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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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accelerate. A frequency–severity view separates two mechanisms before recombining them.",[1797,1798,1801],"span",{"className":1799},[1800],"katex-display",[1797,1802,1805,1881],{"className":1803},[1804],"katex",[1797,1806,1809],{"className":1807},[1808],"katex-mathml",[1810,1811,1814],"math",{"xmlns":1812,"display":1813},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1815,1816,1817,1876],"semantics",{},[1818,1819,1820,1838,1841,1857,1860,1873],"mrow",{},[1821,1822,1823,1835],"msub",{},[1824,1825,1827,1831],"mover",{"accent":1826},"true",[1828,1829,1830],"mi",{},"U",[1832,1833,1834],"mo",{"stretchy":1826},"^",[1828,1836,1837],{},"i",[1832,1839,1840],{},"=",[1842,1843,1844,1851,1853],"msubsup",{},[1824,1845,1846,1849],{"accent":1826},[1828,1847,1848],{},"N",[1832,1850,1834],{"stretchy":1826},[1828,1852,1837],{},[1854,1855,1856],"mtext",{},"ultimate",[1832,1858,1859],{},"×",[1842,1861,1862,1869,1871],{},[1824,1863,1864,1867],{"accent":1826},[1828,1865,1866],{},"A",[1832,1868,1834],{"stretchy":1826},[1828,1870,1837],{},[1854,1872,1856],{},[1832,1874,1875],{"separator":1826},",",[1877,1878,1880],"annotation",{"encoding":1879},"application\u002Fx-tex","\\widehat U_i\n=\\widehat N_i^{\\text{ultimate}}\n\\times\n\\widehat A_i^{\\text{ultimate}},",[1797,1882,1885,2009,2119],{"className":1883,"ariaHidden":1826},[1884],"katex-html",[1797,1886,1889,1894,1997,2002,2006],{"className":1887},[1888],"base",[1797,1890],{"className":1891,"style":1893},[1892],"strut","height:1.0733em;vertical-align:-0.15em;",[1797,1895,1898,1951],{"className":1896},[1897],"mord",[1797,1899,1902],{"className":1900},[1897,1901],"accent",[1797,1903,1906],{"className":1904},[1905],"vlist-t",[1797,1907,1910],{"className":1908},[1909],"vlist-r",[1797,1911,1915,1928],{"className":1912,"style":1914},[1913],"vlist","height:0.9233em;",[1797,1916,1918,1923],{"style":1917},"top:-3em;",[1797,1919],{"className":1920,"style":1922},[1921],"pstrut","height:3em;",[1797,1924,1830],{"className":1925,"style":1927},[1897,1926],"mathnormal","margin-right:0.109em;",[1797,1929,1933,1936],{"className":1930,"style":1932},[1931],"svg-align","width:calc(100% - 0.0556em);margin-left:0.0556em;top:-3.6833em;",[1797,1934],{"className":1935,"style":1922},[1921],[1797,1937,1939],{"style":1938},"height:0.24em;",[1940,1941,1947],"svg",{"xmlns":1942,"width":1943,"height":1944,"viewBox":1945,"preserveAspectRatio":1946},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","100%","0.24em","0 0 1062 239","none",[1948,1949],"path",{"d":1950},"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",[1797,1952,1955],{"className":1953},[1954],"msupsub",[1797,1956,1959,1988],{"className":1957},[1905,1958],"vlist-t2",[1797,1960,1962,1983],{"className":1961},[1909],[1797,1963,1966],{"className":1964,"style":1965},[1913],"height:0.3117em;",[1797,1967,1969,1973],{"style":1968},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[1797,1970],{"className":1971,"style":1972},[1921],"height:2.7em;",[1797,1974,1980],{"className":1975},[1976,1977,1978,1979],"sizing","reset-size6","size3","mtight",[1797,1981,1837],{"className":1982},[1897,1926,1979],[1797,1984,1987],{"className":1985},[1986],"vlist-s","​",[1797,1989,1991],{"className":1990},[1909],[1797,1992,1995],{"className":1993,"style":1994},[1913],"height:0.15em;",[1797,1996],{},[1797,1998],{"className":1999,"style":2001},[2000],"mspace","margin-right:0.2778em;",[1797,2003,1840],{"className":2004},[2005],"mrel",[1797,2007],{"className":2008,"style":2001},[2000],[1797,2010,2012,2016,2108,2112,2116],{"className":2011},[1888],[1797,2013],{"className":2014,"style":2015},[1892],"height:1.1703em;vertical-align:-0.247em;",[1797,2017,2019,2052],{"className":2018},[1897],[1797,2020,2022],{"className":2021},[1897,1901],[1797,2023,2025],{"className":2024},[1905],[1797,2026,2028],{"className":2027},[1909],[1797,2029,2031,2039],{"className":2030,"style":1914},[1913],[1797,2032,2033,2036],{"style":1917},[1797,2034],{"className":2035,"style":1922},[1921],[1797,2037,1848],{"className":2038,"style":1927},[1897,1926],[1797,2040,2043,2046],{"className":2041,"style":2042},[1931],"width:calc(100% - 0.1667em);margin-left:0.1667em;top:-3.6833em;",[1797,2044],{"className":2045,"style":1922},[1921],[1797,2047,2048],{"style":1938},[1940,2049,2050],{"xmlns":1942,"width":1943,"height":1944,"viewBox":1945,"preserveAspectRatio":1946},[1948,2051],{"d":1950},[1797,2053,2055],{"className":2054},[1954],[1797,2056,2058,2099],{"className":2057},[1905,1958],[1797,2059,2061,2096],{"className":2060},[1909],[1797,2062,2065,2077],{"className":2063,"style":2064},[1913],"height:0.8991em;",[1797,2066,2068,2071],{"style":2067},"top:-2.453em;margin-left:-0.109em;margin-right:0.05em;",[1797,2069],{"className":2070,"style":1972},[1921],[1797,2072,2074],{"className":2073},[1976,1977,1978,1979],[1797,2075,1837],{"className":2076},[1897,1926,1979],[1797,2078,2080,2083],{"style":2079},"top:-3.113em;margin-right:0.05em;",[1797,2081],{"className":2082,"style":1972},[1921],[1797,2084,2086],{"className":2085},[1976,1977,1978,1979],[1797,2087,2089],{"className":2088},[1897,1979],[1797,2090,2093],{"className":2091},[1897,2092,1979],"text",[1797,2094,1856],{"className":2095},[1897,1979],[1797,2097,1987],{"className":2098},[1986],[1797,2100,2102],{"className":2101},[1909],[1797,2103,2106],{"className":2104,"style":2105},[1913],"height:0.247em;",[1797,2107],{},[1797,2109],{"className":2110,"style":2111},[2000],"margin-right:0.2222em;",[1797,2113,1859],{"className":2114},[2115],"mbin",[1797,2117],{"className":2118,"style":2111},[2000],[1797,2120,2122,2125,2213],{"className":2121},[1888],[1797,2123],{"className":2124,"style":2015},[1892],[1797,2126,2128,2161],{"className":2127},[1897],[1797,2129,2131],{"className":2130},[1897,1901],[1797,2132,2134],{"className":2133},[1905],[1797,2135,2137],{"className":2136},[1909],[1797,2138,2140,2148],{"className":2139,"style":1914},[1913],[1797,2141,2142,2145],{"style":1917},[1797,2143],{"className":2144,"style":1922},[1921],[1797,2146,1866],{"className":2147},[1897,1926],[1797,2149,2152,2155],{"className":2150,"style":2151},[1931],"width:calc(100% - 0.2778em);margin-left:0.2778em;top:-3.6833em;",[1797,2153],{"className":2154,"style":1922},[1921],[1797,2156,2157],{"style":1938},[1940,2158,2159],{"xmlns":1942,"width":1943,"height":1944,"viewBox":1945,"preserveAspectRatio":1946},[1948,2160],{"d":1950},[1797,2162,2164],{"className":2163},[1954],[1797,2165,2167,2205],{"className":2166},[1905,1958],[1797,2168,2170,2202],{"className":2169},[1909],[1797,2171,2173,2185],{"className":2172,"style":2064},[1913],[1797,2174,2176,2179],{"style":2175},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1797,2177],{"className":2178,"style":1972},[1921],[1797,2180,2182],{"className":2181},[1976,1977,1978,1979],[1797,2183,1837],{"className":2184},[1897,1926,1979],[1797,2186,2187,2190],{"style":2079},[1797,2188],{"className":2189,"style":1972},[1921],[1797,2191,2193],{"className":2192},[1976,1977,1978,1979],[1797,2194,2196],{"className":2195},[1897,1979],[1797,2197,2199],{"className":2198},[1897,2092,1979],[1797,2200,1856],{"className":2201},[1897,1979],[1797,2203,1987],{"className":2204},[1986],[1797,2206,2208],{"className":2207},[1909],[1797,2209,2211],{"className":2210,"style":2105},[1913],[1797,2212],{},[1797,2214,1875],{"className":2215},[2216],"mpunct",[1793,2218,2219,2220,2249,2250,2278],{},"where ",[1797,2221,2223,2236],{"className":2222},[1804],[1797,2224,2226],{"className":2225},[1808],[1810,2227,2228],{"xmlns":1812},[1815,2229,2230,2234],{},[1818,2231,2232],{},[1828,2233,1848],{},[1877,2235,1848],{"encoding":1879},[1797,2237,2239],{"className":2238,"ariaHidden":1826},[1884],[1797,2240,2242,2246],{"className":2241},[1888],[1797,2243],{"className":2244,"style":2245},[1892],"height:0.6833em;",[1797,2247,1848],{"className":2248,"style":1927},[1897,1926]," is ultimate claim count and ",[1797,2251,2253,2266],{"className":2252},[1804],[1797,2254,2256],{"className":2255},[1808],[1810,2257,2258],{"xmlns":1812},[1815,2259,2260,2264],{},[1818,2261,2262],{},[1828,2263,1866],{},[1877,2265,1866],{"encoding":1879},[1797,2267,2269],{"className":2268,"ariaHidden":1826},[1884],[1797,2270,2272,2275],{"className":2271},[1888],[1797,2273],{"className":2274,"style":2245},[1892],[1797,2276,1866],{"className":2277},[1897,1926]," is average ultimate cost per claim.",[2280,2281,2283],"warning",{"title":2282},"Define “one claim” first","A claimant, coverage, event, and claim-file record need not be the same unit. Reopened and nil claims can change counts without changing economic loss. Freeze one operational definition across all periods.",[2285,2286,2288],"h2",{"id":2287},"_1-add-a-cumulative-reported-count-triangle","1. Add a cumulative reported-count triangle",[1793,2290,2291],{},"Harbour Mutual reports:",[2293,2294,2295,2318],"table",{},[2296,2297,2298],"thead",{},[2299,2300,2301,2305,2309,2312,2315],"tr",{},[2302,2303,2304],"th",{},"AY",[2302,2306,2308],{"align":2307},"right","Dev 0",[2302,2310,2311],{"align":2307},"Dev 1",[2302,2313,2314],{"align":2307},"Dev 2",[2302,2316,2317],{"align":2307},"Dev 3",[2319,2320,2321,2339,2356,2371],"tbody",{},[2299,2322,2323,2327,2330,2333,2336],{},[2324,2325,2326],"td",{},"2020",[2324,2328,2329],{"align":2307},"50",[2324,2331,2332],{"align":2307},"80",[2324,2334,2335],{"align":2307},"95",[2324,2337,2338],{"align":2307},"100",[2299,2340,2341,2344,2347,2350,2353],{},[2324,2342,2343],{},"2021",[2324,2345,2346],{"align":2307},"55",[2324,2348,2349],{"align":2307},"88",[2324,2351,2352],{"align":2307},"104",[2324,2354,2355],{"align":2307},"—",[2299,2357,2358,2361,2364,2367,2369],{},[2324,2359,2360],{},"2022",[2324,2362,2363],{"align":2307},"60",[2324,2365,2366],{"align":2307},"96",[2324,2368,2355],{"align":2307},[2324,2370,2355],{"align":2307},[2299,2372,2373,2376,2379,2381,2383],{},[2324,2374,2375],{},"2023",[2324,2377,2378],{"align":2307},"70",[2324,2380,2355],{"align":2307},[2324,2382,2355],{"align":2307},[2324,2384,2355],{"align":2307},[1793,2386,2387],{},"Use the same volume-weighted calculation as chain ladder:",[2293,2389,2390,2403],{},[2296,2391,2392],{},[2299,2393,2394,2397,2400],{},[2302,2395,2396],{},"Count transition",[2302,2398,2399],{"align":2307},"Selected factor",[2302,2401,2402],{"align":2307},"CDF to ultimate",[2319,2404,2405,2479,2548],{},[2299,2406,2407,2410,2476],{},[2324,2408,2409],{},"0 → 1",[2324,2411,2412],{"align":2307},[1797,2413,2415,2443],{"className":2414},[1804],[1797,2416,2418],{"className":2417},[1808],[1810,2419,2420],{"xmlns":1812},[1815,2421,2422,2440],{},[1818,2423,2424,2428,2432,2435,2437],{},[2425,2426,2427],"mn",{},"264",[1828,2429,2431],{"mathvariant":2430},"normal","\u002F",[2425,2433,2434],{},"165",[1832,2436,1840],{},[2425,2438,2439],{},"1.6000",[1877,2441,2442],{"encoding":1879},"264\u002F165=1.6000",[1797,2444,2446,2466],{"className":2445,"ariaHidden":1826},[1884],[1797,2447,2449,2453,2457,2460,2463],{"className":2448},[1888],[1797,2450],{"className":2451,"style":2452},[1892],"height:1em;vertical-align:-0.25em;",[1797,2454,2456],{"className":2455},[1897],"264\u002F165",[1797,2458],{"className":2459,"style":2001},[2000],[1797,2461,1840],{"className":2462},[2005],[1797,2464],{"className":2465,"style":2001},[2000],[1797,2467,2469,2473],{"className":2468},[1888],[1797,2470],{"className":2471,"style":2472},[1892],"height:0.6444em;",[1797,2474,2439],{"className":2475},[1897],[2324,2477,2478],{"align":2307},"1.9950",[2299,2480,2481,2484,2545],{},[2324,2482,2483],{},"1 → 2",[2324,2485,2486],{"align":2307},[1797,2487,2489,2514],{"className":2488},[1804],[1797,2490,2492],{"className":2491},[1808],[1810,2493,2494],{"xmlns":1812},[1815,2495,2496,2511],{},[1818,2497,2498,2501,2503,2506,2508],{},[2425,2499,2500],{},"199",[1828,2502,2431],{"mathvariant":2430},[2425,2504,2505],{},"168",[1832,2507,1840],{},[2425,2509,2510],{},"1.1845",[1877,2512,2513],{"encoding":1879},"199\u002F168=1.1845",[1797,2515,2517,2536],{"className":2516,"ariaHidden":1826},[1884],[1797,2518,2520,2523,2527,2530,2533],{"className":2519},[1888],[1797,2521],{"className":2522,"style":2452},[1892],[1797,2524,2526],{"className":2525},[1897],"199\u002F168",[1797,2528],{"className":2529,"style":2001},[2000],[1797,2531,1840],{"className":2532},[2005],[1797,2534],{"className":2535,"style":2001},[2000],[1797,2537,2539,2542],{"className":2538},[1888],[1797,2540],{"className":2541,"style":2472},[1892],[1797,2543,2510],{"className":2544},[1897],[2324,2546,2547],{"align":2307},"1.2469",[2299,2549,2550,2553,2612],{},[2324,2551,2552],{},"2 → 3",[2324,2554,2555],{"align":2307},[1797,2556,2558,2581],{"className":2557},[1804],[1797,2559,2561],{"className":2560},[1808],[1810,2562,2563],{"xmlns":1812},[1815,2564,2565,2578],{},[1818,2566,2567,2569,2571,2573,2575],{},[2425,2568,2338],{},[1828,2570,2431],{"mathvariant":2430},[2425,2572,2335],{},[1832,2574,1840],{},[2425,2576,2577],{},"1.0526",[1877,2579,2580],{"encoding":1879},"100\u002F95=1.0526",[1797,2582,2584,2603],{"className":2583,"ariaHidden":1826},[1884],[1797,2585,2587,2590,2594,2597,2600],{"className":2586},[1888],[1797,2588],{"className":2589,"style":2452},[1892],[1797,2591,2593],{"className":2592},[1897],"100\u002F95",[1797,2595],{"className":2596,"style":2001},[2000],[1797,2598,1840],{"className":2599},[2005],[1797,2601],{"className":2602,"style":2001},[2000],[1797,2604,2606,2609],{"className":2605},[1888],[1797,2607],{"className":2608,"style":2472},[1892],[1797,2610,2577],{"className":2611},[1897],[2324,2613,2577],{"align":2307},[1793,2615,2616],{},"Projected ultimate counts are therefore approximately 100.0, 109.5, 119.7, and 139.6 for AY 2020–2023. Fractional values are expectations, not literal future files.",[2285,2618,2620],{"id":2619},"_2-examine-average-paid-per-reported-claim","2. Examine average paid per reported claim",[1793,2622,2623],{},"For diagnosis, divide cumulative paid loss by cumulative reported count in the matching cell:",[1797,2625,2627],{"className":2626},[1800],[1797,2628,2630,2694],{"className":2629},[1804],[1797,2631,2633],{"className":2632},[1808],[1810,2634,2635],{"xmlns":1812,"display":1813},[1815,2636,2637,2691],{},[1818,2638,2639,2652,2654,2688],{},[1821,2640,2641,2643],{},[1828,2642,1866],{},[1818,2644,2645,2647,2649],{},[1828,2646,1837],{},[1832,2648,1875],{"separator":1826},[1828,2650,2651],{},"j",[1832,2653,1840],{},[2655,2656,2657,2673],"mfrac",{},[1842,2658,2659,2662,2670],{},[1828,2660,2661],{},"C",[1818,2663,2664,2666,2668],{},[1828,2665,1837],{},[1832,2667,1875],{"separator":1826},[1828,2669,2651],{},[1854,2671,2672],{},"paid",[1842,2674,2675,2677,2685],{},[1828,2676,1848],{},[1818,2678,2679,2681,2683],{},[1828,2680,1837],{},[1832,2682,1875],{"separator":1826},[1828,2684,2651],{},[1854,2686,2687],{},"reported",[1828,2689,2690],{"mathvariant":2430},".",[1877,2692,2693],{"encoding":1879},"A_{i,j}=\\frac{C_{i,j}^{\\text{paid}}}{N_{i,j}^{\\text{reported}}}.",[1797,2695,2697,2765],{"className":2696,"ariaHidden":1826},[1884],[1797,2698,2700,2704,2756,2759,2762],{"className":2699},[1888],[1797,2701],{"className":2702,"style":2703},[1892],"height:0.9694em;vertical-align:-0.2861em;",[1797,2705,2707,2710],{"className":2706},[1897],[1797,2708,1866],{"className":2709},[1897,1926],[1797,2711,2713],{"className":2712},[1954],[1797,2714,2716,2747],{"className":2715},[1905,1958],[1797,2717,2719,2744],{"className":2718},[1909],[1797,2720,2722],{"className":2721,"style":1965},[1913],[1797,2723,2725,2728],{"style":2724},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1797,2726],{"className":2727,"style":1972},[1921],[1797,2729,2731],{"className":2730},[1976,1977,1978,1979],[1797,2732,2734,2737,2740],{"className":2733},[1897,1979],[1797,2735,1837],{"className":2736},[1897,1926,1979],[1797,2738,1875],{"className":2739},[2216,1979],[1797,2741,2651],{"className":2742,"style":2743},[1897,1926,1979],"margin-right:0.0572em;",[1797,2745,1987],{"className":2746},[1986],[1797,2748,2750],{"className":2749},[1909],[1797,2751,2754],{"className":2752,"style":2753},[1913],"height:0.2861em;",[1797,2755],{},[1797,2757],{"className":2758,"style":2001},[2000],[1797,2760,1840],{"className":2761},[2005],[1797,2763],{"className":2764,"style":2001},[2000],[1797,2766,2768,2772,2976],{"className":2767},[1888],[1797,2769],{"className":2770,"style":2771},[1892],"height:3.04em;vertical-align:-1.27em;",[1797,2773,2775,2780,2972],{"className":2774},[1897],[1797,2776],{"className":2777},[2778,2779],"mopen","nulldelimiter",[1797,2781,2783],{"className":2782},[2655],[1797,2784,2786,2963],{"className":2785},[1905,1958],[1797,2787,2789,2960],{"className":2788},[1909],[1797,2790,2793,2872,2883],{"className":2791,"style":2792},[1913],"height:1.77em;",[1797,2794,2796,2799],{"style":2795},"top:-2.143em;",[1797,2797],{"className":2798,"style":1922},[1921],[1797,2800,2802],{"className":2801},[1897],[1797,2803,2805,2808],{"className":2804},[1897],[1797,2806,1848],{"className":2807,"style":1927},[1897,1926],[1797,2809,2811],{"className":2810},[1954],[1797,2812,2814,2863],{"className":2813},[1905,1958],[1797,2815,2817,2860],{"className":2816},[1909],[1797,2818,2821,2842],{"className":2819,"style":2820},[1913],"height:0.967em;",[1797,2822,2824,2827],{"style":2823},"top:-2.4231em;margin-left:-0.109em;margin-right:0.05em;",[1797,2825],{"className":2826,"style":1972},[1921],[1797,2828,2830],{"className":2829},[1976,1977,1978,1979],[1797,2831,2833,2836,2839],{"className":2832},[1897,1979],[1797,2834,1837],{"className":2835},[1897,1926,1979],[1797,2837,1875],{"className":2838},[2216,1979],[1797,2840,2651],{"className":2841,"style":2743},[1897,1926,1979],[1797,2843,2845,2848],{"style":2844},"top:-3.1809em;margin-right:0.05em;",[1797,2846],{"className":2847,"style":1972},[1921],[1797,2849,2851],{"className":2850},[1976,1977,1978,1979],[1797,2852,2854],{"className":2853},[1897,1979],[1797,2855,2857],{"className":2856},[1897,2092,1979],[1797,2858,2687],{"className":2859},[1897,1979],[1797,2861,1987],{"className":2862},[1986],[1797,2864,2866],{"className":2865},[1909],[1797,2867,2870],{"className":2868,"style":2869},[1913],"height:0.413em;",[1797,2871],{},[1797,2873,2875,2878],{"style":2874},"top:-3.23em;",[1797,2876],{"className":2877,"style":1922},[1921],[1797,2879],{"className":2880,"style":2882},[2881],"frac-line","border-bottom-width:0.04em;",[1797,2884,2886,2889],{"style":2885},"top:-3.803em;",[1797,2887],{"className":2888,"style":1922},[1921],[1797,2890,2892],{"className":2891},[1897],[1797,2893,2895,2899],{"className":2894},[1897],[1797,2896,2661],{"className":2897,"style":2898},[1897,1926],"margin-right:0.0715em;",[1797,2900,2902],{"className":2901},[1954],[1797,2903,2905,2952],{"className":2904},[1905,1958],[1797,2906,2908,2949],{"className":2907},[1909],[1797,2909,2911,2932],{"className":2910,"style":2820},[1913],[1797,2912,2914,2917],{"style":2913},"top:-2.4231em;margin-left:-0.0715em;margin-right:0.05em;",[1797,2915],{"className":2916,"style":1972},[1921],[1797,2918,2920],{"className":2919},[1976,1977,1978,1979],[1797,2921,2923,2926,2929],{"className":2922},[1897,1979],[1797,2924,1837],{"className":2925},[1897,1926,1979],[1797,2927,1875],{"className":2928},[2216,1979],[1797,2930,2651],{"className":2931,"style":2743},[1897,1926,1979],[1797,2933,2934,2937],{"style":2844},[1797,2935],{"className":2936,"style":1972},[1921],[1797,2938,2940],{"className":2939},[1976,1977,1978,1979],[1797,2941,2943],{"className":2942},[1897,1979],[1797,2944,2946],{"className":2945},[1897,2092,1979],[1797,2947,2672],{"className":2948},[1897,1979],[1797,2950,1987],{"className":2951},[1986],[1797,2953,2955],{"className":2954},[1909],[1797,2956,2958],{"className":2957,"style":2869},[1913],[1797,2959],{},[1797,2961,1987],{"className":2962},[1986],[1797,2964,2966],{"className":2965},[1909],[1797,2967,2970],{"className":2968,"style":2969},[1913],"height:1.27em;",[1797,2971],{},[1797,2973],{"className":2974},[2975,2779],"mclose",[1797,2977,2690],{"className":2978},[1897],[2293,2980,2981,2995],{},[2296,2982,2983],{},[2299,2984,2985,2987,2989,2991,2993],{},[2302,2986,2304],{},[2302,2988,2308],{"align":2307},[2302,2990,2311],{"align":2307},[2302,2992,2314],{"align":2307},[2302,2994,2317],{"align":2307},[2319,2996,2997,3013,3028,3042],{},[2299,2998,2999,3001,3004,3007,3010],{},[2324,3000,2326],{},[2324,3002,3003],{"align":2307},"2.000",[2324,3005,3006],{"align":2307},"2.250",[2324,3008,3009],{"align":2307},"2.526",[2324,3011,3012],{"align":2307},"2.800",[2299,3014,3015,3017,3020,3023,3026],{},[2324,3016,2343],{},[2324,3018,3019],{"align":2307},"2.182",[2324,3021,3022],{"align":2307},"2.500",[2324,3024,3025],{"align":2307},"2.885",[2324,3027,2355],{"align":2307},[2299,3029,3030,3032,3035,3038,3040],{},[2324,3031,2360],{},[2324,3033,3034],{"align":2307},"2.333",[2324,3036,3037],{"align":2307},"2.708",[2324,3039,2355],{"align":2307},[2324,3041,2355],{"align":2307},[2299,3043,3044,3046,3049,3051,3053],{},[2324,3045,2375],{},[2324,3047,3048],{"align":2307},"2.286",[2324,3050,2355],{"align":2307},[2324,3052,2355],{"align":2307},[2324,3054,2355],{"align":2307},[1793,3056,3057],{},"Values are £m per count only because the teaching triangle is deliberately small. Real work would normally use £000 per claim.",[1793,3059,3060],{},"This ratio is not yet “settled severity”: its numerator is paid to date while its denominator is reported claims to date. It is useful only when we understand the timing mismatch.",[1793,3062,3063],{},"Using the arithmetic mean of observed cell-level ratios gives illustrative average-cost factors:",[2293,3065,3066,3077],{},[2296,3067,3068],{},[2299,3069,3070,3073,3075],{},[2302,3071,3072],{},"Average-cost transition",[2302,3074,2399],{"align":2307},[2302,3076,2402],{"align":2307},[2319,3078,3079,3089,3099],{},[2299,3080,3081,3083,3086],{},[2324,3082,2409],{},[2324,3084,3085],{"align":2307},"1.1438",[2324,3087,3088],{"align":2307},"1.4431",[2299,3090,3091,3093,3096],{},[2324,3092,2483],{},[2324,3094,3095],{"align":2307},"1.1383",[2324,3097,3098],{"align":2307},"1.2616",[2299,3100,3101,3103,3106],{},[2324,3102,2552],{},[2324,3104,3105],{"align":2307},"1.1083",[2324,3107,3105],{"align":2307},[1793,3109,3110],{},"The selection rule is intentionally visible. Alternatives include volume weighting, settled-claim severity, payments-per-settlement, or a regression model with inflation and mix terms.",[2285,3112,3114],{"id":3113},"_3-recombine-the-two-projections","3. Recombine the two projections",[2293,3116,3117,3135],{},[2296,3118,3119],{},[2299,3120,3121,3123,3126,3129,3132],{},[2302,3122,2304],{},[2302,3124,3125],{"align":2307},"Ultimate count",[2302,3127,3128],{"align":2307},"Ultimate average cost",[2302,3130,3131],{"align":2307},"Ultimate loss",[2302,3133,3134],{"align":2307},"Reserve",[2319,3136,3137,3152,3168,3184,3200],{},[2299,3138,3139,3141,3144,3146,3149],{},[2324,3140,2326],{},[2324,3142,3143],{"align":2307},"100.0",[2324,3145,3012],{"align":2307},[2324,3147,3148],{"align":2307},"280.0",[2324,3150,3151],{"align":2307},"0.0",[2299,3153,3154,3156,3159,3162,3165],{},[2324,3155,2343],{},[2324,3157,3158],{"align":2307},"109.5",[2324,3160,3161],{"align":2307},"3.197",[2324,3163,3164],{"align":2307},"350.0",[2324,3166,3167],{"align":2307},"50.0",[2299,3169,3170,3172,3175,3178,3181],{},[2324,3171,2360],{},[2324,3173,3174],{"align":2307},"119.7",[2324,3176,3177],{"align":2307},"3.417",[2324,3179,3180],{"align":2307},"409.0",[2324,3182,3183],{"align":2307},"149.0",[2299,3185,3186,3188,3191,3194,3197],{},[2324,3187,2375],{},[2324,3189,3190],{"align":2307},"139.6",[2324,3192,3193],{"align":2307},"3.299",[2324,3195,3196],{"align":2307},"460.6",[2324,3198,3199],{"align":2307},"300.6",[2299,3201,3202,3208,3210,3212,3217],{},[2324,3203,3204],{},[3205,3206,3207],"strong",{},"Total",[2324,3209],{"align":2307},[2324,3211],{"align":2307},[2324,3213,3214],{"align":2307},[3205,3215,3216],{},"1,499.7",[2324,3218,3219],{"align":2307},[3205,3220,3221],{},"499.7",[1793,3223,3224,3225,2690],{},"The result is close to the £501.5m chain-ladder reserve because both components were derived from the same paid and count observations. The value of the decomposition is not the £1.8m difference; it is the explanation of ",[3205,3226,3227],{},"where development comes from",[2285,3229,3231],{"id":3230},"_4-read-the-signals","4. Read the signals",[2293,3233,3234,3247],{},[2296,3235,3236],{},[2299,3237,3238,3241,3244],{},[2302,3239,3240],{},"Observed pattern",[2302,3242,3243],{},"Plausible mechanism",[2302,3245,3246],{},"Additional evidence",[2319,3248,3249,3260,3271,3282],{},[2299,3250,3251,3254,3257],{},[2324,3252,3253],{},"count factors fall, cost factors stable",[2324,3255,3256],{},"faster reporting",[2324,3258,3259],{},"report-date distributions and operational changes",[2299,3261,3262,3265,3268],{},[2324,3263,3264],{},"counts stable, average cost rises by calendar year",[2324,3266,3267],{},"inflation or claim mix",[2324,3269,3270],{},"price indices, injury mix, repair duration",[2299,3272,3273,3276,3279],{},[2324,3274,3275],{},"average paid cost falls while closure rises",[2324,3277,3278],{},"accelerated small-claim settlement",[2324,3280,3281],{},"open\u002Fclosed counts and payment type",[2299,3283,3284,3287,3290],{},[2324,3285,3286],{},"count and cost both jump",[2324,3288,3289],{},"exposure, catastrophe, coding, or coverage change",[2324,3291,3292],{},"policy and event-level data",[1793,3294,3295],{},"Never infer the mechanism from the triangle alone. The table generates hypotheses to test.",[2285,3297,3299],{"id":3298},"_5-a-more-defensible-practical-implementation","5. A more defensible practical implementation",[1793,3301,3302],{},"For each origin year:",[3304,3305,3306,3314,3320,3323],"ol",{},[3307,3308,3309,3310,3313],"li",{},"Model ",[3205,3311,3312],{},"ultimate claim count"," using cumulative reported or settled counts, with exposure where relevant.",[3307,3315,3309,3316,3319],{},[3205,3317,3318],{},"ultimate average severity"," on a coherent claim population.",[3307,3321,3322],{},"Apply inflation and mix adjustments at the level where they arise.",[3307,3324,3325],{},"Multiply expected count and severity only after addressing dependence:",[1797,3327,3329],{"className":3328},[1800],[1797,3330,3332,3376],{"className":3331},[1804],[1797,3333,3335],{"className":3334},[1808],[1810,3336,3337],{"xmlns":1812,"display":1813},[1815,3338,3339,3373],{},[1818,3340,3341,3344,3348,3351,3354,3356,3358,3360,3362,3364,3366,3368,3371],{},[1828,3342,3343],{},"E",[1832,3345,3347],{"stretchy":3346},"false","[",[1828,3349,3350],{},"S",[1832,3352,3353],{"stretchy":3346},"]",[1832,3355,1840],{},[1828,3357,3343],{},[1832,3359,3347],{"stretchy":3346},[1828,3361,1848],{},[1832,3363,3353],{"stretchy":3346},[1828,3365,3343],{},[1832,3367,3347],{"stretchy":3346},[1828,3369,3370],{},"X",[1832,3372,3353],{"stretchy":3346},[1877,3374,3375],{"encoding":1879},"E[S]=E[N]E[X]",[1797,3377,3379,3407],{"className":3378,"ariaHidden":1826},[1884],[1797,3380,3382,3385,3389,3392,3395,3398,3401,3404],{"className":3381},[1888],[1797,3383],{"className":3384,"style":2452},[1892],[1797,3386,3343],{"className":3387,"style":3388},[1897,1926],"margin-right:0.0576em;",[1797,3390,3347],{"className":3391},[2778],[1797,3393,3350],{"className":3394,"style":3388},[1897,1926],[1797,3396,3353],{"className":3397},[2975],[1797,3399],{"className":3400,"style":2001},[2000],[1797,3402,1840],{"className":3403},[2005],[1797,3405],{"className":3406,"style":2001},[2000],[1797,3408,3410,3413,3416,3419,3422,3425,3428,3431,3435],{"className":3409},[1888],[1797,3411],{"className":3412,"style":2452},[1892],[1797,3414,3343],{"className":3415,"style":3388},[1897,1926],[1797,3417,3347],{"className":3418},[2778],[1797,3420,1848],{"className":3421,"style":1927},[1897,1926],[1797,3423,3353],{"className":3424},[2975],[1797,3426,3343],{"className":3427,"style":3388},[1897,1926],[1797,3429,3347],{"className":3430},[2778],[1797,3432,3370],{"className":3433,"style":3434},[1897,1926],"margin-right:0.0785em;",[1797,3436,3353],{"className":3437},[2975],[1793,3439,3440,3441,3469],{},"holds when severities are identically distributed and independent of ",[1797,3442,3444,3457],{"className":3443},[1804],[1797,3445,3447],{"className":3446},[1808],[1810,3448,3449],{"xmlns":1812},[1815,3450,3451,3455],{},[1818,3452,3453],{},[1828,3454,1848],{},[1877,3456,1848],{"encoding":1879},[1797,3458,3460],{"className":3459,"ariaHidden":1826},[1884],[1797,3461,3463,3466],{"className":3462},[1888],[1797,3464],{"className":3465,"style":2245},[1892],[1797,3467,1848],{"className":3468,"style":1927},[1897,1926],". More generally, use",[1797,3471,3473],{"className":3472},[1800],[1797,3474,3476,3529],{"className":3475},[1804],[1797,3477,3479],{"className":3478},[1808],[1810,3480,3481],{"xmlns":1812,"display":1813},[1815,3482,3483,3526],{},[1818,3484,3485,3487,3489,3491,3493,3495,3497,3500,3524],{},[1828,3486,3343],{},[1832,3488,3347],{"stretchy":3346},[1828,3490,3350],{},[1832,3492,3353],{"stretchy":3346},[1832,3494,1840],{},[1828,3496,3343],{},[1854,3498,3499],{}," ⁣",[1818,3501,3502,3504,3506,3508,3510,3513,3515,3517,3520,3522],{},[1832,3503,3347],{"fence":1826},[1828,3505,3343],{},[1832,3507,3347],{"stretchy":3346},[1828,3509,3350],{},[1832,3511,3512],{},"∣",[1828,3514,1848],{},[1832,3516,1875],{"separator":1826},[1828,3518,3519],{},"Z",[1832,3521,3353],{"stretchy":3346},[1832,3523,3353],{"fence":1826},[1832,3525,1875],{"separator":1826},[1877,3527,3528],{"encoding":1879},"E[S]=E\\!\\left[E[S\\mid N,Z]\\right],",[1797,3530,3532,3559],{"className":3531,"ariaHidden":1826},[1884],[1797,3533,3535,3538,3541,3544,3547,3550,3553,3556],{"className":3534},[1888],[1797,3536],{"className":3537,"style":2452},[1892],[1797,3539,3343],{"className":3540,"style":3388},[1897,1926],[1797,3542,3347],{"className":3543},[2778],[1797,3545,3350],{"className":3546,"style":3388},[1897,1926],[1797,3548,3353],{"className":3549},[2975],[1797,3551],{"className":3552,"style":2001},[2000],[1797,3554,1840],{"className":3555},[2005],[1797,3557],{"className":3558,"style":2001},[2000],[1797,3560,3562,3565,3568,3572,3576,3621,3624],{"className":3561},[1888],[1797,3563],{"className":3564,"style":2452},[1892],[1797,3566,3343],{"className":3567,"style":3388},[1897,1926],[1797,3569],{"className":3570,"style":3571},[2000],"margin-right:-0.1667em;",[1797,3573],{"className":3574,"style":3575},[2000],"margin-right:0.1667em;",[1797,3577,3580,3585,3588,3591,3594,3597,3600,3603,3606,3609,3612,3615,3618],{"className":3578},[3579],"minner",[1797,3581,3347],{"className":3582,"style":3584},[2778,3583],"delimcenter","top:0em;",[1797,3586,3343],{"className":3587,"style":3388},[1897,1926],[1797,3589,3347],{"className":3590},[2778],[1797,3592,3350],{"className":3593,"style":3388},[1897,1926],[1797,3595],{"className":3596,"style":2001},[2000],[1797,3598,3512],{"className":3599},[2005],[1797,3601],{"className":3602,"style":2001},[2000],[1797,3604,1848],{"className":3605,"style":1927},[1897,1926],[1797,3607,1875],{"className":3608},[2216],[1797,3610],{"className":3611,"style":3575},[2000],[1797,3613,3519],{"className":3614,"style":2898},[1897,1926],[1797,3616,3353],{"className":3617},[2975],[1797,3619,3353],{"className":3620,"style":3584},[2975,3583],[1797,3622],{"className":3623,"style":3575},[2000],[1797,3625,1875],{"className":3626},[2216],[1793,3628,2219,3629,3657],{},[1797,3630,3632,3645],{"className":3631},[1804],[1797,3633,3635],{"className":3634},[1808],[1810,3636,3637],{"xmlns":1812},[1815,3638,3639,3643],{},[1818,3640,3641],{},[1828,3642,3519],{},[1877,3644,3519],{"encoding":1879},[1797,3646,3648],{"className":3647,"ariaHidden":1826},[1884],[1797,3649,3651,3654],{"className":3650},[1888],[1797,3652],{"className":3653,"style":2245},[1892],[1797,3655,3519],{"className":3656,"style":2898},[1897,1926]," can represent weather, inflation, or portfolio mix affecting both frequency and severity.",[2285,3659,3661],{"id":3660},"_6-compare-with-chain-ladder","6. Compare with chain ladder",[2293,3663,3664,3677],{},[2296,3665,3666],{},[2299,3667,3668,3671,3674],{},[2302,3669,3670],{},"Question",[2302,3672,3673],{},"Chain ladder",[2302,3675,3676],{},"Frequency–severity",[2319,3678,3679,3690,3701,3712],{},[2299,3680,3681,3684,3687],{},[2324,3682,3683],{},"What is projected?",[2324,3685,3686],{},"aggregate cumulative loss",[2324,3688,3689],{},"counts and cost per claim",[2299,3691,3692,3695,3698],{},[2324,3693,3694],{},"Main strength",[2324,3696,3697],{},"simple, transparent, reproducible",[2324,3699,3700],{},"operational explanation and scenario control",[2299,3702,3703,3706,3709],{},[2324,3704,3705],{},"Main data need",[2324,3707,3708],{},"consistent loss triangle",[2324,3710,3711],{},"aligned count, loss, status, and exposure definitions",[2299,3713,3714,3717,3720],{},[2324,3715,3716],{},"Main risk",[2324,3718,3719],{},"stable pattern assumed",[2324,3721,3722],{},"two models can compound misspecification",[1793,3724,3725],{},"Use frequency–severity as a diagnostic even when the selected reserve remains chain-ladder based.",[2285,3727,3729],{"id":3728},"practice","Practice",[3304,3731,3732,3735,3738],{},[3307,3733,3734],{},"AY 2023 ultimate count is 140 and selected average ultimate cost is £3.5m. Find ultimate loss and reserve from £160m paid.",[3307,3736,3737],{},"A claims-system migration creates duplicate claim-file IDs. Which component is biased first?",[3307,3739,3740,3741,3744],{},"Why might average ",[3205,3742,3743],{},"settled"," claim cost be biased downward at early ages?",[3746,3747,3749],"legacy-details",{"title":3748},"Answers",[3304,3750,3751,3946,3949],{},[3307,3752,3753,3754,3851,3852,3945],{},"Ultimate ",[1797,3755,3757,3787],{"className":3756},[1804],[1797,3758,3760],{"className":3759},[1808],[1810,3761,3762],{"xmlns":1812},[1815,3763,3764,3784],{},[1818,3765,3766,3768,3771,3773,3776,3778,3781],{},[1832,3767,1840],{},[2425,3769,3770],{},"140",[1832,3772,1859],{},[2425,3774,3775],{},"3.5",[1832,3777,1840],{},[1828,3779,3780],{"mathvariant":2430},"£",[2425,3782,3783],{},"490",[1877,3785,3786],{"encoding":1879},"=140\\times3.5=£490",[1797,3788,3790,3803,3822,3840],{"className":3789,"ariaHidden":1826},[1884],[1797,3791,3793,3797,3800],{"className":3792},[1888],[1797,3794],{"className":3795,"style":3796},[1892],"height:0.3669em;",[1797,3798,1840],{"className":3799},[2005],[1797,3801],{"className":3802,"style":2001},[2000],[1797,3804,3806,3810,3813,3816,3819],{"className":3805},[1888],[1797,3807],{"className":3808,"style":3809},[1892],"height:0.7278em;vertical-align:-0.0833em;",[1797,3811,3770],{"className":3812},[1897],[1797,3814],{"className":3815,"style":2111},[2000],[1797,3817,1859],{"className":3818},[2115],[1797,3820],{"className":3821,"style":2111},[2000],[1797,3823,3825,3828,3831,3834,3837],{"className":3824},[1888],[1797,3826],{"className":3827,"style":2472},[1892],[1797,3829,3775],{"className":3830},[1897],[1797,3832],{"className":3833,"style":2001},[2000],[1797,3835,1840],{"className":3836},[2005],[1797,3838],{"className":3839,"style":2001},[2000],[1797,3841,3843,3847],{"className":3842},[1888],[1797,3844],{"className":3845,"style":3846},[1892],"height:0.6944em;",[1797,3848,3850],{"className":3849},[1897],"£490","m; reserve ",[1797,3853,3855,3884],{"className":3854},[1804],[1797,3856,3858],{"className":3857},[1808],[1810,3859,3860],{"xmlns":1812},[1815,3861,3862,3881],{},[1818,3863,3864,3866,3868,3871,3874,3876,3878],{},[1832,3865,1840],{},[2425,3867,3783],{},[1832,3869,3870],{},"−",[2425,3872,3873],{},"160",[1832,3875,1840],{},[1828,3877,3780],{"mathvariant":2430},[2425,3879,3880],{},"330",[1877,3882,3883],{"encoding":1879},"=490-160=£330",[1797,3885,3887,3899,3917,3935],{"className":3886,"ariaHidden":1826},[1884],[1797,3888,3890,3893,3896],{"className":3889},[1888],[1797,3891],{"className":3892,"style":3796},[1892],[1797,3894,1840],{"className":3895},[2005],[1797,3897],{"className":3898,"style":2001},[2000],[1797,3900,3902,3905,3908,3911,3914],{"className":3901},[1888],[1797,3903],{"className":3904,"style":3809},[1892],[1797,3906,3783],{"className":3907},[1897],[1797,3909],{"className":3910,"style":2111},[2000],[1797,3912,3870],{"className":3913},[2115],[1797,3915],{"className":3916,"style":2111},[2000],[1797,3918,3920,3923,3926,3929,3932],{"className":3919},[1888],[1797,3921],{"className":3922,"style":2472},[1892],[1797,3924,3873],{"className":3925},[1897],[1797,3927],{"className":3928,"style":2001},[2000],[1797,3930,1840],{"className":3931},[2005],[1797,3933],{"className":3934,"style":2001},[2000],[1797,3936,3938,3941],{"className":3937},[1888],[1797,3939],{"className":3940,"style":3846},[1892],[1797,3942,3944],{"className":3943},[1897],"£330","m.",[3307,3947,3948],{},"Reported frequency; the resulting average cost may be biased downward because the denominator is inflated.",[3307,3950,3951],{},"Small, simple claims often settle first. Early settled claims are therefore not representative of all claims.",[1793,3953,3954,3955,2690],{},"Next, ",[3956,3957,3959],"a",{"href":3958},".\u002F03-b-f-method","combine observed development with an independent prior",{"title":10,"searchDepth":3961,"depth":3961,"links":3962},2,[3963,3964,3965,3966,3967,3968,3969],{"id":2287,"depth":3961,"text":2288},{"id":2619,"depth":3961,"text":2620},{"id":3113,"depth":3961,"text":3114},{"id":3230,"depth":3961,"text":3231},{"id":3298,"depth":3961,"text":3299},{"id":3660,"depth":3961,"text":3661},{"id":3728,"depth":3961,"text":3729},"Separate claim emergence from average cost to explain why a triangle develops.","md",{"sidebar":3973},{"order":3961},true,{"title":846,"description":3970},"EUuybyyOaqV95GiBief1bp1ZqiXzD6XqqXmFaCJ3vB4",[3978,3980],{"title":842,"path":843,"stem":844,"description":3979,"children":-1},"Calculate a deterministic chain-ladder reserve and expose the assumptions behind every step.",{"title":850,"path":851,"stem":852,"description":3981,"children":-1},"Blend an expected-loss prior with observed maturity without letting early random payments dominate.",1785754734231]