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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Afriat S. (1967) The construction of a utility function from expenditure data. International Economic Review 8: 67–77
Barnhart S. W., Whitney G. A. (1988) Nonparametric analysis in parametric estimation: An application to translog demand systems. Review of Economics and Statistics 70: 149–153
Blackorby C., Primont D., Russell R. R. (1978) Duality, Separability, and Functional Structure. North-Holland, Amsterdam
Blackorby C., Russell R. R. (1994) The conjunction of direct and indirect separability. Journal of Economic Theory 62: 480–498
Brown D., Shannon C. (2000) Uniqueness, stability, and comparative statics in rationalizable Walrasian markets. Econometrica 68: 1529–1539
Cherchye D., Rock B., Vermeulen F. (2010) An Afriat’s theorem for the collective model of household consumption. Journal of Economic Theory 145: 1142–1163
Diewert W. E. (1973) Afriat and revealed preference theory. The Review of Economic Studies 40: 419–425
Diewert W. E., Parkan C. (1978) Tests for the Consistency Of Consumer Data and Nonparametric Index Numbers. Discussion Paper 78-27. Department of Economics, University of British Columbia, Vancouver
Diewert W. E., Parkan C. (1985) Tests for the consistency of consumer data. Journal of Econometrics 30: 127–147
Drake L. M., Fleissig A. R., Swofford J. L. (2003) A semi-nonparametric approach to the demand for UK monetary assets. Economica 70: 99–120
Fleissig A. R., Whitney G. A. (2003) A new PC-based test for Varian’s weak separability conditions. Journal of Business and Economic Statistics 21: 133–143
Forges F., Minelli E. (2009) Afriat’s theorem for general budget sets. Journal of Economic Theory 144: 135–145
Fostel A., Scarf H. E., Todd M. J. (2004) Two proofs of Afriat’s theorem. Economic Theory 24: 211–219
Gross J. (1995) Testing data for consistency with revealed preference. The Review of Economics and Statistics 77: 701–710
Hjertstrand P. (2007) Food demand in Sweden: A non-parametric approach. In: Barnett W.A., Serletis A. (eds) Functional Structure Inference. International Symposia in Economic Theory and Econometrics (ISETE). Elsevier Science, London, pp 157–182
Hjertstrand P. (2009) A Monte Carlo study of the necessary and sufficient conditions for weak separability. In: Binner J.M., Edgerton D.L., Elger T. (eds) Measurement Error—Consequences, Applications and Solutions. Advances in Econometrics (Vol 24). Bingley, UK, Emerald Group Publishing, pp 151–182
Houthakker H. S. (1950) Revealed preference and the utility function. Economica 17: 159–174
Moschini G. (2001) A flexible multistage demand system based on indirect separability. Southern Economic Journal 68: 22–41
Sakai Y. (1977) Revealed favorability, indirect utility, and direct utility. Journal of Economic Theory 14: 113–129
Samuelson P. A. (1938) A note on the pure theory of consumer’s behaviour. Economica 5: 61–71
Serletis A., Shahmoradi A. (2005) Semi-nonparametric estimates of the demand for money in the United States. Macroeconomic Dynamics 9: 542–559
Swofford J. L., Whitney G. A. (1987) Nonparametric tests of utility maximization and weak separability for consumption, leisure and money. The Review of Economics and Statistics 69: 458–464
Swofford J. L., Whitney G. A. (1994) A revealed preference test for weakly separable utility maximization with incomplete adjustment. Journal of Econometrics 60: 235–249
Varian H. R. (1982) The nonparametric approach to demand analysis. Econometrica 50: 945–973
Varian H. R. (1983) Nonparametric tests of consumer behavior. Review of Economic Studies 50: 99–110
Varian H. R. (2006) Revealed preference. In: Szenberg M., Ramrattan L., Gottesman A. A. (eds) Samuelsonian Economics and the Twenty-First Century. Oxford University Press, Oxford, pp 99–115
About this article
Cite this article
Hjertstrand, P., Swofford, J.L. Revealed preference tests for consistency with weakly separable indirect utility. Theory Decis 72, 245–256 (2012). https://doi.org/10.1007/s11238-010-9226-3
- Revealed preference
- Indirect utility
- Weak separability