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Exact Properties of the Maximum Likelihood Estimator in Spatial Autoregressive Models

Hillier, G and Martellosio, F (2015) Exact Properties of the Maximum Likelihood Estimator in Spatial Autoregressive Models [Working Paper]

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Abstract

The (quasi-) maximum likelihood estimator (QMLE) for the autoregres-sive 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 in terms of that of a particular quadratic form. A number of immediate consequences of this result are discussed, and some examples 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.

Item Type: Working Paper
Subjects : subj_Economics
Divisions : Faculty of Arts and Social Sciences > School of Economics
Authors :
AuthorsEmailORCID
Hillier, GUNSPECIFIEDUNSPECIFIED
Martellosio, FUNSPECIFIEDUNSPECIFIED
Date : 2015
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 04 May 2016 15:44
Last Modified : 04 May 2016 15:44
URI: http://epubs.surrey.ac.uk/id/eprint/810630

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