In this paper we develop asymptotic theory for a similarity-based spatial autoregressive (SAR) model. The model is hybrid in the terminology of Gilboa et al. (2006), with the data generating process for a dependent variable containing a rule-based linear component and a case-based term with a similarity structure. The weight of the similarity structure is allowed to vary in the unit interval and to be estimated explicitly. We prove consistency of the quasi-maximum-likelihood estimator and derive its limit distribution. This paper contributes to the literature on SAR and empirical similarity by incorporating a regression-type component in the data generating process, by allowing the similarity structure to accommodate non-ordered data and by estimating explicitly the weight of the similarity, allowing it to be equal to unity. The model we consider is formally similar to a standard SAR model with exogenous regressors and a data-driven weight matrix which depends on a finite set of parameters that have to be estimated. Our setup accommodates strong forms of cross-sectional correlation that are normally ruled out in the standard literature on spatial autoregressions, and also includes as special cases the random walk with a drift model, the local to unit root model (LUR) with a drift and the model for moderate integration with a drift.

Inference in a similarity-based spatial autoregressive model.

Francesca Rossi
2022

Abstract

In this paper we develop asymptotic theory for a similarity-based spatial autoregressive (SAR) model. The model is hybrid in the terminology of Gilboa et al. (2006), with the data generating process for a dependent variable containing a rule-based linear component and a case-based term with a similarity structure. The weight of the similarity structure is allowed to vary in the unit interval and to be estimated explicitly. We prove consistency of the quasi-maximum-likelihood estimator and derive its limit distribution. This paper contributes to the literature on SAR and empirical similarity by incorporating a regression-type component in the data generating process, by allowing the similarity structure to accommodate non-ordered data and by estimating explicitly the weight of the similarity, allowing it to be equal to unity. The model we consider is formally similar to a standard SAR model with exogenous regressors and a data-driven weight matrix which depends on a finite set of parameters that have to be estimated. Our setup accommodates strong forms of cross-sectional correlation that are normally ruled out in the standard literature on spatial autoregressions, and also includes as special cases the random walk with a drift model, the local to unit root model (LUR) with a drift and the model for moderate integration with a drift.
Spatial Autoregression, Similarity Function, Weight Matrix, Quasi-Maximum-Likelihood
File in questo prodotto:
File Dimensione Formato  
wp2022n1.pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: Documento in Pre-print
Licenza: Accesso ristretto
Dimensione 621.25 kB
Formato Adobe PDF
621.25 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/1056055
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact