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A lattice test for additive separability

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  • Matthew Polisson

    () (Institute for Fiscal Studies and Bristol University)

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. 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.
    2. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    3. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804.
    4. John Quah, 2014. "A test for weakly separable preferences," Economics Series Working Papers 708, University of Oxford, Department of Economics.
    5. Andrew Leicester & Zoë Oldfield, 2009. "Using Scanner Technology to Collect Expenditure Data," Fiscal Studies, Institute for Fiscal Studies, vol. 30(Special I), pages 309-337, December.
    6. 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.
    7. Yoram Halevy & Dotan Persitz & Lanny Zrill, 2018. "Parametric Recoverability of Preferences," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1558-1593.
    8. Pierre Dubois & Rachel Griffith & Aviv Nevo, 2014. "Do Prices and Attributes Explain International Differences in Food Purchases?," American Economic Review, American Economic Association, vol. 104(3), pages 832-867, March.
    9. 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.
    10. 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.
    11. Blundell, Richard, 1988. "Consumer Behaviour: Theory and Empirical Evidence--a Survey," Economic Journal, Royal Economic Society, vol. 98(389), pages 16-65, March.
    12. Fleissig, Adrian R. & Whitney, Gerald A., 2008. "A nonparametric test of weak separability and consumer preferences," Journal of Econometrics, Elsevier, vol. 147(2), pages 275-281, December.
    13. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
    14. repec:dau:papers:123456789/4099 is not listed on IDEAS
    15. 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.
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    Cited by:

    1. Federico Echenique, 2019. "New developments in revealed preference theory: decisions under risk, uncertainty, and intertemporal choice," Papers 1908.07561, arXiv.org, revised Dec 2019.

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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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