Economic Theory Of Index Numbers Research Articles

Generation and Distribution of Productivity Gains in French Agriculture. Who are the Winners and the Losers over the Last Fifty Years

This paper offers an approach based on the economic theory of index numbers that revisitsthe classical surplus accounting technique. We measure the productivity gains and the combinedeffects of output and input price variation on French farmers’ income between 1959 and 2011, for thewhole agricultural sector. During this period, total factor productivity grows at an average annual rateof 1.4% mainly due to a decrease of input quantity over the last thirty years while output volume hasstagnated since the end of the nineties. Over the whole period, with a share of nearly 70% of the globalsurplus, the customers appear as the main beneficiaries of these productivity gains through a decreasein agricultural and food prices. Farmers only retained 23% of the surplus corresponding to a lowincrease in farm income. Finally, the suppliers and taxpayers are the losers in the surplus distributionvia respectively a significant decrease of relative intermediate input prices and a substantial growth ofpublic subsidies in favour of the agricultural sector.

Aggregation of Price Risk over Commodities: An Economic Index Number Approach

AbstractThis article extends the economic theory of index numbers to the aggregation of price risk over commodities in production. Superlative indexes of aggregate price risk are related to Tornqvist and Fisher—type output quantity indexes. An application to major crops in Manitoba illustrates the empirical importance of the analysis.

More on stochastic index numbers

There are three major approaches used to estimate index numbers. The first is Fisher's test approach whereby indexes are judged on their ability to satisfy certain criteria. The economic theory of index numbers is the second approach and this deals with their foundations in utility theory. The third approach is a less well-known methodology, but one which is now attracting considerable attention, the stochastic approach which is a new way of viewing index numbers in which uncertainty and statistical ideas play a central role. While providing a point estimate for the index number like the other two approaches, the stochastic approach additionally provides the SE of the point estimate. This article enhances understanding of stochastic index numbers by showing that they are formally equivalent to the familiar optimal combination of forecasts with the individual prices playing the role of n forecasts of the overall rate of inflation. This leads to new analytical results on the impact of adding additional information within the stochastic approach framework. We provide two concrete examples of the sources of such additional information: (i) the quantity theory of money; and (ii) the use of quantity data in addition to price data. We also illustrate some of these theoretical results using real data.

The Measurement of Growth under Embodied Technical Change

De nouvelles statistiques americaines provenant du NIPA contredisent certains des fameux faits stylises de Kaldor et invitent a une reformulation de la theorie moderne de la croissance economique. Parmi ces faits nouveaux, deux sont a mettre en avant plus particulierement : une baisse continue du prix relatif des biens durables et une hausse continue du ratio equipement reel sur PIB reel. Pour etre en accord avec ces nouveaux faits stylises, les modeles de croissance doivent inclure au moins deux secteurs et s’attaquer au probleme de la definition du produit agrege. Dans cet article, nous utilisons la theorie economique des nombres-indices pour definir le taux de croissance du produit reel dans un modele de croissance avec changement technique incorpore. Les principaux resultats sont les suivants : (i) la methode du NIPA mesure la croissance conformement a la theorie economique des nombres-indices, et (ii) lorsque le taux de croissance est mesure comme le fait le NIPA, nous trouvons que la contribution du changement technique incorpore a la croissance du PIB par tete aux Etats-Unis est de 69%. Ceci confirme l’hypothese selon laquelle le changement technique incorpore est important pour la croissance.

Das Ideal des „reinen Preisvergleichs“ / The Principle of "Pure Price Comparison“

Zusammenfassung Dem Laspeyres Preisindex mit einem konstanten Warenkorb wird regelmäßig eine mangelnde theoretische Fundierung vorgeworfen. Es ist zuzugeben, dass dieses bei Praktikern der Preisstatistik nach wie vor beliebte, wenngleich von Theoretikern kritisierte Konzept nicht sehr klar ausformuliert ist. Kann man einen Preisvergleich nur dann als „rein“ bezeichnen, wenn das Wägungsschema (der Warenkorb) konstant gehalten wird? Ist der Gedanke des reinen Preisvergleichs, den zu konkretisieren das Ziel dieses Beitrags ist, kompatibel mit dem Konzept „superlativer“ Indizes? Es zeigt sich, dass das Laspeyres Konzept dem Gedanken des reinen Preisvergleichs am besten entspricht, weil es sowohl eine Zeitreihenbetrachtung als auch eine Ausgabeninterpretation impliziert. Es ist eine Operationalisierung des „reinen“ Vergleichs.

The Measurement of Growth under Embodied Technical Change

New U.S. evidence from NIPA contradicts some of the well-known Kaldor stylized facts, and call for a reformulation of the modem theory of economic growth. Among these new facts, two must be stressed : A permanent decline in the relative price of durable goods, and a permanent increase in the real equipment to real GDP ratio. To be consistent with these new facts, growth models must include at least two sectors and address the problem of defining aggregate output. In this paper, the economic theory of index numbers is used to define the growth rate of real output in a growth model with embodied technical change. The main findings are : (i) NIPA's methodology measures growth in accordance with the economic theory on index numbers, and (ii) when the growth rate is measured as in NIPA, the contribution of embodied technical change to per capital GDP growth in the U.S. is 69%, which reinforce the claim that embodied technical change is important for growth.

Measurement of export prices and changes in product quality

In this paper, the economic theory of index numbers is applied to the construction of industry-level export price indices and export quality indices. These indices are used to make consistent comparisons of export prices and qualities at the same or different points in time. Evidence of quality change over time was found to be an important phenomenon in explaining the variation of unit value indices over time and across countries for some European Union trade flows. About half of the unit value differences among destination countries can be explained by quality differentials. The quality-corrected price indices are potentially useful in any empirical application in which accurate measures of export prices are needed.

Productive restructuring, costs, and profit margins in the industrial countries

By recurring to a restricted cost function and applying recent developments in the economic theory of index numbers, improvements of technological efficiency in the six major industrial countries have been measured and inequality between prices and total unit costs have been rationalized. In such a world price-cost margins different from zero depend upon a non optimal level of utilization of capacity. Moreover, in order to ascertain the level of competitiveness of the various countries (and not the rate of change of competitiveness) Purchasing Power Parity exchange rates which equalize total unit costs were compared with actual exchange rates.

Regional energy input prices in Canadian manufacturing: An index number approach

Index number analysis is used to investigate the intertemporal and interspatial price behaviour of energy inputs in the manufacturing sector in the 10 provinces of Canada. The indices which are used are ones with desirable characteristics from the viewpoint of either descriptive index number theory or the economic theory of index numbers.

Alternative measures of effective exchange rates for agricultural trade

Alternative measures of multilateral exchange-rate changes appropriate for agricultural trade are analyzed. The economic theory of index numbers was consulted in analyzing published exchange-rate indices and in constructing new indices. Comparisons among indices were made for the period 1970-85, and differences were found to be significant. Results were particularly sensitive to the use of global rather than bilateral trade weights used in the U.S. Department of Agriculture index. The relative importance of alternative exchange-rate measures and trade elasticities is illustrated in terms of an agricultural trade model. Copyright 1987 by Oxford University Press.

Multilateral Productivity Comparisons of Selected Asian Developing Countries

The rapid growth experiences of several Asian countries during the past decade raise the need and interest to measure their performances more accurately, and to make sensible comparisons among these countries and other industrialized nations. This study applies the modern economic theory of index numbers for international comparisons of output, input, and productivity for five ASEAN countries (Indonesia, the Philippines, Thailand, Malaysia, and Singapore) and Hong Kong, Taiwan, and Korea. The comparisons are made for nine outputs and three factors across countries over time. The method of bilateral and multilateral translog index numbers developed by Caves, Christensen, and Diewert [1982a] along the line of the Tornqvist-Theil approximation to the Divisia index formula (Diewert [1976], Caves, Christensen, and Diewert [1982b]) is employed to perform international comparisons of productivity. Although the metho dology used is relatively new, it is used in the growth study of the United States and Japan (Jorgenson and Nishimizu [1978]), and in the study of regional performance of Canadian manufacturing (Denny, Fuss and May [1981]) among others. Multilateral productivity index comparison is extended recently by Pittman [1983] to include the undesirable outputs in the production function. This paper is an empirical application of index numbers to measure and compare productivity for several developing Asian countries. The focus is on the analysis of pro ductivity growth of aggregate factors and that of technological differences among various output sectors. It is assumed that each of these countries consists of a group of aggregate

The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity

The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity

Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers

Early in this century economists began to give serious attention to making comparisons using index number techniques. There was extensive debate as to which index number formulas were the most appropriate for carrying out comparisons.1 The debate was extensive in no small part due to the lack of agreement as to criteria for preferring one formula over another. In recent decades there has been a resurgence of interest in index numbers, resulting from discoveries that the properties of index numbers can be directly related to the properties of the underlying aggregator functions that they represent. The underlying functions - production functions, utility functions, etc. - are the building blocks of economic theory, and the study of relationships between these functions and index number formulas has been referred to by Samuelson and Swamy (I974) as the economic theory of index numbers.2 A key development in the economic theory of index numbers has been the demonstration that numerous index number formulas can be explicitly derived from particular aggregator functions. This development provides a powerful new basis for selecting an index number procedure. Rather than starting the selection process with a number of plausible index number formulas, one can specify an aggregator function with desirable properties and derive the corresponding index number procedure. The resulting index is termed exact for that particular aggregator function. Diewert (I976) makes a strong case for limiting the consideration of aggregator functions to those which are flexible, i.e. those which can provide a second order approximation to an arbitrary aggregator function. He has termed index numbers that are exact for flexible aggregator functions 'superlative '. There are two superlative index numbers that are of particular interest - the Fisher Ideal index and the Tornqvist-Theil-translog index. Fisher (I 922) dubbed the following index Ideal since it best satisfied his several criteria for choosing among index numbers:

THE MEASUREMENT OF REAL INCOME

This paper is about the theory of the measurement of real income. By “theory of measurement” I mean the characterization of statistical terms as variables in a model, just as real consumption is characterized as an indicator of utility and the consumer price index is characterized as the cost of attaining a given level of utility in the economic theory of index numbers developed by Konus, Frisch and others half a century ago. I identify five logically distinct and internally‐consistent concepts of real income: maximum sustainable consumption, consumption plus the output of new capital goods, consumption plus the increase in the capital stock where capital can be measured in two quite separate ways, and the sum of actual consumption and consumption forgone in the investment process. The last of these concepts is the most appropriate as a guide to producing long time series of real income for measuring a country's rate of economic growth.

The Economic Theory of Index Numbers

Ti-iIS paper attempts a synthesis of what might be called the classical economic theory of index numbers, developed by Staehle and others,' with the later work of Hicks2 and Samuelson.:3 The problem can be expressed in its simplest form as follows. A given individual consumer is considered in two situations, i and z, usually (but not necessarily) two points of time. Complete price-quantity data are available for the consumer in each of the situations, i.e., the prices of (n + i) commodities, Pl, P', Pl . . P.1p(), and the quantities purchased, ql, ql', q1 . . . ql(n), at situation i, and the corresponding prices and quantities denoted with a suffix z at situation 2. A definite preference map, subject to the usual conditions of convexity, etc., is assumed for the consumer in each situation, but the map for situation i may be different from that for situation 2. The consumer is assumed to have free choice. In particular, nothing will be said about a situation in which there is rationing. Can we define an index of the change in prices and an index of the change in the volume of consumption from situation i to situation z ? If so, can we obtain a measure of each index or, at least, limits for each index ? We can start with the problem of the price index. A perfectly definite index of price change can be defined for the consumer for situation i, which has reference only to the indifference level I, on which the consumer finds himself at this situation. The index, P12 (situation i), is the income which leaves the consumer on the indifference level I, when expended optimally at prices (P2), divided by the actual income expended at prices (Pl). Here the prices (P2) can be regarded as a hypothetical alternative to the prices (Pl) in situation i. There is no reference to the behaviour of the consumer in situation 2 ; the index is independent of the preference map of situation z and of the purchases (q2) made in this situation. We know what purchases (ql) the consumer makes in situation i ; to derive the index we should need to know the purchases, call them (q), he would make if the prices had been (P2) to maintain the same indifference level. We are not interested in what the consumer actually does at prices (p2) in situation 2. By definition, then: