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Testing Convergence Using HAR Inference

In: Essays in Honor of Cheng Hsiao

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  • Jianning Kong
  • Peter C. B. Phillips
  • Donggyu Sul

Abstract

Measurement of diminishing or divergent cross section dispersion in a panel plays an important role in the assessment of convergence or divergence over time in key economic indicators. Econometric methods, known as weakσ-convergence tests, have recently been developed (Kong, Phillips, & Sul, 2019) to evaluate such trends in dispersion in panel data using simple linear trend regressions. To achieve generality in applications, these tests rely on heteroskedastic and autocorrelation consistent (HAC) variance estimates. The present chapter examines the behavior of these convergence tests when heteroskedastic and autocorrelation robust (HAR) variance estimates using fixed-bmethods are employed instead of HAC estimates. Asymptotic theory for both HAC and HAR convergence tests is derived and numerical simulations are used to assess performance in null (no convergence) and alternative (convergence) cases. While the use of HAR statistics tends to reduce size distortion, as has been found in earlier analytic and numerical research, use of HAR estimates in nonparametric standardization leads to significant power differences asymptotically, which are reflected in finite sample performance in numerical exercises. The explanation is that weakσ-convergence tests rely on intentionally misspecified linear trend regression formulations of unknown trend decay functions that model convergence behavior rather than regressions with correctly specified trend decay functions. Some new results on the use of HAR inference with trending regressors are derived and an empirical application to assess diminishing variation in US State unemployment rates is included.

Suggested Citation

  • Jianning Kong & Peter C. B. Phillips & Donggyu Sul, 2020. "Testing Convergence Using HAR Inference," Advances in Econometrics, in: Essays in Honor of Cheng Hsiao, volume 41, pages 25-72, Emerald Group Publishing Limited.
  • Handle: RePEc:eme:aecozz:s0731-905320200000041002
    DOI: 10.1108/S0731-905320200000041002
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    Citations

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    Cited by:

    1. Ramanathan Kasivisvanathan & Henry S. Tilney & Shaman Jhanji & Michelle O’Mahony & Pascale Gruber & David Nicol & Dominic Morgan & Emma Kipps & Shahnawaz Rasheed, 2021. "The ‘hub and spoke model’ for the management of surgical patients during the COVID‐19 pandemic," International Journal of Health Planning and Management, Wiley Blackwell, vol. 36(5), pages 1397-1406, September.
    2. Rodríguez Benavides, Domingo & Mendoza González, Miguel Ángel & Muller Durán, Nancy Ivonne, 2022. "Convergencia regional sigma débil en México: 1970-2019," INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, Asociación Española de Ciencia Regional, issue 54, pages 29-49.

    More about this item

    Keywords

    HAR estimation; HAC estimation; nonparametric studentization; weak σ-convergence; misspecified trend regression; cross-sectional dependence; C33;
    All these keywords.

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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