Per Hjertstrand

Consistent subsets: Computationally feasible methods to compute the Houtman–Maks-index

We provide two methods to compute the largest subset of a set of observations that is consistent with the Generalised Axiom of Revealed Preference. The algorithm provided by Houtman and Maks (1985) is not comput ationally feasible for larger data sets, while our methods are not limited in that respect. The first method is a variation of Gross and Kaisers (1996) approximate algorithm and is only applicable for two-dimensional data sets, but it is very fast and easy to implement. The second method is a mixed-integer linear programming approach that is slightly more involved but still fast and not limited by the dimension of the data set.

What Do Revealed Preference Axioms Reveal About Elasticities of Demand

It is well-known that observed data on prices and quantities of a set of goods is consistent with rational choice if the data satisfy revealed preference. In this paper, we derive estimators for demand and substitution elasticities at the observed data points for datasets satisfying the Strong version of the Strong Axiom of Revealed Preference (SSARP) from Chiappori and Rochet (1987). We find that these estimators are identified only up to a strictly positive parameter, which must be small enough that the utility function rationalizing the dataset satisfies certain properties. We show that the estimated elasticities of substitution approach zero in the limit as this parameter approaches zero. Thus, if the dataset satisfies SSARP, then it is consistent with negligible substitutability between any pair of goods at all observed data points. Our estimators are derived directly from results in Brown and Shannon (2000) and Brown and Kannan (2005).

Indirect Estimation of Semiparametric Binary Choice Models

One of the most cited studies within the field of binary choice models is that of Klein and Spady (1993), in which the authors propose a semiparametric estimator for use when the distribution of the error term is unknown. However, although theoretically appealing, the estimator has been found to be difficult to implement, and therefore not very attractive from an applied point of view. The current study offers an indirect inference-based solution to this problem. The new estimator is not only simple with good small-sample properties, but also consistent and asymptotically normal.

Revealed Preference Tests of Utility Maximization and Weak Separability of Consumption, Leisure and Money with Incomplete Adjustment

Swofford and Whitney (1987) investigated the validity of two types of assumptions that underlie the representative agent models of modern macroeconomics and monetary economics. These assumptions are utility maximization and weak or functional separability that is required for an economic aggregate to exist. To reinvestigate the structure of the representative consumer’s preferences we develop a mixed integer programming revealed preference test with incomplete adjustment. We find that both a narrow official US monetary aggregate, M1, and a broad collection of assets are weakly separable. We further find that a modern analog of money as suggested by Friedman and Schwartz (1963) is also weakly separable. We also find that consumption goods and leisure are separable from all monetary goods. We find no evidence that official US M2 or MZERO are consistent with utility maximization and weak separability. That is, the assets in these measures do not meet the requirement for forming an aggregate over goods that is consistent with economic theory. Finally, we find that three broad categories of consumption goods, durables, nondurables and services, do not meet the weak separability conditions required for forming a consumption aggregate. However, a consumption aggregate of nondurables and services is weakly separable.

A Simple Method to Account for Measurement Errors in Revealed Preference Tests

Revealed preference tests are widely used in empirical applications of consumer rationality. These are static tests, and consequently, lack ability to handle measurement errors in the data. This paper extends and generalizes existing procedures that account for measurement errors in revealed preference tests. In particular, it introduces a very efficient method to implement these procedures, which make them operational for large data sets. The paper illustrates the new method for both classical and Berkson measurement errors models.

Homothetic Efficiency: Theory and Applications

We provide a nonparametric revealed preference approach to demand analysis based on homothetic efficiency. Homotheticity is widely assumed (often implicitly) because it is a convenient and often useful restriction. However, this assumption is rarely tested, and data rarely satisfy testable conditions. To overcome this, we provide a way to estimate homothetic efficiency of consumption choices. The method provides considerably higher discriminatory power against random behavior than the commonly used Afriat efficiency. We use experimental and household survey data to illustrate how our approach is useful for different empirical applications and can provide greater predictive success.

Homothetic Efficiency and Test Power: A Non-Parametric Approach

We provide a nonparametric revealed preference approach to demand analysis based on homothetic efficiency. Homotheticity is a useful restriction but data rarely satisfies testable conditions. To overcome this we provide a way to estimate homothetic efficiency of consumption choices. It generalises Heufers (2013) two-dimensional concept to arbitrary dimensions and is motivated by a form of rationalisation similar to Halevy et al. (2012). The method allows to recover larger preferred and worse sets and provides considerably more preditive success and discriminatory power against random behaviour. An application to experimental and household expenditure data illustrates the potential of our approach.

Homothetic Efficiency. A Non-Parametric Approach

This article provides a robust non-parametric approach to demand analysis based on a concept called homothetic efficiency. Homotheticity is a useful restriction or assumption but data rarely satisfy testable conditions. To overcome this problem, this article provides a way to estimate homothetic efficiency of consumption choices by consumers. The basic efficiency index suggested is similar to Afriats (1972) efficiency index and Varians (1993) violation index. It generalises Heufers (2013b) two-dimensional concept to arbitrary dimensions and is motivated by a form of rationalisation similar to the one proposed by Halevy et al. (2012). The method allows to construct scalar factors which can be used to construct revealed preferred and worse sets. The approach also provides considerably more discriminatory power against irrational behaviour than standard utility maximisation. An application to experimental and household expenditure data illustrates how the method allows to recover preferences and increase test power.