This thesis examines the theoretical underpinnings and practical construction of select economic and financial indexes. Such indexes are used for a variety of purposes, including the measurement of inflation, portfolio return performance, and firm productivity. Chapter 1 motivates interest in economic and financial indexes and introduces the principal ideas in the thesis. Chapter 2 focuses on one potential source of bias in the Canadian consumer price index (CPI) that arises from the emergence of large discount/warehouse stores—the so-called outlet substitution bias. Such outlets have gained market share in Canada in recent years, but current CPI procedures fail to capture the declines in average prices that consumers enjoy when they switch to such outlets. Unrepresentative sampling, and the fact that discount stores often deliver lower rates of price increase can further bias the CPI. Bias estimates for some elementary indexes are computed using data from Statistics Canada's CPI production files for the province of Ontario. It is shown that the effect on the Canadian CPI of inappropriately accounting for such discount outlets can be substantial. Another area in which indexes are frequently used is the stock market. Several stock market indexes exist, including those produced by Dow Jones and Company, Standard and Poor's Corporation, Frank Russell and Company, among others. These indexes differ in two fundamental respects: their composition and their method of computation—with important implications for their usage and interpretation. Chapter 3 introduces the concept of a stock index by asking what, in fact a stock market index is—this is tantamount to considering the purpose for which the index is intended, since stock indexes should be constructed according to their usage. Because stock indexes are most commonly used as measures of returns on portfolios, the main considerations in constructing such return indexes are examined. Chapter 4 uses the Dow Jones Industrial Average (DJIA) as a case study to examine its properties as a return index. It is shown that the DJIA is not the return on a market portfolio consisting of its thirty component stocks: in fact the DJIA measures the return performance on a very particular (and unusual) investment strategy, a fact that is not well understood by institutional investors. An examination of some other popular stock indexes shows that they all differ in their computational formula and that each is consistent with a particular investment strategy. Numerical calculations reveal that the return performance of the DJIA can vary considerably with the choice of basic index number formula, particularly over shorter time horizons. Given the numerous ways of constructing stock market return indexes, the user is left to determine which is 'best' in some sense. The choice of an appropriate (or 'best') formula for a stock market index is formally addressed in chapter 5. The test or axiomatic approach to standard bilateral index number theory as in Eichhorn & Voeller (1983), Diewert (1993a), and Balk (1995) is adapted here. A number of a priori desirable properties (or axioms) are proposed for a stock index whose purpose is to measure the gross return on a portfolio of stocks. It is shown that satisfaction of a certain subset of axioms implies a definite functional form for a stock market return index. Chapter 6 evaluates the various stock indexes is use today in terms of their usefulness as measures of gross returns on portfolios. To this end the axioms developed in chapter 5 are used to provide a common evaluative framework, in the sense that some of the indexes satisfy certain axioms while others do not. It is shown that the shortcomings of the DJIA as a measure of return arise from its failure to satisfy a number of the basic axioms proposed. Notwithstanding this, each index corresponds to a different investment strategy. Thus, when choosing an index for benchmarking purposes an investor should select one which closely matches his/her investment strategy—a choice that cannot be made by appealing to axioms alone.

This thesis examines the theoretical underpinnings and practical construction of select economic and financial indexes. Such indexes are used for a variety of purposes, including the measurement of inflation, portfolio return performance, and firm productivity. Chapter 1 motivates interest in economic and financial indexes and introduces the principal ideas in the thesis. Chapter 2 focuses on one potential source of bias in the Canadian consumer price index (CPI) that arises from the emergence of large discount/warehouse stores—the so-called outlet substitution bias. Such outlets have gained market share in Canada in recent years, but current CPI procedures fail to capture the declines in average prices that consumers enjoy when they switch to such outlets. Unrepresentative sampling, and the fact that discount stores often deliver lower rates of price increase can further bias the CPI. Bias estimates for some elementary indexes are computed using data from Statistics Canada's CPI production files for the province of Ontario. It is shown that the effect on the Canadian CPI of inappropriately accounting for such discount outlets can be substantial. Another area in which indexes are frequently used is the stock market. Several stock market indexes exist, including those produced by Dow Jones and Company, Standard and Poor's Corporation, Frank Russell and Company, among others. These indexes differ in two fundamental respects: their composition and their method of computation—with important implications for their usage and interpretation. Chapter 3 introduces the concept of a stock index by asking what, in fact a stock market index is—this is tantamount to considering the purpose for which the index is intended, since stock indexes should be constructed according to their usage. Because stock indexes are most commonly used as measures of returns on portfolios, the main considerations in constructing such return indexes are examined. Chapter 4 uses the Dow Jones Industrial Average (DJIA) as a case study to examine its properties as a return index. It is shown that the DJIA is not the return on a market portfolio consisting of its thirty component stocks: in fact the DJIA measures the return performance on a very particular (and unusual) investment strategy, a fact that is not well understood by institutional investors. An examination of some other popular stock indexes shows that they all differ in their computational formula and that each is consistent with a particular investment strategy. Numerical calculations reveal that the return performance of the DJIA can vary considerably with the choice of basic index number formula, particularly over shorter time horizons. Given the numerous ways of constructing stock market return indexes, the user is left to determine which is 'best' in some sense. The choice of an appropriate (or 'best') formula for a stock market index is formally addressed in chapter 5. The test or axiomatic approach to standard bilateral index number theory as in Eichhorn & Voeller (1983), Diewert (1993a), and Balk (1995) is adapted here. A number of a priori desirable properties (or axioms) are proposed for a stock index whose purpose is to measure the gross return on a portfolio of stocks. It is shown that satisfaction of a certain subset of axioms implies a definite functional form for a stock market return index. Chapter 6 evaluates the various stock indexes is use today in terms of their usefulness as measures of gross returns on portfolios. To this end the axioms developed in chapter 5 are used to provide a common evaluative framework, in the sense that some of the indexes satisfy certain axioms while others do not. It is shown that the shortcomings of the DJIA as a measure of return arise from its failure to satisfy a number of the basic axioms proposed. Notwithstanding this, each index corresponds to a different investment strategy. Thus, when choosing an index for benchmarking purposes an investor should select one which closely matches his/her investment strategy—a choice that cannot be made by appealing to axioms alone. / Arts, Faculty of / Vancouver School of Economics / Graduate