Composite Commodity Research Articles

The Generalized Composite Commodity Theorem and Food Demand Estimation

AbstractThis article reports tests of aggregation over consumer food products and estimates of aggregate food demand elasticities. Evidence that food demand variables follow unit root processes leads us to build on and simplify existing tests of the Generalized Composite Commodity Theorem. We compute food demand elasticities using a method of cointegration that is shown to apply to a convenient but nonlinear functional form. Estimates are based on consumer reported expenditure data rather than commercial disappearance data.

Testing aggregation consistency across geography and commodities*

Consistent aggregation of production data across commodities and Western USA states was tested using Lewbel's generalised composite commodity theorem. The applicability of the generalised composite commodity theorem for testing consistent geographic aggregation was demonstrated and applied to two groups of states. Consistent commodity aggregation was tested in each state for two output groups and three input groups and in one state for a larger number of groups. Most tests for commodity aggregation supported consistent aggregation of inputs but not outputs. Consistent geographic aggregation was supported for each output and input category across Pacific Northwest states but only for inputs across all Western states.

Tests For Market Integration and the Law of One Price: The Market For Whitefish in France

This paper examines the relationship between causality models and cointegration models in testing for price integration and the Law of One Price (LOP). In our review, we show that cointegration models, which allow for nonstationarity in prices, are a natural extension of the traditional causality methods and not an alternative approach. Hence, the two approaches investigate the same economic hypotheses; however, the choice of modeling method depends on the time series properties of the data. An empirical analysis is provided using prices from the whitefish market in France. With nonstationary price data, the causality approach over rejects the hypothesis of the LOP, whereas conintegration models provide evidence for a well-integrated whitefish market. A generalized version of the composite commodity theorem holds, and prices of most whitefish species can be aggregated into a single commodity price index.

The Generalized Composite Commodity Theorem: Stronger Support in the Presence of Data Limitations

Because of common data limitations, the existing testing framework for the generalized composite commodity theorem (Lewbel, 1996) is incomplete. This note clarifies and strengthens the testing procedure by implementing modified Bonferroni procedures. The conditions are established for consistency between the existing and modified Bonferroni tests. In an empirical application, the Bonferroni tests provide more powerful support for the generalized composite commodity theorem than is obtained from the existing test.

Money as a Mechanism in a Bewley Economy

We study what features an economic environment might possess, such that it would be Pareto efficient for the exchange of goods in that environment to be conducted on spot markets where those goods trade for money. We prove a conjecture that is essentially due to Bewley [1980, 1983]. Monetary spot trading is nearly efficient when there is only a single perishable good (or a composite commodity) at each date and state of the world; random shocks are idiosyncratic, privately observed, and temporary; markets are competitive; and the agents are very patient. This result is a fairly close analogue, for trade using outside, fiat money, of a recent characterization by Levine and Zame [2002] of environments in which spot trade using inside money, in the form of one-period debt payable in a commodity, is nearly Pareto efficient. We also study a example where expansionary monetary mechanism Pareto dominates laissez-faire or contractionary monetary mechanism in an environment with impatient agents.

CAN AGGREGATION ACROSS GOODS BE ACHIEVED BY NEGLECTING THE PROBLEM? PROPERTY INHERITANCE AND AGGREGATION BIAS*

This article studies the problem of composite commodity in two different frameworks. In one case, aggregation across goods is analyzed for elementary goods that satisfy an optimality condition. The unrestricted case is also examined. The notion of an approximate aggregate representation is formalized and shown to be always possible. Can thereby aggregation issues simply be neglected in economic contributions? I show that the standard economic properties of initial functions are not necessarily inherited by the approximate aggregate. The severity of this problem and the size of the aggregation bias across inputs are investigated empirically.

On the Nature of Neighbourhood

The paper advances the conceptualisation of neighbourhood by specifying it as a bundle of spatially based attributes associated with clusters of residences, sometimes in conjunction with other land uses. There follows a discussion of how this 'composite commodity' definition relates to the planning challenge of spatially bounding neighbourhood. The paper then probes the myriad idiosyncrasies associated with the concept of neighbourhood: cross-attribute variation in durability and ability to be priced, relativistic evaluations of attributes and consumption impacts on attributes. It discusses how, within this new paradigmatic context, neighbourhoods are produced by the same actors that consume them: households, property owners, business people and local government. Finally, consideration is given to various aspects of the origins and nature of neighbourhood change and it is argued that neighbourhood dynamics are rife with social inefficiencies.

Aggregation without separability: Composite commodity theorems in quantity-space

In this paper, we provide an obvious extension of the Composite Commodity Theorems to the case of inverse demands, where quantities and not prices can be used for aggregation. First, the Hicks–Leontief commodity theorem is extended to the quantity space, and then its generalised stochastic version is presented.

Willingness to Accept, Willingness to Pay and the Income Effect

The disparity between willingness to pay and willingness to accept in experimental and survey settings remains a troubling anomaly. Willingness-to-accept is almost always higher than WTP, often substantially higher. Our interest lies with the neoclassical explanation of Hanemann, who demonstrates that for exogenous quantity changes, the difference between WTP and WTA depends ratio of the ordinary income elasticity of demand for the good to the Allen-Uzawa elasticity of substitution between the good and a composite commodity. When the elasticity of substitution is low, this ratio will be large. The ratio WTA/WTP will then also be large. We use a result of Sugden to formulate the WTA/WTP ratio as a function of the income effect on WTP. We find that the WTA/WTP ratios provided by our comprehensive literature search imply income elasticities and income effects that are implausibly high; much higher than income effects found in the literature; and much higher than income elasticities estimated in the set of studies from which the WTA/WTP results are drawn. Based on the evidence, it is difficult to accept the idea that the observed ratios of WTA/WTP, garnered from a remarkably large and diverse set of studies, are consistent with a standard neoclassical model. Substitution among goods seems an inadequate explanation for the divergence between WTA and WTP.

Adam Smith’s division of labor and structural changes

This paper considers two different cases of division of labor: (i) the subdivision of different operations in order to produce a particular product in a given firm or plant; (ii) the specialization of firms in the same industry. Division of labor of the former type is limited by demand for output of a particular firm or plant, while division of labor of the latter type is limited by demand for the industry as a whole. It is argued that, in the case of an industry producing a homogenous product, an increase in the scale of production of any particular firm is likely to be associated with changes in the internal division of labor. In the case of inter-firm division of labor, decreasing unit costs may result from lateral disintegration. Finally, in the case of an industry producing a composite commodity (that is, a commodity composed of many different sub-commodities), firms’, disequilibrium behavior may lead to concentration of each firm to fewer sub-commodities, in the anticipation of the entry of new firms, or as a result of it.

Aggregation without Separability: Tests of the United States and Mexican Agricultural Production Data

AbstractThe generalized composite commodity theorem (GCCT) and testing procedure is extended to test for consistent aggregation of the United States and Mexican agricultural production data in each category for which earlier tests rejected homothetic separability. Nonrejected GCCT and separability hypotheses provide empirical support for aggregating all the United States agricultural outputs into as few as two categories: crops and livestock. Mexican agricultural outputs also can be aggregated into as few as two categories. Support for aggregating all outputs into a single category is ambiguous in both countries and is only provided by the GCCT.

Markets for Composite Goods

The usual assumptions about preferences and production technologies are easily justified when they involve elementary goods (differentiated by dates, locations, and states of nature). But it is far less easy to come up with direct justifications when only composite goods are traded. We show that the equilibria defined by the equality of supply and demand of composite goods coincide with the Walrasian equilibria of suitably defined economies whose commodity space is the composite commodity space. This shows in particular that the relevance of the general equilibrium model is essentially independent of the level of commodity aggregation. Journal of Economic Literature Classification Numbers: D50, D51, D61.

On Housing Services

The paper reconsiders the theoretical motivation for studying the housing market by means of the concept “housing services.” The analysis uses a model of consumer behavior that takes into full account the heterogeneity of housing. An assumption about the hedonic price function allows the researcher to define a scalar indicator of housing quality, that can be interpreted as the quantity of housing services available at a constant price per unit if a second assumption about the hedonic price function is made. The central result can be considered as an extension of Hicks' composite commodity theorem to cases in which expenditure on a bundle of characteristics is a nonlinear function of the quantities of these characteristics. The assumptions needed for aggregation impose testable restrictions on the hedonic price function, and a procedure for testing their validity is proposed. The basis of this approach is an econometric method for estimating functions with discrete explanatory variables without imposing assumptions about their functional form. This allows one to test the validity of the aggregation conditions essentially without joint assumptions. The method is applied on the basis of data for the two largest Dutch cities. The conditions for a constant price per unit of housing services are violated. Aggregation of bundles of housing characteristics into a scalar measure, which may alternatively be inter_preted as a quantity of housing services available at a varying price per unit, appears to be possible for the data used. However, the concept housing services loses much of its convenience if it cannot be used in combination with a constant price per unit.

A simple existence proof of demand functions without standard transitivity

This paper discusses the need for transitivity with respect to the existence of demand functions. It is known that one can prove the existence of a demand function without an explicit transitivity axiom, provided a convexity assumption is imposed on preferences, together with the conditions of completeness and continuity. In this paper, it is proved that convexity actually implies transitivity of the weak preference relation on line segments. On the basis of this result, and on the composite commodity concept, a very simple existence proof of demand functions is given, without the use of the standard transitivity axiom.

An expository note on the composite commodity theorem

This note offers an alternative derivation of the composite commodity theorem using only elementary economic and mathematical tools. It offers some insight as to why constancy of relative prices induces separability in the consumers optimization problem. It should be more readily accessible to students in upper level microeconomics courses and prove useful in the classroom in presenting this central theorem of economic analysis.

Quality Variation and Quantity Aggregation in Consumer Demand for Food

AbstractViewing the problem of “quality” variation in consumer demand for food asa problem of valid aggregation over goods leads to new insights. The simple sum of physical quantities, used as the measure of demand in the “quality” literature, is found to be a theoretically arbitrary and potentially misleading measure of demand when goods are heterogenous. Alternative measures of demand derived from restrictions on quality variation, consumer preferences, or relative prices, are investigated. A hypothetical example illustrates the use of a Hicksian composite commodity assumption. The empirical as well as conceptual merits of the various measures are discussed.

Quantity Aggregation in Consumer Demand Analysis when Physical Quantities are Observed

A method for estimating price and income elasticities from cross section data devised by Deaton (1986, 1987, 1988) makes implicit use of the Hicks' composite commodity theorem. Recognition of this fact allows theoretically rigorous definition of aggregate composite quantities. A comparison of elasticities of Hicks' composite with elasticities of simple physical quantity measures for the Ivory Coast and the United States demonstrates that use of physical quantity measures can be severely misleading when commodity heterogeneity is substantial. Copyright 1990 by MIT Press.

A Dynamic Multisector Economywide Model for Kuwait “The Impact on Growth, Welfare and Population Balance”

A dynamic multisector CGE model is constructed to analyze the medium-term path of the Kuwaiti economy. The model is in the applied general equilibrium tradition emphasizing the role of structural factors in the macro-economy and is based on a static within-period and dynamic inter-period components. The first component can be described as a twelve-sector, demand-driven model with a supply-determined oil sector and imports that are treated as a part of composite commodity. The second component expands the short-run adjustment to a medium-term run by capturing the dynamic changes in population structure, capital stock and government assets held abroad. The reference path generated by the model showed a modest growth of GDP components, a slight improvement in Kuwaiti population ratio, and a dramatic drop in per Kuwaiti general fund. Increasing investment expenditure in non-oil sectors improved the per capita Kuwaiti household income but deteriorated the per capita general fund and population balance. The increase in investment income from abroad produced similar effects on per capita income and population balance but improved the performance of the per capita general fund. The increase in participation of Kuwaitis is mainly felt in the population balance. Its effect on GDP growth and per capita indicators is very limited.

Estimating the demand for housing characteristics: A survey and critique

Many economists criticize the concept of the composite commodity'of housing that forms the basis of modern urban economics. As a result, much empirical work has been produced that attempts to estimate the household demand for housing and locational characteristics. The purpose of this paper is to take stock of the literature. The theoretical foundations of the literature and the econometric procedures employed are analyzed and critiqued. In addition, the empirical results are examined in order to identify any patterns that exist. The principal conclusion of this survey is that the theoretical basis is sound, but the econometric applications leave much to be desired. One consequence is that the literature has produced few empirical regularities. Another is that more studies using better estimation procedures and better data are needed before it can be safely argued that the composite commodity concept is replaced by the characteristics approach.

Efficiency and Equity in the Provision of Public Education

The paper focuses on the benefits derived from public elementary and secondary education; monetary values of households' perceived benefits from operating expenditures are estimated. Information concerning the preference mappings of citizens is obtained using a random utility model to analyze micro voting data. The estimated model in turn provides information concerning the efficiency and distributional consequences of public education expenditures. The conclusion is that operating expenditures exceed the estimated efficient level. Furthermore, it may be difficult to justify the inefficiently large expenditures on equity grounds since the estimated distribution of households' perceived benefits, net of local taxes, is pro-rich. G~ OVERNMENT provision of goods and I J~ services has the potential of greatly affecting the welfare of citizens. This paper focuses on the benefits derived from one such service, public elementary and secondary education; monetary values of households' perceived benefits from public education expenditures are estimated. Information concerning the preference mappings of citizens is obtained using a multinomial probit, random utility model to analyze micro voting data. The estimated model in turn provides information concerning the efficiency and distributional consequences of public education expenditures. The conclusion is that operating expenditures exceed the estimated efficient level. Furthermore, it may be difficult to justify the inefficiently large expenditures on equity grounds since the estimated distribution of households' perceived benefits, net of local taxes, is pro-rich. In contrast to this study, a number of studies employ ad hoc rules to measure citizens' benefits from public elementary and secondary education. Initially total benefits are assumed to equal the cost of educational services; this input cost measure of benefits is then allocated to households using some unproven rule of thumb.' When an ad hoc rule is used to allocate a questionable measure of total benefits, the results are even more suspect. Conceptually, it is quite odd to determine (assume) total benefits and then allocate the total to individuals or households. The correct method is first to obtain estimates of individuals' or households' benefits. These estimates can then be used to determine the magnitude of total benefits and analyze how the benefits are distributed across the population. Aaron and McGuire (1970) criticize ad hoc benefit measures and propose the income value measure. For X' units of the politically allocated good X this measure is IV = MRSj X' where MRSj is the marginal rate of substitution of X for a composite commodity evaluated at X' and one's aftertax income. This measure is comparable to measures of the income values of goods purchased in private markets. While Aaron and McGuire argue for preferencebased benefit measures, the lack of information concerning preference mappings necessitates that they assume the shape of the utility function. Even though the results by Maital (1973), based on a similar method, are slightly less restrictive, a number of restrictive assumptions are common to both studies. Not only are households assumed to have identical, separable utility functions, but the existing levels of politically allocated goods are assumed to be efficient, implying the total income value equals the input cost. Also, the allocation of benefits from mixed goods (e.g., public education) between public and private components is based on ad hoc rules. The major contribution of the current study is that the benefit estimates are based on information concerning the preference mappings of individuals as revealed through referenda voting.2 The estiReceived for publication March 9, 1983. Revision accepted for publication June 4, 1984. *State University of New York-Albany. This paper was improved as a result of the advice and encouragement of Kenneth Wertz, John Akin, David Guilkey and James Wilde, as well as the helpful comments of two referees. Financial support for this research was, in part, provided by a Dissertation Research Fellowship from the Brookings Institution. 1 An example is the 1967 Tax Foundation Study. 2NMicro voting data are also used by Rubinfeld (1977) to obtain information about citizens' preferences for public school expenditures; he uniquely estimates the parameters of a demand function up to an unknown multiplicative constant. A micro demand function for education is uniquely estimated by Bergstrom, Rubinfeld, and Shapiro (1982), using a different type of survey data. While the method used here is to directly estimate preference mappings, the information concerning such mappings embedded in such a demand function provides an