IDEAS home Printed from https://ideas.repec.org/p/ifs/ifsewp/15-16.html
   My bibliography  Save this paper

Demand analysis with partially observed prices

Author

Listed:
  • Ian Crawford

    (Institute for Fiscal Studies and Nuffield College, Oxford)

  • Matthew Polisson

    (Institute for Fiscal Studies and University of Bristol)

Abstract

In empirical demand, industrial organization, and labor economics, prices are often unobserved or unobservable since they may only be recorded when an agent transacts. In the absence of any additional information, this partial observability of prices is known to lead to a number of identi?cation problems. However, in this paper, we show that theory-consistent demand analysis remains feasible in the presence of partially observed prices, and hence partially observed implied budget sets, even if we are agnostic about the nature of the missing prices. Our revealed preference approach is empirically meaningful and easy to implement. We illustrate using simple examples.

Suggested Citation

  • Ian Crawford & Matthew Polisson, 2015. "Demand analysis with partially observed prices," IFS Working Papers W15/16, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:ifsewp:15/16
    as

    Download full text from publisher

    File URL: https://www.ifs.org.uk/uploads/publications/wps/WP201516.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Walter Beckert & Richard Blundell, 2008. "Heterogeneity and the Non-Parametric Analysis of Consumer Choice: Conditions for Invertibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(4), pages 1069-1080.
    3. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    4. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    5. Richard Blundell & Martin Browning & Laurens Cherchye & Ian Crawford & Bram De Rock & Frederic Vermeulen, 2015. "Sharp for SARP: Nonparametric Bounds on Counterfactual Demands," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 43-60, February.
    6. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    7. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    8. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
    9. Meghir, Costas & Robin, Jean-Marc, 1992. "Frequency of purchase and the estimation of demand systems," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 53-85.
    10. Neary, J. P. & Roberts, K. W. S., 1980. "The theory of household behaviour under rationing," European Economic Review, Elsevier, vol. 13(1), pages 25-42, January.
    11. Yuichi Kitamura & Jörg Stoye, 2013. "Nonparametric analysis of random utility models: testing," CeMMAP working papers 36/13, Institute for Fiscal Studies.
    12. Varian, Hal R., 1988. "Revealed preference with a subset of goods," Journal of Economic Theory, Elsevier, vol. 46(1), pages 179-185, October.
    13. Arthur Lewbel & Krishna Pendakur, 2009. "Tricks with Hicks: The EASI Demand System," American Economic Review, American Economic Association, vol. 99(3), pages 827-863, June.
    14. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    15. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    16. Richard W. Blundell & Martin Browning & Ian A. Crawford, 2003. "Nonparametric Engel Curves and Revealed Preference," Econometrica, Econometric Society, vol. 71(1), pages 205-240, January.
    17. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    18. P. A. Samuelson, 1947. "Some Implications of "Linearity."," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 15(2), pages 88-90.
    19. Rosa L. Matzkin, 2008. "Identification in Nonparametric Simultaneous Equations Models," Econometrica, Econometric Society, vol. 76(5), pages 945-978, September.
    20. Blundell, Richard & Kristensen, Dennis & Matzkin, Rosa, 2014. "Bounding quantile demand functions using revealed preference inequalities," Journal of Econometrics, Elsevier, vol. 179(2), pages 112-127.
    21. Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
    22. Matthew Polisson & John K.-H. Quah, 2013. "Revealed Preference in a Discrete Consumption Space," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 28-34, February.
    23. Atkinson, A B & Gomulka, J & Stern, N H, 1990. "Spending on Alcohol: Evidence from the Family Expenditure Survey 1970-1983," Economic Journal, Royal Economic Society, vol. 100(402), pages 808-827, September.
    24. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    25. Keen, Michael, 1986. "Zero Expenditures and the Estimation of Engel Curves," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(3), pages 277-286, July.
    26. Richard Blundell & Martin Browning & Ian Crawford, 2007. "Improving Revealed Preference Bounds On Demand Responses," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1227-1244, November.
    27. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    28. 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.
    29. Stefan Hoderlein & Jörg Stoye, 2014. "Revealed Preferences in a Heterogeneous Population," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 197-213, May.
    30. Deaton, Angus & Irish, Margaret, 1984. "Statistical models for zero expenditures in household budgets," Journal of Public Economics, Elsevier, vol. 23(1-2), pages 59-80.
    31. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
    32. E. Rothbarth, 1941. "The Measurement of Changes in Real Income under Conditions of Rationing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 8(2), pages 100-107.
    33. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    34. Haag, Berthold R. & Hoderlein, Stefan & Pendakur, Krishna, 2009. "Testing and imposing Slutsky symmetry in nonparametric demand systems," Journal of Econometrics, Elsevier, vol. 153(1), pages 33-50, November.
    35. Fleissig, Adrian R. & Whitney, Gerald, 2011. "A revealed preference test of rationing," Economics Letters, Elsevier, vol. 113(3), pages 234-236.
    36. Browning, Martin, 1989. "A Nonparametric Test of the Life-Cycle Rational Expectations Hypothesis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 979-992, November.
    37. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
    38. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-829, July.
    39. Stefan Hoderlein & Jörg Stoye, 2015. "Testing stochastic rationality and predicting stochastic demand: the case of two goods," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 313-328, October.
    40. Thomas Demuynck & Ewout Verriest, 2013. "I’Ll Never Forget My First Cigarette: A Revealed Preference Analysis Of The “Habits As Durables” Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(2), pages 717-738, May.
    41. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 419-425.
    42. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Thomas Demuynck & Christian Seel, 2018. "Revealed Preference with Limited Consideration," American Economic Journal: Microeconomics, American Economic Association, vol. 10(1), pages 102-131, February.
    2. Christopher Dobronyi & Christian Gouri'eroux, 2020. "Consumer Theory with Non-Parametric Taste Uncertainty and Individual Heterogeneity," Papers 2010.13937, arXiv.org, revised Jan 2021.
    3. Laurens Cherchye & Bram De Rock & Khushboo Surana, 2024. "Marital Matching, Labor Market Participation and Individual Welfare Analysis," Working Papers ECARES 2024-07, ULB -- Universite Libre de Bruxelles.
    4. Matthew Polisson, 2018. "A lattice test for additive separability," IFS Working Papers W18/08, Institute for Fiscal Studies.
    5. Matthew Polisson, 2018. "A lattice test for additive separability," IFS Working Papers W18/08, Institute for Fiscal Studies.
    6. Dieter Saelens, 2022. "Unitary or collective households? A nonparametric rationality and separability test using detailed data on consumption expenditures and time use," Empirical Economics, Springer, vol. 62(2), pages 637-677, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sam Cosaert & Thomas Demuynck, 2018. "Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 349-361, May.
    2. Cherchye, Laurens & Demuynck, Thomas & Rock, Bram De, 2019. "Bounding counterfactual demand with unobserved heterogeneity and endogenous expenditures," Journal of Econometrics, Elsevier, vol. 211(2), pages 483-506.
    3. Blundell, Richard & Kristensen, Dennis & Matzkin, Rosa, 2014. "Bounding quantile demand functions using revealed preference inequalities," Journal of Econometrics, Elsevier, vol. 179(2), pages 112-127.
    4. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    5. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    6. Hubner, Stefan, 2023. "Identification of unobserved distribution factors and preferences in the collective household model," Journal of Econometrics, Elsevier, vol. 234(1), pages 301-326.
    7. Stefan Hoderlein & Jörg Stoye, 2015. "Testing stochastic rationality and predicting stochastic demand: the case of two goods," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 313-328, October.
    8. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers 60/17, Institute for Fiscal Studies.
    9. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    10. Abi Adams & Richard Blundell & Martin Browning & Ian Crawford, 2015. "Prices versus preferences: taste change and revealed preference," IFS Working Papers W15/11, Institute for Fiscal Studies.
    11. Laura Blow & Richard Blundell, 2018. "A Nonparametric Revealed Preference Approach to Measuring the Value of Environmental Quality," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 69(3), pages 503-527, March.
    12. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    13. Molinari, Francesca, 2020. "Microeconometrics with partial identification," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 355-486, Elsevier.
    14. Dette, Holger & Hoderlein, Stefan & Neumeyer, Natalie, 2016. "Testing multivariate economic restrictions using quantiles: The example of Slutsky negative semidefiniteness," Journal of Econometrics, Elsevier, vol. 191(1), pages 129-144.
    15. Yuichi Kitamura & Jörg Stoye, 2013. "Nonparametric analysis of random utility models: testing," CeMMAP working papers 36/13, Institute for Fiscal Studies.
    16. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    17. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.
    18. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2017. "Household Consumption When the Marriage Is Stable," American Economic Review, American Economic Association, vol. 107(6), pages 1507-1534, June.
    19. 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.
    20. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.

    More about this item

    Keywords

    Demand; missing prices; partial identification; revealed preference;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ifs:ifsewp:15/16. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/ifsssuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.