Consistent EM algorithm for a spatial autoregressive probit model

This paper is concerned with the estimation of spatial autoregressive probit models, which are increasingly used in many empirical settings. Among existing estimators, the EM algorithm for spatial probit models introduced by McMillen (J Reg Sci 32(3):335–348, 1992) is a widely used method, but it la...

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Bibliographic Details
Published inJournal of Spatial Econometrics Vol. 3; no. 1
Main Author Cheng, Wei
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2022
Subjects
Econometrics
Economics
Economics and Finance
Finance
Insurance
Management
Original Paper
Regional/Spatial Science
Statistics for Business
C63
Near-epoch dependence
C13
Consistent estimator
Spatial probit model
EM algorithm
C51
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ISSN2662-2998
2662-298X
DOI10.1007/s43071-022-00022-x

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Summary:This paper is concerned with the estimation of spatial autoregressive probit models, which are increasingly used in many empirical settings. Among existing estimators, the EM algorithm for spatial probit models introduced by McMillen (J Reg Sci 32(3):335–348, 1992) is a widely used method, but it lacks proof of consistency. In this paper, we formally show that it is inconsistent by applying the law of large numbers for dependent and non-identically distributed near-epoch dependence (NED) random fields. We provide a modification of the EM algorithm to yield a consistent estimator. Monte Carlo experiments show that in finite samples, our new EM algorithm outperforms McMillen’s EM algorithm, especially for medium to high levels of spatial dependence.
ISSN:2662-2998
2662-298X
DOI:10.1007/s43071-022-00022-x