IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/08-12.html
   My bibliography  Save this paper

Estimation of random coefficients logit demand models with interactive fixed effects

Author

Listed:
  • Hyungsik Roger Moon

    (Institute for Fiscal Studies and USC)

  • Matthew Shum

    (Institute for Fiscal Studies)

  • Martin Weidner

    (Institute for Fiscal Studies and University College London)

Abstract

We extend the Berry, Levinsohn and Pakes (BLP, 1995) random coefficients discrete-choice demand model, which underlies much recent empirical work in IO. We add interactive fixed effects in the form of a factor structure on the unobserved product characteristics. The interactive fixed effects can be arbitrarily correlated with the observed product characteristics (including price), which accommodates endogeneity and, at the same time, captures strong persistence in market shares across products and markets. We propose a two step least squares-minimum distance (LS-MD) procedure to calculate the estimator. Our estimator is easy to compute, and Monte Carlo simulations show that it performs well. We consider an empirical application to US automobile demand.

Suggested Citation

  • Hyungsik Roger Moon & Matthew Shum & Martin Weidner, 2012. "Estimation of random coefficients logit demand models with interactive fixed effects," CeMMAP working papers CWP08/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:08/12
    as

    Download full text from publisher

    File URL: http://cemmap.ifs.org.uk/wps/cwp081212.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jean‐Pierre Dubé & Jeremy T. Fox & Che‐Lin Su, 2012. "Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation," Econometrica, Econometric Society, vol. 80(5), pages 2231-2267, September.
    2. David Besanko & Ulrich Doraszelski, 2004. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 23-49, Spring.
    3. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    4. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    5. 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.
    6. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    7. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    8. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    9. Amit Gandhi Gandhi & Zhentong Lu & Xiaoxia Shi, 2013. "Estimating demand for differentiated products with error in market shares," CeMMAP working papers 03/13, Institute for Fiscal Studies.
    10. Steve Berry & Oliver B. Linton & Ariel Pakes, 2004. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 613-654.
    11. 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.
    12. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    13. Nevo, Aviv, 2001. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, Econometric Society, vol. 69(2), pages 307-342, March.
    14. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-1395, November.
    15. Ackerberg, Daniel & Lanier Benkard, C. & Berry, Steven & Pakes, Ariel, 2007. "Econometric Tools for Analyzing Market Outcomes," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 63, Elsevier.
    16. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    17. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    18. Christopher R. Knittel & Konstantinos Metaxoglou, 2014. "Estimation of Random-Coefficient Demand Models: Two Empiricists' Perspective," The Review of Economics and Statistics, MIT Press, vol. 96(1), pages 34-59, March.
    19. 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.
    20. Jushan Bai & Serena Ng, 2006. "Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions," Econometrica, Econometric Society, vol. 74(4), pages 1133-1150, July.
    21. Ahn, Seung C. & Lee, Young H. & Schmidt, Peter, 2013. "Panel data models with multiple time-varying individual effects," Journal of Econometrics, Elsevier, vol. 174(1), pages 1-14.
    22. Patrick Bajari & Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan, 2009. "A Simple Nonparametric Estimator for the Distribution of Random Coefficients," NBER Working Papers 15210, National Bureau of Economic Research, Inc.
    23. Amil Petrin, 2002. "Quantifying the Benefits of New Products: The Case of the Minivan," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 705-729, August.
    24. Matthew C. Harding & Jerry Hausman, 2007. "Using A Laplace Approximation To Estimate The Random Coefficients Logit Model By Nonlinear Least Squares," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1311-1328, November.
    25. Rosa L. Matzkin, 2013. "Nonparametric Identification in Structural Economic Models," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 457-486, May.
    26. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    27. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    28. Susanna Esteban & Matthew Shum, 2007. "Durable-goods oligopoly with secondary markets: the case of automobiles," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 332-354, June.
    29. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    30. Christopher R. Knittel & Konstantinos Metaxoglou, 2008. "Estimation of Random Coefficient Demand Models: Challenges, Difficulties and Warnings," NBER Working Papers 14080, National Bureau of Economic Research, Inc.
    31. Ahn, Seung Chan & Hoon Lee, Young & Schmidt, Peter, 2001. "GMM estimation of linear panel data models with time-varying individual effects," Journal of Econometrics, Elsevier, vol. 101(2), pages 219-255, April.
    32. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    33. Hahn, Jinyong & Kuersteiner, Guido, 2011. "Bias Reduction For Dynamic Nonlinear Panel Models With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1152-1191, December.
    34. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
    35. J. Miguel Villas-Boas & Russell S. Winer, 1999. "Endogeneity in Brand Choice Models," Management Science, INFORMS, vol. 45(10), pages 1324-1338, October.
    36. Lee, Nayoung & Moon, Hyungsik Roger & Zhou, Qiankun, 2017. "Many IVs estimation of dynamic panel regression models with measurement error," Journal of Econometrics, Elsevier, vol. 200(2), pages 251-259.
    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. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    2. Walter Beckert & Elaine Kelly, 2021. "Divided by choice? For‐profit providers, patient choice and mechanisms of patient sorting in the English National Health Service," Health Economics, John Wiley & Sons, Ltd., vol. 30(4), pages 820-839, April.
    3. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2017. "Nonparametric identification of random coefficients in endogenous and heterogeneous aggregate demand models," CeMMAP working papers 11/17, Institute for Fiscal Studies.
    4. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2014. "Nonparametric Identification of Endogenous and Heterogeneous Aggregate Demand Models: Complements, Bundles and the Market Level," Boston University - Department of Economics - Working Papers Series 2014-005, Boston University - Department of Economics.
    5. Ando, Tomohiro & Bai, Jushan & Li, Kunpeng, 2022. "Bayesian and maximum likelihood analysis of large-scale panel choice models with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 230(1), pages 20-38.
    6. Daniel Czarnowske & Amrei Stammann, 2020. "Inference in Unbalanced Panel Data Models with Interactive Fixed Effects," Papers 2004.03414, arXiv.org.
    7. Vira Semenova & Matt Goldman & Victor Chernozhukov & Matt Taddy, 2023. "Inference on heterogeneous treatment effects in high‐dimensional dynamic panels under weak dependence," Quantitative Economics, Econometric Society, vol. 14(2), pages 471-510, May.
    8. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2023. "Nonparametric identification of random coefficients in aggregate demand models for differentiated products," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 279-306.
    9. Bokhari, Farasat A.S. & Mariuzzo, Franco, 2018. "Demand estimation and merger simulations for drugs: Logits v. AIDS," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 653-685.
    10. Ando, Tomohiro & Bai, Jushan, 2021. "Large-scale generalized linear longitudinal data models with grouped patterns of unobserved heterogeneity," MPRA Paper 111431, University Library of Munich, Germany.
    11. Thibaut Lamadon & Elena Manresa & Stephane Bonhomme, 2016. "Discretizing Unobserved Heterogeneity," 2016 Meeting Papers 1536, Society for Economic Dynamics.
    12. Lu, Zhentong & Shi, Xiaoxia & Tao, Jing, 2023. "Semi-nonparametric estimation of random coefficients logit model for aggregate demand," Journal of Econometrics, Elsevier, vol. 235(2), pages 2245-2265.
    13. Hugo Freeman & Martin Weidner, 2021. "Linear Panel Regressions with Two-Way Unobserved Heterogeneity," Papers 2109.11911, arXiv.org, revised Aug 2022.
    14. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    15. Hugo Freeman & Martin Weidner, 2021. "Linear panel regressions with two-way unobserved heterogeneity," CeMMAP working papers CWP39/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Galvao, Antonio F. & Wang, Liang, 2015. "Efficient minimum distance estimator for quantile regression fixed effects panel data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 1-26.
    17. Chen, Mingli, 2016. "Estimation of Nonlinear Panel Models with Multiple Unobserved Effects," Economic Research Papers 269326, University of Warwick - Department of Economics.
    18. Miao, Ke & Li, Kunpeng & Su, Liangjun, 2020. "Panel threshold models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 219(1), pages 137-170.
    19. Robert Donnelly & Francisco J.R. Ruiz & David Blei & Susan Athey, 2021. "Counterfactual inference for consumer choice across many product categories," Quantitative Marketing and Economics (QME), Springer, vol. 19(3), pages 369-407, December.
    20. Ye, Xiaoqing & Xu, Juan & Wu, Xiangjun, 2018. "Estimation of an unbalanced panel data Tobit model with interactive effects," Journal of choice modelling, Elsevier, vol. 28(C), pages 108-123.
    21. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.

    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. Hyungsik Roger Moon & Matthew Shum & Martin Weidner, 2017. "Estimation of random coefficients logit demand models with interactive fixed effects," CeMMAP working papers 12/17, Institute for Fiscal Studies.
    2. Hyungsik Roger Roger Moon & Matthew Shum & Martin Weidner, 2014. "Estimation of random coefficients logit demand models with interactive fixed effects," CeMMAP working papers 20/14, Institute for Fiscal Studies.
    3. Hyungsik Roger Roger Moon & Matthew Shum & Martin Weidner, 2012. "Estimation of random coefficients logit demand models with interactive fixed effects," CeMMAP working papers 08/12, Institute for Fiscal Studies.
    4. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    5. Hyungsik Roger Roger Moon & Martin Weidner, 2013. "Dynamic linear panel regression models with interactive fixed effects," CeMMAP working papers 63/13, Institute for Fiscal Studies.
    6. Lu, Zhentong & Shi, Xiaoxia & Tao, Jing, 2023. "Semi-nonparametric estimation of random coefficients logit model for aggregate demand," Journal of Econometrics, Elsevier, vol. 235(2), pages 2245-2265.
    7. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.
    8. Hyungsik Roger Roger Moon & Martin Weidner, 2014. "Dynamic linear panel regression models with interactive fixed effects," CeMMAP working papers 47/14, Institute for Fiscal Studies.
    9. Chen, Mingli & Fernández-Val, Iván & Weidner, Martin, 2021. "Nonlinear factor models for network and panel data," Journal of Econometrics, Elsevier, vol. 220(2), pages 296-324.
    10. Hou, Lei & Li, Kunpeng & Li, Qi & Ouyang, Min, 2021. "Revisiting the location of FDI in China: A panel data approach with heterogeneous shocks," Journal of Econometrics, Elsevier, vol. 221(2), pages 483-509.
    11. Allais, Olivier & Etilé, Fabrice & Lecocq, Sébastien, 2015. "Mandatory labels, taxes and market forces: An empirical evaluation of fat policies," Journal of Health Economics, Elsevier, vol. 43(C), pages 27-44.
    12. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    13. Steven T. Berry & Philip A. Haile, 2021. "Foundations of Demand Estimation," Cowles Foundation Discussion Papers 2301, Cowles Foundation for Research in Economics, Yale University.
    14. Hyungsik Roger Roger Moon & Martin Weidner, 2014. "Linear regression for panel with unknown number of factors as interactive fixed effects," CeMMAP working papers 35/14, Institute for Fiscal Studies.
    15. Byrne, David P. & Imai, Susumu & Jain, Neelam & Sarafidis, Vasilis, 2022. "Instrument-free identification and estimation of differentiated products models using cost data," Journal of Econometrics, Elsevier, vol. 228(2), pages 278-301.
    16. Georg Keilbar & Juan M. Rodriguez-Poo & Alexandra Soberon & Weining Wang, 2022. "A semiparametric approach for interactive fixed effects panel data models," Papers 2201.11482, arXiv.org, revised Mar 2023.
    17. Jörg Breitung & Philipp Hansen, 2021. "Alternative estimation approaches for the factor augmented panel data model with small T," Empirical Economics, Springer, vol. 60(1), pages 327-351, January.
    18. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "Estimation of large dimensional conditional factor models in finance," Working Papers unige:125031, University of Geneva, Geneva School of Economics and Management.
    19. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2023. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," Econometrica, Econometric Society, vol. 91(1), pages 107-146, January.
    20. Hyungsik Roger Moon & Martin Weidner, 2018. "Nuclear Norm Regularized Estimation of Panel Regression Models," Papers 1810.10987, arXiv.org, revised Jun 2023.

    More about this item

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

    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:cemmap:08/12. 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/cmifsuk.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.