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.     

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.     

On the disaggregation of excess demand functions when prices and aggregate income vary independently

Under the assumption that prices and aggregate income can vary independently and that the income distribution scheme is known and homogeneous of degree 1 in prices and aggregate income, I raise the question of the restrictions on aggregate excess demand behavior implied by the postulate of rationality of individual agents. If the number of agents is at least as high as the number of commodities, aggregate excess demand need not satisfy, at a point, any restrictions other than homogeneity of degree 0 and Walras' law. Furthermore, if the number of agents, m, is less than the number of commodities, l, aggregate excess demand can be locally arbitrary when projected on an m-dimensional subspace of the commodity space.     

Consumer demand functions,Spain, 1958–1964

Barten's maximum likelihood method (European Economic Review, Fall 1969) is used to estimate demand systems for Spain, under the assumptions of constant elasticities and constant marginal budget shares, respectively. It is shown in which sense the second assumption gives “better” results. In both cases, the homogeneity restriction is rejected, using the maximum likelihood ratio test. But once homogeneity is imposed, the symmetry restriction cannot be rejected.     

The interest elasticity of household savings: a structural approach with German micro data

This paper empirically investigates the effects of changes in the interest rate as well as in the current and expected future consumer price levels on households’ consumption–savings decision. In a structural demand model applied to German consumption data, we use cross-sectional and longitudinal variation in prices and tax rates to construct individual after-tax interest rates and cluster-specific consumer prices. We find that the compensated own-price elasticities for savings as well as consumption are significantly negative, while the theoretical model implications of homogeneity and symmetry must be rejected. Importantly, we estimate the uncompensated interest rate elasticity of savings, in line with the literature, at around zero. Some heterogeneity in this elasticity is found along the savings and wealth distribution. We conclude that short-term policy-induced variation of net returns to savings is expected to have no significant effects on the level of compound savings.     

The analysis of consumer demand in Greece. Model selection and dynamic specification

The paper analyses the pattern of consumer demand in Greece exploring systematically the questions of the functional form of demand that best fits the data, the appropriate dynamic structure and the empirical validity of the constraints of demand theory. A general dynamic Almost Ideal demand model for four categories of consumer non-durables for the period 1958–1994 is estimated. The maintained specification rejects the static AI, its counterparts implied by the partial adjustment and autoregressive disturbances models and, upon applying a non-nested test, the Rotterdam specification. However, it cannot reject homogeneity and symmetry nor the hypothesis of structural stability.     

The econometric modelling of aggregate consumer behaviour

This paper examines several problems involved in modelling the structure of consumer behaviour. A new model of consumer demand is presented which encompasses the indirect translog, the CES and the LES as special cases, enabling nested comparisons to be made. Within this framework we show that acceptance of zero-degree homogeneity and/or symmetry of the Slutsky matrix is heavily dependent upon the structure within which inferential tests are carried out, and that great care must be utilised in formulating nested hypotheses and drawing inferences on the basis of χ² and F-statistics. We then show that conventional econometric work implies that consumer preferences must be homothetic if symmetry of the Slutsky matrix is imposed. An alternative procedure is suggested and utilised. Finally, we suggest that low Durbin–Watson statistics may arise from misspecification of functional form and may not be due solely to omitted dynamics, as many conjecture.     

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.     

An intertemporal system of dynamic consumer demand functions

This paper constructs and estimates a system of dynamic consumer demand equations under the assumption of rational expectations about anticipated human wealth. The traditional one-period budget constraint is replaced by the lifetime anticipated wealth constraint. Lagged dependent variables are rationalized by an adjustment cost argument. In the model presented, both the dynamic adjustment coefficients as well as the parameters characterizing the underlying long-run preferences are identified and can be estimated. We find that a weak version of the REH cannot be rejected on the data. In common with most empirical studies on demand behaviour we have to reject the symmetry restrictions.     

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.     

Estimating consumer demand in Korea

In this paper, time series annual data on five consumer goods for Korea are analyzed using the neoclassical model of consumer behavior. The approach taken is the indirect utility function and employs a translog form. Various restrictive specifications of consumer preferences with respect to homotheticity and separability are examined and rejected by the likelihood ratio test. Income and price elasticities are estimated, which appear to be generally high relative to those of developed countries. Growth in real income is primarily responsible for changes in commodity demand. Marginal utilities of income and associated income elasticities are calculated, which are consistent with normal expectations.     

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.     

Exact aggregation of consumer demand systems

This paper is divided into two parts which deal with closely connected issues. The first section of the paper explores the structure of consumer demand systems necessary and sufficient for exact aggregation. The second section addresses a related empirical question: what, if anything, do the restrictions imposed on exactly aggregable demand systems buy the econometrician engaged in estimating integrable consumer demands? In particular, if the objective of an empirical exercise is to estimate the demand systems of individual utility maximizing consumers and only aggregate expenditure information and information on the income and demographic composition of the population are available, then under what conditions can the parameters of the estimated aggregate expenditure system be used to uniquely identify the parameters of the underlying individual demand systems?     

Empirical regularities in South African consumption patterns

This article investigates a number of empirical regularities in the South African consumption patterns. The data support the following empirical regularities: (1) variability in consumption systematically exceeds the variability in prices; (2) law of demand; (3) income flexibility is about ?0.5; (4) Engel's law; and (5) the demand hypotheses, demand homogeneity and Slutsky symmetry are acceptable. In contrast to the findings for a number of other countries, another important empirical regularity that consumer's utility function is additive is rejected for the South African consumers. Based on the implied demand elasticity estimates from the preferred model, it is found that food, housing and medical care are necessities, and clothing, furniture, transport and recreation are luxuries and demand for all the commodities are price inelastic.     

The structure of consumer preferences,Federal Republic of Germany, 1950–1973

Summary The objective of this paper is to analyze the structure of consumer preferences and changes in preferences over time. Consumer preferences are represented by an indirect translog utility function with time-varying preferences that is quadratic in the logarithms of its arguments. We consider a system of demand functions associated with parameter restrictions consistent with the theory. We characterize groupwise separability and groupwise homotheticity of preferences and derive for each set of restrictions on preferences parametric restrictions on the corresponding system of demand functions. Empirical results of the tests, based on time series data for FRG consumption expenditures on three commodity groups — durables, non-durables, and energy — are presented.     

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 Estimable Model of Supermarket Behavior: Prices, Distribution Services and Some Effects of Competition

In this paper we present and estimate a simple model of supermarket behavior that has several attractive properties: It permits the incorporation of the (distribution) services provided by a supermarket as an output of supermarkets and a determinant of demand for supermarket products; it generates, as a special case, one of its main competitors in the supermarket literature – the so called full price model of services; and, it can be estimated with a unique data set originally constructed by the Economic Research Service of USDA. The main results of the analysis are three. First, the aggregate demand for a supermarket's products depends critically on distribution services: at the substantive level, a 1% increase in these services increase quantity demanded by 0.4%; at the methodological level, the restrictions on the parameter values implied by the model are critical in the evaluation of functional forms for demand. Second, supermarkets exhibit constant marginal costs with respect to the quantity of output or turnover and substantially declining marginal costs with respect to (distribution) services, which implies substantial multiproduct economies of scale. Third, in response to an exogenous increase in competition those supermarkets that have adopted newer formats such as superstores and that employ newer technology such as optical scanners choose prices and (distribution ) services in ways that increase consumer welfare, whereas those that do not have these characteristics choose prices and services in ways that lower consumer welfare.     

The evolution of consumer preferences in Poland

This note investigates a change of consumer preferences in Poland in the period of 1996–2016. I use the Euler equation–generalized method of moments (GMM) to estimate the structural parameters of the aggregate consumption function to show that consumers in Poland significantly change their attitude to risk during the global financial crisis, when the estimate of the risk-aversion parameter becomes very high, while otherwise close to zero suggesting near risk neutrality. Also, the subjective trade-off between consumption today and tomorrow undergoes an evolution towards lower ‘impatience’. Over-identifying restrictions are tested and the null hypothesis of validity of instruments is not rejected. The stability over time of the estimated parameters is tested and rejected. The evolution of preferences is shown through recursive estimates of the deep parameters, too.     

Consumer behaviour in India: An application of the Rotterdam demand system

The purpose of this paper is to analyse the extent to which the observed data support the postulates of neoclassical theory of consumer behaviour. The absolute price version of the Rotterdam model has been estimated for rural and urban areas of India separately. The results indicate a trade off between theoretical consistency and goodness of fit. The symmetry, but not homogeneity, conditions are found to be empirically valid in rural India. All the other hypotheses are rejected both in rural and urban areas of India. Frequent violation of convexity conditions is also observed. The estimated marginal budget shares, income and price elasticities show marked differences in consumption patterns of rural and urban consumers in India. The effect of foodgrains price rise on the demand for various items is also analysed.     

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.