{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,30]],"date-time":"2026-10-30T18:41:18Z","timestamp":1793385678159,"version":"4.5.0"},"reference-count":58,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T00:00:00Z","timestamp":1770854400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"abstract":"<jats:p>This article proposes and studies two Huber-type estimation approaches, namely, the Huber instrumental variable (IV) estimation and the Huber generalized method of moments (GMM) estimation, for a spatial autoregressive model. We establish the consistency, asymptotic distributions, finite sample breakdown points, and influence functions of these estimators. Simulation studies show that compared to the corresponding traditional estimators (the two-stage least squares estimator, the best IV estimator, and the GMM estimator), our estimators are more robust when the unknown disturbances are long-tailed, and our estimators only lose a little efficiency when the disturbances are short-tailed. Moreover, the Huber GMM estimator also outperforms several robust estimators in the literature. Finally, we apply our estimation method to investigate the impact of the urban heat island effect on housing prices. A package is published on GitHub for practitioners to use in their empirical studies.<\/jats:p>","DOI":"10.1017\/s0266466626100346","type":"journal-article","created":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T08:24:54Z","timestamp":1770884694000},"page":"1-51","source":"Crossref","is-referenced-by-count":1,"title":["ROBUST ESTIMATION FOR THE SPATIAL AUTOREGRESSIVE MODEL"],"prefix":"10.1017","author":[{"given":"Tuo","family":"Liu","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00mcjh785","id-type":"ROR","asserted-by":"publisher"}],"name":"Xiamen University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingbai","family":"Xu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00mcjh785","id-type":"ROR","asserted-by":"publisher"}],"name":"Xiamen University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lung-Fei","family":"Lee","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00wtvfq62","id-type":"ROR","asserted-by":"publisher"}],"name":"Shanghai University of Finance and Economics"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingdan","family":"Mei","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041pakw92","id-type":"ROR","asserted-by":"publisher"}],"name":"Renmin University of China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,2,12]]},"reference":[{"key":"S0266466626100346_r15","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-22799-5"},{"key":"S0266466626100346_r18","doi-asserted-by":"publisher","DOI":"10.3368\/le.90.1.61"},{"key":"S0266466626100346_r10","volume-title":"A unified theory of estimation and inference for nonlinear dynamic models","author":"Gallant","year":"1988"},{"key":"S0266466626100346_r47","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600011233"},{"key":"S0266466626100346_r16","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177703732"},{"key":"S0266466626100346_r38","unstructured":"Liu, T. , & Lee, L. (2023). Estimation and selection of high order spatial autoregressive models with adaptive elastic net. Working paper."},{"key":"S0266466626100346_r46","doi-asserted-by":"publisher","DOI":"10.1016\/j.regsciurbeco.2012.07.009"},{"key":"S0266466626100346_r25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2006.01.007"},{"key":"S0266466626100346_r41","unstructured":"Mallows, C. L. (1975). On some topics in robustness. Bell Telephone Laboratories, Murray Hill, NJ: Technical Memorandum."},{"key":"S0266466626100346_r12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-57338-5_12"},{"key":"S0266466626100346_r61","doi-asserted-by":"crossref","unstructured":"Huber, P. & Ronchetti, E. (2009). Robust Statistics (2nd ed.). John Wiley & Sons, Inc.","DOI":"10.1002\/9780470434697"},{"key":"S0266466626100346_r1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012780"},{"key":"S0266466626100346_r24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.10.025"},{"key":"S0266466626100346_r17","unstructured":"Huber, P. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In Fifth berkeley symposium on mathematical statistics and probability (pp. 221\u2013233) Lucien M. Le Cam, Jerzy Neyman, University of California Press."},{"key":"S0266466626100346_r22","doi-asserted-by":"publisher","DOI":"10.1111\/1468-2354.00027"},{"key":"S0266466626100346_r37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2019.07.001"},{"key":"S0266466626100346_r50","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2019.04.040"},{"key":"S0266466626100346_r3","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1975.10479884"},{"key":"S0266466626100346_r6","doi-asserted-by":"publisher","DOI":"10.1002\/9781119115151"},{"key":"S0266466626100346_r30","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00558.x"},{"key":"S0266466626100346_r5","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-937X.2009.00550.x"},{"key":"S0266466626100346_r21","doi-asserted-by":"publisher","DOI":"10.1023\/A:1007707430416"},{"key":"S0266466626100346_r40","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpubeco.2012.03.002"},{"key":"S0266466626100346_r23","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(01)00064-1"},{"key":"S0266466626100346_r39","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0297.2008.02235.x"},{"key":"S0266466626100346_r60","doi-asserted-by":"publisher","DOI":"10.1086\/700936"},{"key":"S0266466626100346_r48","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03486-6"},{"key":"S0266466626100346_r33","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2022.2041424"},{"key":"S0266466626100346_r53","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(01)00102-6"},{"key":"S0266466626100346_r13","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00373"},{"key":"S0266466626100346_r45","unstructured":"Phillips, P. C. , & Jiang, L. (2025). Cross section curve autoregression: The unit root case. Manuscript."},{"key":"S0266466626100346_r9","volume-title":"Real analysis: Modern techniques and their applications","author":"Folland","year":"1999"},{"key":"S0266466626100346_r51","unstructured":"Su, L. , & Yang, Z. (2011). Instrumental variable quantile estimation of spatial autoregressive models. Working paper."},{"key":"S0266466626100346_r31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.10.004"},{"key":"S0266466626100346_r20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.05.022"},{"key":"S0266466626100346_r26","doi-asserted-by":"publisher","DOI":"10.1086\/692842"},{"key":"S0266466626100346_r58","doi-asserted-by":"publisher","DOI":"10.1080\/00949655.2020.1740223"},{"key":"S0266466626100346_r19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.02.009"},{"key":"S0266466626100346_r55","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.12.005"},{"key":"S0266466626100346_r27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2013.02.004"},{"key":"S0266466626100346_r35","article-title":"Spatial-temporal patterns of summer urban islands and their economic implications in Beijing","author":"Lin","year":"2022","journal-title":"Environmental Science and Pollution Research"},{"key":"S0266466626100346_r43","doi-asserted-by":"publisher","DOI":"10.1016\/j.jenvman.2017.03.095"},{"key":"S0266466626100346_r57","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2017.10.008"},{"key":"S0266466626100346_r14","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177693054"},{"key":"S0266466626100346_r56","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2015.05.004"},{"key":"S0266466626100346_r54","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2023.109917"},{"key":"S0266466626100346_r11","doi-asserted-by":"publisher","DOI":"10.1201\/9781420072884"},{"key":"S0266466626100346_r44","doi-asserted-by":"publisher","DOI":"10.2307\/1913622"},{"key":"S0266466626100346_r36","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.10.035"},{"key":"S0266466626100346_r4","doi-asserted-by":"publisher","DOI":"10.1007\/s00180-018-0845-4"},{"key":"S0266466626100346_r42","volume-title":"Robust statistics: Theory and methods (with R)","author":"Maronna","year":"2019"},{"key":"S0266466626100346_r29","doi-asserted-by":"publisher","DOI":"10.1081\/ETC-120025891"},{"key":"S0266466626100346_r28","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA13660"},{"key":"S0266466626100346_r52","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecosta.2023.01.004"},{"key":"S0266466626100346_r59","doi-asserted-by":"publisher","DOI":"10.5194\/acp-17-5439-2017"},{"key":"S0266466626100346_r2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpubeco.2014.06.011"},{"key":"S0266466626100346_r49","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.08.008"},{"key":"S0266466626100346_r8","doi-asserted-by":"publisher","DOI":"10.1201\/9780429096280"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466626100346","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T08:25:04Z","timestamp":1770884704000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466626100346\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,12]]},"references-count":58,"alternative-id":["S0266466626100346"],"URL":"https:\/\/doi.org\/10.1017\/s0266466626100346","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,12]]}}}