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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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It can reflect repair prices, wages, medical costs, litigation, social attitudes, supply constraints, policy terms, and portfolio mix.",[1797,1798,1800],"h2",{"id":1799},"_1-put-losses-on-a-common-level","1. 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",[1805,1806,1809,1839],"span",{"className":1807},[1808],"katex",[1805,1810,1813],{"className":1811},[1812],"katex-mathml",[1814,1815,1817],"math",{"xmlns":1816},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1818,1819,1820,1834],"semantics",{},[1821,1822,1823],"mrow",{},[1824,1825,1826,1830],"msub",{},[1827,1828,1829],"mi",{},"X",[1831,1832,1833],"mn",{},"0",[1835,1836,1838],"annotation",{"encoding":1837},"application\u002Fx-tex","X_0",[1805,1840,1844],{"className":1841,"ariaHidden":1843},[1842],"katex-html","true",[1805,1845,1848,1853],{"className":1846},[1847],"base",[1805,1849],{"className":1850,"style":1852},[1851],"strut","height:0.8333em;vertical-align:-0.15em;",[1805,1854,1857,1862],{"className":1855},[1856],"mord",[1805,1858,1829],{"className":1859,"style":1861},[1856,1860],"mathnormal","margin-right:0.0785em;",[1805,1863,1866],{"className":1864},[1865],"msupsub",[1805,1867,1871,1903],{"className":1868},[1869,1870],"vlist-t","vlist-t2",[1805,1872,1875,1898],{"className":1873},[1874],"vlist-r",[1805,1876,1880],{"className":1877,"style":1879},[1878],"vlist","height:0.3011em;",[1805,1881,1883,1888],{"style":1882},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[1805,1884],{"className":1885,"style":1887},[1886],"pstrut","height:2.7em;",[1805,1889,1895],{"className":1890},[1891,1892,1893,1894],"sizing","reset-size6","size3","mtight",[1805,1896,1833],{"className":1897},[1856,1894],[1805,1899,1902],{"className":1900},[1901],"vlist-s","​",[1805,1904,1906],{"className":1905},[1874],[1805,1907,1910],{"className":1908,"style":1909},[1878],"height:0.15em;",[1805,1911],{}," and cumulative severity index is ",[1805,1914,1916,1936],{"className":1915},[1808],[1805,1917,1919],{"className":1918},[1812],[1814,1920,1921],{"xmlns":1816},[1818,1922,1923,1933],{},[1821,1924,1925],{},[1824,1926,1927,1930],{},[1827,1928,1929],{},"b",[1827,1931,1932],{},"t",[1835,1934,1935],{"encoding":1837},"b_t",[1805,1937,1939],{"className":1938,"ariaHidden":1843},[1842],[1805,1940,1942,1946],{"className":1941},[1847],[1805,1943],{"className":1944,"style":1945},[1851],"height:0.8444em;vertical-align:-0.15em;",[1805,1947,1949,1952],{"className":1948},[1856],[1805,1950,1929],{"className":1951},[1856,1860],[1805,1953,1955],{"className":1954},[1865],[1805,1956,1958,1980],{"className":1957},[1869,1870],[1805,1959,1961,1977],{"className":1960},[1874],[1805,1962,1965],{"className":1963,"style":1964},[1878],"height:0.2806em;",[1805,1966,1968,1971],{"style":1967},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1805,1969],{"className":1970,"style":1887},[1886],[1805,1972,1974],{"className":1973},[1891,1892,1893,1894],[1805,1975,1932],{"className":1976},[1856,1860,1894],[1805,1978,1902],{"className":1979},[1901],[1805,1981,1983],{"className":1982},[1874],[1805,1984,1986],{"className":1985,"style":1909},[1878],[1805,1987],{},",",[1805,1990,1993],{"className":1991},[1992],"katex-display",[1805,1994,1996,2086],{"className":1995},[1808],[1805,1997,1999],{"className":1998},[1812],[1814,2000,2002],{"xmlns":1816,"display":2001},"block",[1818,2003,2004,2083],{},[1821,2005,2006,2012,2016,2022,2028,2030,2034,2040,2042,2060,2064,2066,2069,2076,2079],{},[1824,2007,2008,2010],{},[1827,2009,1829],{},[1827,2011,1932],{},[2013,2014,2015],"mo",{},"=",[1824,2017,2018,2020],{},[1827,2019,1929],{},[1827,2021,1932],{},[1824,2023,2024,2026],{},[1827,2025,1829],{},[1831,2027,1833],{},[2013,2029,1988],{"separator":1843},[2031,2032],"mspace",{"width":2033},"2em",[1824,2035,2036,2038],{},[1827,2037,1929],{},[1827,2039,1932],{},[2013,2041,2015],{},[2043,2044,2045,2048,2058],"munderover",{},[2013,2046,2047],{},"∏",[1821,2049,2050,2053,2055],{},[1827,2051,2052],{},"s",[2013,2054,2015],{},[1831,2056,2057],{},"1",[1827,2059,1932],{},[2013,2061,2063],{"stretchy":2062},"false","(",[1831,2065,2057],{},[2013,2067,2068],{},"+",[1824,2070,2071,2074],{},[1827,2072,2073],{},"i",[1827,2075,2052],{},[2013,2077,2078],{"stretchy":2062},")",[1827,2080,2082],{"mathvariant":2081},"normal",".",[1835,2084,2085],{"encoding":1837},"X_t=b_tX_0,\n\\qquad\nb_t=\\prod_{s=1}^{t}(1+i_s).",[1805,2087,2089,2146,2294,2396],{"className":2088,"ariaHidden":1843},[1842],[1805,2090,2092,2095,2135,2139,2143],{"className":2091},[1847],[1805,2093],{"className":2094,"style":1852},[1851],[1805,2096,2098,2101],{"className":2097},[1856],[1805,2099,1829],{"className":2100,"style":1861},[1856,1860],[1805,2102,2104],{"className":2103},[1865],[1805,2105,2107,2127],{"className":2106},[1869,1870],[1805,2108,2110,2124],{"className":2109},[1874],[1805,2111,2113],{"className":2112,"style":1964},[1878],[1805,2114,2115,2118],{"style":1882},[1805,2116],{"className":2117,"style":1887},[1886],[1805,2119,2121],{"className":2120},[1891,1892,1893,1894],[1805,2122,1932],{"className":2123},[1856,1860,1894],[1805,2125,1902],{"className":2126},[1901],[1805,2128,2130],{"className":2129},[1874],[1805,2131,2133],{"className":2132,"style":1909},[1878],[1805,2134],{},[1805,2136],{"className":2137,"style":2138},[2031],"margin-right:0.2778em;",[1805,2140,2015],{"className":2141},[2142],"mrel",[1805,2144],{"className":2145,"style":2138},[2031],[1805,2147,2149,2153,2193,2233,2237,2241,2245,2285,2288,2291],{"className":2148},[1847],[1805,2150],{"className":2151,"style":2152},[1851],"height:0.8889em;vertical-align:-0.1944em;",[1805,2154,2156,2159],{"className":2155},[1856],[1805,2157,1929],{"className":2158},[1856,1860],[1805,2160,2162],{"className":2161},[1865],[1805,2163,2165,2185],{"className":2164},[1869,1870],[1805,2166,2168,2182],{"className":2167},[1874],[1805,2169,2171],{"className":2170,"style":1964},[1878],[1805,2172,2173,2176],{"style":1967},[1805,2174],{"className":2175,"style":1887},[1886],[1805,2177,2179],{"className":2178},[1891,1892,1893,1894],[1805,2180,1932],{"className":2181},[1856,1860,1894],[1805,2183,1902],{"className":2184},[1901],[1805,2186,2188],{"className":2187},[1874],[1805,2189,2191],{"className":2190,"style":1909},[1878],[1805,2192],{},[1805,2194,2196,2199],{"className":2195},[1856],[1805,2197,1829],{"className":2198,"style":1861},[1856,1860],[1805,2200,2202],{"className":2201},[1865],[1805,2203,2205,2225],{"className":2204},[1869,1870],[1805,2206,2208,2222],{"className":2207},[1874],[1805,2209,2211],{"className":2210,"style":1879},[1878],[1805,2212,2213,2216],{"style":1882},[1805,2214],{"className":2215,"style":1887},[1886],[1805,2217,2219],{"className":2218},[1891,1892,1893,1894],[1805,2220,1833],{"className":2221},[1856,1894],[1805,2223,1902],{"className":2224},[1901],[1805,2226,2228],{"className":2227},[1874],[1805,2229,2231],{"className":2230,"style":1909},[1878],[1805,2232],{},[1805,2234,1988],{"className":2235},[2236],"mpunct",[1805,2238],{"className":2239,"style":2240},[2031],"margin-right:2em;",[1805,2242],{"className":2243,"style":2244},[2031],"margin-right:0.1667em;",[1805,2246,2248,2251],{"className":2247},[1856],[1805,2249,1929],{"className":2250},[1856,1860],[1805,2252,2254],{"className":2253},[1865],[1805,2255,2257,2277],{"className":2256},[1869,1870],[1805,2258,2260,2274],{"className":2259},[1874],[1805,2261,2263],{"className":2262,"style":1964},[1878],[1805,2264,2265,2268],{"style":1967},[1805,2266],{"className":2267,"style":1887},[1886],[1805,2269,2271],{"className":2270},[1891,1892,1893,1894],[1805,2272,1932],{"className":2273},[1856,1860,1894],[1805,2275,1902],{"className":2276},[1901],[1805,2278,2280],{"className":2279},[1874],[1805,2281,2283],{"className":2282,"style":1909},[1878],[1805,2284],{},[1805,2286],{"className":2287,"style":2138},[2031],[1805,2289,2015],{"className":2290},[2142],[1805,2292],{"className":2293,"style":2138},[2031],[1805,2295,2297,2301,2378,2382,2385,2389,2393],{"className":2296},[1847],[1805,2298],{"className":2299,"style":2300},[1851],"height:3.0477em;vertical-align:-1.2671em;",[1805,2302,2306],{"className":2303},[2304,2305],"mop","op-limits",[1805,2307,2309,2369],{"className":2308},[1869,1870],[1805,2310,2312,2366],{"className":2311},[1874],[1805,2313,2316,2338,2351],{"className":2314,"style":2315},[1878],"height:1.7806em;",[1805,2317,2319,2323],{"style":2318},"top:-1.8829em;margin-left:0em;",[1805,2320],{"className":2321,"style":2322},[1886],"height:3.05em;",[1805,2324,2326],{"className":2325},[1891,1892,1893,1894],[1805,2327,2329,2332,2335],{"className":2328},[1856,1894],[1805,2330,2052],{"className":2331},[1856,1860,1894],[1805,2333,2015],{"className":2334},[2142,1894],[1805,2336,2057],{"className":2337},[1856,1894],[1805,2339,2341,2344],{"style":2340},"top:-3.05em;",[1805,2342],{"className":2343,"style":2322},[1886],[1805,2345,2346],{},[1805,2347,2047],{"className":2348},[2304,2349,2350],"op-symbol","large-op",[1805,2352,2354,2357],{"style":2353},"top:-4.3em;margin-left:0em;",[1805,2355],{"className":2356,"style":2322},[1886],[1805,2358,2360],{"className":2359},[1891,1892,1893,1894],[1805,2361,2363],{"className":2362},[1856,1894],[1805,2364,1932],{"className":2365},[1856,1860,1894],[1805,2367,1902],{"className":2368},[1901],[1805,2370,2372],{"className":2371},[1874],[1805,2373,2376],{"className":2374,"style":2375},[1878],"height:1.2671em;",[1805,2377],{},[1805,2379,2063],{"className":2380},[2381],"mopen",[1805,2383,2057],{"className":2384},[1856],[1805,2386],{"className":2387,"style":2388},[2031],"margin-right:0.2222em;",[1805,2390,2068],{"className":2391},[2392],"mbin",[1805,2394],{"className":2395,"style":2388},[2031],[1805,2397,2399,2403,2444,2448],{"className":2398},[1847],[1805,2400],{"className":2401,"style":2402},[1851],"height:1em;vertical-align:-0.25em;",[1805,2404,2406,2409],{"className":2405},[1856],[1805,2407,2073],{"className":2408},[1856,1860],[1805,2410,2412],{"className":2411},[1865],[1805,2413,2415,2436],{"className":2414},[1869,1870],[1805,2416,2418,2433],{"className":2417},[1874],[1805,2419,2422],{"className":2420,"style":2421},[1878],"height:0.1514em;",[1805,2423,2424,2427],{"style":1967},[1805,2425],{"className":2426,"style":1887},[1886],[1805,2428,2430],{"className":2429},[1891,1892,1893,1894],[1805,2431,2052],{"className":2432},[1856,1860,1894],[1805,2434,1902],{"className":2435},[1901],[1805,2437,2439],{"className":2438},[1874],[1805,2440,2442],{"className":2441,"style":1909},[1878],[1805,2443],{},[1805,2445,2078],{"className":2446},[2447],"mclose",[1805,2449,2082],{"className":2450},[1856],[1793,2452,2453,2454,2483,2484,2642],{},"At constant annual inflation ",[1805,2455,2457,2470],{"className":2456},[1808],[1805,2458,2460],{"className":2459},[1812],[1814,2461,2462],{"xmlns":1816},[1818,2463,2464,2468],{},[1821,2465,2466],{},[1827,2467,2073],{},[1835,2469,2073],{"encoding":1837},[1805,2471,2473],{"className":2472,"ariaHidden":1843},[1842],[1805,2474,2476,2480],{"className":2475},[1847],[1805,2477],{"className":2478,"style":2479},[1851],"height:0.6595em;",[1805,2481,2073],{"className":2482},[1856,1860],", ",[1805,2485,2487,2522],{"className":2486},[1808],[1805,2488,2490],{"className":2489},[1812],[1814,2491,2492],{"xmlns":1816},[1818,2493,2494,2519],{},[1821,2495,2496,2502,2504,2506,2508,2510,2512],{},[1824,2497,2498,2500],{},[1827,2499,1929],{},[1827,2501,1932],{},[2013,2503,2015],{},[2013,2505,2063],{"stretchy":2062},[1831,2507,2057],{},[2013,2509,2068],{},[1827,2511,2073],{},[2513,2514,2515,2517],"msup",{},[2013,2516,2078],{"stretchy":2062},[1827,2518,1932],{},[1835,2520,2521],{"encoding":1837},"b_t=(1+i)^t",[1805,2523,2525,2580,2601],{"className":2524,"ariaHidden":1843},[1842],[1805,2526,2528,2531,2571,2574,2577],{"className":2527},[1847],[1805,2529],{"className":2530,"style":1945},[1851],[1805,2532,2534,2537],{"className":2533},[1856],[1805,2535,1929],{"className":2536},[1856,1860],[1805,2538,2540],{"className":2539},[1865],[1805,2541,2543,2563],{"className":2542},[1869,1870],[1805,2544,2546,2560],{"className":2545},[1874],[1805,2547,2549],{"className":2548,"style":1964},[1878],[1805,2550,2551,2554],{"style":1967},[1805,2552],{"className":2553,"style":1887},[1886],[1805,2555,2557],{"className":2556},[1891,1892,1893,1894],[1805,2558,1932],{"className":2559},[1856,1860,1894],[1805,2561,1902],{"className":2562},[1901],[1805,2564,2566],{"className":2565},[1874],[1805,2567,2569],{"className":2568,"style":1909},[1878],[1805,2570],{},[1805,2572],{"className":2573,"style":2138},[2031],[1805,2575,2015],{"className":2576},[2142],[1805,2578],{"className":2579,"style":2138},[2031],[1805,2581,2583,2586,2589,2592,2595,2598],{"className":2582},[1847],[1805,2584],{"className":2585,"style":2402},[1851],[1805,2587,2063],{"className":2588},[2381],[1805,2590,2057],{"className":2591},[1856],[1805,2593],{"className":2594,"style":2388},[2031],[1805,2596,2068],{"className":2597},[2392],[1805,2599],{"className":2600,"style":2388},[2031],[1805,2602,2604,2608,2611],{"className":2603},[1847],[1805,2605],{"className":2606,"style":2607},[1851],"height:1.0436em;vertical-align:-0.25em;",[1805,2609,2073],{"className":2610},[1856,1860],[1805,2612,2614,2617],{"className":2613},[2447],[1805,2615,2078],{"className":2616},[2447],[1805,2618,2620],{"className":2619},[1865],[1805,2621,2623],{"className":2622},[1869],[1805,2624,2626],{"className":2625},[1874],[1805,2627,2630],{"className":2628,"style":2629},[1878],"height:0.7936em;",[1805,2631,2633,2636],{"style":2632},"top:-3.063em;margin-right:0.05em;",[1805,2634],{"className":2635,"style":1887},[1886],[1805,2637,2639],{"className":2638},[1891,1892,1893,1894],[1805,2640,1932],{"className":2641},[1856,1860,1894],". With 10% inflation, a £80,000 base loss becomes",[1805,2644,2646],{"className":2645},[1992],[1805,2647,2649,2684],{"className":2648},[1808],[1805,2650,2652],{"className":2651},[1812],[1814,2653,2654],{"xmlns":1816,"display":2001},[1818,2655,2656,2681],{},[1821,2657,2658,2661,2663,2666,2673,2675,2678],{},[1831,2659,2660],{},"80,000",[2013,2662,2063],{"stretchy":2062},[1831,2664,2665],{},"1.10",[2513,2667,2668,2670],{},[2013,2669,2078],{"stretchy":2062},[1831,2671,2672],{},"2",[2013,2674,2015],{},[1827,2676,2677],{"mathvariant":2081},"£",[1831,2679,2680],{},"96,800",[1835,2682,2683],{"encoding":1837},"80{,}000(1.10)^2=£96{,}800",[1805,2685,2687,2754],{"className":2686,"ariaHidden":1843},[1842],[1805,2688,2690,2694,2698,2704,2708,2711,2714,2745,2748,2751],{"className":2689},[1847],[1805,2691],{"className":2692,"style":2693},[1851],"height:1.1141em;vertical-align:-0.25em;",[1805,2695,2697],{"className":2696},[1856],"80",[1805,2699,2701],{"className":2700},[1856],[1805,2702,1988],{"className":2703},[2236],[1805,2705,2707],{"className":2706},[1856],"000",[1805,2709,2063],{"className":2710},[2381],[1805,2712,2665],{"className":2713},[1856],[1805,2715,2717,2720],{"className":2716},[2447],[1805,2718,2078],{"className":2719},[2447],[1805,2721,2723],{"className":2722},[1865],[1805,2724,2726],{"className":2725},[1869],[1805,2727,2729],{"className":2728},[1874],[1805,2730,2733],{"className":2731,"style":2732},[1878],"height:0.8641em;",[1805,2734,2736,2739],{"style":2735},"top:-3.113em;margin-right:0.05em;",[1805,2737],{"className":2738,"style":1887},[1886],[1805,2740,2742],{"className":2741},[1891,1892,1893,1894],[1805,2743,2672],{"className":2744},[1856,1894],[1805,2746],{"className":2747,"style":2138},[2031],[1805,2749,2015],{"className":2750},[2142],[1805,2752],{"className":2753,"style":2138},[2031],[1805,2755,2757,2760,2764,2770],{"className":2756},[1847],[1805,2758],{"className":2759,"style":2152},[1851],[1805,2761,2763],{"className":2762},[1856],"£96",[1805,2765,2767],{"className":2766},[1856],[1805,2768,1988],{"className":2769},[2236],[1805,2771,2773],{"className":2772},[1856],"800",[1793,2775,2776],{},"after two years—not £96,000, because inflation compounds.",[1797,2778,2780],{"id":2779},"_2-fixed-nominal-layers-erode","2. Fixed nominal layers erode",[1793,2782,2783,2784,2814,2815,1988],{},"For a fixed attachment ",[1805,2785,2787,2801],{"className":2786},[1808],[1805,2788,2790],{"className":2789},[1812],[1814,2791,2792],{"xmlns":1816},[1818,2793,2794,2799],{},[1821,2795,2796],{},[1827,2797,2798],{},"a",[1835,2800,2798],{"encoding":1837},[1805,2802,2804],{"className":2803,"ariaHidden":1843},[1842],[1805,2805,2807,2811],{"className":2806},[1847],[1805,2808],{"className":2809,"style":2810},[1851],"height:0.4306em;",[1805,2812,2798],{"className":2813},[1856,1860]," and limit ",[1805,2816,2818,2832],{"className":2817},[1808],[1805,2819,2821],{"className":2820},[1812],[1814,2822,2823],{"xmlns":1816},[1818,2824,2825,2830],{},[1821,2826,2827],{},[1827,2828,2829],{},"l",[1835,2831,2829],{"encoding":1837},[1805,2833,2835],{"className":2834,"ariaHidden":1843},[1842],[1805,2836,2838,2842],{"className":2837},[1847],[1805,2839],{"className":2840,"style":2841},[1851],"height:0.6944em;",[1805,2843,2829],{"className":2844,"style":2845},[1856,1860],"margin-right:0.0197em;",[1805,2847,2849],{"className":2848},[1992],[1805,2850,2852,2916],{"className":2851},[1808],[1805,2853,2855],{"className":2854},[1812],[1814,2856,2857],{"xmlns":1816,"display":2001},[1818,2858,2859,2913],{},[1821,2860,2861,2868,2870,2873,2876,2879,2881,2887,2893,2896,2898,2904,2906,2908,2911],{},[1824,2862,2863,2866],{},[1827,2864,2865],{},"C",[1827,2867,1932],{},[2013,2869,2015],{},[1827,2871,2872],{},"min",[2013,2874,2875],{},"⁡",[2013,2877,2878],{"stretchy":2062},"{",[2013,2880,2063],{"stretchy":2062},[1824,2882,2883,2885],{},[1827,2884,1929],{},[1827,2886,1932],{},[1824,2888,2889,2891],{},[1827,2890,1829],{},[1831,2892,1833],{},[2013,2894,2895],{},"−",[1827,2897,2798],{},[1824,2899,2900,2902],{},[2013,2901,2078],{"stretchy":2062},[2013,2903,2068],{},[2013,2905,1988],{"separator":1843},[1827,2907,2829],{},[2013,2909,2910],{"stretchy":2062},"}",[1827,2912,2082],{"mathvariant":2081},[1835,2914,2915],{"encoding":1837},"C_t=\\min\\{(b_tX_0-a)_+,l\\}.",[1805,2917,2919,2976,3078],{"className":2918,"ariaHidden":1843},[1842],[1805,2920,2922,2925,2967,2970,2973],{"className":2921},[1847],[1805,2923],{"className":2924,"style":1852},[1851],[1805,2926,2928,2932],{"className":2927},[1856],[1805,2929,2865],{"className":2930,"style":2931},[1856,1860],"margin-right:0.0715em;",[1805,2933,2935],{"className":2934},[1865],[1805,2936,2938,2959],{"className":2937},[1869,1870],[1805,2939,2941,2956],{"className":2940},[1874],[1805,2942,2944],{"className":2943,"style":1964},[1878],[1805,2945,2947,2950],{"style":2946},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[1805,2948],{"className":2949,"style":1887},[1886],[1805,2951,2953],{"className":2952},[1891,1892,1893,1894],[1805,2954,1932],{"className":2955},[1856,1860,1894],[1805,2957,1902],{"className":2958},[1901],[1805,2960,2962],{"className":2961},[1874],[1805,2963,2965],{"className":2964,"style":1909},[1878],[1805,2966],{},[1805,2968],{"className":2969,"style":2138},[2031],[1805,2971,2015],{"className":2972},[2142],[1805,2974],{"className":2975,"style":2138},[2031],[1805,2977,2979,2982,2985,2989,3029,3069,3072,3075],{"className":2978},[1847],[1805,2980],{"className":2981,"style":2402},[1851],[1805,2983,2872],{"className":2984},[2304],[1805,2986,2988],{"className":2987},[2381],"{(",[1805,2990,2992,2995],{"className":2991},[1856],[1805,2993,1929],{"className":2994},[1856,1860],[1805,2996,2998],{"className":2997},[1865],[1805,2999,3001,3021],{"className":3000},[1869,1870],[1805,3002,3004,3018],{"className":3003},[1874],[1805,3005,3007],{"className":3006,"style":1964},[1878],[1805,3008,3009,3012],{"style":1967},[1805,3010],{"className":3011,"style":1887},[1886],[1805,3013,3015],{"className":3014},[1891,1892,1893,1894],[1805,3016,1932],{"className":3017},[1856,1860,1894],[1805,3019,1902],{"className":3020},[1901],[1805,3022,3024],{"className":3023},[1874],[1805,3025,3027],{"className":3026,"style":1909},[1878],[1805,3028],{},[1805,3030,3032,3035],{"className":3031},[1856],[1805,3033,1829],{"className":3034,"style":1861},[1856,1860],[1805,3036,3038],{"className":3037},[1865],[1805,3039,3041,3061],{"className":3040},[1869,1870],[1805,3042,3044,3058],{"className":3043},[1874],[1805,3045,3047],{"className":3046,"style":1879},[1878],[1805,3048,3049,3052],{"style":1882},[1805,3050],{"className":3051,"style":1887},[1886],[1805,3053,3055],{"className":3054},[1891,1892,1893,1894],[1805,3056,1833],{"className":3057},[1856,1894],[1805,3059,1902],{"className":3060},[1901],[1805,3062,3064],{"className":3063},[1874],[1805,3065,3067],{"className":3066,"style":1909},[1878],[1805,3068],{},[1805,3070],{"className":3071,"style":2388},[2031],[1805,3073,2895],{"className":3074},[2392],[1805,3076],{"className":3077,"style":2388},[2031],[1805,3079,3081,3084,3087,3129,3132,3135,3138,3141],{"className":3080},[1847],[1805,3082],{"className":3083,"style":2402},[1851],[1805,3085,2798],{"className":3086},[1856,1860],[1805,3088,3090,3093],{"className":3089},[2447],[1805,3091,2078],{"className":3092},[2447],[1805,3094,3096],{"className":3095},[1865],[1805,3097,3099,3120],{"className":3098},[1869,1870],[1805,3100,3102,3117],{"className":3101},[1874],[1805,3103,3106],{"className":3104,"style":3105},[1878],"height:0.2583em;",[1805,3107,3108,3111],{"style":1967},[1805,3109],{"className":3110,"style":1887},[1886],[1805,3112,3114],{"className":3113},[1891,1892,1893,1894],[1805,3115,2068],{"className":3116},[2392,1894],[1805,3118,1902],{"className":3119},[1901],[1805,3121,3123],{"className":3122},[1874],[1805,3124,3127],{"className":3125,"style":3126},[1878],"height:0.2083em;",[1805,3128],{},[1805,3130,1988],{"className":3131},[2236],[1805,3133],{"className":3134,"style":2244},[2031],[1805,3136,2829],{"className":3137,"style":2845},[1856,1860],[1805,3139,2910],{"className":3140},[2447],[1805,3142,2082],{"className":3143},[1856],[1793,3145,3146],{},"Consider £50,000 xs £50,000:",[3148,3149,3150,3170],"table",{},[3151,3152,3153],"thead",{},[3154,3155,3156,3160,3164,3167],"tr",{},[3157,3158,3159],"th",{},"Time",[3157,3161,3163],{"align":3162},"right","Indexed loss",[3157,3165,3166],{"align":3162},"Ceded",[3157,3168,3169],{"align":3162},"Retained",[3171,3172,3173,3187],"tbody",{},[3154,3174,3175,3178,3181,3184],{},[3176,3177,1847],"td",{},[3176,3179,3180],{"align":3162},"£80,000",[3176,3182,3183],{"align":3162},"£30,000",[3176,3185,3186],{"align":3162},"£50,000",[3154,3188,3189,3192,3195,3198],{},[3176,3190,3191],{},"after two years at 10%",[3176,3193,3194],{"align":3162},"£96,800",[3176,3196,3197],{"align":3162},"£46,800",[3176,3199,3186],{"align":3162},[1793,3201,3202],{},"More of the same real loss enters the fixed nominal layer. The reinsurer's expected frequency of attachment and expected recovery can rise even if the underlying real-risk distribution is unchanged.",[1793,3204,3205],{},"Once loss exceeds £100,000, this layer is exhausted and further nominal inflation again falls on the insurer.",[1797,3207,3209],{"id":3208},"_3-indexed-layers-preserve-a-real-position","3. Indexed layers preserve a real position",[1793,3211,3212,3213,1988],{},"If attachment and limit are indexed by the same 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me":4264,"style":1887},[1886],[1805,4266,4268],{"className":4267},[1891,1892,1893,1894],[1805,4269,2068],{"className":4270},[2392,1894],[1805,4272,1902],{"className":4273},[1901],[1805,4275,4277],{"className":4276},[1874],[1805,4278,4280],{"className":4279,"style":3126},[1878],[1805,4281],{},[1805,4283,1988],{"className":4284},[2236],[1805,4286],{"className":4287,"style":2244},[2031],[1805,4289,4291,4294],{"className":4290},[1856],[1805,4292,2829],{"className":4293,"style":2845},[1856,1860],[1805,4295,4297],{"className":4296},[1865],[1805,4298,4300,4320],{"className":4299},[1869,1870],[1805,4301,4303,4317],{"className":4302},[1874],[1805,4304,4306],{"className":4305,"style":1879},[1878],[1805,4307,4308,4311],{"style":3520},[1805,4309],{"className":4310,"style":1887},[1886],[1805,4312,4314],{"className":4313},[1891,1892,1893,1894],[1805,4315,1833],{"className":4316},[1856,1894],[1805,4318,1902],{"className":4319},[1901],[1805,4321,4323],{"className":4322},[1874],[1805,4324,4326],{"className":4325,"style":1909},[1878],[1805,4327],{},[1805,4329,2910],{"className":4330},[2447],[1805,4332,2082],{"className":4333},[1856],[1793,4335,4336],{},"This preserves the layer in real terms under a common proportional inflation model. In practice, claim categories inflate differently and wording may index attachment, limit, or neither.",[1797,4338,4340],{"id":4339},"_4-separate-four-effects","4. Separate four effects",[1793,4342,4343],{},"Suppose observed average claim rises 15%. Decompose before applying a trend:",[3148,4345,4346,4359],{},[3151,4347,4348],{},[3154,4349,4350,4353,4356],{},[3157,4351,4352],{},"Effect",[3157,4354,4355],{},"Example",[3157,4357,4358],{},"Needed evidence",[3171,4360,4361,4372,4383,4394],{},[3154,4362,4363,4366,4369],{},[3176,4364,4365],{},"price\u002Fseverity inflation",[3176,4367,4368],{},"parts and labour cost more",[3176,4370,4371],{},"matched claim categories and external indices",[3154,4373,4374,4377,4380],{},[3176,4375,4376],{},"mix",[3176,4378,4379],{},"more bodily injury, fewer glass claims",[3176,4381,4382],{},"claim-type weights and within-type means",[3154,4384,4385,4388,4391],{},[3176,4386,4387],{},"exposure",[3176,4389,4390],{},"more or different vehicles insured",[3176,4392,4393],{},"earned exposure and rating variables",[3154,4395,4396,4399,4402],{},[3176,4397,4398],{},"settlement\u002Freporting",[3176,4400,4401],{},"claims close later or earlier",[3176,4403,4404],{},"report, payment, and closure lags",[1793,4406,4407],{},"An unsegmented mean cannot identify these mechanisms.",[4409,4410,4412],"h3",{"id":4411},"composition-example","Composition example",[1793,4414,4415],{},"If 90% ordinary claims average £2,000 and 10% complex claims average £20,000, portfolio mean is £3,800. If the complex share rises to 20%, mean becomes £5,600—a 47.4% increase with no inflation inside either group.",[1797,4417,4419],{"id":4418},"_5-inflation-creates-calendar-effects-in-reserves","5. Inflation creates calendar effects in reserves",[1793,4421,4422],{},"Claims paid in the same calendar year face similar repair and wage conditions even when they come from different accident years. In a run-off triangle, inflation can therefore align along diagonals.",[1793,4424,4425],{},"A development-age-only chain ladder may absorb old inflation into its factors and project it forward implicitly. That can be too high or too low when inflation regime changes. Useful responses include:",[4427,4428,4429,4433,4436,4439],"ul",{},[4430,4431,4432],"li",{},"bringing incremental claims to a common price level before fitting;",[4430,4434,4435],{},"modelling origin, development, and calendar effects;",[4430,4437,4438],{},"explicit severity trend scenarios;",[4430,4440,4441],{},"separate treatment of large or long-settling claims.",[1793,4443,4444],{},"Do not both pre-inflate data and add the same inflation again in future factors.",[1797,4446,4448],{"id":4447},"_6-stress-the-decision-not-one-parameter","6. Stress the decision, not one parameter",[1793,4450,4451],{},"For each plausible annual trend, recalculate:",[4453,4454,4455,4458,4461,4464,4467,4470],"ol",{},[4430,4456,4457],{},"gross ultimate losses and reserve;",[4430,4459,4460],{},"attachment probability;",[4430,4462,4463],{},"expected ceded loss;",[4430,4465,4466],{},"probability of layer exhaustion;",[4430,4468,4469],{},"net aggregate VaR\u002FTVaR;",[4430,4471,4472],{},"timing and reinstatement premium.",[3148,4474,4475,4488],{},[3151,4476,4477],{},[3154,4478,4479,4482,4485],{},[3157,4480,4481],{},"Stress",[3157,4483,4484],{},"Gross effect",[3157,4486,4487],{},"Fixed layer effect",[3171,4489,4490,4501,4512,4523],{},[3154,4491,4492,4495,4498],{},[3176,4493,4494],{},"uniform severity +10%",[3176,4496,4497],{},"all losses scale",[3176,4499,4500],{},"more attachment, possible exhaustion",[3154,4502,4503,4506,4509],{},[3176,4504,4505],{},"only large losses +15%",[3176,4507,4508],{},"centre may barely move",[3176,4510,4511],{},"high layers change materially",[3154,4513,4514,4517,4520],{},[3176,4515,4516],{},"faster settlement",[3176,4518,4519],{},"payment timing changes",[3176,4521,4522],{},"cash\u002Frecovery timing changes",[3154,4524,4525,4528,4531],{},[3176,4526,4527],{},"high-cost class weight rises",[3176,4529,4530],{},"mixture shifts",[3176,4532,4533],{},"attachment frequency can jump",[1797,4535,4537],{"id":4536},"_7-current-evidence-used-carefully","7. Current evidence, used carefully",[1793,4539,4540],{},"Recent UK motor and liability publications document persistent concern about repair, wage, injury, and social inflation. They are useful external scenarios, but not plug-in parameters for Harbour Mutual:",[4427,4542,4543,4546,4549],{},[4430,4544,4545],{},"ABI's motor claims-inflation discussion reports that its selected motor claims-cost measure grew faster than CPI over 2019–2023; it is an industry-authored summary with its own scope.",[4430,4547,4548],{},"CAS research examines liability insurance inflation through year-end 2024 and emphasises line- and environment-specific effects.",[4430,4550,4551],{},"ABI's 2025 payout release explicitly warns that improved data coverage limits direct absolute year-on-year comparison.",[1793,4553,4554],{},"The defensible use is to create and document scenarios, then calibrate with portfolio data.",[1797,4556,4558],{"id":4557},"practice","Practice",[4453,4560,4561,4564,4567],{},[4430,4562,4563],{},"Inflate £120,000 for three years at 6% annually.",[4430,4565,4566],{},"Under £100,000 xs £50,000, find ceded loss for £80,000, £120,000, and £190,000.",[4430,4568,4569],{},"Why can a general consumer-price index be a poor claims index?",[4571,4572,4574],"legacy-details",{"title":4573},"Answers",[4453,4575,4576,4704,4707],{},[4430,4577,4578,2082],{},[1805,4579,4581,4616],{"className":4580},[1808],[1805,4582,4584],{"className":4583},[1812],[1814,4585,4586],{"xmlns":1816},[1818,4587,4588,4613],{},[1821,4589,4590,4593,4595,4598,4605,4608,4610],{},[1831,4591,4592],{},"120,000",[2013,4594,2063],{"stretchy":2062},[1831,4596,4597],{},"1.06",[2513,4599,4600,4602],{},[2013,4601,2078],{"stretchy":2062},[1831,4603,4604],{},"3",[2013,4606,4607],{},"≈",[1827,4609,2677],{"mathvariant":2081},[1831,4611,4612],{},"142,922",[1835,4614,4615],{"encoding":1837},"120{,}000(1.06)^3\\approx£142{,}922",[1805,4617,4619,4684],{"className":4618,"ariaHidden":1843},[1842],[1805,4620,4622,4626,4630,4636,4639,4642,4645,4675,4678,4681],{"className":4621},[1847],[1805,4623],{"className":4624,"style":4625},[1851],"height:1.0641em;vertical-align:-0.25em;",[1805,4627,4629],{"className":4628},[1856],"120",[1805,4631,4633],{"className":4632},[1856],[1805,4634,1988],{"className":4635},[2236],[1805,4637,2707],{"className":4638},[1856],[1805,4640,2063],{"className":4641},[2381],[1805,4643,4597],{"className":4644},[1856],[1805,4646,4648,4651],{"className":4647},[2447],[1805,4649,2078],{"className":4650},[2447],[1805,4652,4654],{"className":4653},[1865],[1805,4655,4657],{"className":4656},[1869],[1805,4658,4660],{"className":4659},[1874],[1805,4661,4664],{"className":4662,"style":4663},[1878],"height:0.8141em;",[1805,4665,4666,4669],{"style":2632},[1805,4667],{"className":4668,"style":1887},[1886],[1805,4670,4672],{"className":4671},[1891,1892,1893,1894],[1805,4673,4604],{"className":4674},[1856,1894],[1805,4676],{"className":4677,"style":2138},[2031],[1805,4679,4607],{"className":4680},[2142],[1805,4682],{"className":4683,"style":2138},[2031],[1805,4685,4687,4690,4694,4700],{"className":4686},[1847],[1805,4688],{"className":4689,"style":2152},[1851],[1805,4691,4693],{"className":4692},[1856],"£142",[1805,4695,4697],{"className":4696},[1856],[1805,4698,1988],{"className":4699},[2236],[1805,4701,4703],{"className":4702},[1856],"922",[4430,4705,4706],{},"£30,000; £70,000; and £100,000 (the layer limit), respectively.",[4430,4708,4709],{},"Claim baskets include specialised labour, parts, medical care, litigation, and mix effects whose weights and trends differ from household consumption.",[1797,4711,4713],{"id":4712},"sources-and-further-reading","Sources and further reading",[4427,4715,4716,4724,4731],{},[4430,4717,4718],{},[2798,4719,4723],{"href":4720,"rel":4721},"https:\u002F\u002Fforum.casact.org\u002Farticle\u002F121372-understanding-and-coping-with-the-new-normal-in-insurance-inflation",[4722],"nofollow","CAS — Understanding and Coping with the New Normal in Insurance Inflation (2024)",[4430,4725,4726],{},[2798,4727,4730],{"href":4728,"rel":4729},"https:\u002F\u002Fforum.casact.org\u002Farticle\u002F165011-increasing-inflation-on-liability-insurance-impact-as-of-year-end-2024",[4722],"CAS — Increasing Inflation on Liability Insurance: Impact as of Year-End 2024 (2025)",[4430,4732,4733],{},[2798,4734,4737],{"href":4735,"rel":4736},"https:\u002F\u002Fwww.abi.org.uk\u002Fnews\u002Fblog-articles\u002F2025\u002F9\u002Fmotor-claims-inflation-causes-consequences-and-what-comes-next\u002F",[4722],"ABI — Motor claims inflation: causes and consequences (2025)",{"title":10,"searchDepth":4739,"depth":4739,"links":4740},2,[4741,4742,4743,4744,4748,4749,4750,4751,4752],{"id":1799,"depth":4739,"text":1800},{"id":2779,"depth":4739,"text":2780},{"id":3208,"depth":4739,"text":3209},{"id":4339,"depth":4739,"text":4340,"children":4745},[4746],{"id":4411,"depth":4747,"text":4412},3,{"id":4418,"depth":4739,"text":4419},{"id":4447,"depth":4739,"text":4448},{"id":4536,"depth":4739,"text":4537},{"id":4557,"depth":4739,"text":4558},{"id":4712,"depth":4739,"text":4713},"Separate claims inflation from exposure and mix, then test fixed and indexed reinsurance layers.","md",{"sidebar":4756},{"order":4747},true,{"title":898,"description":4753},"L_B-M_Ss68wkdH5zWNyzySHf-mxrmLSh0u4tCt8aapY",[4761,4763],{"title":894,"path":895,"stem":896,"description":4762,"children":-1},"Apply limited layers per risk, occurrence, or aggregate and recognise exhaustion and reinstatement.",{"title":902,"path":903,"stem":904,"description":4764,"children":-1},"Compare quota share and per-loss excess cover on one simulated portfolio without hiding contract assumptions.",1785754736293]