On spatial processes and asymptotic inference under near-epoch dependence

The 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 notio...

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Bibliographic Details
Published in:Journal of econometrics Vol. 170; no. 1; pp. 178 - 190
Main Authors: Jenish, Nazgul, Prucha, Ingmar R.
Format: Journal Article
Language:English
Published: Netherlands Elsevier B.V 01.09.2012
Elsevier
Elsevier Sequoia S.A
Subjects:
Asymptotic methods
Central limit theorem
Econometric models
econometrics
Economic models
Economic theory
Estimation
Generalized method of moments
GMM estimator
Inference
Law of large numbers
Mathematical analysis
Near-epoch dependent processes
Nonlinear analysis
nonlinear models
Normality
Probability theory
Random fields
Statistical models
Stochastic processes
Studies
Theorems
Time series
time series analysis
C31
C10
C21
Random fields
Central limit theorem
GMM estimator
Law of large numbers
Near-epoch dependent processes
ISSN:0304-4076, 1872-6895
Online Access:Get full text
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Summary:The 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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ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2012.05.022