Aggregation theory and statistical index numbers

• Main Author: Nesmith, Travis Dean
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.2000
• Subjects: Aggregates; Central banks; Copyright; Cost of living; Decentralization; Decision making; Dissertations & theses; Dynamic programming; Economic growth; Economic justification; Economic theory; Economists; Expenditures; Federal Reserve monetary policy; GDP; Gross Domestic Product; Inheritances; Interest rates; Macroeconomics; Market prices; Nobel prizes; Present value; Seasonal variations; Shadow prices; Stock exchanges; Uncertainty; Utility functions
• ISBN: 0599780037; 9780599780033

Aggregation theory and index numbers straddle the divide between theory and practice in economics. They also straddle the divide between microeconomics and macroeconomics. Aggregation theory and statistical index numbers answer the fundamental question, “In a complex and high-dimensional economy, how can economic behavior and activity be comprehensibly measured?” This thesis extends aggregation theory to address three different challenges: interest rates; seasonality; and uncertainty. These topics are addressed within the framework of a neoclassical consumer decision problem that is developed in the second chapter. Prior to taking up the three topics, Chapters 3–5 thoroughly review duality and separability, functional structure, and economic aggregation theory and statistical indexes respectively. Following this review, the theoretical support for interest rate aggregation is examined. Although the literature on interest rates is voluminous, the extant literature on interest rate aggregation consists largely of three articles Moore, Porter, and Small (1990) and Barnett and Xu (1998, 2000). Interest rate aggregation is shown to be generally inconsistent with user cost aggregation. A new definition of an interest rate aggregate, that is consistent, is proposed and its theoretical properties are examined. The import of seasonality for the construction of economic indexes is addressed by Diewert (1980, 1983, 1998, and 1999). He convincingly argues that seasonality violates the basic models that underlie economic aggregates and indexes, because seasonality implies time inseparability His development assumed homothetic preferences. This assumption is relaxed which extends the previous work. A new economic justification for his rolling year index is also developed. To this point, the thesis focuses on the perfect certainty case. Barnett (1994), Barnett and Liu (1995), and Barnett, Liu, and Jensen (1997) generalized monetary aggregation theory to include risk bearing monetary assets. In this thesis, their models are extended to include other durable goods. The existence and uniqueness of the models' solutions is proved. The major contributions are a decentralization theorem and the construction of dual aggregates. Finally, risk neutrality is shown to be necessary and sufficient for two-stage budgeting in the presence of uncertainty.