{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,30]],"date-time":"2026-10-30T06:07:46Z","timestamp":1793340466516,"version":"4.5.0"},"reference-count":59,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T00:00:00Z","timestamp":1675641600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:p>This paper studies the non-Gaussian pseudo maximum likelihood (PML) estimation of a spatial autoregressive (SAR) model with SAR disturbances. If the spatial weights matrix \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466623000026_inline1.png\"\/><jats:tex-math>\n$M_{n}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> for the SAR disturbances is normalized to have row sums equal to 1 or the model reduces to a SAR model with no SAR process of disturbances, the non-Gaussian PML estimator (NGPMLE) for model parameters except the intercept term and the variance \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466623000026_inline2.png\"\/><jats:tex-math>\n$\\sigma _{0}^{2}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> of independent and identically distributed (i.i.d.) innovations in the model is consistent. Without row normalization of \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466623000026_inline3.png\"\/><jats:tex-math>\n$M_{n}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, the symmetry of i.i.d. innovations leads to consistent NGPMLE for model parameters except \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466623000026_inline4.png\"\/><jats:tex-math>\n$\\sigma _{0}^{2}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. With neither row normalization of \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466623000026_inline5.png\"\/><jats:tex-math>\n$M_{n}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> nor the symmetry of innovations, a location parameter can be added to the non-Gaussian pseudo likelihood function to achieve consistent estimation of model parameters except \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466623000026_inline6.png\"\/><jats:tex-math>\n$\\sigma _{0}^{2}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. The NGPMLE with no added parameter can have a significant efficiency improvement upon the Gaussian PML estimator and the generalized method of moments estimator based on linear and quadratic moments. We also propose a non-Gaussian score test for spatial dependence, which can be locally more powerful than the Gaussian score test. Monte Carlo results show that our NGPMLE with no added parameter and the score test based on it perform well in finite samples.<\/jats:p>","DOI":"10.1017\/s0266466623000026","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T10:22:27Z","timestamp":1675678947000},"page":"1120-1158","source":"Crossref","is-referenced-by-count":1,"title":["CONSISTENT NON-GAUSSIAN PSEUDO MAXIMUM LIKELIHOOD ESTIMATORS OF SPATIAL AUTOREGRESSIVE MODELS"],"prefix":"10.1017","volume":"40","author":[{"given":"Fei","family":"Jin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuqin","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2023,2,6]]},"reference":[{"key":"S0266466623000026_r10","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1111\/j.2517-6161.1980.tb01108.x","article-title":"On the Cliff\u2013Ord test for spatial autocorrelation","volume":"42","author":"Burridge","year":"1980","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"S0266466623000026_r47","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2010.08.001"},{"key":"S0266466623000026_r17","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2013.840239"},{"key":"S0266466623000026_r56","doi-asserted-by":"publisher","DOI":"10.1017\/CCOL0521252806"},{"key":"S0266466623000026_r24","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1765(91)90238-G"},{"key":"S0266466623000026_r49","doi-asserted-by":"crossref","first-page":"2111","DOI":"10.1016\/S1573-4412(05)80005-4","volume-title":"Handbook of Econometrics","volume":"4","author":"Newey","year":"1994"},{"key":"S0266466623000026_r46","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2020.07.032"},{"key":"S0266466623000026_r14","doi-asserted-by":"crossref","DOI":"10.1002\/9781119115151","volume-title":"Statistics for Spatial Data","author":"Cressie","year":"1993"},{"key":"S0266466623000026_r34","unstructured":"Jin, F. , Lee, L.F. , & Yang, K. 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