Index numbers are also differentiated according to the number of commodities or products included in the comparison. Sinclair december 28, 2001 forthcoming in the hans theil memorial special issue of the journal of agricultural and applied economics william a. Operational identification of the complete class of. Exact and superlative price and quantity indicators core. All papers are available in pdfformat on the internet. Erwin diewert published an article that suggested a relatively simple way to approximate the theoretical costofliving index. E exact and superlative index numbers, journal of econometrics, 4, 1976, 115145. This raises the question of which superlative index should be used. The university of british columbia publications record date of most recent revision please initial name in full. Exact and superlative welfare change indicators, economic. If and only if the quadratic function f is defined by 2. Introduction one of the most troublesome problems facing national income accountants and econometricians who are forced to construct some data series, is the question of which functional form for an index number should be used. This paper proposes to clarify some important questions that are still open in the field of index number theory. Exactness implies that a particular index number can be.
Index numbers, stochastic, test and economic approaches to index number theory. The paper rationalizes certain functional forms for index numbers with functional forms for the underlying aggregator function. An aggregator functional form is said to be flexible if it can provide a second order approximation to an arbitrary twice differentiable linearly homo geneous. The differential approach to superlative index number theory. Erwin diewert1 department of economics university of british columbia vancouver, canada, v6t 1z1 email. This result has significant implications for the index number literature. When the exact index number approach and diewerts numerical analysis approximation results for superlative index numbers are applied, the a priori. Erwin diewert 2010, on the stochastic approach to index numbers. Diewert 1976 wrote his first paper on superlative indexes in 19733 but it took about 20 years for the idea to diffuse into statistical agencies. Index numbers are used to aggregate detailed information on prices and quantities. The differential approach to superlative index number.
Diewert s superlative index numbers, defined to be exact for secondorder aggregator functions, unify index number theory with aggregation theory but have been difficult to identify. Discussion paper 0701, university of british columbia. Available formats pdf please select a format to send. Geologarithmic price indices satisfying the axioms of monotonicity, basis reversibility and factor reversibility have been investigated by marco fattore 2010, who has shown that the superlative fisher price index does not belong to this family of indices. Each component in this decomposition represents the. An index number functional form is said to be superlative if it is exact i. Aug 17, 2017 index numbers are used to reduce and summarize this overwhelming abundance of microeconomic information. The present paper looks for counterparts to his results in the difference context, for both flexible homothetic and flexible nonhomothetic preferences. Operational identification of the complete class of superlative index numbers.
Walter diewert economics working papers from vancouver school of economics. Erwin and hide exact and superlative price and quantity. Jan 25, 2020 the base of this chapter is diewert, w. Chapter 8 bilateral and multilateral comparisons of. This paper proposes to clarify some important questions that are still open in thefield of index number theory. Diewert defined superlative price and quantity indexes as observable indexes which were exact for a ratio of unit cost functions or for a ratio of linearly homogeneous utility functions. A superlative indicator for the luenbergerhicksmoorsteen. An important body of literature initiated by diewert 1976 seeks to find superlative index numbers for which the approximation holds under the assumption of. Diewert 1976a has suggested the use of a superlative index number for mula. Diewertfunctional form in the theory of production and consumer demand. Working papers journal articles books and chapters software components. Economic theory and beas alternative quantity and price indexes. Exact index numbers are empirical index number formula that are equal to an underlying theoretical index, provided that the.
Diewert university of british columbia, vancouver, canada received february 1974, revised version received june 1975. Pdf the differential approach to superlative index number. Flexibleweight index numbers by referring to more general functional forms of aggregator functions, diewert 1976 discovered another class of exact index numbers, which he called superlative using a term that. Diewert 1976 on exact and superlative index numbers is a basic paper. Diewert defined superlative price and quantity indices as observable indices that were exact for a ratio of unit cost functions or for a ratio of linearly homogeneous utility functions. Diewert 1976 defined p and q to be superlative indexes if either p is exact for a flexible.
A superlative index number formula for the hicksmoorsteen. Diewert very often, an index number used in an economic model has been constructed in two. Northholland publishing company exact and superlative index numbers w. In addition, some new exact decompositions of the percentage change in the fisher and walsh superlative indexes into n components are derived. A flexible aggregator is a secondorder approximation to an arbitrary production, cost, utility or distance function. The paris oecdimf workshop on real estate price indexes. Erwin diewert september 10, 1995 professor of economics at the university of british columbia and research associate at the national bureau of economic research. A quantity index q is defined to be superlative if it is exact for a neo classical.
In a most recent publication diewert diewert 19 76. A simple index, also known as a relative, is a comparison involving only one item but an index whose calculation is based on several items is known as an aggregate or composite index. Diewerts 1976 superlative index numbers, defined to be exact for second order aggregator functions, unify index number theory with aggregation theory, but have been difficult to identify. An important body of literature initiated by diewert 1976 seeks to find superlative index numbers for which the approximation holds under the assumption of i economic optimizing behavior and. However, experience with scanner data has shown that the use of chained superlative indexes leads to chain drift. Christensen, the economic journal 92 march 1982, pp. Journal of econometrics 42, 115146, reprinted as chapter 8 in diewert and nakamura 1993. Diewert 1976 defines a quantity price index as superlative if it is exact for a flexible aggregator unit cost function.
The use of superlative index links in the swedish cpi. Pdf the differential approach to superlative index. When the exact index number approach and diewert s numerical analysis approximation results for superlative index numbers are applied, the a priori information requirements for choosing an index number formula are reduced to a list of general characteristics of the production scenario. If an index number is linearly homogeneous and a second order approximation in a formal manner that we define, we prove the index to be in the superlative index number class of. Hence index numbers impinge on virtually every empirical investigation in economics. That approach to monetary aggregation was derived and advocated by william a. Using this, it is possible to compute an index number that describes the price development from. An aggregator unit cost function is flexible if it can provide a secondorder approximation to an arbitrary twice differentiable linearly homogeneous aggregator unit cost function.
Using these estimates, we develop an exact aggregate price index and find that the upward bias in the conventional import price index over this time period was 28 percent or 1. Erwin diewerta, b amethods and informatics department,statistics netherlands p. Abstract index numbers are used to aggregate detailed information on prices and quantities into scalar measures of price and quantity levels or their growth. The traditional economic approach to index number theory is based on a ratio of cost functions. An index can rigorously apply microeconomic and aggregationtheoretic foundations in the construction of monetary aggregates. Diewert university of british columbia, vancouver, canada received february 1974, revised version received june 1975 the paper rationalizes certain functional forms for index numbers with functional forms for the underlying aggregator function. An important body of literature initiated by diewert 1976 seeks to find superlative index numbers for which the approximation holds under the assumption of i economic optimizing behavior and ii a technology that can be represented up to the second order by a flexible functional form.
Diewert coined the term superlative for an index number functional form that is exact for a behavioral relationship with a functional form that is flexible. Diewert 1978 showed that all known superlative index numbers approximate each other to the second order, and that in actual comparisons the two most widely used superlative indexes fisher and tornqvist are numerically very close. Chapter 8 cost of living indexes and exact index numbers. Superlative indices are price or quantity indices that are exact for a. Diewerts superlative index numbers, defined to be exact for secondorder aggregator functions, unify index number theory with aggregation theory but have been difficult to identify. Caves dw, christensen lr, diewert we 1982 the economic theory of index numbers and the measurement of input, output, and productivity. Walras theory of capital formation and the existence of a temporary equilibrium. Barnett 1980 and has led to the construction of monetary aggregates based on diewert s 1976 class of superlative quantity index numbers. Erwin diewert for a variety of reasons, it is useful to be able to make accurate comparisons of the relative consumption or real output between countries or between re gions within a country. The paper shows that a certain family of index number formulae is exact for the flexible quadratic mean of order r aggregator function. The theory of exact and superlative index numbers revisited. Index numbers were, in fact, defined to be superlative by diewert 1976, p.
Erwin introduced the now standard concepts of flexible functional forms in econometrics and superlative index numbers in productivity measurement both. Diewert s superlative index numbers, defined to be exact for second order aggregator functions, unify index number theory with aggregation theory, but have been difficult to identify. Superlative indices are price or quantity indices that are exact for a flexible aggregator. In section 2 below, we note that the geks multilateral index number method that was. Barnett is professor of economics at washington university. Diewert s 1976 superlative index numbers, defined to be exact for second order aggregator functions, unify index number theory with aggregation theory, but have been difficult to identify. Eurostat, unece, world bank, 2004, producer price index manual. International policy discussion in property price indices.
Diewert 1976 calls index number formulae that have this property superlative. Exact index numbers are empirical index number formula that are equal to an underlying theoretical index, provided that the consumer has preferences that can be represented by. Exact index numbers are empirical index number formula that are equal to an underlying theoretical index, provided that the consumer has preferences that can be represented by certain functional forms. The differential approach to superlative index number theory by william a. Exact and superlative index numbers 1976 citeseerx. Professor erwin diewert has made significant contributions to a variety of areas, including duality theory, index number theory, user cost, functional form specification, international trade and revealed preference theory. As we saw at the end of the last chapter, these superlative month to month indexes can be subject to a considerable amount of chain drift. Thus we will define exact price and quantity indexes and present two definitions for a superlative price. Oecd glossary of statistical terms superlative indices. Exact and superlative welfare change indicators exact and superlative welfare change indicators diewert, w. An index number is said to be exact for a function if it is identically equal to the ratio of numerical. Economics working papers from vancouver school of economics. Multilateral comparisons of output, input, and productivity using superlative index numbers dw caves, lr christensen, we diewert the economic journal 92 365, 7386, 1982. We present a new approach to finding elements of this class.
Multilateral comparisons of output, input, and productivity using superlative index numbers douglas w. Pdf exact and superlative index number researchgate. Superlative indices definition oecd glossary of statistical terms. We provide an operational identification of the complete class of superlative index numbers to track the exact aggregator functions of economic aggregation theory. Axiomatic and economic approaches to international. This paper revisits the theory of exact and superlative index numbers that was developed in a seminal article by diewert 1976 and is still dominating the. Then diewert 1976 defined p and q to be superlative indexes if either p is exact. Erwin diewert early in this century economists began to give serious attention to making comparisons using index number techniques. Sorry, we are unable to provide the full text but you may find it at the following locations. If an index number is linearly homogeneous and a second order approximation in a formal manner that we define, we prove the index to be in the superlative index number class of nonparametric functions. Index number concepts, measures and decompositions of.
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