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Abstract:
The paper presents a general theory of the aggregation of prices and quantities that unifies the field and relates topics that in the past have been treated separately and unsatisfactorily, or not at all. The theory does without the common but unrealistic assumptions of homotheticity, or representative agents and is valid with or without an explicit utility maximization assumption. Two different derivations are given, one in continuous time, using Divisia integrals, and one employing more traditional discrete arguments. The unifying concept is the money metric, which is interpreted as a partial welfare indicator, rather than as a comprehensive welfare measure. On this basis, a consistent set of chained price and quantity indexes for a set of additive time series, such as those in the national income and product accounts, is derived. All variants of the theory lead to Törnqvist indexes defined on the appropriate data set. A numerical example confirms that in the non-homothetic case, these indexes are superior both to Fisher's "ideal" index and to the consumer surplus approximation.

Chain Indexes, Consumer Surplus, Cost-of-living, Divisia Integral, Money Metric Price Index, Quantity Index, Real Consumption, Tornqvist Index

Abstract:
This paper has two sources: One is my own research in three broad areas: business cycles, economic measurement and social choice. In all of these fields I attempted to apply the basic precepts of the scientific method as it is understood in the natural sciences. I found that my effort at using natural science methods in economics was met with little understanding and often considerable hostility. I found economics to be driven less by common sense and empirical evidence, then by various ideologies that exhibited either a political or a methodological bias, or both. This brings me to the second source: Several books have appeared recently that describe in historical terms the ideological forces that have shaped either the direct areas in which I worked, or a broader background. These books taught me that the ideological forces in the social sciences are even stronger than I imagined on the basis of my own experiences.

The scientific method is the antipode to ideology. I feel that the scientific work that I have done on specific, long standing and fundamental problems in economics and political science have given me additional insights into the destructive role of ideology beyond the history of thought orientation of the works I will be discussing.

Business cycles, Ideology, Science, Voting, Welfare measurement

Abstract:
The paper provides a rigorous derivation of the "welfare triangle approximation" (WTA), which is at the center of cost benefit analysis. The result is generalized by showing that the WTA is one of two dual expressions, one of which approximates the change in real consumption, the other the change in the cost-of-living. The result is based on a correction of a proof attempted by Hicks. Many other derivations are also given, each based on a different definition of the theoretical functions to be approximated. The final result is the following: Each of the empirical variations corresponds to a range of theoretical variations. The edges of the range are theoretical Laspeyres and Paasche variations which are approximated linearly; the interior region of the range is approximated quadratically; the center of the range is replicated exactly by the empirical measures.

Abstract:
The paper provides a rigorous derivation of the "welfare triangle approximation" (WTA), which is at the center of cost benefit analysis. The result is generalized by showing that the WTA is one of two dual expressions, one of which approximates the change in real consumption, the other the change in the cost-of-living. The result is based on a correction of a proof attempted by Hicks. Many other derivations are also given, each based on a different definition of the theoretical functions to be approximated. The final result is the following: Each of the empirical variations corresponds to a range of theoretical variations. The edges of the range are theoretical Laspeyres and Paasche variations which are approximated linearly; the interior region of the range is approximated quadratically; the center of the range is replicated exactly by the empirical measures.

Key Words: Cost-of-living, Consumer Surplus, Money Metric, Real Consumption, Welfare measurement

Abstract:
The paper discusses measurement, primarily in economics, from both analytical and historical perspectives. The historical section traces the commitment to ordinalism on the part of economic theorists from the doctrinal disputes between classical economics and marginalism, through the struggle of orthodox economics against socialism down to the cold-war alliance between mathematical social science and anti-communist ideology. In economics the commitment to ordinalism led to the separation of theory from the quantitative measures that are computed in practice: price and quantity indexes, consumer surplus and real national product. The commitment to ordinality entered political science, via Arrow's 'impossibility theorem', effectively merging it with economics, and ensuring its sterility. How can a field that has as its central result the impossibility of democracy contribute to the design of democratic institutions?

The analytical part of the paper deals with the quantitative measures mentioned above. I begin with the conceptual clarification that what these measures try to achieve is a restoration of the money metric that is lost when prices are variable. I conclude that there is only one measure that can be embedded in a satisfactory economic theory, free from unreasonable restrictions. It is the Törnqvist index as an approximation to its theoretical counterpart the Divisia index.

The statistical agencies have at various times produced different measures for real national product and its components, as well as related concepts. I argue that all of these are flawed and that a single deflator should be used for the aggregate and the components. Ideally this should be a chained Törnqvist price index defined on aggregate consumption.

The social sciences are split. The economic approach is abstract, focused on the assumption of rational and informed behavior, and tends to the political right. The sociological approach is empirical, stresses the non-rational aspects of human behavior and tends to the political left. I argue that the split is due to the fact that the empirical and theoretical traditions were never joined in the social sciences as they were in the natural sciences. I also argue that measurement can potentially help in healing this split.

collective choice, consumer surplus, money metric, price and quantity indexes, welfare measurement

Abstract:
We test the quantity theory of money (QTM) using a novel approach and a large new sample. We do not follow the usual approach of first differentiating the logarithm of the Cambridge equation to obtain an equation relating the growth rate of real GDP, the growth rate of money and inflation. These variables must then again be 'integrated' by averaging in order to obtain stable relationships. Instead we suggest a much simpler procedure for testing directly the stability of the coefficient of the Cambridge equation. For 125 countries and post-war data we find the coefficient to be surprisingly stable. We do not select for high inflation episodes as was done in most empirical studies; inflation rates do not even appear in our data set.

Much work supporting the QTM has been done by economic historians and at the University of Chicago by Milton Friedman and his associates. The QTM was a foundation stone of the monetarist revolution. Subsequently belief in it waned. The currently dominant New Keynesian School, implicitly or explicitly denies the validity of the QTM. We survey this history and argue that the QTM is valid and New Keynesians are wrong.

Keynesian theory, quantity theory of money

Abstract:
The paper reports the principal findings of a long term research project on the description and explanation of business cycles. The research strongly confirmed the older view that business cycles have large systematic components that take the form of investment cycles. These quasi-periodic movements can be represented as low order, stochastic, dynamic processes with complex eigenvalues. Specifically, there is a fixed investment cycle of about 8 years and an inventory cycle of about 4 years. Maximum entropy spectral analysis was employed for the description of the cycles and continuous time econometrics for the explanatory models. The central explanatory mechanism is the second order accelerator, which incorporates adjustment costs both in relation to the capital stock and the rate of investment. By means of parametric resonance it was possible to show, both theoretically and empirically how cycles aggregate from the micro to the macro level. The same mathematical tool was also used to explain the international convergence of cycles. I argue that the theory of investment cycles was abandoned for ideological, not for evidential reasons. Methodological issues are also discussed.

Continuous time econometrics, investment cycle, inventory cycle, maximum entropy spectral analysis, parametric resonance

Abstract:
The paper challenges the 'orthodox doctrine' of collective choice theory according to which Arrow's 'general possibility theorem' precludes rational decision procedures generally and implies that in particular all voting procedures must be flawed. I point out that all voting procedures are cardinal and that Arrow's result, based on preference orderings cannot apply to them. All voting procedures that have been proposed, with the exception of approval voting, involve restrictions on voters expressions of their preferences. These restrictions, not any general impossibility, are the cause of various well known pathologies. In the class of unrestricted voting procedures I favor 'evaluative voting' under which a voter can vote for or against any alternative, or abstain. I give a historical/conceptual analysis of the origins of theorists' aversion to cardinal analysis in collective choice and voting theories.

Arrow's paradox, approval voting, cardinal collective choice, instant runoff voting, plurality voting, voting paradoxes

Abstract:
The paper continues the author's work on a general theory for the aggregation of prices and quantities in relation to the money metric. The focus here is on the National Income and Product Accounts (NIPAs). It is shown that the measures that are currently being produced are seriously defective. This is true particularly with respect to real magnitudes and applies to traditional measures as well as those introduced more recently. Some further problems are discussed, that while less fundamental, may still seriously bias empirical results that rely on NIPA data.

Abstract:
The international movement to convert the real (deflated) components of the NIPAs to chain indexes, in order to assure timeliness, has introduced grave inconsistencies. Most importantly, the components no longer add up to the totals. The U.S. accounts which employ a Fisher chain have additional inconsistencies. For example, the product of the price and quantity indexes does not reproduce the change in nominal expenditure. The paper presents a unified approach to the construction of price and quantity measures which can be chained while maintaining every kind of consistency. The solution is based on a combination of elements from the theories of price indexes and consumer surplus.

Abstract:
The international movement to convert the real (deflated) components of the NIPAs to chain indexes, in order to assure timeliness, has introduced grave inconsistencies. Most importantly, the components no longer add up to the totals. The U.S. accounts which employ a Fisher chain have additional inconsistencies. For example, the product of the price and quantity indexes does not reproduce the change in nominal expenditure. The paper presents a unified approach to the construction of price and quantity measures which can be chained while maintaining every kind of consistency. The solution is based on a combination of elements from the theories of price indexes and consumer surplus.

Abstract:
In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow's theorem, all voting methods must be seriously flawed. Arrow's theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper, I point out that all voting methods are cardinal and, therefore, outside the reach of Arrow's result.

Parallel to Arrow's ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this, I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting.

A conclusion of the paper is that the defects of conventional voting methods result not from Arrow's theorem, but rather from restrictions imposed on voters' expression of their preferences.

The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior.

Approval voting, cardinal collective choice, evaluative voting, strategic voting, voting paradoxes

Abstract:
Utilitarian voting (UV) is defined in this paper as any voting rule that allows the voter to rank all of the alternatives by means of the scores permitted under a given voting scale. Specific UV rules that have been proposed are approval voting, allowing the scores 0, 1; range voting, allowing all numbers in an interval as scores; evaluative voting, allowing the scores -1, 0, 1.

The paper deals extensively with Arrow's impossibility theorem that has been interpreted as precluding a satisfactory voting mechanism. I challenge the relevance of the ordinal framework in which that theorem is expressed and argue that instead utilitarian, i.e. cardinal social choice theory is relevant for voting. I show that justifications of both utilitarian social choice and of majority rule can be modified to derive UV. The most elementary derivation of UV is based on the view that no justification exists for restricting voters' freedom to rank the alternatives on a given scale.

Approval voting, Arrow's impossibility theorem, cardinal collective choice, evaluative voting, majority rule, range voting, utilitarian voting

Abstract:
Utilitarian voting (UV) is defined in this paper as any voting rule that allows the voter to rank all of the alternatives by means of the scores permitted under a given voting scale. Specific UV rules that have been proposed are approval voting, allowing the scores 0, 1; range voting, allowing all numbers in an interval as scores; evaluative voting, allowing the scores -1, 0, 1.

The paper deals extensively with Arrow's impossibility theorem that has been interpreted as precluding a satisfactory voting mechanism. I challenge the relevance of the ordinal framework in which that theorem is expressed and argue that instead utilitarian, i.e. cardinal social choice theory is relevant for voting. I show that justifications of both utilitarian social choice and of majority rule can be modified to derive UV. The most elementary derivation of UV is based on the view that no justification exists for restricting voters' freedom to rank the alternatives on a given scale.

Approval voting, Arrow's impossibility theorem, cardinal collective choice, evaluative voting, majority rule, range voting, utilitarian voting

Abstract:
The paper elaborates the idea that voting is an instance of the aggregation of judgments, this being a more general concept than the aggregation of preferences. To aggregate judgments one must first measure them. I show that such aggregation has been unproblematic whenever it has been based on an independent and unrestricted scale. The scales analyzed in voting theory are either context dependent or subject to unreasonable restrictions. This is the real source of the diverse 'paradoxes of voting' that would better be termed 'voting pathologies'. The theory leads me to advocate what I term evaluative voting. It can also be called utilitarian voting as it is based on having voters express their cardinal preferences. The alternative that maximizes the sum wins. This proposal operationalizes, in an election context, the abstract cardinal theories of collective choice due to Fleming and Harsanyi. On pragmatic grounds, I argue for a three valued scale for general elections.

Approval voting, cardinal utility, instant runoff voting, plurality voting, voting paradoxes

Abstract:
The most important economic measures are monetary. They have many different names, are derived in different theories and employ different formulas. Yet, they all attempt to do basically the same thing: to separate a change in nominal value into a 'real part' due to the changes in quantities and an inflation due to the changes of prices. Examples are: real national product and its components, the GNP deflator, the CPI, various measures related to consumer surplus, as well as the large number of formulas for price and quantity indexes that have been proposed.

The theories that have been developed to derive these measures are largely unsatisfactory. The axiomatic theory of indexes does not make clear which economic problem a particular formula can be used to solve. The economic theories are for the most part based on unrealistic assumption. For example, the theory of the CPI is usually developed for a single consumer with homothetic preferences and then applied to a large aggregate of diverse consumers with non-homothetic preferences.

In this paper I develop a unitary theory that can be used in all situations in which monetary measures have been used. The theory implies a uniquely optimal measure which turns out to be the Törnqvist index. I review, and partly reinterpret the derivations of this index in the literature and provide several new derivations.

The paper also covers several related topics, particularly the presently unsatisfactory determination of the components of real GDP.

consumer price index, consumer surplus, money metric, price and quantity indexes, welfare measurement

Abstract:
The paper discusses conceptual errors in the methodologies for computing the national income and product accounts (NIPAs). Recent changes in methodology introduced by the statistical agencies have not touched some of these deficiencies and in other cases have substituted new problems for old ones. Unresolved conceptual problems involve the computation of GDP sectors in real terms, the definition of the GDP deflator and real national income, among others. The paper is addressed to: a. the producers of NIPA statistic, hoping to motivate them to improve their methods, b. the users of these statistics who should know exactly what they are getting and make optimal choices among the available alternatives. The paper also clarifies some general issues pertaining to the construction of price and quantity indexes.

Economic growth, GDP deflator, price index, quanity index, real GDP, welfare measurement

Abstract:
The paper presents a general theory of the aggregation of prices and quantities that unifies the field and relates topics that in the past have been treated separately and unsatisfactorily, or not at all. The theory does without the common but unrealistic assumptions of homotheticity, or representative agents and is valid with or without an explicit utility maximization assumption. Two different derivations are given, one in continuous time, using Divisia integrals, and one employing more traditional discrete arguments. The unifying concept is the money metric, which is interpreted as a partial welfare indicator, rather than as a comprehensive welfare measure. On this basis, a consistent set of chained price and quantity indexes for a set of additive time series, such as those in the national income and product accounts, is derived. All variants of the theory lead to Törnqvist indexes defined on the appropriate data set. A numerical example confirms that in the non-homothetic case, these indexes are superior both to Fisher's "ideal" index and to the consumer surplus approximation.

Chain Indexes, Consumer Surplus, Cost-of-living, Divisia Integral, Money Metric Price Index, Quantity Index, Real Consumption, Tornqvist Index