{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T22:27:35Z","timestamp":1792016855666,"version":"4.4.0"},"reference-count":24,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2016,2,21]],"date-time":"2016-02-21T00:00:00Z","timestamp":1456012800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J of Applied Econometrics"],"published-print":{"date-parts":[[2017,3]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>\n                    The cluster robust variance estimator (CRVE) relies on the number of clusters being sufficiently large. Monte Carlo evidence suggests that the \u2018rule of 42\u2019 is not true for unbalanced clusters. Rejection frequencies are higher for datasets with 50 clusters proportional to US state populations than with 50 balanced clusters. Using critical values based on the wild cluster bootstrap performs much better. However, this procedure fails when a small number of clusters is treated. We explain why CRVE\n                    <jats:italic>t<\/jats:italic>\n                    \u00a0statistics and the wild bootstrap fail in this case, study the \u2018effective number\u2019 of clusters and simulate placebo laws with dummy variable regressors. Copyright \u00a9 2016 John Wiley &amp; Sons, Ltd.\n                  <\/jats:p>","DOI":"10.1002\/jae.2508","type":"journal-article","created":{"date-parts":[[2016,2,21]],"date-time":"2016-02-21T21:58:43Z","timestamp":1456091923000},"page":"233-254","source":"Crossref","is-referenced-by-count":404,"title":["Wild Bootstrap Inference for Wildly Different Cluster Sizes"],"prefix":"10.1002","volume":"32","author":[{"given":"James G.","family":"MacKinnon","sequence":"first","affiliation":[{"name":"Department of Economics Queen's University  Ontario Kingston Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthew D.","family":"Webb","sequence":"additional","affiliation":[{"name":"Department of Economics Carleton University  Ontario Ottawa Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2016,2,21]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.ap08746"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1162\/rest.90.2.191"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.2307\/j.ctvcm4j72"},{"key":"e_1_2_11_5_1","first-page":"169","article-title":"Bias reduction in standard errors for linear regression with multi\u2010stage samples","volume":"28","author":"Bell RM","year":"2002","journal-title":"Survey Methodology"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1162\/003355304772839588"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2011.01.007"},{"key":"e_1_2_11_8_1","doi-asserted-by":"crossref","unstructured":"BrewerM CrossleyTF JoyceR.2013.Inference with difference\u2010in\u2010differences revisited.Technical Report Institute for Fiscal Studies.","DOI":"10.2139\/ssrn.2363229"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.3368\/jhr.50.2.317"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1162\/rest.90.3.414"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00639"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00049"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.08.003"},{"key":"e_1_2_11_14_1","volume-title":"Econometric Theory and Methods","author":"Davidson R","year":"2004"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1162\/rest.89.2.221"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.08046"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00552"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.2307\/1911134"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/73.1.13"},{"key":"e_1_2_11_20_1","unstructured":"MacKinnonJG WebbMD.2016.Randomization inference for difference\u2010in\u2010differences with few treated clusters.Technical Report Department of Economics Working Paper 1355 Queen's University."},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(85)90158-7"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.2307\/2109724"},{"key":"e_1_2_11_23_1","unstructured":"WebbMD.2014.Reworking wild bootstrap based inference for clustered errors. 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