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.     

Towards a more general approach to testing the time additivity hypothesis

A new procedure is proposed for re-examining the assumption of additivity of preferences over time which, although untenable, is usually maintained in intertemporal analyses of consumption and labour supply. The method is an extension of a famous work by Browning. However, it is more general in permitting the estimation of intertemporal demand systems, which are explicit in an unobservable variable (price of utility), but may lack a closed form representation in terms of observable variables such as prices and total outlay. It also makes extensive use of duality theory to solve the endogeneity problem encountered in Browning's study. Applying this method with an appropriate estimator to the Australian aggregate data, it is found that the time additivity hypothesis is decisively rejected, which is consistent with Browning's conclusion.     

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.     

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.     

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.     

Uncertain vacancies and unemployment equilibria

The paper develops a dynamic implicit contracts model to consider the rationale for rejections of qualified applicants in the search process and to explore the implications for unemployment rates under equilibrium in the labor market. The implications are similar to traditional search models, although the effects of stochastic output prices upon equilibrium unemployment can be directly determined. A nearly invariant natural rate result pertains. A stochastic sales-rations variant of the model leads to equilibrium unemployment rates that depend upon both neoclassical and Keynesian factors.     

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 demand for local public goods: choosing an appropriate functional form

The demand for public goods is typically specified in direct form (prices are assumed exogenous, quantities are the choice variable) based on cross-section data. The fact that public goods are characterized by jointness suggests that the indirect form (quantity exogenous) may be more appropriate than the direct form. In addition, it is not likely that cross-sectional data will satisfy integrability. In this paper integrability. In this paper integrability is tested for in both the direct and indirect form using data on a typical cross-section of municipalities. It is found that the homogeneity, equality and symmetry conditions are violated in both the direct and indirect forms.     

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.     

Internal Relative Price Stationarity in Long-Run Purchasing Power Parity

This study demonstrates that the joint relationship among domestic traded-goods prices, dometic nontraded-goods prices, foreign traded-goods prices, and foreign nontraded-goods prices is important to understanding rejections or confirmations of long-run PPP. This joint relationship is defined as the "cross-country internal relative price structure." For nine of the ten pairs of countries studied, the cross-country internal relative price structure is found to be stationary; thus, factors other than the influence of nontraded-goods prices must be responsible for the rejections of long-run PPP.     

Excess demand functions with incomplete markets—a global result

The purpose of this paper is to give a global characterization of excess demand functions in a two-period exchange economy with incomplete real asset markets. We show that continuity, homogeneity and Walras’ law characterize the aggregate excess demand functions on any compact price set which maintains the dimension of the budget set.     

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.     

The determinants of international reserves in the emerging countries: a nonlinear approach

In this article, we adopt a nonlinear approach to examine the dynamics of the international reserves holdings by the emerging economies. To do so, we estimate the demand for international reserves with a Panel Smooth Transition Regression (PSTR) model that loosens two restricting hypotheses, homogeneity and time-stability. We find evidence for the presence of a nonlinear behaviour in the demand for international reserves, a result that is new to the literature. The coefficients are found to change smoothly, as a function of two threshold variables – out of five candidates tested in total. Our specification accounts for the acceleration of foreign exchange reserves accumulation that the linear specifications fail to explain.     

A comparison of technology in centrally-planned and market-type economies

The present paper considers the role of technical progress in centrally-planned and market-type economies using a case study approach of Czechoslovakia and Austria. The paper goes beyond the usual treatment of productivities of prime factors in that the demand for intermediate inputs is specifically considered. The empirical analysis is based on the input-output approach which consists of testing the ‘fundamental’ properties of the input-output tables including triangularity, physical homogeneity and bloc decomposability. The comparisons include new sensitivity tests of ‘critical’ values and new methods of matrix triangulation. It is found that the ‘fundamental’ structures of both Czechoslovakia and Austria were triangular in form and formed a hierarchical arrangement. The findings suggest that the forces generating ‘fundamental’ properties of production structure in developed market economies can be also found in centrally-planned economies.     

Price adjustment in an atomistic market

This paper considers the price adjustment process in a market which retains the characteristics of a perfectly competitive market except that individual firms are price-setters. Buyers, unaware initially of what prices which firms are charging, indulge in search by contacting a sample of firms and buy (according to a demand curve) from the lowest-price firm encountered. Firms set prices to maximise profits over their perceived (or estimated) demand curve, and update their estimated demand curve in accordance with the observed change in demand between successive time periods. It is shown that the price distribution converges to a degenerate distribution centred on the monopoly price.     

Input substitution,economies of scale and productivity growth in the US upholstered furniture industry

Cost, factor demand and productivity growth are considered in the upholstered furniture industry over 1958–87. Factors are divided into labour, capital and materials. It is found that all inputs are substitutes in production although substitution elasticities are small. Factor demand is price-inelastic for all inputs. The industry operates around minimum average cost. Productivity growth is small but significant. The results indicate that labour will continue to be important in the industry. However, regional comparative advantage is not related to labour alone; the results suggest that policies to attract or retain the industry must consider the low degree of factor substitution.     

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.     

Demand for parimutuel horse race wagering with special reference to telephone betting

Parimutuel horse race wagering (handle), measured in real terms, has been steadily declining for the past several decades. In an attempt to reverse this trend, a number of racetracks in the United States have instituted telephone betting systems which allow wagering from an ‘off-track’ location. The present study investigates the demand for parimutuel horse race wagering when a telephone betting system is implemented. Two demand equations are estimated for a racetrack, one for on-track (live race) handle and another for total (on-track plus telephone betting) handle. As expected, it is found that the telephone betting system has led to a decline in on-track wagering but surprisingly, it has also led to decline in total wagering, although not to the same extent as in on-track wagering. Thus, off-track wagering generated through the telephone betting system has not been sufficient to offset the loss in on-track handle. In addition to the effect of the telephone betting system, it is found that the takeout rate (price of wagering), the price of admissions, racing quality, racing days, and competition from professional sports and another racetrack in the market area are significant determinants of the demand for wagering. Demand is found to be elastic with respect to the takeout rate, inelastic with respect to the price of admissions and parking, and almost unitary elastic with respect to income.     

Fads or bubbles?

This paper tests between fads and bubbles using a switching regression to distinguish between competing models. Two main features of the bubbles model distinguish it from the fads model. First, the bubbles model implies that returns are drawn from regimes which differ in the way returns vary with deviations from fundamental prices. Second, the bubbles model implies that deviations from fundamental price will help predict regime switches. Using US data for 1926–89, we find evidence which is consistent with the fads model even when we allow for variation in expected dividend growth rates and expected discount rates. However, the restrictions which the fads model implies for a more general switching-regression specification are rejected. The rejections point in the direction of the bubbles model, although not all of the implications of the bubbles model are supported by the data. First Version Received: October 2000/Final Version Received: October 2001     

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.