Model selection and model averaging for matrix exponential spatial models

Ye Yang*, Osman Doğan, Suleyman Taspinar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we focus on a model specification problem in spatial econometric models when an empiricist needs to choose from a pool of candidates for the spatial weights matrix. We propose a model selection (MS) procedure for the matrix exponential spatial specification (MESS), when the true spatial weights matrix may not be in the set of candidate spatial weights matrices. We show that the selection estimator is asymptotically optimal in the sense that asymptotically it is as efficient as the infeasible estimator that uses the best candidate spatial weights matrix. The proposed selection procedure is also consistent in the sense that when the data generating process involves spatial effects, it chooses the true spatial weights matrix with probability approaching one in large samples. We also propose a model averaging (MA) estimator that compromises across a set of candidate models. We show that it is asymptotically optimal. We further flesh out how to extend the proposed selection and averaging schemes to higher order specifications and to the MESS with heteroscedasticity. Our Monte Carlo simulation results indicate that the MS and MA estimators perform well in finite samples. We also illustrate the usefulness of the proposed MS and MA schemes in a spatially augmented economic growth model.

Original languageEnglish
Pages (from-to)827-858
Number of pages32
JournalEconometric Reviews
Issue number8
Publication statusPublished - 2022
Externally publishedYes

Bibliographical note

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© 2022 Taylor & Francis Group, LLC.


  • AMSE
  • Asymptotic optimality
  • matrix exponential spatial models
  • MESS
  • model averaging
  • model selection


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