Determinants of food consumption in rural Sierra Leone: Application of the quadratic expenditure system to the consumption-leisure component of a household-firm model

This paper reports the application of a quadratic expenditure system with demographic variables to the household consumption-leisure choice component of a household-firm model. A system of seven commodities is estimated: including five foods, non-food and leisure. Appropriate for such a level of disaggregation a demand system is used, the Quadratic Expenditure System, which allows for a flexible relationship between full income and commodity expenditures without sacrificing parsimony in parameters. Demographic data on households are explicitly incorporated into the model allowing for a richer specification than can be achieved by using per capita variables. The data are from a cross-section survey of households in rural Sierra Leone. Price variation exists by region, permitting estimation of a complete demand system. Engel curves are found to be significantly non-linear, with marginal expenditure on rice, the major staple, declining with higher income. Most foods are found to be reasonably price responsive with sizeable own price substitution effects, declining with higher income. Aggregate labor supply is found to be price inelastic.     

An Engel Curve Analysis of Household Expenditure in New Zealand*

In this paper we estimate systems of Engel curves for expenditure on eight commodity groups by New Zealand households. Six model specifications are considered, and the preferred results are based on the Almost Ideal Demand System. The estimated expenditure elasticities and marginal budget shares are quite insensitive, at the sample mean, to the choice of functional form. The results are compared with those from other Australasian, British and American studies.     

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.     

More or better? Measuring quality versus quantity in food consumption

As people become richer they get the opportunity of consuming more but also qualitatively better goods. This holds for a basic commodity like food as well. We investigate food consumption in Russia, taking into account both expenditure and nutrition value in terms of calories. We analyse how food consumption patterns change with increasing income by considering both “quantity Engel curves” and “quality Engel curves.” The former describe the functional dependence of calories consumed on total expenditure. The latter trace out the dependence of unit value per calorie on total expenditure. We compare income elasticities of quantity with income elasticities of unit value and quality. In Russian household survey data for years 2000–2002 the reaction of quality to income changes is significantly stronger than the reaction of quantity to income changes suggesting that Russian households tend to choose higher quality food items as income rises.     

Using inverted Engel curves to estimate material standards of living in a household

This article demonstrates how to estimate latent total consumption expenditure or material standard of living in households by inverting estimated Engel curves. While the conventional estimator, total purchase expenditure, is unbiased for latent total household consumption expenditure, it is not variance minimizing since it is an un-weighted sum. In two stages, this article derives a variance-minimizing, unbiased estimator by first estimating and inverting Engel curves; then combining the estimators from the inverted Engel curves. The employed latent variable method allows for utilization of non-expenditure relations. The suggested method may help improve the accuracy in studies of consumption inequality and tax evasion.      

On the Functional Form of Engel Curves: The Australian Household Expenditure Survey 1975–76*

This paper considers the properties of a class of models which is based on the Addilog demand system. These models not only fulfil the adding-up criterion but also ensure that the predicted expenditures are non-negative and a subset of these models permits the existence of saturation levels for certain commodities. A goodness of fit comparison between this class and other systems of Engel curves favours the Addilog model. The estimated expenditure elasticities compare favourably with previous estimates of Australian household expenditure patterns and it is observed that the elasticities for health and alcohol and tobacco expenditures have decreased substantially from their levels in the late 1960s.     

An intertemporal analysis of expenditure elasticities under three expenditure specifications for Sri Lanka

Household income has been identified as one of the major determinants of demand for household goods. In addition, other household characteristics, such as household size and composition are also found to be important factors that influence household consumption decisions. This study, using four waves (2006/07, 2009/10, 2012/13 and 2016) of Sri Lankan Household Income and Expenditure Survey data, estimates three different specifications (namely, household expenditure, per-capita expenditure and expenditure per equivalent adult) of a complete system of Box-Cox Engel curves to incorporate household size and compositional differences into the model specification. A comparison of elasticity estimates across the three specifications indicates that amongst the three, the best performing model is the one utilizing household expenditure. An intertemporal analysis of expenditure elasticities indicates that although the magnitude of expenditure elasticities has changed, the necessity or luxury classification of household commodities has mostly remained unchanged for the period 2006 ? 2016 in Sri Lanka.     

On the estimation of 'an implicitly additive demand system'

Motivated by a lack of Engel flexibility in commonly used demand systems, Rimmer and Powell developed a new demand system. This system, referred to AIDADS, is implicitly, directly additive, possesses marginal budget shares and thus Engel elasticities, that vary nonlinearly with expenditure such that predicted budget shares are restricted to the [0,1] interval. Due to these attractive Engel properties, AIDADS represents a significant contribution to the literature on demand analysis. This paper presents an alternative estimation procedure to the one used by Rimmer and Powell and examines its properties via a case study. The proposed approach avoids a linear approximation employed in Rimmer and Powell's estimation framework. Based on a small Monte Carlo study, it appears that the approach produces more accurate estimates of the parameters and Engel elasticities.     

The displaced exponential as an Engel curve

An exponential function, vertically displaced, is considered as a relationship between expenditure on a particular commodity and total expenditure or total income. Economic properties are derived. The function is fitted to UK data, and fits more closely than quadratic functions.     

A trigonometric flexible consumer demand system

Abstract.  This paper proposes the first ever empirical specification of a trigonometric demand system. The new model is potentially useful because of some attractive features. It is flexible, amenable to exact aggregation over consumers, possessed of trigonometric Engel curves, which can oscillate, and able to have an unusually large regular region. With comparisons between the new model and two other popular models, an illustration is given for Japanese demand for non‐durables and services. The new model shows relatively gentle Engel curves with an inflection point on each of them, which seem reasonable, given that aggregate expenditure is used in parameter estimation. JEL classification: C51, D12     

Is the Engel curve approach viable in the estimation of alternative PPPs?

Conventional estimates of purchasing power parities (PPP) rely on cross-country price data. Using Engel curves, Almås (Am Econ Rev 102:1093–1117, 2012) was, however, able to show that PPPs contain substantial bias. Since constructing conventional estimates is expensive and time consuming, Almås’ idea of employing Engel curves is welcome. This article examines the viability of the Engel curve approach to PPP and its sensitivity to differences in relative prices and preferences by estimating Engel curves not only between countries but also for regions within a given country. My empirical evidence from the United States and Norway suggests that the differences can be problematic, but not sufficiently to discredit the new methodology. A pragmatic approach to PPP estimation between countries that are different is to compute a PPP band, rather than a point estimate. I present a practical example of this using expenditure data from 2001, which yields a band for NOK and US dollar.     

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.     

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.     

Imposing local curvature in the QUAIDS

In this paper, we build on Ryan and Wales (1998), Moschini (1999), and Serletis and Shahmoradi (2007) and impose curvature conditions locally on the quadratic Almost Ideal Demand System (AIDS) model of Banks et al. (1997), an extension of the simple AIDS model of Deaton and Muellbauer (1980) that can generate quadratic Engel curves [that is, rank-three demand systems, in the terminology of Lewbel (1991)]. In doing so, we exploit the Slutsky matrix of second order derivatives of the indirect utility function.     

On the Estimation of Total Expenditure Elasticities from Derived Engel Functions with Applications to Australian Micro-Data*

This paper proposes a method of estimating total expenditure elasticities based on the implicit Engel equations derived from the Lorenz curve of total expenditure and concentration curves of commodity-specific expenditures. The proposed procedure is computationally easy to implement and produces elasticity estimates which appear to satisfy the adding-up criterion well For illustration, the method is applied to the 1984 Household Expenditure Survey and an attempt is made to compare the present estimates with those generated in previous Australian studies.     

Optimally uniform commodity taxes,taste differences and lump-sum grants

Optimal commodity taxes for an economy with many households should be at a uniform proportional rate under certain conditions. These include (i) linear and parallel Engel curves with intercepts dependent on household composition, (ii) separability between goods and labour, and (iii) optimal demogrants.     

Back to Engel? Some evidence for the hierarchy of needs

Using UK household expenditure data spanning over four decades (1960–2000), this paper employs Engel’s needs-based approach to analyzing household expenditure patterns and finds evidence for the existence of a stable hierarchy of expenditure patterns at low levels of household income. Second, we investigate how rising household income influences the manner in which total expenditure is distributed across Engel’s expenditure categories. Our results suggest that i) total household expenditure is distributed across Engel’s expenditure categories in an increasingly even manner as household income increases and ii) over time, there has been an acceleration in the rate at which household expenditure patterns become diversified as household income rises. Finally, we consider how the shape of Engel Curves may help shed light on the relationship between goods and the underlying needs they serve.     

Functional form of engel curves for foodstuffs

Employing individual household expenditure data for six foodstuffs we test five three-parameter and four two-parameter Engel curves against a more general form. All two-parameter functions must be rejected, including Working's function; it appears that a transformation of the budget share is in order to capture the observed curvature.     

A globally flexible,quadratic almost ideal demand system: an application to demand for meats and fish in Taiwan

A new demand system, called a globally flexible, quadratic almost ideal demand system (GF–QUAIDS), integrates both the quadratic Engel curve and the Fourier series. This novel GF–QUAIDS model is applied to study the demand for meats and fish in Taiwan. Empirical results show that the GF–QUAIDS fits the data well and that, by using the likelihood ratio test, its nested models are rejected, including the locally flexible functional form and the linear Engel curve. Nevertheless, other empirical model-selection measures indicate that the GF–QUAIDS can be as good as its famous nested models such as the AIDS, QUAIDS and GF–AIDS.     

Using Engel curves to estimate bias in the Canadian CPI as a cost of living index

Abstract.  Semiparametric Engel curves are used to infer bias in the Canadian CPI as a Cost of Living Index. The budget share of food has long been used as an indicator of welfare. We compare households with the same levels of CPI deflated total expenditure over the period 1978–2000. Differences in the expenditure share of food are attributed to the CPI failing to capture changes in costs of living. We employ a novel econometric approach using a single index penalized linear spline model. Over the period, we find that the CPI overstated changes in the cost of living between 1.33 and 1.86% for the four household types considered. JEL classification: D1, C1