IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v207y2018i2p285-306.html
   My bibliography  Save this article

Subvector inference when the true parameter vector may be near or at the boundary

Author

Listed:
  • Ketz, Philipp

Abstract

Extremum estimators are not asymptotically normally distributed when the estimator satisfies the restrictions on the parameter space – such as the non-negativity of a variance parameter – andthe true parameter vector is near or at the boundary. This possible lack of asymptotic normality makes it difficult to construct tests for testing subvector hypotheses that control asymptotic size in a uniform sense and have good local asymptotic power irrespective of whether the true parameter vector is at, near, or far from the boundary. We propose a novel estimator that is asymptotically normally distributed even when the true parameter vector is near or at the boundary and the objective function is not defined outside the parameter space. The proposed estimator allows the implementation of a new test based on the Conditional Likelihood Ratio statistic that is easy-to-implement, controls asymptotic size, and has good local asymptotic power properties. Furthermore, we show that the test enjoys certain asymptotic optimality properties when the parameter of interest is scalar. In an application of the random coefficients logit model (Berry, Levinsohn and Pakes, 1995) to the European car market, we find that, for most parameters, the new test leads to tighter confidence intervals than the two-sided t-test commonly used in practice.

Suggested Citation

  • Ketz, Philipp, 2018. "Subvector inference when the true parameter vector may be near or at the boundary," Journal of Econometrics, Elsevier, vol. 207(2), pages 285-306.
  • Handle: RePEc:eee:econom:v:207:y:2018:i:2:p:285-306
    DOI: 10.1016/j.jeconom.2018.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440761830143X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jeconom.2018.08.003?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    2. Reynaert, Mathias & Verboven, Frank, 2014. "Improving the performance of random coefficients demand models: The role of optimal instruments," Journal of Econometrics, Elsevier, vol. 179(1), pages 83-98.
    3. 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.
    4. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    5. Nevo, Aviv, 2001. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, Econometric Society, vol. 69(2), pages 307-342, March.
    6. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    7. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    8. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    9. David T. Frazier & Eric Renault, 2016. "Indirect Inference With(Out) Constraints," Papers 1607.06163, arXiv.org, revised Aug 2019.
    10. Jason Abrevaya & Shu Shen, 2014. "Estimation Of Censored Panel‐Data Models With Slope Heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(4), pages 523-548, June.
    11. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    12. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    13. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    14. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "Applications of subsampling, hybrid, and size-correction methods," Journal of Econometrics, Elsevier, vol. 158(2), pages 285-305, October.
    15. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(3), pages 295-313, December.
    16. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    17. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    18. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(2), pages 426-468, April.
    19. Yogesh Tripathi & Somesh Kumar, 2007. "Estimating a positive normal mean," Statistical Papers, Springer, vol. 48(4), pages 609-629, October.
    20. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    21. Andrews, Donald W K, 2002. "Generalized Method of Moments Estimation When a Parameter Is on a Boundary," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 530-544, October.
    22. Moreira, Humberto Ataíde & Moreira, Marcelo J., 2013. "Contributions to the Theory of Optimal Tests," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 747, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    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. Centorrino, Samuele & Pérez-Urdiales, María, 2023. "Maximum likelihood estimation of stochastic frontier models with endogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 82-105.
    2. Aditi Dimri & Véronique Gille & Philipp Ketz, 2021. "Measuring sex-selective abortion: How many women abort?," Working Papers halshs-03495964, HAL.
    3. Rao, Akhil & Burgess, Matthew & Kaffine, Daniel, 2020. "Orbital-use fees could more than quadruple the value of the space industry," MPRA Paper 112708, University Library of Munich, Germany.
    4. Jehiel, Philippe & Singh, Juni, 2021. "Multi-state choices with aggregate feedback on unfamiliar alternatives," Games and Economic Behavior, Elsevier, vol. 130(C), pages 1-24.
    5. Ketz, Philipp, 2019. "Testing overidentifying restrictions with a restricted parameter space," Economics Letters, Elsevier, vol. 185(C).
    6. Philipp Ketz & Adam McCloskey, 2021. "Short and Simple Confidence Intervals when the Directions of Some Effects are Known," Papers 2109.08222, arXiv.org.
    7. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    8. Ketz, Philipp, 2019. "On asymptotic size distortions in the random coefficients logit model," Journal of Econometrics, Elsevier, vol. 212(2), pages 413-432.
    9. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    10. Philipp Ketz, 2022. "Allowing for weak identification when testing GARCH-X type models," Papers 2210.11398, arXiv.org.
    11. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Dec 2022.
    12. Gregory Fletcher Cox, 2024. "A Simple and Adaptive Confidence Interval when Nuisance Parameters Satisfy an Inequality," Papers 2409.09962, arXiv.org.
    13. Timo Schenk, 2023. "Time-Weighted Difference-in-Differences: Accounting for Common Factors in Short T Panels," Tinbergen Institute Discussion Papers 23-004/III, Tinbergen Institute.
    14. David T. Frazier & Eric Renault, 2016. "Indirect Inference With(Out) Constraints," Papers 1607.06163, arXiv.org, revised Aug 2019.
    15. Giuseppe Cavaliere & Zeng-Hua Lu & Anders Rahbek & Yuhong Yang, 2021. "MinP Score Tests with an Inequality Constrained Parameter Space," Papers 2107.06089, arXiv.org.
    16. Fan, Yanqin & Shi, Xuetao, 2023. "Wald, QLR, and score tests when parameters are subject to linear inequality constraints," Journal of Econometrics, Elsevier, vol. 235(2), pages 2005-2026.

    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. Ketz, Philipp, 2019. "On asymptotic size distortions in the random coefficients logit model," Journal of Econometrics, Elsevier, vol. 212(2), pages 413-432.
    2. Gregory Fletcher Cox, 2024. "A Simple and Adaptive Confidence Interval when Nuisance Parameters Satisfy an Inequality," Papers 2409.09962, arXiv.org.
    3. Ketz, Philipp, 2019. "Testing overidentifying restrictions with a restricted parameter space," Economics Letters, Elsevier, vol. 185(C).
    4. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    5. Philipp Ketz & Adam McCloskey, 2021. "Short and Simple Confidence Intervals when the Directions of Some Effects are Known," Papers 2109.08222, arXiv.org.
    6. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    7. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    8. Fan, Yanqin & Shi, Xuetao, 2023. "Wald, QLR, and score tests when parameters are subject to linear inequality constraints," Journal of Econometrics, Elsevier, vol. 235(2), pages 2005-2026.
    9. Stépahne Auray & Nicolas Lepage-Saucier & Purevdorj Tuvaandor, 2018. "Doubly Robust GMM Inference and Differentiated Products Demand Models," Working Papers 2018-13, Center for Research in Economics and Statistics.
    10. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    11. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    12. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    13. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    14. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    15. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    16. Wang, Wenjie & Doko Tchatoka, Firmin, 2018. "On Bootstrap inconsistency and Bonferroni-based size-correction for the subset Anderson–Rubin test under conditional homoskedasticity," Journal of Econometrics, Elsevier, vol. 207(1), pages 188-211.
    17. Chen, Heng & Fan, Yanqin & Liu, Ruixuan, 2016. "Inference for the correlation coefficient between potential outcomes in the Gaussian switching regime model," Journal of Econometrics, Elsevier, vol. 195(2), pages 255-270.
    18. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Dec 2022.
    19. Xu Cheng & Winston Wei Dou & Zhipeng Liao, 2022. "Macro‐Finance Decoupling: Robust Evaluations of Macro Asset Pricing Models," Econometrica, Econometric Society, vol. 90(2), pages 685-713, March.
    20. Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978R2, Cowles Foundation for Research in Economics, Yale University, revised Jan 2019.

    More about this item

    Keywords

    Boundary; Asymptotic normality; Admissibility; Random coefficients;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

    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:207:y:2018:i:2:p:285-306. 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.