{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T12:41:50Z","timestamp":1790772110417,"version":"4.1.0"},"reference-count":50,"publisher":"The Econometric Society","issue":"2","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004853","name":"Chinese University of Hong Kong","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004853","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009743","name":"Swenson College of Science and Engineering, University of Minnesota Duluth","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100009743","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000155","name":"Social Sciences and Humanities Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000155","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008240","name":"Fonds de Recherche du Qu\u00e9bec-Soci\u00e9t\u00e9 et Culture","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008240","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>In this paper, we introduce a method of generating bootstrap samples with unknown patterns of cross\u2010 sectional\/spatial dependence, which we call the spatial dependent wild bootstrap. This method is a spatial counterpart to the wild dependent bootstrap of Shao (2010) and generates data by multiplying a vector of independently and identically distributed external variables by the eigendecomposition of a bootstrap kernel. We prove the validity of our method for studentized and unstudentized statistics under a linear array representation of the data. Simulation experiments document the potential for improved inference with our approach. We illustrate our method in a firm\u2010level regression application investigating the relationship between firms' sales growth and the import activity in their local markets using unique firm\u2010level and imports data for Canada.<\/jats:p>","DOI":"10.3982\/qe1626","type":"journal-article","created":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T05:06:37Z","timestamp":1683781597000},"page":"511-569","source":"Crossref","is-referenced-by-count":20,"title":["Bootstrap inference under cross\u2010sectional dependence"],"prefix":"10.3982","volume":"14","author":[{"given":"Timothy G.","family":"Conley","sequence":"first","affiliation":[{"name":"Department of Economics, Western University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S\u00edlvia","family":"Gon\u00e7alves","sequence":"additional","affiliation":[{"name":"Department of Economics, McGill University"},{"name":"CIREQ"},{"name":"CIRANO"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Min Seong","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Connecticut"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benoit","family":"Perron","sequence":"additional","affiliation":[{"name":"D\u00e9partement de sciences \u00e9conomiques, Universit\u00e9 of Montr\u00e9al"},{"name":"CIREQ"},{"name":"CIRANO"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2023]]},"reference":[{"key":"quan200260-bib-0001","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1086\/682384","volume":"34","author":"Acemoglu","year":"2016","journal-title":"Journal of Labor Economics"},{"key":"quan200260-bib-0002","doi-asserted-by":"crossref","first-page":"817","DOI":"10.2307\/2938229","volume":"59","author":"Andrews","year":"1991","journal-title":"Econometrica"},{"issue":"4","key":"quan200260-bib-0003","doi-asserted-by":"crossref","first-page":"1799","DOI":"10.1093\/qje\/qju026","volume":"129","author":"Autor","year":"2014","journal-title":"The Quarterly Journal of Economics"},{"key":"quan200260-bib-0004","volume-title":"An Introduction to Stochastic Processes","author":"Bartlett","year":"1955"},{"issue":"1","key":"quan200260-bib-0005","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.jinteco.2005.06.002","volume":"68","author":"Bernard","year":"2006","journal-title":"Journal of International Economics"},{"key":"quan200260-bib-0006","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.jeconom.2011.01.007","volume":"165 (2)","author":"Bester","year":"2011","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0007","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1017\/S0266466614000814","volume":"32","author":"Bester","year":"2016","journal-title":"Econometric Theory"},{"key":"quan200260-bib-0008","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1162\/rest.90.3.414","volume":"90","author":"Cameron","year":"2008","journal-title":"Review of Economics and Statistics"},{"key":"quan200260-bib-0009","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.3982\/ECTA16557","volume":"88","author":"Cavaliere","year":"2020","journal-title":"Econometrica"},{"key":"quan200260-bib-0010","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/S0304-4076(01)00070-7","volume":"105","author":"Chen","year":"2001","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0011","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0304-4076(98)00084-0","volume":"92","author":"Conley","year":"1999","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0012","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1086\/367681","volume":"111","author":"Conley","year":"2003","journal-title":"Journal of Political Economy"},{"issue":"2","key":"quan200260-bib-0013","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1023\/A:1015676113101","volume":"7","author":"Conley","year":"2002","journal-title":"Journal of Economic Growth"},{"key":"quan200260-bib-0014","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.jeconom.2006.09.003","volume":"140","author":"Conley","year":"2007","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0015","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1002\/jae.670","volume":"17","author":"Conley","year":"2002","journal-title":"Journal of Applied Econometrics"},{"key":"quan200260-bib-0016","doi-asserted-by":"crossref","unstructured":"Conley, Timothy G., S\u00edlvia Gon\u00e7alves, Min Seong Kim, and Benoit Perron (2023), \u201cSupplement to \u2018Bootstrap inference under cross-sectional dependence\u2019.\u201d Quantitative Economics Supplemental Material, 14, https:\/\/doi.org\/10.3982\/QE1626.","DOI":"10.3982\/QE1626"},{"key":"quan200260-bib-0017","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1111\/1468-2354.00026","volume":"40","author":"Davidson","year":"1999","journal-title":"International Economic Review"},{"key":"quan200260-bib-0018","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.jeconom.2019.04.035","volume":"212","author":"Djogbenou","year":"2019","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0019","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1006\/jmva.2001.2056","volume":"83","author":"Gneiting","year":"2002","journal-title":"Journal of Multivariate Analysis"},{"key":"quan200260-bib-0020","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1017\/S0266466610000496","volume":"27","author":"Gon\u00e7alves","year":"2011","journal-title":"Econometric Theory"},{"key":"quan200260-bib-0021","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S0304-4076(03)00204-5","volume":"119","author":"Gon\u00e7alves","year":"2004","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0022","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.jeconom.2016.09.008","volume":"196","author":"Hidalgo","year":"2017","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0023","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1198\/jbes.2009.08046","volume":"28","author":"Ibragimov","year":"2010","journal-title":"Journal of Business and Economics Statistics"},{"key":"quan200260-bib-0024","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.jeconom.2006.09.005","volume":"140","author":"Kelejian","year":"2007","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0025","doi-asserted-by":"crossref","first-page":"1130","DOI":"10.1017\/S0266466605050565","volume":"21","author":"Kiefer","year":"2005","journal-title":"Econometric Theory"},{"key":"quan200260-bib-0026","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.jeconom.2010.10.002","volume":"160","author":"Kim","year":"2011","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0027","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.jeconom.2013.07.002","volume":"177","author":"Kim","year":"2013","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0028","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1515\/2156-6674.1006","volume":"1","author":"Kline","year":"2012","journal-title":"Journal of Econometric Methods"},{"key":"quan200260-bib-0029","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.jeconom.2012.06.001","volume":"171","author":"Kline","year":"2012","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0030","unstructured":"Kojevnikov, Denis (2021), \u201cThe bootstrap for network dependent processes.\u201d Working paper, Tilburg University."},{"key":"quan200260-bib-0031","doi-asserted-by":"crossref","first-page":"1774","DOI":"10.1214\/009053606000000551","volume":"34","author":"Lahiri","year":"2006","journal-title":"The Annals of Statistics"},{"key":"quan200260-bib-0032","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jeconom.2015.08.001","volume":"190","author":"Lee","year":"2016","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0033","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1093\/biomet\/73.1.13","volume":"73","author":"Liang","year":"1986","journal-title":"Biometrika"},{"key":"quan200260-bib-0034","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1017\/S0266466612000175","volume":"28","author":"Martellosio","year":"2012","journal-title":"Econometric Theory"},{"key":"quan200260-bib-0035","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1111\/j.1467-9892.2010.00679.x","volume":"31","author":"McMurry","year":"2010","journal-title":"Journal of Time Series Analysis"},{"key":"quan200260-bib-0036","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/0304-4076(86)90021-7","volume":"32","author":"Moulton","year":"1986","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0037","doi-asserted-by":"crossref","first-page":"2901","DOI":"10.3982\/ECTA19465","volume":"90","author":"M\u00fcller","year":"2022","journal-title":"Econometrica"},{"key":"quan200260-bib-0038","first-page":"468","volume":"69","author":"Nordman","year":"2007","journal-title":"Sankhya"},{"key":"quan200260-bib-0039","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1016\/j.jspi.2006.06.033","volume":"137","author":"Phillips","year":"2007","journal-title":"Journal of Statistical Planning and Inference"},{"key":"quan200260-bib-0040","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1017\/S0266466610000484","volume":"27","author":"Politis","year":"2011","journal-title":"Econometric Theory"},{"key":"quan200260-bib-0041","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.jeconom.2011.09.033","volume":"167","author":"Robinson","year":"2011","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0042","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.jeconom.2011.05.002","volume":"165","author":"Robinson","year":"2012","journal-title":"Journal of Econometrics"},{"key":"quan200260-bib-0043","unstructured":"Sandoval, Aldo (2020), \u201cImport wholesalers and the effect of trade on Canadian producers.\u201d Ontario, Working paper, University of Western, http:\/\/www.aldouwoecon.com."},{"key":"quan200260-bib-0044","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1198\/jasa.2009.tm08744","volume":"105","author":"Shao","year":"2010","journal-title":"Journal of the American Statistical Association"},{"key":"quan200260-bib-0045","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1494-6","volume-title":"Interpolation of Spatial Data: Some Theory for Kriging","author":"Stein","year":"1999"},{"key":"quan200260-bib-0046","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1162\/REST_a_00441","volume":"97","author":"Sun","year":"2015","journal-title":"Review of Economics and Statistics"},{"key":"quan200260-bib-0047","volume-title":"Globalization","author":"Utar","year":"2017"},{"key":"quan200260-bib-0048","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511802256","volume-title":"Asymptotic Statistics","author":"Vaart","year":"1998"},{"key":"quan200260-bib-0049","volume-title":"Correlation Theory of Stationary and Related Random Functions","author":"Yaglom","year":"1987"},{"key":"quan200260-bib-0050","first-page":"1329","volume":"41","author":"Zhang","year":"2013","journal-title":"Annals of Statistics"}],"container-title":["Quantitative Economics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.3982\/QE1626","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T05:09:30Z","timestamp":1683781770000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/QE1626"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"references-count":50,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023]]}},"alternative-id":["10.3982\/QE1626"],"URL":"https:\/\/doi.org\/10.3982\/qe1626","relation":{},"ISSN":["1759-7323"],"issn-type":[{"value":"1759-7323","type":"print"}],"subject":[],"published":{"date-parts":[[2023]]}}}