[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2006.02541.html
   My bibliography  Save this paper

Testing Finite Moment Conditions for the Consistency and the Root-N Asymptotic Normality of the GMM and M Estimators

Author

Listed:
  • Yuya Sasaki
  • Yulong Wang
Abstract
Common approaches to inference for structural and reduced-form parameters in empirical economic analysis are based on the consistency and the root-n asymptotic normality of the GMM and M estimators. The canonical consistency (respectively, root-n asymptotic normality) for these classes of estimators requires at least the first (respectively, second) moment of the score to be finite. In this article, we present a method of testing these conditions for the consistency and the root-n asymptotic normality of the GMM and M estimators. The proposed test controls size nearly uniformly over the set of data generating processes that are compatible with the null hypothesis. Simulation studies support this theoretical result. Applying the proposed test to the market share data from the Dominick's Finer Foods retail chain, we find that a common \textit{ad hoc} procedure to deal with zero market shares in analysis of differentiated products markets results in a failure to satisfy the conditions for both the consistency and the root-n asymptotic normality.

Suggested Citation

  • Yuya Sasaki & Yulong Wang, 2020. "Testing Finite Moment Conditions for the Consistency and the Root-N Asymptotic Normality of the GMM and M Estimators," Papers 2006.02541, arXiv.org, revised Sep 2020.
    • Handle: RePEc:arx:papers:2006.02541
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2006.02541
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Graham Elliott & Ulrich K. Müller & Mark W. Watson, 2015. "Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis," Econometrica, Econometric Society, vol. 83, pages 771-811, March.
    2. Inoue, Atsushi & Rossi, Barbara, 2011. "Testing for weak identification in possibly nonlinear models," Journal of Econometrics, Elsevier, vol. 161(2), pages 246-261, April.
    3. Sanderson, Eleanor & Windmeijer, Frank, 2016. "A weak instrument F-test in linear IV models with multiple endogenous variables," Journal of Econometrics, Elsevier, vol. 190(2), pages 212-221.
    4. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    5. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(2), pages 151-175, April.
    6. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    7. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
    8. Victor Chernozhukov & Iván Fernández-Val, 2011. "Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 559-589.
    9. Ulrich K. Müller & Yulong Wang, 2017. "Fixed- Asymptotic Inference About Tail Properties," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1334-1343, July.
    10. J. M. C. Santos Silva & Silvana Tenreyro, 2006. "The Log of Gravity," The Review of Economics and Statistics, MIT Press, vol. 88(4), pages 641-658, November.
    11. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    12. 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.
    13. Wright, Jonathan H., 2003. "Detecting Lack Of Identification In Gmm," Econometric Theory, Cambridge University Press, vol. 19(2), pages 322-330, April.
    14. Qi-Man Shao & Hao Yu & Jun Yu, 2001. "Do Stock Returns Follow a Finite Variance Distribution?," Annals of Economics and Finance, Society for AEF, vol. 2(2), pages 467-486, November.
    15. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    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. Kaiser, Ulrich & Mendez, Susan J. & Rønde, Thomas & Ullrich, Hannes, 2014. "Regulation of pharmaceutical prices: Evidence from a reference price reform in Denmark," Journal of Health Economics, Elsevier, vol. 36(C), pages 174-187.
    2. Joonhwi Joo & Ali Hortacsu, 2016. "Semiparametric estimation of CES demand system with observed and unobserved product characteristics," 2016 Meeting Papers 36, Society for Economic Dynamics.
    3. Amit Gandhi & Jean-François Houde, 2019. "Measuring Substitution Patterns in Differentiated-Products Industries," NBER Working Papers 26375, National Bureau of Economic Research, Inc.
    4. 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.
    5. Sergey Lychagin & Joris Pinkse & Margaret E. Slade & John Van Reenen, 2016. "Spillovers in Space: Does Geography Matter?," Journal of Industrial Economics, Wiley Blackwell, vol. 64(2), pages 295-335, June.
    6. Wang, Yulong & Xiao, Zhijie, 2022. "Estimation and inference about tail features with tail censored data," Journal of Econometrics, Elsevier, vol. 230(2), pages 363-387.
    7. Jan De Loecker & Paul T. Scott, 2016. "Estimating market power Evidence from the US Brewing Industry," NBER Working Papers 22957, National Bureau of Economic Research, Inc.
    8. André de Palma & Julien Monardo, 2017. "The General Nesting Logit (GNL) Model using Aggregate Data," Working Papers hal-01552455, HAL.
    9. 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.
    10. 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.
    11. Pham, Vivienne & Prentice, David, 2010. "An empirical analysis of the counterfactual: a merger and divestiture in the Australian cigarette industry," MPRA Paper 26713, University Library of Munich, Germany.
    12. Lou, Weifang & Prentice, David & Yin, Xiangkang, 2008. "The Effects of Product Ageing on Demand: The Case of Digital Cameras," MPRA Paper 13407, University Library of Munich, Germany.
    13. Friberg, Richard & Huse, Cristian, 2012. "How to use demand systems to evaluate risky projects, with an application to automobile production," CEPR Discussion Papers 9266, C.E.P.R. Discussion Papers.
    14. Paul Scott, 2017. "Estimating Market Power: Evidence from the US Brewing Industry," 2017 Meeting Papers 389, Society for Economic Dynamics.
    15. Moon, Hyungsik Roger & Shum, Matthew & Weidner, Martin, 2018. "Estimation of random coefficients logit demand models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 613-644.
    16. Victor Couture & Jessie Handbury, 2017. "Urban Revival in America, 2000 to 2010," NBER Working Papers 24084, National Bureau of Economic Research, Inc.
    17. Mogens Fosgerau & Julien Monardo & André de Palma, 2024. "The Inverse Product Differentiation Logit Model," American Economic Journal: Microeconomics, American Economic Association, vol. 16(4), pages 329-370, November.
    18. Brett R. Gordon & Wesley R. Hartmann, 2016. "Advertising competition in presidential elections," Quantitative Marketing and Economics (QME), Springer, vol. 14(1), pages 1-40, March.
    19. Sungho Park & Sachin Gupta, 2012. "Comparison of SML and GMM estimators for the random coefficient logit model using aggregate data," Empirical Economics, Springer, vol. 43(3), pages 1353-1372, December.
    20. Givord, Pauline & Grislain-Letrémy, Céline & Naegele, Helene, 2018. "How do fuel taxes impact new car purchases? An evaluation using French consumer-level data," Energy Economics, Elsevier, vol. 74(C), pages 76-96.

    More about this item

    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:arx:papers:2006.02541. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.