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Properties of the maximum likelihood estimator in spatial autoregressive models

Properties of the maximum likelihood estimator in spatial autoregressive models
Properties of the maximum likelihood estimator in spatial autoregressive models
The (quasi-) maximum likelihood estimator (MLE) for the autoregressive parameter in a spatial autoregressive model cannot in general be written explicitly in terms of the data. The only known properties of the estimator have hitherto been its first-order asymptotic properties (Lee, 2004, Econometrica), derived under specific assumptions on the evolution of the spatial weights matrix involved. In this paper we show that the exact cumulative distribution function of the estimator can, under mild assumptions, be written down explicitly. A number of immediate consequences of the main result are discussed, and several examples of theoretical and practical interest are analyzed in detail. The examples are of interest in their own right, but also serve to illustrate some unexpected features of the distribution of the MLE. In particular, we show that the distribution of the MLE may not be supported on the entire parameter space, and may be nonanalytic at some points in its support.
44/2013
University of Southampton
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Martellosio, Federico
4fa40068-a4be-4f23-be6f-83cbdc33685b
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Martellosio, Federico
4fa40068-a4be-4f23-be6f-83cbdc33685b

Hillier, Grant and Martellosio, Federico (2013) Properties of the maximum likelihood estimator in spatial autoregressive models (CeMMap Working Paper, , (doi:10.1920/wp.cem.2013.4413), 44/2013) Southampton, GB. University of Southampton 43pp.

Record type: Monograph (Working Paper)

Abstract

The (quasi-) maximum likelihood estimator (MLE) for the autoregressive parameter in a spatial autoregressive model cannot in general be written explicitly in terms of the data. The only known properties of the estimator have hitherto been its first-order asymptotic properties (Lee, 2004, Econometrica), derived under specific assumptions on the evolution of the spatial weights matrix involved. In this paper we show that the exact cumulative distribution function of the estimator can, under mild assumptions, be written down explicitly. A number of immediate consequences of the main result are discussed, and several examples of theoretical and practical interest are analyzed in detail. The examples are of interest in their own right, but also serve to illustrate some unexpected features of the distribution of the MLE. In particular, we show that the distribution of the MLE may not be supported on the entire parameter space, and may be nonanalytic at some points in its support.

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Published date: 12 September 2013
Organisations: Economics

Identifiers

Local EPrints ID: 357085
URI: https://eprints.soton.ac.uk/id/eprint/357085
PURE UUID: 54ca7690-c976-4351-9502-c0b40d30244e
ORCID for Grant Hillier: ORCID iD orcid.org/0000-0003-3261-5766

Catalogue record

Date deposited: 04 Oct 2013 12:40
Last modified: 27 Jul 2019 00:38

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