Indirect Utility Function Research Articles

Revealed Preference Tests for Weak Separability: An Integer Programming Approach

We focus on the revealed preference conditions that characterize the collection of finite data sets that are consistent with the maximization of a weakly separable utility function. From a theoretical perspective, we show that verifying these revealed preference conditions is a difficult problem, i.e. it is NP-complete. From a practical perspective, we present an integer programming approach that can verify the revealed preference conditions in a straightforward way, which is particularly attractive in view of empirical analysis. We demonstrate the versatility of this integer programming approach by showing that it also allows for testing homothetic separability and weak separability of the indirect utility function. We illustrate the practical usefulness of the approach by an empirical application to Spanish household consumption data.

Risk Aversion and Portfolio Selection in a Continuous-Time Model

The comparative statics of the optimal portfolios across individuals is carried out for the Black-Scholes market model. It turns out that the indirect utility functions inherit the order of risk aversion (in the Arrow-Pratt sense) from the von Neumann-Morgenstern utility functions, and therefore, a more risk-averse agent would invest less wealth (in absolute value) in the risky asset.

HOW DOES INFORMATION PROVISION AFFECT RESIDENTIAL ENERGY CONSERVATION? EVIDENCE FROM A FIELD EXPERIMENT

This paper attempts to measure the benefits of information about efficient usage of electric appliances consumers receive through energy conservation, using data from a Japanese experiment. In the experiment, households could easily obtain information on how to achieve efficient usage of electric appliances through a display installed at their residence. The data were used to estimate a utility-consistent, discrete−continuous model of display usage and electricity demand. Full information maximum likelihood estimates of a translog indirect utility function and electricity cost share function indicate that information provision contributed to energy conservation and to welfare improvements of consumers in the experiment.

Global restrictions on the parameters of the CDES indirect utility function

This paper extends the analytical and empirical application of the basic indirect utility function of Houthakker–Hanoch—called the CDES specification (constant differences of elasticities of substitution). The non-homothetic CDES preferences are the natural parametric extension on the global domain of the homothetic CES preferences with many commodities, and CDES can conveniently be used in specifying CGE multisector models with a demand side satisfying observable Engel curve patterns. Moreover, all Marshallian own-price elasticities are no longer restricted to exceed one, and positive and negative cross-price effects are allowed for in empirical demand analyses. Explicit calculations of the Allen elasticities of substitution are instrumental in demonstrating the economic implications of the parameters of indirect utility functions with global regularity properties and flexibility of the derived demand systems.

Preferences estimation without approximation

We devise an estimation methodology which allows preferences estimation and comparative statics analysis without a reliance on Taylor’s approximations and the indirect utility function.

Identities for Homogeneous Utility Functions

Using a homogeneous and continuous utility function that represents a household's preferences, this paper proves explicit identities between most of the different objects that arise from the utility maximization and the expenditure minimization problems. The paper also outlines the homogeneity properties of each object. Finally, we show explicit algebraic ways to go from the indirect utility function to the expenditure function and from the Marshallian demand to the Hicksian demand and vice versa, without the need of any other function, thus simplifying the integrability problem avoiding the use of differential equations.

Portfolio selection and duality under mean variance preferences

This paper uses duality to analyze an investor’s behavior in a n-asset portfolio selection problem when the investor has mean variance preferences. The indirect utility and wealth requirement functions are used to derive Roy’s identity, Shephard’s lemma and the Slutsky equation. In our simple Slutsky equation the income effect is characterized by decreasing absolute risk aversion (DARA) and the substitution effect is always positive [negative] with respect to an asset’s holding if the asset’s mean return [risk] increases. Substitution effect and income effect work in the same direction presupposed mean variance preferences display DARA.

Identification and Semiparametric Estimation of Equilibrium Models of Local Jurisdictions

We develop a new model of household sorting in a system of residential neighborhoods. We show that this model is partially identified without imposing parametric restrictions on the distribution of unobserved tastes for neighborhood quality and the shape of the indirect utility function. The proof of identification is constructive and can be used to derive a new semiparameteric estimator. Our empirical application focuses on residential choices in the Pittsburgh metropolitan area. We find that sorting of households with children exhibit more stratification by income than sorting of households without children. (JEL C51, D12, H41, J12, R21, R23)

Estimation of Consumer Demand Functions When the Observed Prices are the Same for All Sample Units

With the advent of the almost ideal demand system (AIDS) of Deaton and Muellbauer, the estimation of consumer demand functions revolves around specifications that use flexible functional forms of the indirect utility function. This dual approach has put on the backburner the traditional primal approach because the direct utility function exists only in a latent state. The lack of explicit, analytical invertibility of either system, however, is an indication that focusing exclusively on the dual side of the consumer problem is equivalent to disregard potentially important and independent information residing with the primal side. This paper suggests that efficient estimates (in the sense of using all the available information) of the demand functions require the joint estimation of all the primal and dual relations. The specification of this objective assumes that risk neutral households maximize their expected utility subject to their expected budget constraint. This theoretical framework leads to a two-step procedure that produces consistent and efficient estimates of the model’s parameters. The generality of the approach proposed here can handle also the frequently encountered case when all the sample units face the same observed commodity prices. Finally, we present a general solution of the nonlinear errors-in-variables problem with a novel estimation procedure that avoids the pitfalls of the traditional approach.

Revealed preference tests for consistency with weakly separable indirect utility

Since Varian (Econometrica 50:945–973, 1982; Review of Economic Studies 50:90–110, 1983) made checking for consistency with revealed preference conditions more accessible to empirical researchers; researchers have often used revealed preference procedures to test their maintained hypotheses and narrow the scope of their demand studies. The tests developed by Varian are for the direct utility function, while researchers estimating demand systems often find it convenient to model consumer behavior with an indirect utility function. Unfortunately structure revealed in the direct utility function does not necessarily follow for the indirect utility function. To remedy this problem, we set forth conditions for checking consumer data for consistency with revealed preference conditions for minimization and weak separability of the indirect utility function.

Econometric Effects of Utility Order-Preserving Transformations in Discrete Choice Models

In the random utility modelling context, choice probabilities are unaffected by increasing linear transformations of the systematic utility; hence its empirical specification is derived on the basis that only differences in utility matters and that the scale of utility is arbitrary. We argue that choice probabilities remain unchanged if these linear transformations are made under the deterministic perspective of a single individual choosing several times. But, in the random utility setting, parameter estimates might be significantly affected by these transformations. In particular we focus on the effect of two order-preserving transformations usually applied in the derivation of the representative utility from the conditional indirect utility function: adding a constant to the utility of all alternatives and multiplying each alternative utility by a constant. We concentrate on the two most popular specifications in transport mode choice: the “wage rate” (Train and McFadden Transport Res 12:349–353, 1978) and the “expenditure rate” (Jara-Diaz and Farah Transport Res 22B:159–171, 1987) specifications. Using a collection of synthetic datasets generated in a new fashion directly from the conditional indirect utility function, i.e. before applying any expansion or transformation, we demonstrate how taking this class of order-preserving transformations could lead to misinterpretation of the econometric results, such as detecting randomly distributed and correlated parameters and/or income and time effects which are in fact not present.

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.

A welfare estimation of beach recreation with aggregate data

A single-site travel cost recreation demand model for a representative agent visiting a beach is employed that uses an indirect utility function. Alternative specifications of the expected demand function are estimated with aggregate time-series data from a local beach park. The estimated parameters are used to compute the value of the consumer surplus. The recreational value of the park is expectedly sensitive to the functional form used. Also, own-price and income elasticities for various functional forms vary. The results from the Box–Cox procedure suggest that the semi-log function is the most appropriate for the data used in this study. Confidence intervals are calculated to deal with the reliability problem of the consumer surplus estimates. An alternative algorithm, which assumes omitted variable as the source of the error in the demand function, is also presented.

Hicksian Welfare Measures and the Normative Endowment Effect

We show that the Hicksian welfare measures of compensating variation and equivalent variation coincide if one of them is evaluated at a compensated income. The measures are nondecreasing in income if the varied attribute and income are complementary, and indirect utility is concave in income. Income monotonicity implies the normative endowment effect, which refers to a situation where the equivalent variation exceeds the compensating variation. We provide additional sufficient conditions for the normative endowment effect based on various properties of the compensated income and proximity of income to indifference points, respectively. Lastly, we discuss empirical implications, notably that in the global absence of an endowment effect both Hicksian welfare measures must be independent of income and the indirect utility function additively separable in income.

Portfolio selection in multidimensional general and partial moment space

This paper develops a general approach for the single period portfolio optimization problem in a multidimensional general and partial moment space. A shortage function is defined that looks for possible increases in odd moments and decreases in even moments. A main result is that this shortage function ensures sufficient conditions for global optimality. It also forms a natural basis for developing tests on the influence of additional moments. Furthermore, a link is made with an approximation of an arbitrary order of a general indirect utility function. This non-parametric efficiency measurement framework permits to differentiate mainly between portfolio efficiency and allocative efficiency. Finally, information can, in principle, be inferred about the revealed risk aversion, prudence, temperance and other higher-order risk characteristics of investors.

A Cautionary Note on Designing Discrete Choice Experiments: A Comment on Lusk and Norwood's “Effect of Experiment Design on Choice‐Based Conjoint Valuation Estimates”

AbstractRecent Monte Carlo work on choosing experimental designs for discrete choice experiments seemed to greatly simplify this choice for applied researchers. It suggested that (a) commonly used designs can generate unbiased estimates for indirect utility function specifications with main effects only and main effects plus higher order terms, and (b) random designs are more efficient than main effects designs. We show that these results are very specific to the particular indirect utility specifications studied and do not generalize well. We further show that conclusions drawn concerning random designs are problematic and potentially dangerous for applied researchers.

Think twice before you book? Modelling the choice of public vs private dentist in a choice experiment

This study concerns the choice of primary dental service provider by consumers. If the health service delivery system allows individuals to choose between public-care providers or if complementary private services are available, it is typically assumed that utilisation is a three-stage decision process. The patient first makes a decision to seek care, and then chooses the service provider. The final stage, involving decisions over the amount and form of treatment, is not considered here. The paper reports a discrete choice experiment (DCE) designed to evaluate attributes affecting individuals' choice of dental-care provider. The feasibility of the DCE approach in modelling consumers' choice in the context of non-acute need for dental care is assessed. The aim is to test whether a separate two-stage logit, a multinomial logit, or a nested logit best fits the choice process of consumers. A nested logit model of indirect utility functions is estimated and inclusive value (IV) constraints are tested for modelling implications. The results show that non-trading behaviour has an impact on the choice of appropriate modelling technique, but is to some extent dependent on the choice of scenarios offered. It is concluded that for traders multinomial logit is appropriate, whereas for non-traders and on average the nested logit is the method supported by the analyses. The consistent finding in all subgroup analyses is that the traditional two-stage decision process is found to be implausible in the context of consumer's choice of dental-care provider.

Assessing the value of museums with a combined discrete choice/count data model

This article assesses the value of Dutch museums using information about destination choice as well as about the number of trips undertaken by an actor. Destination choice is analysed by means of a mixed logit model, and a count data model is used to explain trip generation. We use a utility-consistent framework in which the discrete choice model for destination choice is linked to an indirect utility function. The results are used to compute the compensating variation of particular museums and of the total group of museums in the sample.

Testing expected utility maximization under price and quantity risk with a heterogeneous panel

Refutable implications based on the curvature properties of the indirect utility function for the competitive firm operating under uncertainty are extended to the case of both price and quantity uncertainty. Using unit roots and cointegration tests for heterogeneous panels, a model of US agricultural production is developed based on the time-series properties of a panel of state-level data. Most refutable hypotheses under output price and output quantity risk are not rejected, but symmetry conditions implied by a twice-continuously-differentiable indirect utility function are rejected. The same test conclusions are obtained from a traditional model that presumes stationarity in all variables.

Preferences Estimation Without Approximation

We devise an estimation methodology which allows preferences estimation and comparative statics analysis without reliance on Taylor's approximations and the indirect utility function.