802,4060,4062],{"className":4061},[2046],[1802,4063,4065],{"className":4064},[2051],[1802,4066,4068],{"className":4067,"style":2480},[2055],[1802,4069,4070,4073],{"style":2495},[1802,4071],{"className":4072,"style":2064},[2063],[1802,4074,4076],{"className":4075},[2068,2069,2070,2071],[1802,4077,2002],{"className":4078},[1845,2071],[1802,4080,2017],{"className":4081},[1845],[1798,4083,4084,4085,4162,4163,4191,4192,4252],{},"The covariance matrix supplies ",[1802,4086,4088,4118],{"className":4087},[1805],[1802,4089,4091],{"className":4090},[1809],[1811,4092,4093],{"xmlns":1813},[1815,4094,4095,4115],{},[1818,4096,4097,4099,4101,4103,4105,4107,4109,4112],{},[1821,4098,1823],{},[1907,4100,1985],{"stretchy":1984},[1821,4102,1823],{},[1907,4104,1915],{},[1922,4106,1924],{},[1907,4108,2005],{"stretchy":1984},[1821,4110,4111],{"mathvariant":2001},"\u002F",[1922,4113,4114],{},"2",[1825,4116,4117],{"encoding":1827},"K(K+1)\u002F2",[1802,4119,4121,4146],{"className":4120,"ariaHidden":1832},[1831],[1802,4122,4124,4128,4131,4134,4137,4140,4143],{"className":4123},[1836],[1802,4125],{"className":4126,"style":4127},[1840],"height:1em;vertical-align:-0.25em;",[1802,4129,1823],{"className":4130,"style":1847},[1845,1846],[1802,4132,1985],{"className":4133},[2421],[1802,4135,1823],{"className":4136,"style":1847},[1845,1846],[1802,4138],{"className":4139,"style":2113},[1976],[1802,4141,1915],{"className":4142},[2117],[1802,4144],{"className":4145,"style":2113},[1976],[1802,4147,4149,4152,4155,4158],{"className":4148},[1836],[1802,4150],{"className":4151,"style":4127},[1840],[1802,4153,1924],{"className":4154},[1845],[1802,4156,2005],{"className":4157},[2520],[1802,4159,4161],{"className":4160},[1845],"\u002F2"," distinct equations, while unrestricted ",[1802,4164,4166,4179],{"className":4165},[1805],[1802,4167,4169],{"className":4168},[1809],[1811,4170,4171],{"xmlns":1813},[1815,4172,4173,4177],{},[1818,4174,4175],{},[1821,4176,3642],{},[1825,4178,3642],{"encoding":1827},[1802,4180,4182],{"className":4181,"ariaHidden":1832},[1831],[1802,4183,4185,4188],{"className":4184},[1836],[1802,4186],{"className":4187,"style":1841},[1840],[1802,4189,3642],{"className":4190,"style":3752},[1845,1846]," has ",[1802,4193,4195,4213],{"className":4194},[1805],[1802,4196,4198],{"className":4197},[1809],[1811,4199,4200],{"xmlns":1813},[1815,4201,4202,4210],{},[1818,4203,4204],{},[2762,4205,4206,4208],{},[1821,4207,1823],{},[1922,4209,4114],{},[1825,4211,4212],{"encoding":1827},"K^2",[1802,4214,4216],{"className":4215,"ariaHidden":1832},[1831],[1802,4217,4219,4223],{"className":4218},[1836],[1802,4220],{"className":4221,"style":4222},[1840],"height:0.8141em;",[1802,4224,4226,4229],{"className":4225},[1845],[1802,4227,1823],{"className":4228,"style":1847},[1845,1846],[1802,4230,4232],{"className":4231},[2042],[1802,4233,4235],{"className":4234},[2046],[1802,4236,4238],{"className":4237},[2051],[1802,4239,4241],{"className":4240,"style":4222},[2055],[1802,4242,4243,4246],{"style":3597},[1802,4244],{"className":4245,"style":2064},[2063],[1802,4247,4249],{"className":4248},[2068,2069,2070,2071],[1802,4250,4114],{"className":4251},[1845,2071]," entries. Additional restrictions are required. Common approaches include:",[4254,4255,4256,4272],"table",{},[4257,4258,4259],"thead",{},[4260,4261,4262,4266,4269],"tr",{},[4263,4264,4265],"th",{},"Restriction",[4263,4267,4268],{},"Meaning",[4263,4270,4271],{},"Main risk",[4273,4274,4275,4287,4298,4309,4320],"tbody",{},[4260,4276,4277,4281,4284],{},[4278,4279,4280],"td",{},"recursive\u002FCholesky",[4278,4282,4283],{},"some contemporaneous effects are zero under an ordering",[4278,4285,4286],{},"conclusions inherit the ordering",[4260,4288,4289,4292,4295],{},[4278,4290,4291],{},"long-run",[4278,4293,4294],{},"specified shocks have zero long-run effects on selected variables",[4278,4296,4297],{},"sensitive to long-horizon estimation",[4260,4299,4300,4303,4306],{},[4278,4301,4302],{},"sign",[4278,4304,4305],{},"responses obey theory-based signs over selected horizons",[4278,4307,4308],{},"set identification and researcher choices",[4260,4310,4311,4314,4317],{},[4278,4312,4313],{},"external instrument",[4278,4315,4316],{},"a proxy correlates with one shock but not others",[4278,4318,4319],{},"instrument relevance and exclusion",[4260,4321,4322,4325,4328],{},[4278,4323,4324],{},"narrative",[4278,4326,4327],{},"historically documented episodes reveal a shock",[4278,4329,4330],{},"episode classification and representativeness",[1798,4332,4333],{},"Identification is an economic argument represented by matrix restrictions.",[1793,4335,4337],{"id":4336},"r-laboratory-ordering-changes-the-named-shock","R laboratory: ordering changes the named shock",[1798,4339,4340,4341,4369,4370,4440],{},"Consider a reduced-form VAR(1) with the same ",[1802,4342,4344,4357],{"className":4343},[1805],[1802,4345,4347],{"className":4346},[1809],[1811,4348,4349],{"xmlns":1813},[1815,4350,4351,4355],{},[1818,4352,4353],{},[1821,4354,1920],{},[1825,4356,1920],{"encoding":1827},[1802,4358,4360],{"className":4359,"ariaHidden":1832},[1831],[1802,4361,4363,4366],{"className":4362},[1836],[1802,4364],{"className":4365,"style":1841},[1840],[1802,4367,1920],{"className":4368},[1845,1846]," and ",[1802,4371,4373,4391],{"className":4372},[1805],[1802,4374,4376],{"className":4375},[1809],[1811,4377,4378],{"xmlns":1813},[1815,4379,4380,4388],{},[1818,4381,4382],{},[1897,4383,4384,4386],{},[1821,4385,2012],{"mathvariant":2001},[1821,4387,1969],{},[1825,4389,4390],{"encoding":1827},"\\Sigma_u",[1802,4392,4394],{"className":4393,"ariaHidden":1832},[1831],[1802,4395,4397,4400],{"className":4396},[1836],[1802,4398],{"className":4399,"style":2536},[1840],[1802,4401,4403,4406],{"className":4402},[1845],[1802,4404,2012],{"className":4405},[1845],[1802,4407,4409],{"className":4408},[2042],[1802,4410,4412,4432],{"className":4411},[2046,2047],[1802,4413,4415,4429],{"className":4414},[2051],[1802,4416,4418],{"className":4417,"style":2273},[2055],[1802,4419,4420,4423],{"style":2149},[1802,4421],{"className":4422,"style":2064},[2063],[1802,4424,4426],{"className":4425},[2068,2069,2070,2071],[1802,4427,1969],{"className":4428},[1845,1846,2071],[1802,4430,2079],{"className":4431},[2078],[1802,4433,4435],{"className":4434},[2051],[1802,4436,4438],{"className":4437,"style":2086},[2055],[1802,4439],{}," under two recursive orderings.",[4442,4443],"web-r",{"code64":4444,"layout":4445,"locale":7,"title":4446},"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","vertical","Compare recursive impulse responses under two orderings",[1798,4448,4449],{},"Both factorizations reproduce the same reduced-form covariance. Yet the response of variable 2 on impact differs because “a shock to variable 1” has been defined differently. Statistical fit cannot select the ordering.",[1793,4451,4453],{"id":4452},"local-projections","Local projections",[1798,4455,4456,4457,4485],{},"At each horizon ",[1802,4458,4460,4473],{"className":4459},[1805],[1802,4461,4463],{"className":4462},[1809],[1811,4464,4465],{"xmlns":1813},[1815,4466,4467,4471],{},[1818,4468,4469],{},[1821,4470,3529],{},[1825,4472,3529],{"encoding":1827},[1802,4474,4476],{"className":4475,"ariaHidden":1832},[1831],[1802,4477,4479,4482],{"className":4478},[1836],[1802,4480],{"className":4481,"style":3541},[1840],[1802,4483,3529],{"className":4484},[1845,1846],", a local projection estimates",[1802,4487,4489],{"className":4488},[1882],[1802,4490,4492,4580],{"className":4491},[1805],[1802,4493,4495],{"className":4494},[1809],[1811,4496,4497],{"xmlns":1813,"display":1891},[1815,4498,4499,4577],{},[1818,4500,4501,4518,4520,4527,4529,4536,4542,4544,4553,4560,4562,4575],{},[1897,4502,4503,4505],{},[1821,4504,1902],{},[1818,4506,4507,4510,4512,4514,4516],{},[1821,4508,4509],{},"i",[1907,4511,1974],{"separator":1832},[1821,4513,1905],{},[1907,4515,1915],{},[1821,4517,3529],{},[1907,4519,1909],{},[1897,4521,4522,4525],{},[1821,4523,4524],{},"α",[1821,4526,3529],{},[1907,4528,1915],{},[1897,4530,4531,4534],{},[1821,4532,4533],{},"θ",[1821,4535,3529],{},[1897,4537,4538,4540],{},[1821,4539,2705],{},[1821,4541,1905],{},[1907,4543,1915],{},[1993,4545,4546,4549,4551],{},[1821,4547,4548],{"mathvariant":2001},"Γ",[1821,4550,3529],{},[1821,4552,2002],{"mathvariant":2001},[1897,4554,4555,4558],{},[1821,4556,4557],{},"w",[1821,4559,1905],{},[1907,4561,1915],{},[1897,4563,4564,4567],{},[1821,4565,4566],{},"e",[1818,4568,4569,4571,4573],{},[1821,4570,1905],{},[1907,4572,1915],{},[1821,4574,3529],{},[1907,4576,1974],{"separator":1832},[1825,4578,4579],{"encoding":1827},"y_{i,t+h}\n=\\alpha_h+\\theta_h s_t+\\Gamma_h^\\top w_t+e_{t+h},",[1802,4581,4583,4657,4715,4813,4922],{"className":4582,"ariaHidden":1832},[1831],[1802,4584,4586,4590,4648,4651,4654],{"className":4585},[1836],[1802,4587],{"className":4588,"style":4589},[1840],"height:0.7167em;vertical-align:-0.2861em;",[1802,4591,4593,4597],{"className":4592},[1845],[1802,4594,1902],{"className":4595,"style":4596},[1845,1846],"margin-right:0.0359em;",[1802,4598,4600],{"className":4599},[2042],[1802,4601,4603,4640],{"className":4602},[2046,2047],[1802,4604,4606,4637],{"className":4605},[2051],[1802,4607,4610],{"className":4608,"style":4609},[2055],"height:0.3361em;",[1802,4611,4613,4616],{"style":4612},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1802,4614],{"className":4615,"style":2064},[2063],[1802,4617,4619],{"className":4618},[2068,2069,2070,2071],[1802,4620,4622,4625,4628,4631,4634],{"className":4621},[1845,2071],[1802,4623,4509],{"className":4624},[1845,1846,2071],[1802,4626,1974],{"className":4627},[2405,2071],[1802,4629,1905],{"className":4630},[1845,1846,2071],[1802,4632,1915],{"className":4633},[2117,2071],[1802,4635,3529],{"className":4636},[1845,1846,2071],[1802,4638,2079],{"className":4639},[2078],[1802,4641,4643],{"className":4642},[2051],[1802,4644,4646],{"className":4645,"style":2294},[2055],[1802,4647],{},[1802,4649],{"className":4650,"style":2092},[1976],[1802,4652,1909],{"className":4653},[2096],[1802,4655],{"className":4656,"style":2092},[1976],[1802,4658,4660,4664,4706,4709,4712],{"className":4659},[1836],[1802,4661],{"className":4662,"style":4663},[1840],"height:0.7333em;vertical-align:-0.15em;",[1802,4665,4667,4671],{"className":4666},[1845],[1802,4668,4524],{"className":4669,"style":4670},[1845,1846],"margin-right:0.0037em;",[1802,4672,4674],{"className":4673},[2042],[1802,4675,4677,4698],{"className":4676},[2046,2047],[1802,4678,4680,4695],{"className":4679},[2051],[1802,4681,4683],{"className":4682,"style":4609},[2055],[1802,4684,4686,4689],{"style":4685},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1802,4687],{"className":4688,"style":2064},[2063],[1802,4690,4692],{"className":4691},[2068,2069,2070,2071],[1802,4693,3529],{"className":4694},[1845,1846,2071],[1802,4696,2079],{"className":4697},[2078],[1802,4699,4701],{"className":4700},[2051],[1802,4702,4704],{"className":4703,"style":2086},[2055],[1802,4705],{},[1802,4707],{"className":4708,"style":2113},[1976],[1802,4710,1915],{"className":4711},[2117],[1802,4713],{"className":4714,"style":2113},[1976],[1802,4716,4718,4722,4764,4804,4807,4810],{"className":4717},[1836],[1802,4719],{"className":4720,"style":4721},[1840],"height:0.8444em;vertical-align:-0.15em;",[1802,4723,4725,4729],{"className":4724},[1845],[1802,4726,4533],{"className":4727,"style":4728},[1845,1846],"margin-right:0.0278em;",[1802,4730,4732],{"className":4731},[2042],[1802,4733,4735,4756],{"className":4734},[2046,2047],[1802,4736,4738,4753],{"className":4737},[2051],[1802,4739,4741],{"className":4740,"style":4609},[2055],[1802,4742,4744,4747],{"style":4743},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1802,4745],{"className":4746,"style":2064},[2063],[1802,4748,4750],{"className":4749},[2068,2069,2070,2071],[1802,4751,3529],{"className":4752},[1845,1846,2071],[1802,4754,2079],{"className":4755},[2078],[1802,4757,4759],{"className":4758},[2051],[1802,4760,4762],{"className":4761,"style":2086},[2055],[1802,4763],{},[1802,4765,4767,4770],{"className":4766},[1845],[1802,4768,2705],{"className":4769},[1845,1846],[1802,4771,4773],{"className":4772},[2042],[1802,4774,4776,4796],{"className":4775},[2046,2047],[1802,4777,4779,4793],{"className":4778},[2051],[1802,4780,4782],{"className":4781,"style":2056},[2055],[1802,4783,4784,4787],{"style":2149},[1802,4785],{"className":4786,"style":2064},[2063],[1802,4788,4790],{"className":4789},[2068,2069,2070,2071],[1802,4791,1905],{"className":4792},[1845,1846,2071],[1802,4794,2079],{"className":4795},[2078],[1802,4797,4799],{"className":4798},[2051],[1802,4800,4802],{"className":4801,"style":2086},[2055],[1802,4803],{},[1802,4805],{"className":4806,"style":2113},[1976],[1802,4808,1915],{"className":4809},[2117],[1802,4811],{"className":4812,"style":2113},[1976],[1802,4814,4816,4820,4871,4913,4916,4919],{"className":4815},[1836],[1802,4817],{"className":4818,"style":4819},[1840],"height:1.1461em;vertical-align:-0.247em;",[1802,4821,4823,4826],{"className":4822},[1845],[1802,4824,4548],{"className":4825},[1845],[1802,4827,4829],{"className":4828},[2042],[1802,4830,4832,4863],{"className":4831},[2046,2047],[1802,4833,4835,4860],{"className":4834},[2051],[1802,4836,4838,4849],{"className":4837,"style":2480},[2055],[1802,4839,4840,4843],{"style":2483},[1802,4841],{"className":4842,"style":2064},[2063],[1802,4844,4846],{"className":4845},[2068,2069,2070,2071],[1802,4847,3529],{"className":4848},[1845,1846,2071],[1802,4850,4851,4854],{"style":2495},[1802,4852],{"className":4853,"style":2064},[2063],[1802,4855,4857],{"className":4856},[2068,2069,2070,2071],[1802,4858,2002],{"className":4859},[1845,2071],[1802,4861,2079],{"className":4862},[2078],[1802,4864,4866],{"className":4865},[2051],[1802,4867,4869],{"className":4868,"style":2514},[2055],[1802,4870],{},[1802,4872,4874,4878],{"className":4873},[1845],[1802,4875,4557],{"className":4876,"style":4877},[1845,1846],"margin-right:0.0269em;",[1802,4879,4881],{"className":4880},[2042],[1802,4882,4884,4905],{"className":4883},[2046,2047],[1802,4885,4887,4902],{"className":4886},[2051],[1802,4888,4890],{"className":4889,"style":2056},[2055],[1802,4891,4893,4896],{"style":4892},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1802,4894],{"className":4895,"style":2064},[2063],[1802,4897,4899],{"className":4898},[2068,2069,2070,2071],[1802,4900,1905],{"className":4901},[1845,1846,2071],[1802,4903,2079],{"className":4904},[2078],[1802,4906,4908],{"className":4907},[2051],[1802,4909,4911],{"className":4910,"style":2086},[2055],[1802,4912],{},[1802,4914],{"className":4915,"style":2113},[1976],[1802,4917,1915],{"className":4918},[2117],[1802,4920],{"className":4921,"style":2113},[1976],[1802,4923,4925,4929,4978],{"className":4924},[1836],[1802,4926],{"className":4927,"style":4928},[1840],"height:0.6389em;vertical-align:-0.2083em;",[1802,4930,4932,4935],{"className":4931},[1845],[1802,4933,4566],{"className":4934},[1845,1846],[1802,4936,4938],{"className":4937},[2042],[1802,4939,4941,4970],{"className":4940},[2046,2047],[1802,4942,4944,4967],{"className":4943},[2051],[1802,4945,4947],{"className":4946,"style":4609},[2055],[1802,4948,4949,4952],{"style":2149},[1802,4950],{"className":4951,"style":2064},[2063],[1802,4953,4955],{"className":4954},[2068,2069,2070,2071],[1802,4956,4958,4961,4964],{"className":4957},[1845,2071],[1802,4959,1905],{"className":4960},[1845,1846,2071],[1802,4962,1915],{"className":4963},[2117,2071],[1802,4965,3529],{"className":4966},[1845,1846,2071],[1802,4968,2079],{"className":4969},[2078],[1802,4971,4973],{"className":4972},[2051],[1802,4974,4976],{"className":4975,"style":2217},[2055],[1802,4977],{},[1802,4979,1974],{"className":4980},[2405],[1798,4982,4983,4984,5055,5056,5126,5127,5209],{},"where ",[1802,4985,4987,5005],{"className":4986},[1805],[1802,4988,4990],{"className":4989},[1809],[1811,4991,4992],{"xmlns":1813},[1815,4993,4994,5002],{},[1818,4995,4996],{},[1897,4997,4998,5000],{},[1821,4999,2705],{},[1821,5001,1905],{},[1825,5003,5004],{"encoding":1827},"s_t",[1802,5006,5008],{"className":5007,"ariaHidden":1832},[1831],[1802,5009,5011,5015],{"className":5010},[1836],[1802,5012],{"className":5013,"style":5014},[1840],"height:0.5806em;vertical-align:-0.15em;",[1802,5016,5018,5021],{"className":5017},[1845],[1802,5019,2705],{"className":5020},[1845,1846],[1802,5022,5024],{"className":5023},[2042],[1802,5025,5027,5047],{"className":5026},[2046,2047],[1802,5028,5030,5044],{"className":5029},[2051],[1802,5031,5033],{"className":5032,"style":2056},[2055],[1802,5034,5035,5038],{"style":2149},[1802,5036],{"className":5037,"style":2064},[2063],[1802,5039,5041],{"className":5040},[2068,2069,2070,2071],[1802,5042,1905],{"className":5043},[1845,1846,2071],[1802,5045,2079],{"className":5046},[2078],[1802,5048,5050],{"className":5049},[2051],[1802,5051,5053],{"className":5052,"style":2086},[2055],[1802,5054],{}," is the identified shock or treatment-like innovation and ",[1802,5057,5059,5077],{"className":5058},[1805],[1802,5060,5062],{"className":5061},[1809],[1811,5063,5064],{"xmlns":1813},[1815,5065,5066,5074],{},[1818,5067,5068],{},[1897,5069,5070,5072],{},[1821,5071,4557],{},[1821,5073,1905],{},[1825,5075,5076],{"encoding":1827},"w_t",[1802,5078,5080],{"className":5079,"ariaHidden":1832},[1831],[1802,5081,5083,5086],{"className":5082},[1836],[1802,5084],{"className":5085,"style":5014},[1840],[1802,5087,5089,5092],{"className":5088},[1845],[1802,5090,4557],{"className":5091,"style":4877},[1845,1846],[1802,5093,5095],{"className":5094},[2042],[1802,5096,5098,5118],{"className":5097},[2046,2047],[1802,5099,5101,5115],{"className":5100},[2051],[1802,5102,5104],{"className":5103,"style":2056},[2055],[1802,5105,5106,5109],{"style":4892},[1802,5107],{"className":5108,"style":2064},[2063],[1802,5110,5112],{"className":5111},[2068,2069,2070,2071],[1802,5113,1905],{"className":5114},[1845,1846,2071],[1802,5116,2079],{"className":5117},[2078],[1802,5119,5121],{"className":5120},[2051],[1802,5122,5124],{"className":5123,"style":2086},[2055],[1802,5125],{}," contains controls and lags. The sequence ",[1802,5128,5130,5154],{"className":5129},[1805],[1802,5131,5133],{"className":5132},[1809],[1811,5134,5135],{"xmlns":1813},[1815,5136,5137,5151],{},[1818,5138,5139,5142,5148],{},[1907,5140,5141],{"stretchy":1984},"{",[1897,5143,5144,5146],{},[1821,5145,4533],{},[1821,5147,3529],{},[1907,5149,5150],{"stretchy":1984},"}",[1825,5152,5153],{"encoding":1827},"\\{\\theta_h\\}",[1802,5155,5157],{"className":5156,"ariaHidden":1832},[1831],[1802,5158,5160,5163,5166,5206],{"className":5159},[1836],[1802,5161],{"className":5162,"style":4127},[1840],[1802,5164,5141],{"className":5165},[2421],[1802,5167,5169,5172],{"className":5168},[1845],[1802,5170,4533],{"className":5171,"style":4728},[1845,1846],[1802,5173,5175],{"className":5174},[2042],[1802,5176,5178,5198],{"className":5177},[2046,2047],[1802,5179,5181,5195],{"className":5180},[2051],[1802,5182,5184],{"className":5183,"style":4609},[2055],[1802,5185,5186,5189],{"style":4743},[1802,5187],{"className":5188,"style":2064},[2063],[1802,5190,5192],{"className":5191},[2068,2069,2070,2071],[1802,5193,3529],{"className":5194},[1845,1846,2071],[1802,5196,2079],{"className":5197},[2078],[1802,5199,5201],{"className":5200},[2051],[1802,5202,5204],{"className":5203,"style":2086},[2055],[1802,5205],{},[1802,5207,5150],{"className":5208},[2520]," forms the response.",[1798,5211,5212],{},"Local projections make horizon-specific controls and nonlinearities convenient, but:",[2584,5214,5215,5218,5221,5224],{},[2587,5216,5217],{},"overlapping horizons require serial-correlation-robust inference;",[2587,5219,5220],{},"the shock still requires identification;",[2587,5222,5223],{},"flexible horizon-by-horizon estimates can be noisy;",[2587,5225,5226],{},"post-selection of controls or horizons changes inference.",[1798,5228,5229,5236,5237,5242],{},[5230,5231,5235],"a",{"href":5232,"rel":5233},"https:\u002F\u002Fwww.aeaweb.org\u002Farticles?id=10.1257%2F0002828053828518",[5234],"nofollow","Jordà (2005)"," introduced this approach for impulse responses. ",[5230,5238,5241],{"href":5239,"rel":5240},"https:\u002F\u002Fonlinelibrary.wiley.com\u002Fdoi\u002F10.3982\u002FECTA17813",[5234],"Plagborg-Møller and Wolf (2021)"," establish the population equivalence between unrestricted LP and VAR impulse responses under common identification; regularisation and finite-sample choices drive practical differences.",[1793,5244,5246],{"id":5245},"finance-and-economics-use-vars-differently","Finance and economics use VARs differently",[4254,5248,5249,5262],{},[4257,5250,5251],{},[4260,5252,5253,5256,5259],{},[4263,5254,5255],{},"Use",[4263,5257,5258],{},"Finance",[4263,5260,5261],{},"Economics",[4273,5263,5264,5275,5286,5297,5308],{},[4260,5265,5266,5269,5272],{},[4278,5267,5268],{},"system",[4278,5270,5271],{},"returns, volatility, liquidity, flows, yields",[4278,5273,5274],{},"output, inflation, employment, rates, money",[4260,5276,5277,5280,5283],{},[4278,5278,5279],{},"horizon",[4278,5281,5282],{},"often short and high-frequency",[4278,5284,5285],{},"monthly to multi-year",[4260,5287,5288,5291,5294],{},[4278,5289,5290],{},"innovation label",[4278,5292,5293],{},"market, liquidity, order-flow, volatility shock",[4278,5295,5296],{},"monetary, fiscal, supply, demand shock",[4260,5298,5299,5302,5305],{},[4278,5300,5301],{},"key threat",[4278,5303,5304],{},"asynchronous trading and rapidly changing covariance",[4278,5306,5307],{},"policy anticipation, simultaneity, regime change",[4260,5309,5310,5313,5316],{},[4278,5311,5312],{},"evidence beyond fit",[4278,5314,5315],{},"executable timing and market mechanism",[4278,5317,5318],{},"institutional timing and identification restrictions",[1798,5320,5321],{},"In finance, connectedness or variance decomposition is descriptive unless shocks are identified. In economics, a policy response is structural only to the extent that the restrictions isolate an exogenous policy disturbance.",[1793,5323,5325],{"id":5324},"identification-checklist","Identification checklist",[1798,5327,5328],{},"Before reporting an impulse response, state:",[5330,5331,5332,5335,5338,5341,5344,5347,5350],"ol",{},[2587,5333,5334],{},"the reduced-form variables, transformations, frequency, and lags;",[2587,5336,5337],{},"the matrix restriction or instrument defining the shock;",[2587,5339,5340],{},"why that restriction matches institutional timing;",[2587,5342,5343],{},"shock scale and sign;",[2587,5345,5346],{},"whether the response is cumulative, in levels, or in growth;",[2587,5348,5349],{},"uncertainty method and horizon multiplicity;",[2587,5351,5352],{},"sensitivity to ordering, lag length, sample, trends, and alternative identification.",[1793,5354,5356],{"id":5355},"practice","Practice",[5330,5358,5359,5432,5435],{},[2587,5360,5361,5362,5431],{},"Does a diagonal ",[1802,5363,5365,5382],{"className":5364},[1805],[1802,5366,5368],{"className":5367},[1809],[1811,5369,5370],{"xmlns":1813},[1815,5371,5372,5380],{},[1818,5373,5374],{},[1897,5375,5376,5378],{},[1821,5377,2012],{"mathvariant":2001},[1821,5379,1969],{},[1825,5381,4390],{"encoding":1827},[1802,5383,5385],{"className":5384,"ariaHidden":1832},[1831],[1802,5386,5388,5391],{"className":5387},[1836],[1802,5389],{"className":5390,"style":2536},[1840],[1802,5392,5394,5397],{"className":5393},[1845],[1802,5395,2012],{"className":5396},[1845],[1802,5398,5400],{"className":5399},[2042],[1802,5401,5403,5423],{"className":5402},[2046,2047],[1802,5404,5406,5420],{"className":5405},[2051],[1802,5407,5409],{"className":5408,"style":2273},[2055],[1802,5410,5411,5414],{"style":2149},[1802,5412],{"className":5413,"style":2064},[2063],[1802,5415,5417],{"className":5416},[2068,2069,2070,2071],[1802,5418,1969],{"className":5419},[1845,1846,2071],[1802,5421,2079],{"className":5422},[2078],[1802,5424,5426],{"className":5425},[2051],[1802,5427,5429],{"className":5428,"style":2086},[2055],[1802,5430],{}," solve all structural identification problems?",[2587,5433,5434],{},"If reversing a Cholesky order changes the conclusion, what has been learned?",[2587,5436,5437],{},"Can an LP turn a poorly identified innovation into a causal shock?",[5439,5440,5442],"legacy-details",{"title":5441},"Answers",[5330,5443,5444,5447,5450],{},[2587,5445,5446],{},"No. It removes contemporaneous correlation under the reduced form but does not attach economic labels without assumptions.",[2587,5448,5449],{},"The substantive result depends on contemporaneous zero restrictions and must be justified or reported as fragile.",[2587,5451,5452],{},"No. LP changes response estimation, not the credibility of the shock.",[1798,5454,5455,5456,2017],{},"Next: ",[5230,5457,454],{"href":5458},"..\u002F07-state-space-nowcasting\u002F",{"title":10,"searchDepth":5460,"depth":5460,"links":5461},2,[5462,5463,5464,5465,5466,5467,5468,5469],{"id":1795,"depth":5460,"text":1796},{"id":2681,"depth":5460,"text":2682},{"id":3612,"depth":5460,"text":3613},{"id":4336,"depth":5460,"text":4337},{"id":4452,"depth":5460,"text":4453},{"id":5245,"depth":5460,"text":5246},{"id":5324,"depth":5460,"text":5325},{"id":5355,"depth":5460,"text":5356},"Separate multivariate forecasting from structural shocks using companion matrices, impact restrictions, and impulse responses.","md",{"sidebar":5473},{"order":5474},6,true,{"title":448,"description":5470},"4n7fiiVztmgIDd_7Mued1PCqaPJ_x81qVx8aSHKvYiM",[5479,5481],{"title":442,"path":443,"stem":444,"description":5480,"children":-1},"Diagnose spurious levels, derive reduced-rank error correction, and distinguish financial spreads from economic equilibria.",{"title":454,"path":455,"stem":456,"description":5482,"children":-1},"Use Kalman prediction and update matrices for latent financial states, macroeconomic nowcasts, missing releases, and ragged edges.",1785754724240]