Properties of the maximum likelihood estimator in spatial autoregressive models

Grant Hillier () and Federico Martellosio
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Grant Hillier: Institute for Fiscal Studies and University of Southampton
Federico Martellosio: Institute for Fiscal Studies

No CWP44/13, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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 analysed 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. Supplementary material relating to this working paper can be viewed here

Keywords: spatial autoregression; maximum likelihood estimation; group interaction; networks; complete bipartite graph (search for similar items in EconPapers)
JEL-codes: C12 C21 (search for similar items in EconPapers)
Date: 2013-09-19
New Economics Papers: this item is included in nep-ecm, nep-lam, nep-ltv, nep-neu and nep-ure
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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