Utility theoretic semi-logarithmic incomplete demand systems in a natural experiment: Forest fire impacts on recreational values and use

This study develops a utility theoretic demand model for an arbitrary number of goods that handles correlation between goods and over time. The bivariate compound Poisson estimator is applied to a semi-logarithmic incomplete demand system to estimate the demand for wilderness recreation and the associated welfare measures both prior to and post a 40,000 acre wilderness fire in Washington. Forest fires can simultaneously affect the environmental qualities of many recreational sites; this highlights the need for a utility theoretic demand system approach for modeling consumer behavior that handles the dynamic behavioral and statistical interdependencies over goods and time. Results suggest an increase in consumer welfare per trip post fire, after an initial period of low values, relative to before the fire.     

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.     

Statistical inference in cross-country demand systems

Consumption data on eight goods in 15 countries are used for testing and estimating a system of demand equations across countries. The estimated income elasticities are compared with those of Clements et al. (1979) and Houthakker (1957).     

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.     

Dynamic almost ideal demand systems: an empirical analysis of alcohol expenditure in Ireland

This paper presents a dynamic form of the Almost Ideal Demand System (AIDS). Three versions of the static AIDS model are employed to determine the preferred long-run equilibrium model and represents the short-run dynamics by an error correction mechanism. This estimation procedure is then applied to alcohol expenditure in Ireland. The estimated point elasticities are consistent with previous studies and a priori expectations. Beer and spirits are found to be price inelastic in both the short and long run. While wine is price inelastic in the short run and price elastic in the long run.     

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997     

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.     

Goodness of fit and outliers in cross-country demand systems

For a 10-good consumer demand system, the fit for 30 countries in the sample is compared with that for five countries outside the sample.     

Empirical demand systems incorporating intertemporal consumption dynamics

This article presents and estimates demand systems by explicitly incorporating intertemporal consumption behavior as summarized by the Euler equation. Demand systems are characterized by two indirect utility functions which are effectively globally regular and can better approximate nonlinear Engel curves. Furthermore, an exact and nonlinear Euler equation is derived without a log approximation. This equation is estimated jointly with the demand functions by a careful implementation of the orthogonality conditions using generalized method of moments. We illustrate the techniques by estimating the demand system and Euler equation for Australian aggregate data. Results generally indicate that the proposed methods are promising. The estimated rate of time preference is fairly small while the restrictions producing the moment equations are not rejected. Estimated Frisch price elasticities, which are relevant in an intertemporal setting, appear reasonable, and the intertemporal elasticity of substitution for consumption is found to be small, which are consistent with the findings in earlier studies.     

Recreation demand estimation and valuation in spatially connected systems

Recreation demand models frequently are used to explain outdoor recreation behavior and to estimate willingness to pay for changes in environmental quality at recreation sites. Among the most commonly used recreation demand models are site choice models based on the multinomial logit framework, which account for the spatial relationships between each recreator's home and multiple alternative destinations thereby capturing the substitution possibilities among recreation sites. However, standard applications of this framework typically do not account for the possibility of spatial connections among the sites via movements of the target species, such as fish in connected water bodies in recreational angling applications or terrestrial species in hunting or wildlife viewing applications. In this paper we examine aspects of environmental valuation and natural resource dynamics that generally are addressed separately. Specifically, we show that in such spatially connected systems, a “reduced form” application of the standard site choice modeling approach, using proxy measures of environmental quality rather than direct measures of species abundances, can produce biased estimates of willingness to pay for environmental improvements. Furthermore, we show that under some conditions poorly targeted environmental improvements in spatially connected systems can lead to welfare decreases. In such systems a structural model of recreator site choices and species sorting behavior and population dynamics may be required to fully account for the spatial linkages among sites and the feedback effects between recreators and the target species.     

Advertising in demand systems: testing a Galbraithian hypothesis

In this paper we argue that the influence of advertising upon the inter-product distribution of demand is a system-wide phenomenon which is investigated better through a demand equation system rather than through single equation methods. Attention is focused upon a dynamic version of Deaton Muellbauer's AIDS model modified to include advertising terms. Within this framework using data on consumer's non-durable expenditure in the UK we carry out a preliminary test of Galbraith' hypothesis that advertising may affect the composition of aggregate consumer demand.     

Inverse demand systems and choice of functional form

Barten (Empirical Economics 18 (1993) 129) recently advocated estimation of a synthetic demand system that mechanically nests four other popular differential demand models. This paper follows a similar strategy, but in the context of four inverse share-equation demand systems: The Inverse Translog Demand System (ITLDS); the Inverse Almost Ideal Demand System (IAIDS); the Inverse Lewbel Demand System (ILDS); and the Inverse Non-Separable Linear Expenditure System (INLES). Each of these specifications is artificially nested in a Hybrid Inverse Demand System (HIDS). An empirical application to three categories of quarterly U.S. meat demand data over the period 1961-1996 indicates the HIDS is a preferred specification.     

The rank and model specification of demand systems: an empirical analysis using United States microdata

A rank-three demand system is estimated with United States Consumer Expenditure Survey microdata. A unique price data set is also used, which permits the analysis of effects of systematic errors in price variables. It is found that errors in price variables bias test results for the rank-three hypothesis, in particular towards rejection. Other test results are affected to a lesser extent. Estimating smaller systems of demand equations, even when conditioning on excluded goods, yields significantly different results. Another important conclusion is that model specification is statistically significantly different for households of varying family sizes and housing tenure statuses. JEL Classifications: C31, D12.
Le rang et la spécification du modèle des systèmes de demande: une analyse empirique utilisant des microdonnées américaines. On calibre un système de demande de rang trois à l'aide de microdonnées américaines tirées de la United States Consumer Expenditures Survey. Un ensemble unique de prix est utilisé afin de permettre l'analyse des effets d'erreurs systématiques dans les variables de prix. Il appert que les erreurs dans les variables de prix distorsionnent les résultats du test de l'hypothèse de rang trois en faveur d'un rejet. D'autres résultats de tests sont affectés à un moindre degré. Si l'on calibre de plus petits systèmes d'équations de demande, même en posant des conditions sur des biens exclus, des résultats qui diffèrent de manière significative s'ensuivent. Une autre conclusion importante est que la spécification du modèle est différente de manière statistiquement significative pour les ménages selon la taille de la famille et le statut domiciliaire.     

Applications of robust estimation techniques in demand analysis

Estimates are presented of the demand for tobacco in Italy in the context of a demand system approach. The grouping of goods is based on Varian's non-parametric test for weak separability. The parametric demand model is Banks, Blundell and Lewbel's QUAIDS model, which combines the empirical flexibility of quadratic logarithmic Engel curves with integrability. Estimation is by iterative GMM procedure. The estimates are used in an analysis of welfare-improving tax reforms which incorporates distributional data. The results are discussed with respect to the special features of the Italian tobacco market.     

Demographic variables in demand systems: The case for generality

This paper provides evidence in favour of greater generality in the demographic demand literature. We propose two demographic demand procedures. One extends the Gorman model by allowing non additive interaction between overheads and Barten scaling. The other extends Price Scaling, by allowing the equivalence scale to vary with utility, and offers a test of Equivalence Scale Exactness (ESE). The rejection of ESE is robust to the assumed demand functional forms (RNLPS, QAIDS), to items chosen, and the estimation method (MLE, GMM). The results show that published cell averages yield well determined estimates of the demographic generalisation parameters.This paper was written during my visit to the UBC in Vancouver, Canada in 1992/93. I am grateful to two anonymous referees for their helpful remarks on an earlier version. The disclaimer applies.     

An applied analysis of brand demand structure

The demand literature is concerned with the optimal allocation of expenditure at varied but usually high levels of commodity aggregation. Much less aggregation however is required for business applications. In applied business settings, interest centres upon the different brands of the same commodity because policy formulation takes place at the level of the individual brand. This paper considers application of formal demand analysis to brand demand data. A theoretically plausible demand system is invoked to describe inter-brand allocation of expenditure, test restrictions imposed by economic theory and yield empirically determined insights into brand demand structure.     

Invariance, price indices and estimation in almost ideal demand systems

Two issues are addressed in this paper. First, we explore the issue of price index invariance in the linearized Almost Ideal demand system. We establish that the Stone index, which lacks invariance, and the recently proposed invariant Laspeyres, Paasche and Tornqvist indices all generate biased and inconsistent estimators. Monte Carlo evidence shows that invariance does not necessarily lead to better estimates of price and income elasticities insofar as the Stone and Paasche indices are unambiguously inferior to the Laspeyres and Tornqvist indices, especially if prices are not strongly positively correlated. Second, we examine the merits of the widely used conditional ML estimator of the non-linear Almost Ideal system in which a prior value is chosen for the “subsistence” parameter. We find that the bias and trace mean square error increases induced by conditional estimation are modest. The choice between the linearized and the non-linear models favors the latter although in some cases linear methods are as good as non-linear. First Version Received: January 1999 / Final Version Received: March 2000     

Using the cost function to generate Marshallian demand systems

Limited data means that prior structure is needed when working with large demand systems. The cost function is a convenient vehicle for generating demand systems incorporating such structure. While the cost function directly yields Hicksian demand functions they will not usually have an explicit representation as Marshallian demand equations i.e. in terms of the observable variables. With fast hardware and modern software, however, this need not hinder the estimation of the (implied) Marshallian demand equations. This paper develops the formal theory for using cost functions in this context, and reports on initial trials on the operational feasibility of the method. First version received: September 1997/final version accepted: July 1999     

Industrial coal demand in China: A provincial analysis

The general concern on the environmental implications of the rising demand for coal registered in China during the last few years has induced considerable research effort to produce accurate forecasts of China's energy requirements. Nevertheless, no previous study has modelled the coal demand in China at provincial level. The aim of this paper is twofold. First, we estimate and forecast the Chinese demand for coal using panel data disaggregated by provinces and accounting for spatial heterogeneity. Second, given the spatial nature of the data, we explicitly capture the spatial autocorrelation among provinces using spatial econometrics. In particular, we specify the Chinese industrial coal demand at provincial level with fixed-effect spatial models. The empirical results show that the fixed-effect spatial ADL model is able to capture the existing interdependence between provinces. This model forecasts an average annual increase in coal demand to 2010 of nearly 2%.