Robert J. Shiller
- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198294184
- eISBN:
- 9780191596926
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198294182.003.0006
- Subject:
- Economics and Finance, Macro- and Monetary Economics, Financial Economics
When creating indices intended for use in cash settlement of futures contracts (or perpetual claims or options, or swaps, or other over‐the‐counter forward contracts or retail insurance contracts), ...
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When creating indices intended for use in cash settlement of futures contracts (or perpetual claims or options, or swaps, or other over‐the‐counter forward contracts or retail insurance contracts), it is critical that that each index represents value associated with a standard claim on future income (or services). The contract settlement must reflect the price of claims on income streams, so that the market can be used to hedge the risk associated with the claims, but the problem is that the available observations on prices or incomes may apply to dissimilar claims, and that standardization in the indices used to settle contracts is essential to liquidity in these markets. This chapter first reviews some existing index number methods, and then extends these methods to deal with the problems described. Chain index and hedonic index number methods are reviewed, and ordinary repeated‐measures indices (like the repeat sales indices) are shown to be in a sense a special case of these, and to have strong parallels to some existing indices used to settle contracts. The last part of the chapter introduces the hedonic repeated‐measures index to allow for control of changing price of quality variables, while retaining the repeated‐measures design.Less
When creating indices intended for use in cash settlement of futures contracts (or perpetual claims or options, or swaps, or other over‐the‐counter forward contracts or retail insurance contracts), it is critical that that each index represents value associated with a standard claim on future income (or services). The contract settlement must reflect the price of claims on income streams, so that the market can be used to hedge the risk associated with the claims, but the problem is that the available observations on prices or incomes may apply to dissimilar claims, and that standardization in the indices used to settle contracts is essential to liquidity in these markets. This chapter first reviews some existing index number methods, and then extends these methods to deal with the problems described. Chain index and hedonic index number methods are reviewed, and ordinary repeated‐measures indices (like the repeat sales indices) are shown to be in a sense a special case of these, and to have strong parallels to some existing indices used to settle contracts. The last part of the chapter introduces the hedonic repeated‐measures index to allow for control of changing price of quality variables, while retaining the repeated‐measures design.
Robert J. Shiller
- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198294184
- eISBN:
- 9780191596926
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198294182.003.0008
- Subject:
- Economics and Finance, Macro- and Monetary Economics, Financial Economics
Most published economic indices are revised after they are first published—information does not come in all at once, and timely publication dictates that the preliminary index numbers be later ...
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Most published economic indices are revised after they are first published—information does not come in all at once, and timely publication dictates that the preliminary index numbers be later revised. The repeated‐measures indices developed in the preceding chapters are vulnerable to revisions after especially long intervals of time, since they have the property that, unless the repeated measures come sequentially (which they do not necessarily), there will be revisions in the indices after the index numbers are first produced, even if the raw data used then were perfectly accurate and complete. There are other index number construction methods, such as ordinary‐least‐squares regression‐per‐period hedonic regressions, that do not normally produce revisions; this would at first seem to be an advantage, but an index number construction method that does not produce revisions is not a virtue if new information tends to arrive that implies revisions and is just ignored. This chapter addresses the whole problem of index number revisions in the following sections: Variance components in regression‐per‐period hedonics; Interval‐linked indices; Indices that are derived by conditioning on lagged index values. The final section of the chapter draws some sort of interpretation of what has gone before.Less
Most published economic indices are revised after they are first published—information does not come in all at once, and timely publication dictates that the preliminary index numbers be later revised. The repeated‐measures indices developed in the preceding chapters are vulnerable to revisions after especially long intervals of time, since they have the property that, unless the repeated measures come sequentially (which they do not necessarily), there will be revisions in the indices after the index numbers are first produced, even if the raw data used then were perfectly accurate and complete. There are other index number construction methods, such as ordinary‐least‐squares regression‐per‐period hedonic regressions, that do not normally produce revisions; this would at first seem to be an advantage, but an index number construction method that does not produce revisions is not a virtue if new information tends to arrive that implies revisions and is just ignored. This chapter addresses the whole problem of index number revisions in the following sections: Variance components in regression‐per‐period hedonics; Interval‐linked indices; Indices that are derived by conditioning on lagged index values. The final section of the chapter draws some sort of interpretation of what has gone before.
Robert J. Shiller
- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198294184
- eISBN:
- 9780191596926
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198294182.003.0007
- Subject:
- Economics and Finance, Macro- and Monetary Economics, Financial Economics
This chapter addresses the fact that creating index numbers for settlement of contracts requires some judgement, and that no single method is likely to be applicable to all circumstances—there are ...
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This chapter addresses the fact that creating index numbers for settlement of contracts requires some judgement, and that no single method is likely to be applicable to all circumstances—there are trade‐offs, and choices have to be made with limited information. Before applying a repeated‐measures method like the ones defined in the preceding chapter, a decision has to be made as to whether there are enough repeated measures to ensure that the standard errors are not going to be too high, and whether there is enough unmeasured quality variation across subjects to warrant the increase in error variances caused by the addition of many subject dummies. A choice has to be made as to which kinds of hedonic variables, if any, to include in the analysis, and not all quality measures are appropriate for index number construction, so a choice needs to be made as to whether these variables or the subject dummies are to be constrained in any of various ways. Prior information of an imprecise nature may be used to put probabilistic, rather than rigid, restrictions on the regression coefficients. There are also some fundamentally different variants of the hedonic repeated‐measures regression methods that could be considered, methods in which quality is inferred as an observed factor associated with each subject (factor analytic methods), and methods in which a separate selection equation is used to correct for possible selection bias in the mechanism by which it is determined which subjects are to be measured (selection bias correction methods).Less
This chapter addresses the fact that creating index numbers for settlement of contracts requires some judgement, and that no single method is likely to be applicable to all circumstances—there are trade‐offs, and choices have to be made with limited information. Before applying a repeated‐measures method like the ones defined in the preceding chapter, a decision has to be made as to whether there are enough repeated measures to ensure that the standard errors are not going to be too high, and whether there is enough unmeasured quality variation across subjects to warrant the increase in error variances caused by the addition of many subject dummies. A choice has to be made as to which kinds of hedonic variables, if any, to include in the analysis, and not all quality measures are appropriate for index number construction, so a choice needs to be made as to whether these variables or the subject dummies are to be constrained in any of various ways. Prior information of an imprecise nature may be used to put probabilistic, rather than rigid, restrictions on the regression coefficients. There are also some fundamentally different variants of the hedonic repeated‐measures regression methods that could be considered, methods in which quality is inferred as an observed factor associated with each subject (factor analytic methods), and methods in which a separate selection equation is used to correct for possible selection bias in the mechanism by which it is determined which subjects are to be measured (selection bias correction methods).
Robert J. Shiller
- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198294184
- eISBN:
- 9780191596926
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198294182.001.0001
- Subject:
- Economics and Finance, Macro- and Monetary Economics, Financial Economics
This book, which is part of the distinguished Clarendon Lectures in Economics series, puts forward a unique and authoritative set of detailed proposals for establishing new markets for the management ...
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This book, which is part of the distinguished Clarendon Lectures in Economics series, puts forward a unique and authoritative set of detailed proposals for establishing new markets for the management of the biggest economic risks facing governments and society. Robert Shiller argues that we have largely the wrong financial markets, and that establishing new ones may fundamentally alter and diminish international economic fluctuations (and thus enable better risk management) and reduce the inequality of incomes. Shiller argues that although some risks, such as natural disaster or temporary unemployment, are shared by society, most risks are borne by the individual, and standards of living are determined by luck. He investigates whether a new technology of markets could make risk sharing possible and shows how new contracts could be designed to hedge all manner of risks to the individual's living standards. He proposes new international markets for perpetual claims on national incomes, and on components and aggregates of national incomes, concluding that these markets may well dwarf our stock markets in their activity and significance. He also argues for new liquid international markets for residential and commercial property. Establishing such unprecedented new markets presents some important technical problems that Shiller attempts to solve with proposals for implementing futures markets on perpetual claims on incomes, and for the construction of index numbers for cash settlement of risk management contracts. These new markets could fundamentally alter and diminish international economic fluctuations, and reduce the inequality of incomes around the world. Much of the book is technical, and it is intended mostly for economists, contract designers at futures and options exchanges, originators of swaps and other financial deals, and designers of retail products associated with risk management (such as insurance, pension plans, and mortgages). However, the material within the book is mostly arranged so that a non‐technical reader can follow the broad themes, and until Ch. 6, most of the technical material is relegated to appendices.Less
This book, which is part of the distinguished Clarendon Lectures in Economics series, puts forward a unique and authoritative set of detailed proposals for establishing new markets for the management of the biggest economic risks facing governments and society. Robert Shiller argues that we have largely the wrong financial markets, and that establishing new ones may fundamentally alter and diminish international economic fluctuations (and thus enable better risk management) and reduce the inequality of incomes. Shiller argues that although some risks, such as natural disaster or temporary unemployment, are shared by society, most risks are borne by the individual, and standards of living are determined by luck. He investigates whether a new technology of markets could make risk sharing possible and shows how new contracts could be designed to hedge all manner of risks to the individual's living standards. He proposes new international markets for perpetual claims on national incomes, and on components and aggregates of national incomes, concluding that these markets may well dwarf our stock markets in their activity and significance. He also argues for new liquid international markets for residential and commercial property. Establishing such unprecedented new markets presents some important technical problems that Shiller attempts to solve with proposals for implementing futures markets on perpetual claims on incomes, and for the construction of index numbers for cash settlement of risk management contracts. These new markets could fundamentally alter and diminish international economic fluctuations, and reduce the inequality of incomes around the world. Much of the book is technical, and it is intended mostly for economists, contract designers at futures and options exchanges, originators of swaps and other financial deals, and designers of retail products associated with risk management (such as insurance, pension plans, and mortgages). However, the material within the book is mostly arranged so that a non‐technical reader can follow the broad themes, and until Ch. 6, most of the technical material is relegated to appendices.
S. N. Afriat
- Published in print:
- 1987
- Published Online:
- November 2003
- ISBN:
- 9780198284611
- eISBN:
- 9780191595844
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198284616.001.0001
- Subject:
- Economics and Finance, Microeconomics
This book approaches various aspects of economics that have to do with choice, and the opportunity for it, such as individual and social choice, production, optimal programming, and the market. The ...
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This book approaches various aspects of economics that have to do with choice, and the opportunity for it, such as individual and social choice, production, optimal programming, and the market. The topics belong mostly to microeconomics, but they also have other connections. The object is to state a view about choice and value and to give an account of the logical apparatus. With this there is a wish to present limited matters fairly completely and unproblematically, and where there is some issue about their nature to consider that also. The book consists of six parts, each containing several chapters.Parts I–IV deal with generalities about choice, individual or social, and representative economic topics. The remaining parts have more concern with straightforwardly mathematical subjects, which have an application or interpretation for economics but need not be exclusively connected there. Chapters often are fairly self‐contained or belong to sequences that can be taken more or less on their own. The topics are in the main fabric of economic theory, and most students encounter them. A preamble at the start of every chapter tells what it is about; from this and possibly some further scanning, the main ideas should be easily gathered by those who might not be concerned with all details. Expository materials and reworkings of published fragments have been joined with unpublished work from past and recent years. In all there is a view about choice and ‘the optimum’ in economics surely acceptable to some and perhaps what they have always thought but undoubtedly not to everyone.Less
This book approaches various aspects of economics that have to do with choice, and the opportunity for it, such as individual and social choice, production, optimal programming, and the market. The topics belong mostly to microeconomics, but they also have other connections. The object is to state a view about choice and value and to give an account of the logical apparatus. With this there is a wish to present limited matters fairly completely and unproblematically, and where there is some issue about their nature to consider that also. The book consists of six parts, each containing several chapters.
Parts I–IV deal with generalities about choice, individual or social, and representative economic topics. The remaining parts have more concern with straightforwardly mathematical subjects, which have an application or interpretation for economics but need not be exclusively connected there. Chapters often are fairly self‐contained or belong to sequences that can be taken more or less on their own. The topics are in the main fabric of economic theory, and most students encounter them. A preamble at the start of every chapter tells what it is about; from this and possibly some further scanning, the main ideas should be easily gathered by those who might not be concerned with all details. Expository materials and reworkings of published fragments have been joined with unpublished work from past and recent years. In all there is a view about choice and ‘the optimum’ in economics surely acceptable to some and perhaps what they have always thought but undoubtedly not to everyone.
W. M. Gorman
C. Blackorby and A. F. Shorrocks (eds)
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198285212
- eISBN:
- 9780191596322
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198285213.003.0016
- Subject:
- Economics and Finance, Microeconomics
This paper was presented at the European Meeting of the Econometric Society in Innsbruck in 1953; it has never been published, survives in several drafts, and was the first attempt to try to put ...
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This paper was presented at the European Meeting of the Econometric Society in Innsbruck in 1953; it has never been published, survives in several drafts, and was the first attempt to try to put together the issues raised by aggregation and equilibrium conditions. Klein (1946) posed the problem of aggregating inputs and outputs in an economy's production function when there are no equilibrium conditions restricting the allocation of commodities. This problem was solved by Nataf (1948) who derived the general forms of the aggregates and the economy technologies that are consistent with the Klein aggregation problem. Gorman here analyses the usefulness of the aggregates that solve the Klein problem, arguing that these Klein aggregates are not useful for many purposes in their general form, and proposing additional requirements that useful Klein aggregates should satisfy. For several of these additional requirements, Gorman derives the circumstances in which such aggregates exist.Less
This paper was presented at the European Meeting of the Econometric Society in Innsbruck in 1953; it has never been published, survives in several drafts, and was the first attempt to try to put together the issues raised by aggregation and equilibrium conditions. Klein (1946) posed the problem of aggregating inputs and outputs in an economy's production function when there are no equilibrium conditions restricting the allocation of commodities. This problem was solved by Nataf (1948) who derived the general forms of the aggregates and the economy technologies that are consistent with the Klein aggregation problem. Gorman here analyses the usefulness of the aggregates that solve the Klein problem, arguing that these Klein aggregates are not useful for many purposes in their general form, and proposing additional requirements that useful Klein aggregates should satisfy. For several of these additional requirements, Gorman derives the circumstances in which such aggregates exist.
Robert C. Feenstra and Marshall B. Reinsdorf
- Published in print:
- 2007
- Published Online:
- February 2013
- ISBN:
- 9780226044491
- eISBN:
- 9780226044507
- Item type:
- chapter
- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226044507.003.0017
- Subject:
- Economics and Finance, Microeconomics
This chapter examines the relatively neglected issue of estimating sample variance in the context of constructing exact index numbers. Published index numbers are rarely accompanied by an indicator ...
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This chapter examines the relatively neglected issue of estimating sample variance in the context of constructing exact index numbers. Published index numbers are rarely accompanied by an indicator of variability, and it is thus difficult to assess whether a new estimate is significantly different from the previous one. The chapter applies the analysis to the specific case of total factor productivity (TFP) indexes, and examines the question of whether TFP growth in Singapore has been negative or positive, which has become an issue of considerable controversy.Less
This chapter examines the relatively neglected issue of estimating sample variance in the context of constructing exact index numbers. Published index numbers are rarely accompanied by an indicator of variability, and it is thus difficult to assess whether a new estimate is significantly different from the previous one. The chapter applies the analysis to the specific case of total factor productivity (TFP) indexes, and examines the question of whether TFP growth in Singapore has been negative or positive, which has become an issue of considerable controversy.
Marc Fleurbaey and Didier Blanchet
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199767199
- eISBN:
- 9780199332557
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199767199.003.0004
- Subject:
- Economics and Finance, Public and Welfare
This chapter reviews old and recent arguments for and against monetary aggregates as social welfare indicators. It is organized as follows. Sections 3.1 and 3.2 examine two different ...
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This chapter reviews old and recent arguments for and against monetary aggregates as social welfare indicators. It is organized as follows. Sections 3.1 and 3.2 examine two different revealed-preference arguments that can be used to link the sign of welfare variations with the evolution of total consumption at market prices. Section 3.3 reviews the theory of index numbers, which has the more ambitious goal of providing cardinal measures of welfare. Section 3.4 focuses on the more modest, but perhaps more promising idea of decomposing social welfare into factors separately representing efficiency and equity. Section 3.5 introduces the problem of imputing prices for nonmarketed goods and computing a “full income.” The chapter concludes that economic theory does not provide much support for relying on the market value of total consumption as a proxy for social welfare.Less
This chapter reviews old and recent arguments for and against monetary aggregates as social welfare indicators. It is organized as follows. Sections 3.1 and 3.2 examine two different revealed-preference arguments that can be used to link the sign of welfare variations with the evolution of total consumption at market prices. Section 3.3 reviews the theory of index numbers, which has the more ambitious goal of providing cardinal measures of welfare. Section 3.4 focuses on the more modest, but perhaps more promising idea of decomposing social welfare into factors separately representing efficiency and equity. Section 3.5 introduces the problem of imputing prices for nonmarketed goods and computing a “full income.” The chapter concludes that economic theory does not provide much support for relying on the market value of total consumption as a proxy for social welfare.
Sydney Afriat
- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780199670581
- eISBN:
- 9780191773785
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670581.001.0001
- Subject:
- Economics and Finance, Econometrics, Microeconomics
A theft amounting to £1 was a capital offence in 1260 and a judge in 1610 affirmed the law could not then be applied since £1 was no longer what it was. Such association of money with a date is well ...
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A theft amounting to £1 was a capital offence in 1260 and a judge in 1610 affirmed the law could not then be applied since £1 was no longer what it was. Such association of money with a date is well recognized for its importance in very many connections. Thus arises the need to know how to convert an amount at one date into the right amount at another date. In other words, a price index. The longstanding question concerning how such an index should be constructed is known as ‘The Index Number Problem’. The ordinary consumer price index or CPI represents a practical response to the need. The truth of a price index is an issue giving rise to extensive thought and theory to which an impressive number of economists have each contributed. However, there have been hold-ups at a basic level. The approach brings the subject into involvement with constructions on the basis of finite data, in particular of price indices, and of utility, already well known in a form usually referred to as ‘Afriat's Theorem’. But utility is subject to constant returns, also possibly approximate. Despite a general importance for economic life and decades of outstanding professional attention, there had been no resolution of the Index Number Problem, nor had there been a real idea what could be meant by such a resolution. However, the method now proposed does convey what could be meant, and it undoubtedly represents the resolution.Less
A theft amounting to £1 was a capital offence in 1260 and a judge in 1610 affirmed the law could not then be applied since £1 was no longer what it was. Such association of money with a date is well recognized for its importance in very many connections. Thus arises the need to know how to convert an amount at one date into the right amount at another date. In other words, a price index. The longstanding question concerning how such an index should be constructed is known as ‘The Index Number Problem’. The ordinary consumer price index or CPI represents a practical response to the need. The truth of a price index is an issue giving rise to extensive thought and theory to which an impressive number of economists have each contributed. However, there have been hold-ups at a basic level. The approach brings the subject into involvement with constructions on the basis of finite data, in particular of price indices, and of utility, already well known in a form usually referred to as ‘Afriat's Theorem’. But utility is subject to constant returns, also possibly approximate. Despite a general importance for economic life and decades of outstanding professional attention, there had been no resolution of the Index Number Problem, nor had there been a real idea what could be meant by such a resolution. However, the method now proposed does convey what could be meant, and it undoubtedly represents the resolution.
S. N. Afriat
- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780199670581
- eISBN:
- 9780191773785
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670581.003.0007
- Subject:
- Economics and Finance, Econometrics, Microeconomics
The price index, a pervasive and old institution of economics, is a number issued by the Statistical Office that should tell anyone the ratio of costs for maintaining a given standard of living in ...
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The price index, a pervasive and old institution of economics, is a number issued by the Statistical Office that should tell anyone the ratio of costs for maintaining a given standard of living in two periods where prices differ. This picturesque indication amounts to a definition that is the basis for our approach. An immediate consequence by simple argument is the ‘New Formula’, where price indices are determined as ratios of numbers with the role of price levels that are solutions of a system of inequalities. Work on the approach continues and the system of inequalities is a reminder of a half century of experience including the present chapter.Less
The price index, a pervasive and old institution of economics, is a number issued by the Statistical Office that should tell anyone the ratio of costs for maintaining a given standard of living in two periods where prices differ. This picturesque indication amounts to a definition that is the basis for our approach. An immediate consequence by simple argument is the ‘New Formula’, where price indices are determined as ratios of numbers with the role of price levels that are solutions of a system of inequalities. Work on the approach continues and the system of inequalities is a reminder of a half century of experience including the present chapter.
S. N. Afriat
- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780199670581
- eISBN:
- 9780191773785
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670581.003.0009
- Subject:
- Economics and Finance, Econometrics, Microeconomics
The proposal that demand is governed by utility leads to the question of how to arrive at the utility, from evidence provided by the demand. For while demand is, in principle, directly observable, ...
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The proposal that demand is governed by utility leads to the question of how to arrive at the utility, from evidence provided by the demand. For while demand is, in principle, directly observable, utility is not; it is just discussed, usually for its part in an explanation of demand. The question became a basis for mathematical questions making an enlargement of ‘mathematical economics’ where a host have contributed a variety of fragments. This chapter has to deal specifically with two construction topics, involving a demand function, or a finite demand correspondence. Pareto (1901) touched the utility construction question, dealing with a demand function, and remarked it could be done by solving certain partial differential equations. These referred to the inverse of the function. Volterra (1906) pointed out, in a review of Pareto, that the existence of a solution was not always assured but required certain ‘integrability conditions’, such as had been provided by a theorem of Frobenius. Thereafter the question became known as the ‘integrability problem’. Antonelli (1886) provided equivalent conditions, stated in the form of a symmetry. Slutsky (1915) did the same, by differentiation of first order Lagrange conditions, and brought into view the further necessary (in fact, more than necessary) second-order conditions. The approach gained a currency after rediscovery by Hicks and Allen (1934). Besides symmetry, the Slutsky matrix was required to have a negativity condition, intermediate between its being non-positive and negative definite and different from both. That this negativity requirement found by these discoverers had to be spurious is demonstrated by ‘The Case of the Vanishing Slutsky Matrix’ found by Afriat (1972), where there is a continuously differentiable demand function that has a utility but the Slutsky coefficients all vanish identically, as would be impossible under the negativity condition of Slutsky and the others. Lionel McKenzie (1957) made an elegant departure when he identified the Slutsky coefficient matrix with the matrix of second derivatives of a utility-cost function, so necessarily both symmetric and non-positive definite. The issue of sufficiency that had always remained completely without mention was taken up and settled by Afriat (1980). Afriat (1977, 1980) dealt with the same question when the demand function is replaced by a finite demand correspondence (1956, 1960), with the result now usually referred to as ‘Afriat's Theorem’.Less
The proposal that demand is governed by utility leads to the question of how to arrive at the utility, from evidence provided by the demand. For while demand is, in principle, directly observable, utility is not; it is just discussed, usually for its part in an explanation of demand. The question became a basis for mathematical questions making an enlargement of ‘mathematical economics’ where a host have contributed a variety of fragments. This chapter has to deal specifically with two construction topics, involving a demand function, or a finite demand correspondence. Pareto (1901) touched the utility construction question, dealing with a demand function, and remarked it could be done by solving certain partial differential equations. These referred to the inverse of the function. Volterra (1906) pointed out, in a review of Pareto, that the existence of a solution was not always assured but required certain ‘integrability conditions’, such as had been provided by a theorem of Frobenius. Thereafter the question became known as the ‘integrability problem’. Antonelli (1886) provided equivalent conditions, stated in the form of a symmetry. Slutsky (1915) did the same, by differentiation of first order Lagrange conditions, and brought into view the further necessary (in fact, more than necessary) second-order conditions. The approach gained a currency after rediscovery by Hicks and Allen (1934). Besides symmetry, the Slutsky matrix was required to have a negativity condition, intermediate between its being non-positive and negative definite and different from both. That this negativity requirement found by these discoverers had to be spurious is demonstrated by ‘The Case of the Vanishing Slutsky Matrix’ found by Afriat (1972), where there is a continuously differentiable demand function that has a utility but the Slutsky coefficients all vanish identically, as would be impossible under the negativity condition of Slutsky and the others. Lionel McKenzie (1957) made an elegant departure when he identified the Slutsky coefficient matrix with the matrix of second derivatives of a utility-cost function, so necessarily both symmetric and non-positive definite. The issue of sufficiency that had always remained completely without mention was taken up and settled by Afriat (1980). Afriat (1977, 1980) dealt with the same question when the demand function is replaced by a finite demand correspondence (1956, 1960), with the result now usually referred to as ‘Afriat's Theorem’.
S. N. Afriat
- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780199670581
- eISBN:
- 9780191773785
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670581.003.0008
- Subject:
- Economics and Finance, Econometrics, Microeconomics
A first step in the examination of an act is to view it as a choice. With a choice there is the problem of accounting for the singularity of what is done which differentiates it in the variety of ...
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A first step in the examination of an act is to view it as a choice. With a choice there is the problem of accounting for the singularity of what is done which differentiates it in the variety of what might have been done. The account should involve a principle that applies uniformly to the possibilities, yet singles out the particular act, in terms of its cause, the motive, or objective. Value is a term serving that principle, with preference as a concept for its expression. Whatever the scope of the concept of choice and systematization of choice by preference, here to have attention, it remains just a model, a form of representation, a scheme that can always be applied to behaviour in some fashion, even without assured significance. The model of a choice system based on a preference order is a habit in particular for economics; even in a more general perspective, order appears as an almost invariable component in measurement, though there may be some puzzle about that. Principles concerning choice and preference are to be considered and illustrated, in particular in regard to the analysis of consumption. An approach to the theory of consumption is developed by considering a scheme of consumption data, and then questions that might be asked of that data.Less
A first step in the examination of an act is to view it as a choice. With a choice there is the problem of accounting for the singularity of what is done which differentiates it in the variety of what might have been done. The account should involve a principle that applies uniformly to the possibilities, yet singles out the particular act, in terms of its cause, the motive, or objective. Value is a term serving that principle, with preference as a concept for its expression. Whatever the scope of the concept of choice and systematization of choice by preference, here to have attention, it remains just a model, a form of representation, a scheme that can always be applied to behaviour in some fashion, even without assured significance. The model of a choice system based on a preference order is a habit in particular for economics; even in a more general perspective, order appears as an almost invariable component in measurement, though there may be some puzzle about that. Principles concerning choice and preference are to be considered and illustrated, in particular in regard to the analysis of consumption. An approach to the theory of consumption is developed by considering a scheme of consumption data, and then questions that might be asked of that data.