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Non-Standard Confidence Sets for Ratios and Tipping Points with Applications to Dynamic Panel Data

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  • Jean-Thomas Bernard
  • Ba Chu
  • Lynda Khalaf
  • Marcel Voia

Abstract

We study estimation uncertainty when the object of interest contains one or more ratios of parameters. The ratio of parameters is a discontinuous parameter transformation; it has been shown that traditional confidence intervals often fail to cover a true ratio with reliable probability. Constructing confidence sets for ratios using Fieller s method is a viable solution as the method can avoid the discontinuity problem. This paper proposes an extension of the multivariate Fieller method beyond standard contexts, focusing on asymptotically mixed normal estimators that commonly arise in dynamic regressions with persistent covariates. We show that the asymptotic distribution of the pivotal statistic used for constructing a Fieller s confidence set remains a standard Chi-squared; and in many instances, the Wald-type test statistic ‘self-normalizes’ and thus the rates of convergence need not be known. An extensive simulation study illustrates the finite sample properties of the proposed method using both the Pooled Mean Group (PMG) estimator and Arellano and Bond s (1991) (AnB) estimator in a dynamic polynomial panel regression. Our method is demonstrated to work well in small samples, even in some persistent contexts.

Suggested Citation

  • Jean-Thomas Bernard & Ba Chu & Lynda Khalaf & Marcel Voia, 2019. "Non-Standard Confidence Sets for Ratios and Tipping Points with Applications to Dynamic Panel Data," Annals of Economics and Statistics, GENES, issue 134, pages 79-108.
  • Handle: RePEc:adr:anecst:y:2019:i:134:p:79-108
    DOI: 10.15609/annaeconstat2009.134.0079
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    File URL: https://www.jstor.org/stable/10.15609/annaeconstat2009.134.0079
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    References listed on IDEAS

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    More about this item

    Keywords

    Fieller's Theorem; Ratios of Parameters; Delta Method; the Pooled Mean Group (PMG) Estimator; the Arellano and BondMmethod; Dynamic Polynomial Panels; Wald-Type Tests;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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