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


  • Ketz, Philipp


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

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    References listed on IDEAS

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    Cited by:

    1. Ketz, Philipp, 2019. "Testing overidentifying restrictions with a restricted parameter space," Economics Letters, Elsevier, vol. 185(C).
    2. Ketz, Philipp, 2019. "On asymptotic size distortions in the random coefficients logit model," Journal of Econometrics, Elsevier, vol. 212(2), pages 413-432.
    3. Giuseppe Cavaliere & Heino Bohn Nielsen & Rasmus Søndergaard Pedersen & Anders Rahbek, 2018. "Bootstrap Inference On The Boundary Of The Parameter Space With Application To Conditional Volatility Models," Discussion Papers 18-10, University of Copenhagen. Department of Economics.
    4. Gregory Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222,
    5. Philippe Jehiel & Juni Singh, 2019. "Multi-state choices with aggregate feedback on unfamiliar alternatives," Working Papers halshs-02183444, HAL.
    6. Samuele Centorrino & Mar'ia P'erez-Urdiales, 2020. "Maximum Likelihood Estimation of Stochastic Frontier Models with Endogeneity," Papers 2004.12369,, revised Apr 2020.
    7. David T. Frazier & Eric Renault, 2016. "Indirect Inference With(Out) Constraints," Papers 1607.06163,, revised Aug 2019.

    More about this item


    Boundary; Asymptotic normality; Admissibility; Random coefficients;

    JEL classification:

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


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