On spatial processes and asymptotic inference under near-epoch dependence
AbstractThe development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the notion of near-epoch dependent (NED) processes used in the time series literature to random fields. The class of processes that is NED on, say, an α-mixing process, is shown to be closed under infinite transformations, and thus accommodates models with spatial dynamics. This would generally not be the case for the smaller class of α-mixing processes. The paper then derives a central limit theorem and law of large numbers for NED random fields. These limit theorems allow for fairly general forms of heterogeneity including asymptotically unbounded moments, and accommodate arrays of random fields on unevenly spaced lattices. The limit theorems are employed to establish consistency and asymptotic normality of GMM estimators. These results provide a basis for inference in a wide range of models with spatial dependence.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 170 (2012)
Issue (Month): 1 ()
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Web page: http://www.elsevier.com/locate/jeconom
Random fields; Near-epoch dependent processes; Central limit theorem; Law of large numbers; GMM estimator;
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- 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
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