Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/azt/cemmap/43-17.html
   My bibliography  Save this paper

Monte Carlo confidence sets for identified sets

Author

Listed:
  • Xiaohong Chen
  • Timothy M. Christensen
  • Elie Tamer
Abstract
In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full parameters and of subvectors in models defined through a likelihood or a vector of moment equalities or inequalities. These CSs are based on level sets of optimal sample criterion functions (such as likelihood or optimally-weighted or continuously-updated GMM criterions). The level sets are constructed using cutoffs that are computed via Monte Carlo (MC) simulations directly from the quasi-posterior distributions of the criterions. We establish new Bernstein-von Mises (or Bayesian Wilks) type theorems for the quasi-posterior distributions of the quasi-likelihood ratio (QLR) and profile QLR in partially-identified regular models and some non-regular models. These results imply that our MC CSs have exact asymptotic frequentist coverage for identified sets of full parameters and of subvectors in partially-identified regular models, and have valid but potentially conservative coverage in models with reduced-form parameters on the boundary. Our MC CSs for identified sets of subvectors are shown to have exact asymptotic coverage in models with singularities. We also provide results on uniform validity of our CSs over classes of DGPs that include point and partially identified models. We demonstrate good finite-sample coverage properties of our procedures in two simulation experiments. Finally, our procedures are applied to two non-trivial empirical examples: an airline entry game and a model of trade flows.

Suggested Citation

  • Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2017. "Monte Carlo confidence sets for identified sets," CeMMAP working papers 43/17, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:43/17
    DOI: 10.1920/wp.cem.2017.4317
    as

    Download full text from publisher

    File URL: https://www.cemmap.ac.uk/wp-content/uploads/2020/08/CWP4317.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.1920/wp.cem.2017.4317?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
    ---><---

    References listed on IDEAS

    as
    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 25(3), pages 669-709, June.
    3. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    4. A. Norets & X. Tang, 2014. "Semiparametric Inference in Dynamic Binary Choice Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 1229-1262.
    5. Brendan Kline & Elie Tamer, 2016. "Bayesian inference in a class of partially identified models," Quantitative Economics, Econometric Society, vol. 7(2), pages 329-366, July.
    6. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    7. J. M. C. Santos Silva & Silvana Tenreyro, 2015. "Trading Partners and Trading Volumes: Implementing the Helpman–Melitz–Rubinstein Model Empirically," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 93-105, February.
    8. Armstrong, Timothy B., 2014. "Weighted KS statistics for inference on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 181(2), pages 92-116.
    9. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    10. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
    11. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    12. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    13. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2008. "Estimating Trade Flows: Trading Partners and Trading Volumes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(2), pages 441-487.
    14. Chen, Xiaohong & Gao, Fuchang, 2017. "A reverse Gaussian correlation inequality by adding cones," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 84-87.
    15. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    16. Hyungsik Roger Moon & Frank Schorfheide, 2012. "Bayesian and Frequentist Inference in Partially Identified Models," Econometrica, Econometric Society, vol. 80(2), pages 755-782, March.
    17. 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.
    18. Keisuke Hirano & Jack R. Porter, 2003. "Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support," Econometrica, Econometric Society, vol. 71(5), pages 1307-1338, September.
    19. Edward Herbst & Frank Schorfheide, 2014. "Sequential Monte Carlo Sampling For Dsge Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1073-1098, November.
    20. Victor Chernozhukov & Han Hong, 2004. "Likelihood Estimation and Inference in a Class of Nonregular Econometric Models," Econometrica, Econometric Society, vol. 72(5), pages 1445-1480, September.
    21. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    22. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    23. Flinn, C. & Heckman, J., 1982. "New methods for analyzing structural models of labor force dynamics," Journal of Econometrics, Elsevier, vol. 18(1), pages 115-168, January.
    24. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
    25. Xiaohong Chen & Elie Tamer & Alexander Torgovitsky, 2011. "Sensitivity Analysis in Semiparametric Likelihood Models," Cowles Foundation Discussion Papers 1836, Cowles Foundation for Research in Economics, Yale University.
    26. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    27. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, March.
    28. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, January.
    29. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
    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. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    2. Xiaohong Chen & Timothy Christensen & Keith O’Hara & Elie Tamer, 2016. "MCMC Confidence sets for Identified Sets," Cowles Foundation Discussion Papers 2037R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2016.
    3. Xiaohong Chen & Timothy M. Christensen & Keith O'Hara & Elie Tamer, 2016. "MCMC confidence sets for identified sets," CeMMAP working papers 28/16, Institute for Fiscal Studies.
    4. Sasaki, Yuya & Takahashi, Yuya & Xin, Yi & Hu, Yingyao, 2023. "Dynamic discrete choice models with incomplete data: Sharp identification," Journal of Econometrics, Elsevier, vol. 236(1).
    5. Liao, Yuan & Simoni, Anna, 2019. "Bayesian inference for partially identified smooth convex models," Journal of Econometrics, Elsevier, vol. 211(2), pages 338-360.
    6. Yuan Liao & Anna Simoni, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," Papers 1212.3267, arXiv.org, revised Nov 2013.
    7. Yuan Liao & Anna Simoni, 2016. "Bayesian Inference for Partially Identified Convex Models: Is it Valid for Frequentist Inference?," Departmental Working Papers 201607, Rutgers University, Department of Economics.
    8. Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2014. "Inference for functions of partially identified parameters in moment inequality models," CeMMAP working papers CWP05/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Brendan Kline & Elie Tamer, 2016. "Bayesian inference in a class of partially identified models," Quantitative Economics, Econometric Society, vol. 7(2), pages 329-366, July.
    10. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    11. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    12. Kate Ho & Adam M. Rosen, 2015. "Partial Identification in Applied Research: Benefits and Challenges," NBER Working Papers 21641, National Bureau of Economic Research, Inc.
    13. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    14. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Kyungchul Song, 2009. "Point Decisions for Interval-Identified Parameters," PIER Working Paper Archive 09-036, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    16. Christian Bontemps & Thierry Magnac, 2017. "Set Identification, Moment Restrictions, and Inference," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 103-129, September.
    17. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    18. Armstrong, Timothy B., 2015. "Asymptotically exact inference in conditional moment inequality models," Journal of Econometrics, Elsevier, vol. 186(1), pages 51-65.
    19. Armstrong, Timothy B. & Chan, Hock Peng, 2016. "Multiscale adaptive inference on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 194(1), pages 24-43.
    20. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.

    More about this item

    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:azt:cemmap:43/17. 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: Dermot Watson (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.