Slutsky Symmetry Research Articles

Dynamic modelling of consumption patterns using LA-AIDS: a comparative study of developed versus developing countries

The traditional applied demand system estimation assumes that when consumer income and commodity prices change, the consumers instantaneously fully adjust to a new consumption equilibrium level and use a static demand system such as Static Linear Almost Ideal Demand System (Static LA-AIDS) for estimation. However, in real-life situations, such an assumption does not hold as consumers take time to settle to a new consumption equilibrium level. Hence, dynamic demand system estimations generate more nuanced insights into the short-run dynamics of consumer demand. This paper estimates two forms of dynamic versions of AIDS, Dynamic LA-AIDS and the error-corrected LA-AIDS, and compares the results with the Static LA-AIDS. The paper also models the consumption patterns of consumers in developed and developing countries and provides a comparative analysis of implied elasticities using recent data. The results show that the dynamic models support demand theory hypotheses—demand homogeneity and Slutsky symmetry—more than the static model. The estimated mean own-price elasticities reveal that the demand in the short-run and long-run is price inelastic across all countries. Long-run and short-run income elasticities demonstrated notable variation across various commodity groups and country groups. For example, the restaurant meal is a luxury in the short-run for all countries. In the long-run, it is a necessity in developed countries and a luxury in developing countries. Food and housing are necessities; durables, transport and recreation are luxuries in developed and developing countries in the long-run and short-run.

What do Consumers Consider Before They Choose? Identification from Asymmetric Demand Responses

AbstractConsideration set models generalize discrete-choice models by relaxing the assumption that consumers consider all available options. Determining which options were considered has previously required either survey data or restrictions on how attributes affect consideration or utility. We provide an alternative route. In full-consideration models, choice probabilities satisfy a symmetry property analogous to Slutsky symmetry in continuous-choice models. This symmetry breaks down in consideration set models when changes in characteristics perturb consideration. We show that consideration probabilities are constructively identified from the resulting asymmetries. We validate our approach in a lab experiment where consideration sets are known and then apply our framework to study a “smart default” policy in Medicare Part D, wherein consumers are automatically reassigned to lower-cost prescription drug plans with the option of opting out. Full-consideration models imply that such a policy will be ineffective because consumers will opt out to avoid switching costs. Allowing for inattention, we find that defaulting all consumers to lower-cost options produces negligible welfare benefits on average, but defaulting only consumers who would save at least $300 produces large benefits.

Demand for animal‐derived food in selected Asian countries: A system‐wide analysis

AbstractFood consumption patterns in Asia show a trend away from staples toward high protein food derived from animal and dairy products, fruit and vegetables, fats and oils. Such changes in food consumption patterns are due to rising incomes, urbanization, globalization, and modernization of marketing infrastructure. In this article, we analyze the demand for the animal‐derived food group comprising meat (chicken, beef, pork, and mutton), eggs and fish, and derive income and price elasticities in seven Asian countries using the system‐wide approach. Demand homogeneity and Slutsky symmetry properties were tested and found to be compatible with the data. Our findings reveal that animal‐derived food as a group is a necessity (except in Taiwan) and its demand is price inelastic (except in Taiwan and Sri Lanka). The implied unconditional demand elasticities reveal that, in all countries (except beef in Japan and Taiwan), chicken, beef, pork, mutton, eggs and fish (except in Taiwan) are all necessities and the demand for all types of animal‐derived food in all seven countries are mostly price inelastic. The cross‐price elasticity estimates are mostly found to be positive, meaning that there is a higher degree of substitutability between chicken, beef, pork, mutton, eggs, and fish.

دراسة تحلیلیة للقدرة التنافسیة السعریة لصادرات البرتقال المصری فی أهم الأسواق

A Linear Approximation Almost Ideal Demand System was used to provide more reliable and detailed information about competitive ability of the Egyptian oranges export in major markets: Russia, Saudi Arabia, Netherlands and United Kingdom. The model is estimated by iterated seemingly unrelated regression (ItSUR) estimators with adding up, homogeneity, and Slutsky symmetry conditions imposed. Significance level of estimated marginal shares, expenditure elasticities, signs of own price Slutsky parameters, and Cournot own price elasticities indicated that the model fit the data reasonably well. At the level of the average annual increase rate of the Egyptian orange exports to the studied four markets, the Egyptian orange exports have a distinguish place in all these markets, especially in the Russian and Saudi markets. Between 200-2016, this rate increased by 15.7, 8.4, 3.8 and 3.9 thousand tons in the Russian, Saudi, Netherlands and UK markets, respectively. The results of the research indicate that in case of increasing the total expenditure of oranges in the mentioned markets, the development of the marginal shares of the major four exporting sources is clearly in favor of the Egyptian exports in the Russian and Saudi markets. The high estimated expenditure elasticities of the imported oranges, 1.67 in Russia, 1.13 in Saudi Arabia, 1.08 in Netherlands and 0.71 in the UK, show that the Egyptian oranges are preferred by the customers of these four markets. The results indicate that increasing Orange expenditure by 10% will increase the demand for imports of Egyptian oranges by 10.7%, 11.3%, 11.8% and 7.1% in the studied markets, respectively. The results illustrate that the cournot own price elasticity of the imported Egyptian oranges in the Russian market is relatively high (-1.14), which means that the orange export to the Russian market is very sensitive to the price changes of its own. Other own price elasticities -0.69, -0.37 and -0.39 in the Saudi, Netherlands and UK markets, respectively, are moderate, indicating that there are other factors beside price influencing the preference of the customers of these three markets. The cross price elasticities in all four markets show that the Egyptian orange export are affected by price changes of other sources, however the major impact is due to the price changes of the South African Exports, the main competitor of the Egyptian orange export, especially in the Netherland market.

Integrability of Demand in Incomplete Markets: Kreps-Porteus-Selden Preferences

We provide necessary and sufficient conditions such that consumption and asset demands in an incomplete market setting can be rationalized by Kreps-Porteus-Selden preferences and provide a means for recovering the underlying unique representations of risk and time preferences. The incompleteness of asset markets introduces two serious problems in attempting to use the classic Slutsky symmetry and negative semideniteness properties employed in certainty demand analysis. First, contingent claim prices are not unique and second, they do not vary independently. Non-uniqueness is a key obstacle to rationalizing conditional asset demand by a representation of risk preferences. Non-independence precludes proving the existences of an overall Kreps-Porteus-Selden representation dened over consumption and contingent claims and hence the existence of a representation of time preferences. Mechanisms are provided for overcoming both obstacles.

Are Generalized Extreme Value Class Discrete Choice Demand Models Rationalizable as a Representative Consumer's Behavior?

In general, they are not. Most discrete choice demand systems generated from McFadden’s Generalized Extreme Value (GEV) class fail to satisfy the Slutsky symmetry whenever the budget constraint binds. Failing to satisfy the Slutsky symmetry implies that they are not integrable in the sense of Hurwicz and Uzawa (1971), and thus, they are not rationalizable as a representative consumer’s behavior. The only possible economically and econometrically meaningful exception that we find is the simple multinomial logit model in which the mean utility is log-linear in prices.

Empirical analysis of Australian consumption patterns

This paper presents an empirical analysis of Australian private consumption patterns utilising a system-wide approach to analyse how the dominant component, private consumption, is allocated among ten broad groups of consumer goods. Australian consumers, on average, allocate about two-thirds of their income on food, housing, transport and recreation. We considered three demand models, the AIDS, Rotterdam and CBS demand systems, for estimation. The estimated income elasticities reveal that food, alcohol and tobacco, housing and medical care are necessities. All the own-price elasticities are negative and less than one in absolute value (except for recreation), indicating that demand for most goods is price inelastic. In addition, we tested the demand theory hypotheses, homogeneity, Slutsky symmetry and preference independence and found them to be acceptable.

REGRESSOR DIMENSION REDUCTION WITH ECONOMIC CONSTRAINTS: THE EXAMPLE OF DEMAND SYSTEMS WITH MANY GOODS

Microeconomic theory often yields models with multiple nonlinear equations, nonseparable unobservables, nonlinear cross equation restrictions, and many potentially multicolinear covariates. We show how statistical dimension reduction techniques can be applied in models with these features. In particular, we consider estimation of derivatives of average structural functions in large consumer demand systems, which depend nonlinearly on the prices of many goods. Utility maximization imposes nonlinear cross equation constraints including Slutsky symmetry, and preference heterogeneity yields demand functions that are nonseparable in unobservables. The standard method of achieving dimension reduction in demand systems is to impose strong, empirically questionable economic restrictions such as separability. In contrast, the validity of statistical methods of dimension-reduction such as principal components has not hitherto been studied in contexts like these. We derive the restrictions implied by utility maximization on dimension-reduced demand systems and characterize the implications for identification and estimation of structural marginal effects. We illustrate the results by reporting estimates of the effects of gasoline prices on the demands for many goods, without imposing any economic separability assumptions.

Quantifying price-driven wireless substitution in telephony

For the better part of a decade, a non-trivial and steadily increasing share of households in the United States has come to rely exclusively on wireless technology for their voice communications needs. Aggregate data show clearly (1) that the share of wireless-only households has risen steadily in recent years; while (2) the price of wireless service has fallen substantially relative to traditional landline service. The aggregate data are therefore consistent with the hypothesis that wireless/wireline cross-price elasticities are positive and economically significant. However, econometric corroboration of this conjecture has proven elusive in the existing empirical literature, which has relied on datasets compiled at the turn of the millennium, when wireless substitution was very limited. Partly in response to this dearth of econometric evidence, regulators and competition authorities in the US have generally been reluctant to conclude that wireless voice service represents a meaningful economic substitute for traditional wireline telephony. In the absence of reliable econometric estimates, even the sign of the relevant cross-price elasticities is an open question: The majority of US households maintain both a landline and at least one wireless connection, so it is unclear, ex ante, whether the two services are substitutes or complements. Thus, it is critical to identify consumer behavior at the margin. Using state-level panel data from a relatively recent time period (2001–2007), this study develops and estimates a demand system that permits evaluation of the own-price, cross-price, and income elasticities of demand for wireless and wireline telephony in the United States. A one percent decrease in the price of wireless service is estimated to decrease the demand for fixed-line service by approximately 1.2–1.3%, and the parameter estimates imply that the Slutsky symmetry holds for the demand system. These results substantially exceed prior econometric estimates from the existing empirical literature, and provide evidence that wireless voice service has evolved into a strong economic substitute for traditional landline service. The parameter estimates from the demand system suggest that roughly two thirds of observed landline attrition in the United States over the sample period is attributable to the observed decline in the relative price of wireless service.

US import demand for apple: source differentiated almost ideal demand system approach

We adopted a restricted version of Source Differentiated Almost Ideal Demand System (RSDAIDS) to analyse the US import demand for fresh apples, apple juice and other processed apples after differentiating each type of apple by import origins. Seasonality and time trend variables were included in the RSDAIDS model and the general demand restrictions of adding-up, homogeneity and slutsky symmetry were imposed. The system of equations is then estimated using Seemingly Unrelated Regression (SUR) and the results of the estimation are presented in the form of parameter estimates, as well as price and expenditure elasticities.

A note on demand functions with uncertainty

Demand functions with “additive” and “multiplicative” uncertainty can fail to satisfy the “Slutsky symmetry” conditions required for demand to be based on utility maximization. This makes welfare analysis infeasible, which is important in many applications. Additive uncertainty can also generate negative demand realizations, and this can create non-trivial analytical problems.

Semiparametric indirect utility and consumer demand

A semiparametric model of consumer demand is considered. In the model, the indirect utility function is specified as a partially linear, where utility is nonparametric in expenditure and parametric (with fixed- or varying-coefficients) in prices. Because the starting point is a model of indirect utility, rationality restrictions like homogeneity and Slutsky symmetry are easily imposed. The resulting model for expenditure shares (as functions of expenditures and prices) is locally given by a fraction whose numerator is partially linear, but whose denominator is nonconstant and given by the derivative of the numerator. The basic insight is that given a local polynomial model for the numerator, the denominator is given by a lower order local polynomial. The model can thus be estimated using modified versions of local polynomial modeling techniques. For inference, a new asymmetric version of the wild bootstrap is introduced. Monte Carlo evidence that the proposed technique’s work is provided as well as an implementation of the model on Canadian consumer expenditure and price micro-data.

Semiparametric estimation of consumer demand systems in real expenditure

AbstractMicrodata concerning consumer demand typically show considerable variation in real expenditures, but very little variation in prices. We propose a semiparametric strategy for the consumer demand problem in which expenditure share equations are estimated nonparametrically in the real expenditure direction and estimated parametrically (with fixed or varying coefficients) in price directions. In our model, Engel curves are unrestricted: demands may have any rank. Because the demand model is derived from a cost function, it may be restricted to satisfy integrability and used for consumer surplus calculations. Since real expenditure is unobserved, but rather estimated under the model, we face a semiparametric model with a nonparametrically generated regressor. We show efficient convergence rates for parametric and nonparametric components. We illustrate the feasibility of our proposed strategy using Canadian expenditure and price data: Engel curves display curvature which cannot be encompassed by standard parametric models. We also find that the rationality restriction of Slutsky symmetry is rejected in the fixed‐coefficients model, but not in the varying‐coefficients model. Copyright © 2009 John Wiley & Sons, Ltd.

Semiparametric Estimation of Consumer Demand Systems in Real Expenditure

Consumer demand microdata typically exhibit a great deal of expenditure variation but not very much price variation. In this paper, we propose a semiparametric approach to the consumer demand problem in which expenditure share equations are nonparametric in the real expenditure direction and parametric (with fixed coefficients) in price directions. Here, Engel curves are unrestricted so that demands may have any rank. We also consider a 'varying coefficients' extension in which price effects depend on real expenditure. Because the demand model is derived from a model of cost, it may be restricted to satisfy integrability and used for consumer surplus calculations. Since real expenditure is not observed, but rather estimated under the model, we face a semiparametric model with a nonparametrically generated regressor. We show efficient convergence rates for parametric and nonparametric components. The estimation procedures are introduced for both cases, under integrability restrictions and without. Further we give specification tests to check these integrability restrictions. An empirical illustration with Canadian price and expenditure data shows that Engel curves display curvature which cannot be encompassed by standard parametric models. In addition, we find that although the rationality restriction of Slutsky symmetry is rejected in our fixed coefficients model, it is not rejected in the varying coefficients extension.

Testing and imposing Slutsky symmetry in nonparametric demand systems

Maximization of utility implies that consumer demand systems have a Slutsky matrix which is everywhere symmetric. However, previous non- and semi-parametric approaches to the estimation of consumer demand systems do not give estimators that are restricted to satisfy this condition, nor do they offer powerful tests of this restriction. We use nonparametric modeling to test and impose Slutsky symmetry in a system of expenditure share equations over prices and expenditure. In this context, Slutsky symmetry is a set of nonlinear cross-equation restrictions on levels and derivatives of consumer demand equations. The key insight is that due to the differing convergence rates of levels and derivatives and due to the fact that the symmetry restrictions are linear in derivatives, both the test and the symmetry restricted estimator behave asymptotically as if these restrictions were (locally) linear. We establish large and finite sample properties of our methods, and show that our test has advantages over the only other comparable test. All methods we propose are implemented with Canadian micro-data. We find that our nonparametric analysis yields statistically significantly and qualitatively different results from traditional parametric estimators and tests.

A public good version of the collective household model: an empirical approach with an application to British household data

In this paper we consider an empirical collective household model of time allocation for two-earner households. The novelty of this paper is that we estimate a version of the collective household model, where the internally produced goods and externally purchased goods are assumed to be public. The empirical results suggest that (1) Preferences of men and women differ; (2) Although there are significant individual variations, on average the utility functions of men and women are equally weighted in the household utility function; (3) Differences in the ratio of the partners’ hourly wages are explanatory for how individual utilities are weighted in the household utility function. (4) The female’s preference for household production is influenced by family size, but this does not hold for the male; (5) Both the male and the female have a backward-bending labor supply curve; (6) Labor-supply curves are forward-bending with respect to the partner’s wage rate; (7) Our model rejects the unitary Slutsky symmetry condition.

A Public Good Version of the Collective Household Model: An Empirical Approach with an Application to British Household Data

In this paper we consider an empirical collective household model of time allocation for two-earner households. The novelty of this paper is that we estimate a version of the collective household model, where the internally produced goods and the externally purchased goods are assumed to be public. The empirical results suggest that: (1) Preferences of men and women differ; (2) Although there are significant individual variations, on average the utility functions of men and women are equally weighted in the household utility function; (3) Differences in the ratio of the partners' hourly wages are explanatory for how individual utilities are weighted in the household utility function. (4) The female's preference for household production is influenced by family size, but this does not hold for the male; (5) Both the male and the female have a backward-bending labor supply curve; (6) Labor-supply curves are forward-bending with respect to the partner's wage rate; (7) Our model rejects the unitary Slutsky symmetry condition.

A Public Good Version of the Collective Household Model: An Empirical Approach with an Application to British Household Data

In this paper we consider an empirical collective household model of time allocation for two-earner households. The novelty of this paper is that we estimate a version of the collective household model, where the internally produced goods and the externally purchased goods are assumed to be public. The empirical results suggest that: (1) Preferences of men and women differ; (2) Although there are significant individual variations, on average the utility functions of men and women are equally weighted in the household utility function; (3) Differences in the ratio of the partners' hourly wages are explanatory for how individual utilities are weighted in the household utility function. (4) The female's preference for household production is influenced by family size, but this does not hold for the male; (5) Both the male and the female have a backward-bending labor supply curve; (6) Labor-supply curves are forward-bending with respect to the partner's wage rate; (7) Our model rejects the unitary Slutsky symmetry condition.

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.

Similarities in the Consumption Patterns of the Five Asian Tigers

The five countries of Hong Kong, Japan, Korea, Singapore and Taiwan are considered to be the major Asian economic ‘Tigers’ behind Asia's growth in the late 1900s. In this paper, we analyze the consumption patterns of these five countries, using the most recent consumption data and employing the system‐wide approach. We find that the consumption data from these five countries support a number of empirical regularities, including the ‘law of demand’ and ‘Engel's law’. Based on the estimation results, we find that in all five countries, food, housing and medical care (except in Taiwan) are necessities, while clothing, durables (except in Singapore) and transport are luxuries. Demand for all the commodities is price inelastic. Furthermore, we find that the demand hypothesis, homogeneity, is acceptable for all five countries while Slutsky symmetry is acceptable only for Hong Kong, Singapore and Taiwan. We also find that the preference‐independence hypothesis is acceptable for all countries except Japan. Overall, consumption patterns of consumers appear to be similar across the five countries, while some differences exist between Japan and the other four countries.