IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v205y2018i2p402-422.html
   My bibliography  Save this article

Exact and higher-order properties of the MLE in spatial autoregressive models, with applications to inference

Author

Listed:
  • Hillier, Grant
  • Martellosio, Federico

Abstract

The quasi-maximum likelihood estimator for the autoregressive parameter in a spatial autoregression usually cannot be written explicitly in terms of the data. A rigorous analysis of the first-order asymptotic properties of the estimator, under some assumptions on the evolution of the spatial design matrix, is available in Lee (2004), but very little is known about its exact or higher-order properties. In this paper we first 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. Simple examples are used to illustrate important exact properties of the estimator that follow from this representation. In general models a complete exact analysis is not possible, but a higher-order (saddlepoint) approximation is made available by the main result. We use this approximation to construct confidence intervals for the autoregressive parameter. Coverage properties of the proposed confidence intervals are studied by Monte Carlo simulation, and are found to be excellent in a variety of circumstances.

Suggested Citation

  • Hillier, Grant & Martellosio, Federico, 2018. "Exact and higher-order properties of the MLE in spatial autoregressive models, with applications to inference," Journal of Econometrics, Elsevier, vol. 205(2), pages 402-422.
    • Handle: RePEc:eee:econom:v:205:y:2018:i:2:p:402-422
    DOI: 10.1016/j.jeconom.2018.01.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407618300587
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2018.01.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    2. Ma, Yingying & Lan, Wei & Zhou, Fanying & Wang, Hansheng, 2020. "Approximate least squares estimation for spatial autoregressive models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    3. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.

    More about this item

    Keywords

    Spatial autoregression; Maximum likelihood estimation; Group interaction; Social networks; Complete bipartite graph; Saddlepoint;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:205:y:2018:i:2:p:402-422. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.