The implications of a third-order translog demand system and some empirical results

In this paper a homogeneity and symmetry unconstrained variant of the “third-order translog”, representing a third-order approximation to an indirect utility function, is derived. Using Christensen, Jorgenson and Lau's (1975) data, and subsequent observations to 1986, we estimate this third-order translog, and show that it dominates the homogeneity and symmetry unconstrained translog. The restrictions implied by homogeneity and symmetry, conditional on our third-order translog are also rejected. These results are of interest since they demonstrate that standard restrictions implied by the theory of consumer behaviour can be rejected even in the context of a fairly general model which has been estimated using aggregate, time-series data. However, it has been found that the inclusion of dynamic effects sometimes leads to non-rejection of theoretical restrictions (Anderson and Blundell 1983). Unfortunately, the use of aggregate, time-series data to estimate a dynamic, third-order translog would be problematic, since exact aggregation restrictions are imposeda priori and observations are limited. This suggests that it would be more appropriate to estimate the third-order translog using cross-sectional micro-data sets with many observations. This type of data is now available, and can be used to estimate systems of consumer demands. Furthermore, these data sets contain extensive information on demographic characteristics which, having recently been found to be important determinants of demand (Barnes and Gillingham 1984) can be included in general demand systems of the third-order translog type.     

The allocation of consumer expenditures in a Swedish macroeconomic model

The paper presents and estimates demand functions for components of consumer expenditures in Sweden, based on quarterly data for 1963–72. The model employed, while simple, possesses some attractive features. Income elasticities may be different from unity and complementary as well as substitutionary cross price effects are allowed. Aggregation restrictions hold at all points in time. Additional restrictions such as symmetry and zeroes are added. Results for Sweden from the model are compared to earlier findings by Dahlman and Klevmarken, Goldberger and Gamaletsos, Lluch and Powell, and Parks, who have tested double-logarithmic forms, the Linear Expenditure System, and the Rotterdam model.     

Bartlett adjustments for systems of linear equations with linear restrictions

Simple matrix formulae are derived for calculating a Bartlett adjustment to the likelihood ratio test statistic for testing linear parameter restrictions in a system of linear equations. For the special case of column and/or row restrictions on the matrix of coefficients the adjustment is a simple function of matrix dimensions being invariant to sample observations and the error covariance matrix. An example of testing for homogeneity and symmetry in a demand system is given.     

An almost ideal demand system for alcoholic beverages in British Columbia

An almost ideal demand system for alcoholic beverages in British Columbia is estimated based on five beverage categories. Estimates of the model unrestricted and restricted to satisfy homogeneity and symmetry are presented. The restrictions are tested: as is common in applied demand analysis a number of rejections are encountered, although within-equation tests tend to support homogeneity. The rejections which are encountered are not mitigated by the inclusion of dynamic elements. The Slutsky matrix is used to examine the concavity of the expenditure function, which is found to be mildly violated. Marshallian and Hicksian own-, cross-price, and income elasticities are calculated and are found to be largely consistent with previous findings, although some noteworthy results are obtained.     

Testing the integrability of consumer demand functions: Federal Republic of Germany, 1950–1973

The purpose of this paper is to implement a new econometric methodology for testing the theory of consumer behavior. We begin by fitting systems of indirect and direct demand functions without requiring integrability. We then impose restrictions on the parameters of these functions implied by integrability. We test restrictions corresponding to homogeneity, summability, symmetry, nonnegativity, and monotonicity of systems of demand functions. We formulate tests based on two-sided critical intervals for restrictions that take the form of equalities. We employ tests based on one-sided critical intervals for restrictions that take the form of inequalities. We present empirical results for tests of integrability for German time series data on personal consumption expenditures for the period 1950–1973.     

Stochastic generalizations of demand systems with an application to telecommunications

Systems of demand equations are considered for at least two reasons. First, they offer a theoretical completeness, and second, they embody a number of restrictions which lead to a more parsimonious specification concerning the number of parameters. As it turns out, the quantity and quality of the data are often such that the demand systems considered are not restrictive enough in the sense that large numbers of parameters still remain which cannot be estimated with ‘great precision’. Paradoxically, the restrictions that are considered are often rejected by the data.In this paper we propose a system of random coefficient telecommunications demand equations in a panel data framework. These equations correspond to alternative ways (which have different costs) of placing a call. The system is formulated in such a way that it incorporates the homogeneity condition, as well as stochastic versions of the symmetry and weak separability restrictions. The stochastic versions are given in terms of moments and so they do not have to hold in each individual case. Under certain conditions they reduce to their deterministic counterparts. Finally, we empirically implement the model and compare the results to what they would be in a corresponding deterministic framework.     

Long-run relations between private and public sector wages in Sweden

Using a maximum likelihood cointegration approach we find two long-run relationships between central government, local government, and private sector wages in Sweden. This means that there is one common trend for the three sectoral wages. Private sector wages are weakly exogenous for the estimation of the long-run relationships. This suggests that the private sector is the wage leader. Testing linear restrictions on the estimated cointegrating space, we reject stationarity for the three relative wages using likelihood ratio-tests. The hypotheses of homogeneity for the two cointegrating vectors, i.e., that wages do not diverge in the long run, is also rejected.     

A dynamic specification of an AIDS import allocation model

In this paper we use the first-order autoregressive scheme in order to introduce dynamics into the AIDS model. We also consider the theoretical restrictions of additivity, homogeneity and symmetry, and use two different specifications of the covariance matrix. We estimate the models using import allocation data for the UK 1952–1979 of five EEC countries and test different specifications against each other.     

Advertising effects in complete demand systems

A rationale for including advertising in complete demand systems is presented. An advertising analogue of the Slutsky equation is derived, and properties of the expenditure and indirect utility functions characterized. Empirical estimates of a complete demand system incorporating dynamic advertising effects support neoclassical restrictions; we do not reject homogeneity, or symmetry at the 1% level. This represents surprisingly strong support for neoclassical theory relative to prior parametric studies.     

The integrability of consumer demand functions

The purpose of this paper is to characterize the class of systems of consumer demand functions that are representable as ratios of first-order polynomial functions and are integrable. Starting from a general system of consumer demand functions representable as ratios, we impose successively the restrictions corresponding to homogeneity, summability, symmetry, non-negativity, and monotonicity. We find that the only such systems which are capable of modeling arbitrary own- and cross-substitution effects are the systems generated by transcendental logarithmic utility functions.     

Joint Allocation of Leisure and Consumption Commodities: A Japanese Extended Consumer Demand System 1979—90

In this study we estimate the parameters of a household expenditure function which includes joint choice of leisure and consumption commodities in scope without a separability assumption. We have used Japanese prices, wage rate, labour supply, and expenditure data on ten commodity groups, collected from 47 cities over 12 years. This data set has the advantage that separate observations are available for each data point for all the variables. We employed the AI demand system, for estimation. Controlling for time-specific effects, the result implied a definite rejection of the weak separability of labour supply and commodity choice, and non-rejection of the homogeneity and symmetry restrictions on the demand system. All the own-price elasticities are significantly negative, and both substitutes and complements are observed across commodity groups. As for the negativity, all but one of the eigenvalues of the substitution matrix are negative. The result as a whole showed consistency with demand theory. The estimated compensated labour supply elasticity is 0.39, which is in reasonable agreement with the previous studies.     

Generalized habit formation in an Inverse Almost Ideal Demand System: An application to meat expenditures in the U.S.

The Inverse Almost Ideal Demand System (IAIDS) model of Moschini and Vissa (1992) and Eales and Unnevehr (1994) is extended to include: (1) general, nonlinear, nonadditive habit effects; and (2) a specification for habit stock terms that allows purchases from the distant past to influence current consumption (long memory). The resulting models are compared with a linear habit effects model and a static specification. The empirical estimation is on U.S. quarterly meat expenditures (1961–1993), with each model being subjected to a battery of misspecification tests. Results of these tests, along with tests of homogeneity and symmetry restrictions, indicate clearly that the most generalized dynamic specification-the one with nonlinear, nonadditive long-memory habit stock effects-is preferred. Furthermore, persistence effects are found to be qualitatively important in that flexibility, consumption scale, and habit flexibility estimates differ, in some instances substantially, between alternative specifications.     

Empirical Regularities in Cross-Country Alcohol Consumption*

This paper analyses the demand for the three beverages: beer, wine and spirits, within alcohol, at a cross-country level for 10 countries: Australia, Canada, Finland, France, Japan, New Zealand, Norway, Sweden, the UK and the US. A number of empirical regularities were found at the cross-country level. This includes: (i) the demand theory hypotheses, homogeneity and symmetry are generally acceptable; (ii) the additive utility hypothesis is also acceptable even for such narrowly defined commodities; (iii) in nine out of the 10 countries, beer is considered as a necessity, in half of the countries wine is a necessity and in all the countries spirits are a luxury; and (iv)in all the countries, the demand for beer, wine and spirits are price inelastic.     

The forecasting ability of a cointegrated VAR system of the UK tourism demand for France, Spain and Portugal

This paper uses the vector autoregressive (VAR) methodology as an alternative to Deaton and Muellbauer’s Almost Ideal Demand System (AIDS), to establish the long-run relationships between I(1) variables: tourism shares, tourism prices and UK tourism budget. With appropriate testing, the deterministic components and sets of exogenous and endogenous variables of the VAR are established, and Johansen’s rank test is used to determine the number of cointegrated vectors in the system. The cointegrated VAR structural form is identified and the long-run structural parameters are estimated. Theoretical restrictions such as homogeneity and symmetry are tested and not rejected by the VAR structure. The fully restricted cointegrated VAR model reveals itself a theoretically consistent and statistically robust means to analyse the long-run demand behaviour of UK tourists, and an accurate multi-step forecaster of the destinations’ shares when compared with unrestricted reduced form and first differenced VARs, or even with the structural AIDS model.     

Retesting symmetry and homogeneity in a cointegrated demand system with bootstrapping: The case of meat demand in Greece

A small Almost Ideal Demand System is estimated for Greek meat consumption using the Johansen procedure in conjunction with parametric bootstrapping and Bartlett corrections. Asymptotic Wald and likelihood ratio tests broadly support the predicted number of cointegrating relationships but reject symmetry and homogeneity. Bootstrapping and Bartlett corrections give support to symmetry and homogeneity but give less support for the predicted number of cointegrating relationships.Jel classification: C32 D12First version received: September 2001/Final version received: March 2003     

Economic and demographic factors in U.S. alcohol demand: A growth-accounting analysis

During the 1980s, per capita consumption of absolute ethanol in the U.S. declined by 14 percent. In 1979, consumption was 2.94 gallons per capita compared to 2.52 gallons in 1989. The objective of this paper is to explain the decline in consumption, both for total ethanol and by beverage. The historical growth of ethanol demand is decomposed into several components, with emphasis on the role of relative prices, real income, and demographic factors. Using the Rotterdam model of a demand system, I first estimate the conditional demand for ethanol for each of the three beverages (beer, wine, distilled spirits). Second, I estimate the composite demand for total ethanol. Both sets of estimates are obtained using quarterly data for the period 1974–90. The estimates are tested for conformity with the theoretical restrictions of homogeneity, symmetry, and negativity. The decomposition analysis indicates a positive net effect for the combined impact of autonomous trend, real income growth, and relative price changes, both for total ethanol and each of the three beverages. The negative growth of per capita ethanol consumption is attributable to an increase in the proportion of the population aged 65 and over and a simultaneous decline in the proportion of the population aged 18–29.     

A linear demand system within a seemingly unrelated time series equations framework

A seemingly unrelated time series equations framework for the linear almost ideal (AID) demand system is considered. The framework is applied to a consumer demand system covering nine non-durable commodities. Within a specification where the static linear AID system is augmented by latent variables representing stochastic trends and seasonality, demand homogeneity is tested; both in each equation and in the system as a whole. Income and own-price elasticities are calculated under homogeneity restrictions. Although the homogeneous model is formally rejected by statistical tests, it performs well with respect to interpretability, parameter stability and forecasting.     

经济波动同步性、需求冲击与供给冲击——来自海湾国家的实证分析

本文运用结构向量自回归模型,将海湾六国产出的同步波动性和遭受冲击的对称性联系起来。研究发现,1977-2006年间海湾六国遭受需求冲击的对称程度要高于供给冲击,对称性的需求冲击对维持六国经济周期的同步性既显著又重要,而供给冲击的对称性对维持六国经济周期的同步性几乎没有作用;另外,本文没有发现供给和需求冲击的对称性对经济周期的同步波动有滞后影响。本文实证研究的结果对于海湾六国未来单一货币的汇率制度选择具有重要的参考意义。     

Should a team be homogeneous?

Should an organization hire people with similar backgrounds or with different backgrounds? We formulate this question within the framework of team theory. The team is formed by n agents. The type of each agent is endogenous and determines his information structure and his cost for the team. We show that the sign of complementarity between jobs determines workforce homogeneity. With positive complementarities, the team should be composed of agents of the same type, while, with negative complementarities, workforce heterogeneity is optimal. These results do not rely on the restrictions on the way uncertainty is modeled or on the feasible set of agent types: they can be explained in terms of correlation between errors committed by different agents.     

Smuggling around the world: evidence from a structural equation model

This article uses a Multiple Indicators Multiple Causes (MIMIC) model to analyse the determinants of smuggling. The analysis reveals that higher corruption and a lower rule of law encourage smuggling. Tariffs and trade restrictions are important push factors, while a higher Black Market Premium (BMP) discourages smugglers. Based on the MIMIC estimates, we calculate an index of smuggling which provides a ranking for 54 countries. We find that smuggling is rampant in Cameroon, Pakistan and Kenya while it is least prevalent in Switzerland, Finland and Sweden.