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Saddlepoint Approximations for Spatial Panel Data Models

Author

Listed:
  • Chaonan Jiang

    (University of Geneva - Geneva School of Economics and Management)

  • Davide La Vecchia

    (University of Geneva - Geneva School of Economics and Management - Research Center for Statistics)

  • Elvezio Ronchetti

    (University of Geneva - Research Center for Statistics)

  • O. Scaillet

    (University of Geneva GSEM and GFRI; Swiss Finance Institute; University of Geneva - Research Center for Statistics)

Abstract

We develop new higher-order asymptotic techniques for the Gaussian maximum likelihood estimator of the parameters in a spatial panel data model, with fixed effects, time-varying covariates, and spatially correlated errors. We introduce a new saddlepoint density and tail area approximation to improve on the accuracy of the extant asymptotics. It features relative error of order O(m to the power of -1) for m = n(T -1) with n being the cross-sectional dimension and T the time-series dimension. The main theoretical tool is the tilted-Edgeworth technique. It yields a density approximation that is always non-negative, does not need resampling, and is accurate in the tails. We provide an algorithm to implement our saddlepoint approximation and we illustrate the good performance of our method via numerical examples. Monte Carlo experiments show that, for the spatial panel data model with fixed effects and T = 2, the saddlepoint approximation yields accuracy improvements over the routinely applied first-order asymptotics and Edgeworth expansions, in small to moderate sample sizes, while preserving analytical tractability. An empirical application on the investment-saving relationship in OECD countries shows disagreement between testing results based on first-order asymptotics and saddlepoint techniques, which questions some implications based on the former.

Suggested Citation

  • Chaonan Jiang & Davide La Vecchia & Elvezio Ronchetti & O. Scaillet, 2019. "Saddlepoint Approximations for Spatial Panel Data Models," Swiss Finance Institute Research Paper Series 19-18, Swiss Finance Institute, revised Mar 2019.
  • Handle: RePEc:chf:rpseri:rp1918
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    More about this item

    Keywords

    Spatial statistics; Panel data; Small samples; Saddlepoint approximation;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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