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Monte Carlo simulations show that the proposed test has more power relative to both a bootstrap approach based on the KLIC and an approach that involves multiple testing for differences of individual parts of the density. In addition, the test is computationally much faster than the KLIC\u2010based one, which relies on simulations, and allows for comparisons across multiple groups. Using density expectations from the ECB Survey of Professional Forecasters and the US\u00a0Survey of Consumer Expectations, we show the usefulness of the test in detecting possible changes in density expectations over time and across different types of forecasters.<\/jats:p>","DOI":"10.1002\/jae.3080","type":"journal-article","created":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T10:10:44Z","timestamp":1719223844000},"page":"1104-1122","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Testing for differences in survey\u2010based density expectations: A compositional data approach"],"prefix":"10.1002","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0890-8809","authenticated-orcid":false,"given":"Jonas","family":"Dovern","sequence":"first","affiliation":[{"name":"School of Business, Economics and Society Friedrich\u2010Alexander\u2010Universit\u00e4t Erlangen\u2010N\u00fcrnberg  Nuremberg Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2229-1112","authenticated-orcid":false,"given":"Alexander","family":"Glas","sequence":"additional","affiliation":[{"name":"Pensions and Sustainable Financial Markets, ZEW\u00a0\u2013\u00a0Leibniz Centre for European Economic Research  Mannheim Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4627-1928","authenticated-orcid":false,"given":"Geoff","family":"Kenny","sequence":"additional","affiliation":[{"name":"European Central Bank  Frankfurt am Main Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,6,24]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1982.tb01195.x"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-4109-0"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmoneco.2021.05.006"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/iere.12113"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jebo.2021.04.036"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/for.1023"},{"key":"e_1_2_8_8_1","unstructured":"Bassetti F. 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