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

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  • 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
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. David T. Frazier & Eric Renault, 2016. "Indirect Inference With(Out) Constraints," Papers 1607.06163, arXiv.org, revised Aug 2016.

    More about this item

    Keywords

    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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