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Inference on Higher-Order Spatial Autoregressive Models with Increasingly Many Parameters

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  • Gupta, A
  • Robinson, PM

Abstract

This paper develops consistency and asymptotic normality of parameter estimates for a higher-order spatial autoregressive model whose order, and number of regressors, are allowed to approach infinity slowly with sample size. Both least squares and instrumental variables estimates are examined, and the permissible rate of growth of the dimension of the parameter space relative to sample size is studied. Besides allowing the number of estimable parameters to increase with the data, this has the advantage of accommodating explicitly some asymptotic regimes that arise in practice. Illustrations are discussed, in particular settings where the need for such theory arises quite naturally. A Monte Carlo study analyses various implications of the theory in finite samples. For empirical researchers our work has implications for the choice of model. In particular if the structure of the spatial weights matrix assumes a partitioning of the data then spatial parameters should be allowed to vary over clusters.

Suggested Citation

  • Gupta, A & Robinson, PM, 2013. "Inference on Higher-Order Spatial Autoregressive Models with Increasingly Many Parameters," Economics Discussion Papers 23417, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:23417
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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
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    More about this item

    Keywords

    Spatial autoregression; increasingly many parameters; central limit theorem; rate of convergence; spatial panel data;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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