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Directionally Differentiable Econometric Models

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  • Cho, Jin Seo
  • White, Halbert

Abstract

The current article examines the limit distribution of the quasi-maximum likelihood estimator obtained from a directionally differentiable quasi-likelihood function and represents its limit distribution as a functional of a Gaussian stochastic process indexed by direction. In this way, the standard analysis that assumes a differentiable quasi-likelihood function is treated as a special case of our analysis. We also examine and redefine the standard quasi-likelihood ratio, Wald, and Lagrange multiplier test statistics so that their null limit behaviors are regular under our model framework.

Suggested Citation

  • Cho, Jin Seo & White, Halbert, 2018. "Directionally Differentiable Econometric Models," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1101-1131, October.
  • Handle: RePEc:cup:etheor:v:34:y:2018:i:05:p:1101-1131_00
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    References listed on IDEAS

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    1. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    2. King, Maxwell L & Shively, Thomas S, 1993. "Locally Optimal Testing When a Nuisance Parameter Is Present Only under the Alternative," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 1-7, February.
    3. Jin Seo Cho & Halbert White, 2017. "Supplements to "Directionally Differentiable Econometric Models"," Working papers 2017rwp-103a, Yonsei University, Yonsei Economics Research Institute.
    4. 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.
    5. Cho, Jin Seo & White, Halbert, 2011. "Generalized runs tests for the IID hypothesis," Journal of Econometrics, Elsevier, vol. 162(2), pages 326-344, June.
    6. Jin Seo Cho & Isao Ishida & Halbert White, 2013. "Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions (published in: Essays in Nonlinear Time Series Econometrics, Festschrift in Honor of Timo Teras," Working papers 2013rwp-55, Yonsei University, Yonsei Economics Research Institute.
    7. Baek, Yae In & Cho, Jin Seo & Phillips, Peter C.B., 2015. "Testing linearity using power transforms of regressors," Journal of Econometrics, Elsevier, vol. 187(1), pages 376-384.
    8. Wooldridge, Jeffrey M. & White, Halbert, 1988. "Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 4(2), pages 210-230, August.
    9. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
    10. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
    11. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    12. Cho, Jin Seo & Ishida, Isao, 2012. "Testing for the effects of omitted power transformations," Economics Letters, Elsevier, vol. 117(1), pages 287-290.
    13. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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    Cited by:

    1. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jul 2020.
    2. Jin Seo Cho & Halbert White, 2017. "Supplements to "Directionally Differentiable Econometric Models"," Working papers 2017rwp-103a, Yonsei University, Yonsei Economics Research Institute.
    3. Dakyung Seong & Jin Seo Cho & Timo Terasvirta, 2019. "Comprehensive Testing of Linearity against the Smooth Transition Autoregressive Model," Working papers 2019rwp-151, Yonsei University, Yonsei Economics Research Institute.
    4. Sergio Firpo & Antonio F. Galvao & Thomas Parker, 2019. "Uniform inference for value functions," Papers 1911.10215, arXiv.org, revised Oct 2022.
    5. Firpo, Sergio & Galvao, Antonio F. & Kobus, Martyna & Parker, Thomas & Rosa-Dias, Pedro, 2020. "Loss Aversion and the Welfare Ranking of Policy Interventions," IZA Discussion Papers 13176, Institute of Labor Economics (IZA).

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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