Spatial autoregressions with an extended parameter space and similarity-based weights

Francesca Rossi, Offer Lieberman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We provide in this paper asymptotic theory for a spatial autoregressive model (SAR, henceforth) in which the spatial coefficient, λ, is allowed to be less than or equal to unity, as well as consistent with a local to unit root (LUR) model and of the moderate integration (MI) from unity type, and the spatial weights are allowed to be similarity-based and data driven. Other special cases of our setting include the random walk, a model in which all the weights are equal, the standard SAR model in which λ<1 and the similarity based autoregression in which λ=1 and data do not display a natural order. As the norming rates for the asymptotic theory are very different in the λ<1 - compared with the λ=1 and LUR cases, we resort to random norming that treats all cases in a uniform manner. It turns out that standard CLT results prevail in a large class of models in which the infinity norm of the inverse of the weighting structure that characterizes the reduced-form process is Onγ, γ∈[0,1), and is non-standard in the case γ=1. We use a shifted profile likelihood to obtain results which are valid for all cases. A small simulation experiment supports our findings and the usefulness of our model is illustrated with an empirical application of the Boston housing data set in which the estimate of λ appeared to be very close to unity.

Original languageEnglish
Pages (from-to)1770-1798
Number of pages29
JournalJournal of Econometrics
Issue number2
StatePublished - Aug 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.


  • Quasi-maximum-likelihood
  • Similarity function
  • Spatial autoregression
  • Weight matrix


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