IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v222y2021i1p4-43.html
   My bibliography  Save this article

A survey of preference estimation with unobserved choice set heterogeneity

Author

Listed:
  • Crawford, Gregory S.
  • Griffith, Rachel
  • Iaria, Alessandro

Abstract

We provide an introduction to the estimation of discrete choice models when choice sets are heterogeneous and unobserved to the econometrician. We survey the two most popular approaches: “integrating over” and “differencing out” unobserved choice sets. Inspired by Chamberlain (1980)’s original idea of constructing sufficient statistics from observed choices, we introduce the term “sufficient set” to refer to any combination of observed choices that lies within the true but unobserved choice set. The concept of sufficient set helps to unify notation and organize our thinking, to map econometric assumptions onto economic models, and to implement both methods in practice.

Suggested Citation

  • Crawford, Gregory S. & Griffith, Rachel & Iaria, Alessandro, 2021. "A survey of preference estimation with unobserved choice set heterogeneity," Journal of Econometrics, Elsevier, vol. 222(1), pages 4-43.
    • Handle: RePEc:eee:econom:v:222:y:2021:i:1:p:4-43
    DOI: 10.1016/j.jeconom.2020.07.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407620302463
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2020.07.024?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kate Ho & Joseph Hogan & Fiona Scott Morton, 2017. "The impact of consumer inattention on insurer pricing in the Medicare Part D program," RAND Journal of Economics, RAND Corporation, vol. 48(4), pages 877-905, December.
    2. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    3. de Palma, Andre & Picard, Nathalie & Waddell, Paul, 2007. "Discrete choice models with capacity constraints: An empirical analysis of the housing market of the greater Paris region," Journal of Urban Economics, Elsevier, vol. 62(2), pages 204-230, September.
    4. Gary S. Becker & Kevin M. Murphy, 1993. "A Simple Theory of Advertising as a Good or Bad," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 941-964.
    5. Gabrielle Fack & Julien Grenet & Yinghua He, 2019. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," American Economic Review, American Economic Association, vol. 109(4), pages 1486-1529, April.
    6. Pierre Dubois & Rachel Griffith & Martin O'Connell, 2020. "How Well Targeted Are Soda Taxes?," American Economic Review, American Economic Association, vol. 110(11), pages 3661-3704, November.
    7. Fox, Jeremy T. & Kim, Kyoo il & Yang, Chenyu, 2016. "A simple nonparametric approach to estimating the distribution of random coefficients in structural models," Journal of Econometrics, Elsevier, vol. 195(2), pages 236-254.
    8. Gabrielle Fack & Julien Grenet & Yinghua He, 2019. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," American Economic Review, American Economic Association, vol. 109(4), pages 1486-1529, April.
    9. Paola Manzini & Marco Mariotti, 2014. "Stochastic Choice and Consideration Sets," Econometrica, Econometric Society, vol. 82(3), pages 1153-1176, May.
    10. Xavier Gabaix, 2014. "A Sparsity-Based Model of Bounded Rationality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1661-1710.
    11. Andrew Caplin & Mark Dean & Daniel Martin, 2011. "Search and Satisficing," American Economic Review, American Economic Association, vol. 101(7), pages 2899-2922, December.
    12. Ali Hortaçsu & Seyed Ali Madanizadeh & Steven L. Puller, 2017. "Power to Choose? An Analysis of Consumer Inertia in the Residential Electricity Market," American Economic Journal: Economic Policy, American Economic Association, vol. 9(4), pages 192-226, November.
    13. Timothy J. Gilbride & Greg M. Allenby, 2004. "A Choice Model with Conjunctive, Disjunctive, and Compensatory Screening Rules," Marketing Science, INFORMS, vol. 23(3), pages 391-406, October.
    14. Jeremy T. Fox, 2007. "Semiparametric estimation of multinomial discrete-choice models using a subset of choices," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1002-1019, December.
    15. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    16. Patrick Bajari & Jeremy Fox & Stephen Ryan, 2008. "Evaluating wireless carrier consolidation using semiparametric demand estimation," Quantitative Marketing and Economics (QME), Springer, vol. 6(4), pages 299-338, December.
    17. Hausman, Jerry A. & Ruud, Paul A., 1987. "Specifying and testing econometric models for rank-ordered data," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 83-104.
    18. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    19. Christopher R. Walters, 2018. "The Demand for Effective Charter Schools," Journal of Political Economy, University of Chicago Press, vol. 126(6), pages 2179-2223.
    20. Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan & Patrick Bajari, 2011. "A simple estimator for the distribution of random coefficients," Quantitative Economics, Econometric Society, vol. 2(3), pages 381-418, November.
    21. Elisabeth Honka, 2014. "Quantifying search and switching costs in the US auto insurance industry," RAND Journal of Economics, RAND Corporation, vol. 45(4), pages 847-884, December.
    22. , & ,, 2011. "Search, choice, and revealed preference," Theoretical Economics, Econometric Society, vol. 6(1), January.
    23. Kfir Eliaz & Ran Spiegler, 2011. "Consideration Sets and Competitive Marketing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 235-262.
    24. Ruud, Paul A., 1984. "Tests of Specification in Econometrics," Department of Economics, Working Paper Series qt4kq8m0hf, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    25. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 225-238.
    26. John D. Hey & Chris Orme, 2018. "Investigating Generalizations Of Expected Utility Theory Using Experimental Data," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 3, pages 63-98, World Scientific Publishing Co. Pte. Ltd..
    27. Michaela Draganska & Michael Mazzeo & Katja Seim, 2009. "Beyond plain vanilla: Modeling joint product assortment and pricing decisions," Quantitative Marketing and Economics (QME), Springer, vol. 7(2), pages 105-146, June.
    28. Patrick Bajari & Jeremy T. Fox & Stephen P. Ryan, 2007. "Linear Regression Estimation of Discrete Choice Models with Nonparametric Distributions of Random Coefficients," American Economic Review, American Economic Association, vol. 97(2), pages 459-463, May.
    29. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-1240, September.
    30. Jason Abaluck & Abi Adams, 2017. "What do consumers consider before they choose? Identification from asymmetric demand responses," IFS Working Papers W17/09, Institute for Fiscal Studies.
    31. Freyberger, Joachim, 2015. "Asymptotic theory for differentiated products demand models with many markets," Journal of Econometrics, Elsevier, vol. 185(1), pages 162-181.
    32. Levon Barseghyan & Maura Coughlin & Francesca Molinari & Joshua C. Teitelbaum, 2021. "Heterogeneous Choice Sets and Preferences," Econometrica, Econometric Society, vol. 89(5), pages 2015-2048, September.
    33. Martin Gaynor & Carol Propper & Stephan Seiler, 2016. "Free to Choose? Reform, Choice, and Consideration Sets in the English National Health Service," American Economic Review, American Economic Association, vol. 106(11), pages 3521-3557, November.
    34. Pierre Dubois & Rachel Griffith & Martin O’Connell, 2018. "The Effects of Banning Advertising in Junk Food Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 396-436.
    35. Ching, Andrew T. & Erdem, Tülin & Keane, Michael P., 2014. "A simple method to estimate the roles of learning, inventories and category consideration in consumer choice," Journal of choice modelling, Elsevier, vol. 13(C), pages 60-72.
    36. Jason Abaluck & Abi Adams, 2017. "What Do Consumers Consider Before They Choose? Identification from Asymmetric Demand Responses," NBER Working Papers 23566, National Bureau of Economic Research, Inc.
    37. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    38. Frejinger, E. & Bierlaire, M. & Ben-Akiva, M., 2009. "Sampling of alternatives for route choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 43(10), pages 984-994, December.
    39. Janet Currie & Stefano DellaVigna & Enrico Moretti & Vikram Pathania, 2010. "The Effect of Fast Food Restaurants on Obesity and Weight Gain," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 32-63, August.
    40. Michelle Sovinsky Goeree, 2008. "Limited Information and Advertising in the U.S. Personal Computer Industry," Econometrica, Econometric Society, vol. 76(5), pages 1017-1074, September.
    41. Basar, Gözen & Bhat, Chandra, 2004. "A parameterized consideration set model for airport choice: an application to the San Francisco Bay Area," Transportation Research Part B: Methodological, Elsevier, vol. 38(10), pages 889-904, December.
    42. Bierlaire, M. & Bolduc, D. & McFadden, D., 2008. "The estimation of generalized extreme value models from choice-based samples," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 381-394, May.
    43. Christopher T. Conlon & Julie Holland Mortimer, 2013. "Demand Estimation under Incomplete Product Availability," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 1-30, November.
    44. , & ,, 2013. "Choice by iterative search," Theoretical Economics, Econometric Society, vol. 8(3), September.
    45. Yufeng Huang & Bart J. Bronnenberg, 2018. "Pennies for Your Thoughts: Costly Product Consideration and Purchase Quantity Thresholds," Marketing Science, INFORMS, vol. 37(6), pages 1009-1028, November.
    46. Sophia Ying Li & Joe Mazur & Yongjoon Park & James W. Roberts & Andrew Sweeting & Jun Zhang, 2018. "Endogenous and Selective Service Choices After Airline Mergers," NBER Working Papers 24214, National Bureau of Economic Research, Inc.
    47. D’Haultfœuille, Xavier & Iaria, Alessandro, 2016. "A convenient method for the estimation of the multinomial logit model with fixed effects," Economics Letters, Elsevier, vol. 141(C), pages 77-79.
    48. Jacob Goeree & Charles Holt & Thomas Palfrey, 2005. "Regular Quantal Response Equilibrium," Experimental Economics, Springer;Economic Science Association, vol. 8(4), pages 347-367, December.
    49. Babur De Los Santos & Ali Hortacsu & Matthijs R. Wildenbeest, 2012. "Testing Models of Consumer Search Using Data on Web Browsing and Purchasing Behavior," American Economic Review, American Economic Association, vol. 102(6), pages 2955-2980, October.
    50. Kenneth E. Train & Daniel L. McFadden & Moshe Ben-Akiva, 1987. "The Demand for Local Telephone Service: A Fully Discrete Model of Residential Calling Patterns and Service Choices," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 109-123, Spring.
    51. Chiang, Jeongwen & Chib, Siddhartha & Narasimhan, Chakravarthi, 1998. "Markov chain Monte Carlo and models of consideration set and parameter heterogeneity," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 223-248, November.
    52. Guevara, C. Angelo & Ben-Akiva, Moshe E., 2013. "Sampling of alternatives in Logit Mixture models," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 185-198.
    53. Kenneth E. Train & Clifford Winston, 2007. "Vehicle Choice Behavior And The Declining Market Share Of U.S. Automakers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1469-1496, November.
    54. Jean-Pierre Dubé & Günter Hitsch & Puneet Manchanda, 2005. "An Empirical Model of Advertising Dynamics," Quantitative Marketing and Economics (QME), Springer, vol. 3(2), pages 107-144, June.
    55. Guevara, C. Angelo & Ben-Akiva, Moshe E., 2013. "Sampling of alternatives in Multivariate Extreme Value (MEV) models," Transportation Research Part B: Methodological, Elsevier, vol. 48(C), pages 31-52.
    56. Alon Eizenberg, 2014. "Upstream Innovation and Product Variety in the U.S. Home PC Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 1003-1045.
    57. Hickman, William & Mortimer, Julie Holland, 2016. "Demand Estimation with Availability Variation," SocArXiv qe69j, Center for Open Science.
    58. Botond Koszegi & Adam Szeidl, 2013. "A Model of Focusing in Economic Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 53-104.
    59. Florian Heiss & Daniel McFadden & Joachim Winter & Amelie Wuppermann & Bo Zhou, 2016. "Inattention and Switching Costs as Sources of Inertia in Medicare Part D," NBER Working Papers 22765, National Bureau of Economic Research, Inc.
    60. McFadden, Daniel, 1987. "Regression-based specification tests for the multinomial logit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 63-82.
    61. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    62. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
    63. Andrew Leicester & Zoe Oldfield, 2009. "An analysis of consumer panel data," IFS Working Papers W09/09, Institute for Fiscal Studies.
    64. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    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. Yao, Rui & Bekhor, Shlomo, 2022. "A variational autoencoder approach for choice set generation and implicit perception of alternatives in choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 273-294.
    2. Nail Kashaev & Natalia Lazzati & Ruli Xiao, 2023. "Peer Effects in Consideration and Preferences," Papers 2310.12272, arXiv.org, revised Jan 2024.
    3. Daniel Kornbluth & Alexey Kushnir, 2024. "Undergraduate Course Allocation through Competitive Markets," Papers 2412.05691, arXiv.org.
    4. Victor Aguirregabiria & Alessandro Iaria & Senay Sokullu, 2023. "Identification and Estimation of Demand Models with Endogenous Product Entry and Exit," Working Papers tecipa-755, University of Toronto, Department of Economics.
    5. Tran, Hung & Mai, Tien, 2024. "Network-based representations and dynamic discrete choice models for multiple discrete choice analysis," Transportation Research Part B: Methodological, Elsevier, vol. 184(C).
    6. Siddhartha Chib & Kenichi Shimizu, 2023. "Scalable Estimation of Multinomial Response Models with Random Consideration Sets," Papers 2308.12470, arXiv.org, revised Aug 2024.
    7. Alonso Alfaro-Urena & Paolo Zacchia, 2024. "Matching to Suppliers in the Production Network: an Empirical Framework," CERGE-EI Working Papers wp775, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    8. Ante Sterc, 2022. "Limited Consideration in the Investment Fund Choice," CERGE-EI Working Papers wp729, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    9. Cristina Gualdani & Shruti Sinha, 2023. "Identification in Discrete Choice Models with Imperfect Information," Working Papers 949, Queen Mary University of London, School of Economics and Finance.
    10. Takeshi Fukasawa, 2024. "The Biases in Applying Static Demand Models Under Dynamic Demand," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 65(2), pages 561-594, September.
    11. Sydney Schreiner Wertz, 2023. "Business dynamism, educational attainment, and residential location choice," Journal of Regional Science, Wiley Blackwell, vol. 63(4), pages 1026-1046, September.
    12. Roy Allen, 2024. "Exogenous Consideration and Extended Random Utility," Papers 2405.13945, arXiv.org.
    13. Takeshi Fukasawa, 2022. "The Biases in Applying Static Demand Models under Dynamic Demand," Discussion Paper Series DP2022-18, Research Institute for Economics & Business Administration, Kobe University, revised Jul 2022.
    14. Han, Yafei & Pereira, Francisco Camara & Ben-Akiva, Moshe & Zegras, Christopher, 2022. "A neural-embedded discrete choice model: Learning taste representation with strengthened interpretability," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 166-186.
    15. C. Angelo Guevara, 2022. "A Note on "A survey of preference estimation with unobserved choice set heterogeneity" by Gregory S. Crawford, Rachel Griffith, and Alessandro Iaria," Papers 2205.00852, arXiv.org.

    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. Griffith, Rachel & Crawford, Gregory & Iaria, Alessandro, 2016. "Preference Estimation with Unobserved Choice Set Heterogeneity using Sufficient Sets," CEPR Discussion Papers 11675, C.E.P.R. Discussion Papers.
    2. Kashaev, Nail & Aguiar, Victor H., 2022. "A random attention and utility model," Journal of Economic Theory, Elsevier, vol. 204(C).
    3. Victor H. Aguiar & Maria Jose Boccardi & Nail Kashaev & Jeongbin Kim, 2023. "Random utility and limited consideration," Quantitative Economics, Econometric Society, vol. 14(1), pages 71-116, January.
    4. Levon Barseghyan & Francesca Molinari & Matthew Thirkettle, 2021. "Discrete Choice under Risk with Limited Consideration," American Economic Review, American Economic Association, vol. 111(6), pages 1972-2006, June.
    5. Levon Barseghyan & Maura Coughlin & Francesca Molinari & Joshua C. Teitelbaum, 2021. "Heterogeneous Choice Sets and Preferences," Econometrica, Econometric Society, vol. 89(5), pages 2015-2048, September.
    6. Nikhil Agarwal & Paulo J. Somaini, 2022. "Demand Analysis under Latent Choice Constraints," NBER Working Papers 29993, National Bureau of Economic Research, Inc.
    7. Valentino Dardanoni & Paola Manzini & Marco Mariotti & Christopher J. Tyson, 2020. "Inferring Cognitive Heterogeneity From Aggregate Choices," Econometrica, Econometric Society, vol. 88(3), pages 1269-1296, May.
    8. Helmers, Christian & Krishnan, Pramila & Patnam, Manasa, 2019. "Attention and saliency on the internet: Evidence from an online recommendation system," Journal of Economic Behavior & Organization, Elsevier, vol. 161(C), pages 216-242.
    9. Cristina Gualdani & Shruti Sinha, 2019. "Identification in discrete choice models with imperfect information," Papers 1911.04529, arXiv.org, revised Dec 2023.
    10. Xavier Gabaix, 2017. "Behavioral Inattention," NBER Working Papers 24096, National Bureau of Economic Research, Inc.
    11. Jason Abaluck & Abi Adams, 2017. "What Do Consumers Consider Before They Choose? Identification from Asymmetric Demand Responses," NBER Working Papers 23566, National Bureau of Economic Research, Inc.
    12. Lu, Zhentong, 2022. "Estimating multinomial choice models with unobserved choice sets," Journal of Econometrics, Elsevier, vol. 226(2), pages 368-398.
    13. Jason Abaluck & Abi Adams, 2017. "What do consumers consider before they choose? Identification from asymmetric demand responses," IFS Working Papers W17/09, Institute for Fiscal Studies.
    14. Victor H. Aguiar & Nail Kashaev, 2019. "Identification and Estimation of Discrete Choice Models with Unobserved Choice Sets," Papers 1907.04853, arXiv.org, revised Jun 2021.
    15. Han Qiu, 2018. "An Inattention Model for Traveler Behavior with e-Coupons," Papers 1901.05070, arXiv.org.
    16. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Y. Ozbay, 2012. "Revealed Attention," American Economic Review, American Economic Association, vol. 102(5), pages 2183-2205, August.
    17. Jason Abaluck & Giovanni Compiani, 2020. "A Method to Estimate Discrete Choice Models that is Robust to Consumer Search," NBER Working Papers 26849, National Bureau of Economic Research, Inc.
    18. Michael Grubb, 2015. "Failing to Choose the Best Price: Theory, Evidence, and Policy," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 47(3), pages 303-340, November.
    19. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Aguiar, Victor H. & Boccardi, Maria Jose & Dean, Mark, 2016. "Satisficing and stochastic choice," Journal of Economic Theory, Elsevier, vol. 166(C), pages 445-482.

    More about this item

    Keywords

    Discrete choice models; Panel data; Unobserved choice sets; Unobserved heterogeneity; Sufficient sets;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:eee:econom:v:222:y:2021:i:1:p:4-43. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.