Testing for Rationality, Separability and Efficiency

Abstract: This thesis aims to propose, evaluate and apply test procedures for rationality, weak separability and efficiency. In particular, it focuses on nonparametric revealed preference procedures. This approach has the advantage of not having to stipulate any functional form for the utility function, unlike the parametric approach which relies on finding a suitable functional form for the utility function. Many nonparametric approaches to testing rationality and weak separability are based on what is referred to in the literature as Afriat’s theorem. The significance of this theorem is that if the observed data satisfy some testable conditions, then the data may be rationalized by a well-behaved utility function that possesses such properties as being non-satiated, continuous, monotonic and concave. Chapter 2 provides a generalization of Afriat's theorem. It is shown that the concavity condition in the theorem may be relaxed to the weaker assumption of semistrict quasi-concavity. In particular, revealed preference conditions are used to check whether a finite data set can be generated by a non-satiated, continuous, monotone and semistrict quasi-concave utility function. In addition, it is shown that a data set can be checked for consistency with economic theory by solving a simple linear programming problem. Chapter 3 investigates the properties of nonparametric revealed preference tests for weak separability by means of Monte Carlo experiments. A block of goods is said to be weakly separable from all other goods when the marginal rate of substitution between any pair of goods in the separable block does not depend on the quantities consumed of any good that is not in the block. A main finding of this thesis is that the bias of the sequential test proposed by Fleissig and Whitney (2003) is low, but that the performance of the test deteriorates substantially when measurement errors are added to the data. The theoretically unbiased test by Swofford and Whitney (1994) is found to suffer from an empirical bias, most probably because the test is heavily dependent on efficient nonlinear optimization routines. Chapter 4, using a data set that comprises yearly observations from 1963-2002 examines separability structures and the demand for food in the Swedish food market. A data-orientated search method based on the multistep test procedure proposed by Jones, Elger, Edgerton and Dutkowsky (2005) is applied to find an appropriate structuring of goods in the demand analysis. Most agricultural studies assume that animalia products, beverage products and vegetabilia products constitute separable groupings. It is shown that this is a misleading assumption when analysing Swedish food data. Chapter 5, co-authored with Kerstin Enflo, addresses the issue of Western European regional productivity growth and convergence by means of data envelopment analysis (DEA), decomposing labor productivity into efficiency change, technical change and capital accumulation. A main finding is that the relative ranking of efficiency scores obtained using DEA is stable with regard to bias-corrections. The decomposition shows that, on average, capital accumulation and technological change have played roughly equally large roles, whereas efficiency changes have contributed negatively.