Statistical Indexes Course

Lesson 1 • Populations, Samples, and Parameters

Defines population parameters versus sample statistics and explains why indexes often estimate unobservable quantities. Links sampling design to index reliability.

Lesson 2 • Measurement Error and Data Quality

Identifies systematic and random error sources that distort index values. Introduces validity and reliability as quality criteria for any statistical measure.

Lesson 3 • Variables, Scales, and Data Types

Covers nominal, ordinal, interval, and ratio scales and their implications for index construction. Establishes the measurement vocabulary used throughout the course.

Lesson 1 • What Is an Index Number?

Defines an index number as a ratio expressing change relative to a reference point. Situates indexes within broader statistical measurement practice.

Lesson 2 • Simple Price and Quantity Indexes

Constructs single-item price and quantity relatives and interprets percentage change. Provides the arithmetic foundation for multi-item composite indexes.

Lesson 3 • Selecting and Shifting the Base Period

Explains criteria for choosing a reference period and the mechanics of rebasing an index series. Addresses how base choice affects comparability over time.

Lesson 4 • Index Interpretation and Communication

Translates raw index values into meaningful statements about change, level, and comparison. Covers common misinterpretations and how to avoid them.

Lesson 1 • Comparing Formula Performance

Uses empirical datasets to quantify differences among Laspeyres, Paasche, and Fisher results. Builds judgment for formula choice in applied settings.

Lesson 2 • Laspeyres Price Index

Derives the Laspeyres formula using base-period weights and explains its upward substitution bias. Demonstrates calculation with multi-item basket data.

Lesson 3 • Fisher Ideal Index

Constructs the Fisher index as the geometric mean of Laspeyres and Paasche and verifies its axiomatic properties. Evaluates trade-offs between accuracy and data cost.

Lesson 4 • Axiomatic and Economic Approaches

Introduces the test approach and the economic approach to evaluating index formulas. Connects theoretical criteria to real-world formula selection decisions.

Lesson 1 • Value Indexes and Deflation

Constructs value indexes and uses price indexes to deflate nominal series into real terms. Demonstrates the price-quantity decomposition identity.

Lesson 2 • Chain-Linking Quantity Indexes

Explains chain-linking as a method to update weights annually and reduce substitution bias. Covers the additivity problem unique to chain-linked volume measures.

Lesson 3 • Real Output and Productivity Measures

Applies quantity indexes to measure real output growth and labor productivity. Connects index methodology to national accounts and business performance analysis.

Lesson 1 • Composite Index Design Framework

Outlines the end-to-end process from conceptual framework to published composite index. Establishes design decisions that affect validity and comparability.

Lesson 2 • Weighting Schemes and Justification

Compares equal weighting, expert-based weighting, and statistical weighting methods such as PCA. Addresses the political and methodological dimensions of weight assignment.

Lesson 3 • Normalization and Rescaling Methods

Covers min-max, z-score, and distance-to-reference normalization techniques. Explains how normalization choice affects relative rankings in the composite.

Lesson 4 • Sensitivity and Uncertainty Analysis

Applies Monte Carlo simulation and variance decomposition to quantify composite index uncertainty. Identifies which design choices most influence final rankings.

Lesson 1 • New Goods and Outlet Substitution

Handles the introduction of new products and shifts in consumer purchasing channels within a price index. Covers rotation procedures and scanner data integration.

Lesson 2 • Consumer Price Index Construction

Traces the full CPI production cycle from household expenditure surveys to published index. Covers basket design, outlet sampling, and price collection procedures.

Lesson 3 • Quality Adjustment Methods

Addresses the challenge of price change when product quality changes and introduces hedonic and overlap methods. Ensures measured price change reflects pure price, not quality.

Lesson 4 • Producer and Trade Price Indexes

Distinguishes producer price indexes from consumer price indexes and explains import and export price measurement. Addresses transfer pricing and border valuation issues.

Lesson 1 • Factor and Smart Beta Indexes

Introduces factor-based index construction targeting value, momentum, quality, and low-volatility premia. Connects factor index design to systematic investment strategies.

Lesson 2 • Corporate Actions and Index Maintenance

Explains how dividends, splits, mergers, and delistings are handled to maintain index continuity. Covers divisor adjustment as the standard continuity mechanism.

Lesson 3 • Index Performance Measurement

Calculates total return, risk-adjusted return, and tracking error for market indexes. Provides tools for evaluating index quality as a benchmark.

Lesson 4 • Fixed Income and Commodity Indexes

Extends index methodology to bond markets and commodity futures, addressing unique valuation and roll challenges. Highlights differences from equity index construction.

Lesson 1 • Multilateral Price Comparisons

Extends bilateral index methods to simultaneous multi-country price comparisons using GEKS and other multilateral methods. Addresses transitivity and characteristicity trade-offs.

Lesson 2 • Emerging Methodological Challenges

Surveys unresolved issues including digital economy measurement, free goods, and personalized price indexes. Prepares students to engage with frontier methodological debates.

Lesson 3 • Index Governance and Quality Frameworks

Applies international quality frameworks to index production, covering independence, transparency, and user consultation. Positions governance as essential to index credibility.

Lesson 4 • Big Data and Alternative Data Sources

Evaluates scanner data, web-scraped prices, and administrative records as supplements to traditional surveys. Addresses representativeness, coverage, and real-time index production.