Exact Properties of the Maximum Likelihood Estimator in Spatial Autoregressive Models

Grant Hillier and Federico Martellosio
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Grant Hillier: CeMMAP and University of Southampton
Federico Martellosio: University of Surrey

No 716, School of Economics Discussion Papers from School of Economics, University of Surrey

Abstract: The (quasi-) maximum likelihood estimator (QMLE) 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 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.

JEL-codes: C12 C21 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2016-05
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-sog and nep-ure
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Persistent link: https://EconPapers.repec.org/RePEc:sur:surrec:0716

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