Properties of the maximum likelihood estimator in spatial autoregressive models

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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. Terms of use: Documents in

Spillover dynamics for systemic risk measurement using spatial financial time series models

“…1 The ML Estimator (MLE) for spatial models with static dependence parameter was first studied in Ord (1975) in the context of cross-sectional data sets. Lee (2004) derives asymptotic properties of the Quasi MLE (QMLE) for n → ∞, and Hillier and Martellosio (2013) investigate its finite sample distribution. Large n and large T asymptotics for QMLE of the spatial model with static dependence parameter are studied in Yu et al (2008).…”

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“…In Hillier and Martellosio (2013) we presented a general result, equation (2.1) above, giving an expression for the exact distribution function of the quasi-maximum likelihood estimator for λ in equation (1.3), valid for any distribution of ε. Some examples of the application 24 In the unbalanced case, the columns of the fixed effects matrix span an eigenspace of W (as in the balanced case).…”

“…The class of Group Interaction models was discussed briefly in Hillier and Martellosio (2013) (hereafter H&M), and some exact results given for the pure balanced case. After some preliminaries, given in the next section, in Section 3 we provide a complete analysis of the properties ofλ ML , and of exact inference procedures based upon it, for the pure balanced model.…”