Consistency without compactness of the parameter space in spatial econometrics

Tuo Liu, Xingbai Xu and Lung-fei Lee

Economics Letters, 2022, vol. 210, issue C

Abstract: When studying the consistency of an estimator without a closed-form solution for a spatial econometric model, we usually assume that the parameter space is compact. However, compactness assumptions are restrictive as we need to know the boundaries of parameter spaces. We establish a consistency theorem for concave objective functions. We apply this result to rebuild the consistency of the quasi maximum likelihood estimator (QMLE) of a spatial autoregressive (SAR) model and a SAR Tobit model. Their log-likelihood functions are not concave, but they can be concave after proper reparameterization as in Olsen (1978).

Keywords: Non-compact parameter space; MLE; Spatial autoregressive model; Spatial autoregressive Tobit model; Concave log-likelihood (search for similar items in EconPapers)
JEL-codes: C01 C18 C21 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:210:y:2022:i:c:s0165176521004675

DOI: 10.1016/j.econlet.2021.110224

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