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A lattice test for additive separability

Author

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  • Matthew Polisson

    (Institute for Fiscal Studies and University of Bristol)

Abstract

We derive necessary and sufficient conditions for a finite data set of price and demand observations to be consistent with an additively separable preference. We do so without imposing concavity on any of the subutility functions or convexity of the budget set a priori, thereby generalizing earlier results. Our simple and intuitive lattice test easily accommodates departures from rationality, or errors, which subsequently facilitates a rich empirical analysis. We apply our econometric techniques to the food consumption of a panel of British households. The primary empirical finding is that additive separability has considerable success in explaining the data.

Suggested Citation

  • Matthew Polisson, 2018. "A lattice test for additive separability," IFS Working Papers W18/08, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:ifsewp:18/08
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    References listed on IDEAS

    as
    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. Matthew Polisson & John K.-H. Quah & Ludovic Renou, 2020. "Revealed Preferences over Risk and Uncertainty," American Economic Review, American Economic Association, vol. 110(6), pages 1782-1820, June.
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    5. John Quah, 2014. "A test for weakly separable preferences," Economics Series Working Papers 708, University of Oxford, Department of Economics.
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    8. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    9. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram & Hjertstrand, Per, 2015. "Revealed preference tests for weak separability: An integer programming approach," Journal of Econometrics, Elsevier, vol. 186(1), pages 129-141.
    10. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
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    13. Swofford, James L & Whitney, Gerald A, 1988. "Comparison of Nonparametric Tests of Weak Separability for Annual and Quarterly Data on Consumption, Leisure, and Money," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(2), pages 241-246, April.
    14. Swofford, James L & Whitney, Gerald A, 1987. "Nonparametric Tests of Utility Maximization and Weak Separability for Consumption, Leisure and Money," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 458-464, August.
    15. Matthew Polisson & John K.-H. Quah & Ludovic Renou, 2020. "Revealed Preferences over Risk and Uncertainty," American Economic Review, American Economic Association, vol. 110(6), pages 1782-1820, June.
    16. Fleissig, Adrian R & Whitney, Gerald A, 2003. "A New PC-Based Test for Varian's Weak Separability Conditions," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 133-144, January.
    17. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762.
    18. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 99-110.
    19. Fleissig, Adrian R. & Whitney, Gerald A., 2007. "Testing additive separability," Economics Letters, Elsevier, vol. 96(2), pages 215-220, August.
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    22. Ian Crawford & Matthew Polisson, 2015. "Demand Analysis with Partially Observed Prices," Discussion Papers in Economics 15/12, Division of Economics, School of Business, University of Leicester, revised Dec 2016.
    23. Timothy K. M. Beatty & Ian A. Crawford, 2011. "How Demanding Is the Revealed Preference Approach to Demand?," American Economic Review, American Economic Association, vol. 101(6), pages 2782-2795, October.
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    Cited by:

    1. Marco Castillo & Mikhail Freer, 2023. "A general revealed preference test for quasilinear preferences: theory and experiments," Experimental Economics, Springer;Economic Science Association, vol. 26(3), pages 673-696, July.
    2. Federico Echenique, 2020. "New Developments in Revealed Preference Theory: Decisions Under Risk, Uncertainty, and Intertemporal Choice," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 299-316, August.
    3. Mikhail Freer & Marco Castillo, 2021. "A General Revealed Preference Test for Quasilinear Preferences: Theory and Experiments," Papers 2111.01248, arXiv.org, revised Dec 2022.

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    More about this item

    Keywords

    additive separability; consumer demand; lattice test; revealed preference;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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