Errors of aggregation and errors of specification in a consumer demand model: a theoretical note

Abstract .  Consumer demand models based on the concept of a representative or average consumer suffer from aggregation error. Misspecification of the underlying micro utility-maximizing model, which is virtually inevitable, also results in error. This note provides a theoretical investigation of the relationship between the two types of error. Misspecified expenditure support functions for demand systems at the micro level induce the same misspecified structure in the corresponding expenditure functions at the macro level, and the errors at the two levels are shown to be of similar order.     

Demographic versus expenditure flexibility in Engel curves

We consider the effects of demographic and expenditure variables on consumer demand in a system of Engel curves using a smooth coefficient semiparametric model where the expenditure effects on the budget shares vary nonparametrically with demographic variables such as the age of head and number of children in the household. Our findings, based on UK micro data, suggest that with a smooth coefficient semiparametric model there is no need for nonlinear logarithmic expenditure effects in the budget shares. Furthermore, we find evidence of a trade-off between demographic and expenditure effects in Engel curves and that a rank-2 system of Engel curves where the logarithmic expenditure effects are allowed to vary with demographic characteristics either nonparametrically or as a third degree polynomial function cannot be rejected against a rank-3 (quadratic logarithmic) model. The implications on household behavior and welfare are also examined. We would like to thank an anonymous referee and Baldev Raj, the editor, for useful comments and suggestions. We would also like to thank the University of Cyprus for financial support, Theofanis Mamuneas for stimulating discussions and the Office of National Statistics for making available the UK Family Expenditure Survey data through the ESRC Data Archive. The last author would also like to acknowledge the financial support from SSHRC of Canada.     

Effects of Changes in Household Size,Consumer Taste & Preferences on Demand Pattern in India

Current research in applied demand analysis has been addressing the twin issues of degree of non-linearity or curvature of the Engel curves and the ability to capture price effects appropriately by the demand system. Further, in addition to income and prices, the role of demographic variables like household size, composition and dynamic aspects like consumer taste & preferences are also being ’ emphasized in recent literature. Continuous efforts are being made to modify the existing models and propose new ones to incorporate the above developments. The purpose of this study is to re-examine the usefulness of the popular linear expenditure system vis-à-vis the two other flexible models viz. Nasse expenditure system, a generalization of the linear expenditure system itself, and the almost ideal demand system in the above context for India.The empirical results indicate wide variation in marginal budget shares and demand elasticities across income groups, rural-urban sectors and alternative models. The household size and consumer taste & preferences are found to be statistically significant. The results confirm the earlier findings that there are significant changes in consumer tastes away from cereals and pulses in favor of other food and nonfood commodities. The results also show that flexible models, which are theoretically superior, gave unacceptable positive price responses for some commodities and violated second order conditions of utility maximization. It is found that some ad-hoc separability restrictions are needed, thereby limiting the flexibility of the model, to get negative own-price responses in these models. But, second order conditions are still violated. The tests of nested hypotheses also confirm the need for inclusion of household size, consumer taste, income group and rural-urban dummies along with their interaction variables in the demand system.

     

Consumer allocation models: Choice of functional form

The functional form of consumer allocation models should be able to satisfy theoretical properties derived from the theory of consumer demand. The paper sketches four approaches that meet this condition. Of course, also empirical performance matters. Next to naive goodness-of-fit comparison, non-nested hypothesis testing can be employed. The latter technique is applied to a comparison of four versions of differential demand systems: the Rotterdam system, a version of the Almost Ideal Demand (AID) system, the CBS system and the NBR system. These systems are artificially nested in a more general model using scalar weights in contrast to Barten and McAleer (1991) who use matrix weights for this purpose. Annual data over the period 1921–1981 for The Netherlands for four major groups of consumer expenditure have been used for the empirical application. The CBS system dominates the others.     

我国居民消费需求与社会保障水平的动态分析——基于中国19902009年经验数据

文章利用我国1990-2009年居民人均消费支出PCS和社会保障支出PPS数据，采用协整检验和误差修正模型等计量技术，检验社会保障水平对于居民消费的影响。在计量分析的基础上，认为拉动居民消费需求的关键在于完善社会保障制度、实现国民收入水平的持续稳定增加，增强国民的消费信心；同时还要扩宽社会保障基金的筹资渠道，加快重大民生工程建设，改善人们的消费预期，引导和促进居民扩大消费需求。     

Sensitivity of ‘optimal’ commodity tax rates to alternative demand functional forms: An econometric case study of India

This study investigates, on a nine commodity disaggregation of Indian budget data (NSS, 28th round), the sensitivity of ‘optimal’ commodity tax rates to alternative demand systems. LES and RNLPS. ‘Optimality’ is used here in the very special sense of being conditional on observed expenditure and fixed consumer prices. The alternative sets of tax rates agree at low levels of ‘inequality aversion’ but disagree widely at ‘Rawlsian’ levels. LES is heavily rejected in favour of its one-parameter generalisation, RNLPS. The results suggest that LES price elasticities should not be used in ‘optimal’ tax calculations. The ‘optimal’ tax rates imply only a modest redistribution.     

Fiscal policy simulations – a comparison of UK models

The problem of endowing large applied general equilibrium models with numerical values for parameters is formidable. For example, a complete set of own- and cross-price elasticities of demands for the MONASH model of the Australianeconomy involves in excess of 50000 items. Invoking the minimal assumptions that demand is generated by utility maximization reduces the load to about 26000 - obviously still a number much too large for unrestrained econometric estimation. To obtain demand systems estimates for a dozen or so generic commodities at a top level of aggregation (categories like ‘food’, ‘clothing and footwear’, etc.), typically Johansen's lead has been followed, and directly additive preferences imposed upon the underlying utility function. With the move beyond one-step linearized solutions of applied general equilibrium models, the functional form of the demand system adopted becomes an issue. The most celebrated of the additive-preference demand systems, the linear expenditure system (LES), has one drawback for empirical work; namely, the constancy of marginal budget shares (MBSs) - a liability shared with the Rotterdam system. To get around this, Theil and Clements used Holbrook Working's Engel specification in conjunction with additive preferences; unfortunately both Working's formulation and Deaton and Muellbauer's AIDS have the problem that, under large changes in real incomes, budget shares can stray outside the [0, 1] interval. It was such behaviour that led Cooper and McLaren to devise systems with better regularity properties. These systems, however, are not globally compatible with any additive preference system. In this paper we specify, and estimate, at the six-commodity level, an implicitly directly additive-preference demand system which allows MBSs to vary as a function of total real expenditure and which is globally regular throughout that part of the the price-expenditure space in which the consumer is at least affluent enough to meet subsistence requirements.     

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?     

城镇居民不同收入群体消费行为分析

按照家庭收入由低到高将城镇居民划分成四个收入群体,并应用带有家庭属性的AIDS模型分析每个收入群体的消费行为。研究结果表明,随着家庭收入的上升,城镇居民对于大多数商品消费的支出弹性和价格弹性呈下降趋势;城镇居民家庭用品和交通通讯消费富有支出弹性和价格弹性。因此,政府提高低收入群体的收入水平,通过财政政策使家庭用品和交通通讯商品的价格降低,可以有效地刺激城镇居民的消费。     

A BOX–COX CONSUMER DEMAND SYSTEM NESTING THE ALMOST IDEAL MODEL*

This article proposes a consumer demand system that has a generalized functional form characterized by the Box–Cox transformation. The new model offers a wider range of responses to both price and expenditure changes than the existing price independent generalized linear models, including the almost ideal demand system. Even with these features, its functional form is relatively simple and easy to interpret and implement. An empirical illustration is given for Japanese demand for nondurable goods and services. The results show that the new model is preferable to the nested models in terms of relative explanatory power and producing reasonable elasticities.     

Conditional and unconditional food demand elasticities in a dynamic multistage demand system

This paper estimates conditional and unconditional demand elasticities in a three stage analysis of consumer demand for food and non-food items in Greece. A dynamic version of the AIDS model is specified and estimated, and full system misspecification tests applied. Correction formulas for price and expenditure elasticities are used to calculate unconditional elasticities from conditional demand sub-systems. All food items rank as price inelastic. Deviations between the calculated conditional and unconditional price and expenditure elasticities are found to be significant, demonstrating the importance of correcting conditional elasticities before they can be used for policy purposes or welfare analyses.     

Development of the extended linear expenditure system from simple saving assumptions

The extended linear expenditure system (ELES) can be developed as an atemporal maximization of a Stone-Geary utility function wherein saving is treated as a good in itself. The key to this development is the a priori specification of the ‘subsistence quantity’ of saving, γ_{n + 1}, to be zero. Thus, the intertemporal maximization approach to the ELES is equivalent to specifying a Klein-Rubin saving function with γ_{n + 1} = 0 for a linear expenditure system (LES) based on permanent income rather than total expenditure. Any income concept - current, normal, or permanent, for example - is acceptable for the ELES developed from the atemporal maximization.     

The extended linear expenditure system

The purpose of this paper is to derive the aggregate consumption function associated with the linear expenditure system (LES) from simple utility maximization procedures. The parameter set (β, γ) of LES plus an added parameter (μ: the ratio of the subjective rate of discount to the market rate of interest) characterize the consumption-savings and the expenditure allocation decisions under the Klein-Rubin utility function. The term p′y appears in the aggregate consumption function.The distinction between subjective, planning time and historical time (a continuum of initial points of optimal plans) is basic here: thus the focus on solutions at t = 0.     

Hoglex Demand Systems and Welfare Policy in Major Asean Developing Countries: A Bayesian Analysis Using Expenditure Unit Records

The HOGLEX demand system (Tran Van Hoa (1983, 1985)) is integrable and flexible in the sense that it is based on utility maximization and encompasses most other well-known demand systems (e.g., LINEX, AIDS) in the literature on consumer behaviour (Laitinen et al. (1983)). HOGLEX studies to date have been based on conventional OLS or MLE methods and panel aggregate income and price data, and restricted to investigating consumption patterns. The paper elaborates on three important subsets of the HOGLEX demand system and, using household expenditure unit records from two major ASEAN developing countries (i.e., Thailand and the Philippines), estimates by the Bayesian method these subsets for 20 socio-demographic cohorts, and discusses their substantial implications in social security and welfare policy analysis. We also estimate the models in the more practical case of measurement errors in total expenditure and compare the results with those without measurement errors.

     

The effect on consumption of household size and composition

The paper is about effects of household composition on household demand. Demand functions where prices are multiplied by consumer unit numbers (Barten-functions) are discussed theoretically and empirically. The theoretical part shows how Barten-functions may be derived from a simple model of distribution and decision-making within the household, incorporating the possibility of joint consumption. Regression analysis of two Norwegian surveys of consumer expenditure is used to inaminate the predictive power of Barten-functions. Equivalent adult scales are computed by a method of approximation using the budget percentage of foodstuffs.     

Maximum likelihood estimation of linear expenditure systems with serially correlated errors: An application

The present paper uses Canadian data for the period 1947–1972 and three commodity groups to examine the empirical importance of restrictions imposed by autocorrelated disturbances on the static linear expenditure system, LES. For comparison a simple habit persistence model is also estimated. Results of applications of likelihood ratio tests indicate that autocorrelation is present in the data, that a simple habit persistence hypothesis on the structure is implied and that the restrictions imposed by the form of the utility function and maximization problem are inconsistent with the data whether or not adjusted for the autocorrelation in errors. Despite these differences, the estimated price and income elasticities remain fairly constant across the various specifications of the LES that were considered.     

非参数估计方法在长江和珠江三角洲地区城镇居民消费支出分析中的应用

本文给出商品消费支出份额Working-Leser非均匀面板数据固定效应和随机效应模型的非参数局部线性估计方法,并用之估计和比较珠三角和长三角两地区城镇居民各类商品消费支出结构。利用支出弹性分析方法,分析和比较两地区城镇居民的消费结构差异。     

Engel curves and systems of demand functions

The functional forms of the Engel curves implied by several popular complete systems of demand functions are discussed. Among the systems are those generated by generalized quadratic indirect utility (the translog system, the generalized Leontief system, etc.), the linear and quadratic expenditure systems, and Deaton and Muellbauer's PIGL and AIDS. A new system, which can produce the Engel curves of all these systems as special cases, is suggested. The different Engel curves are tested against data from a Norwegian survey of consumer expenditure. This is done both in a complete system of Engel curves for eight commodities and commodity by commodity.     

收入增长中城乡居民畜产品消费结构趋势实证研究——以浙江省为例

基于浙江省城乡居民固定观测点的调查数据,细分不同产品种类,采用扩展线形支出系统（ELES）模型,实证研究了收入增长过程中城乡居民畜产品消费结构的变动趋势。研究结果显示：随着人均收入的增加,浙江省城镇居民畜产品的消费变化主要表现为猪肉消费的减少及奶类消费的增加;农村居民对家禽类产品有较高的边际预算份额及较大的需求收入弹性。     

Consumer expenditure,the demand for money,and the Hall hypothesis

Although a considerable amount of work has been conducted on the validity of the Hall hypothesis, as applied to consumer expenditure, there has been negligible empirical work on the Hall hypothesis as applied to the demand for money. In this paper the Hallian hypothesis is applied to consumer expenditure and the demand for money using quarterly data for six countries.