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The test is able to detect a wide class of deviations from the null hypothesis. The test statistic is based on the estimates from the restricted semiparametric model, can be computed in a regression\u2010based way, and is asymptotically standard normal under the null. I apply the test to Environmental Engel Curves and find that while the relationship between income and emissions may be quadratic, its shape changes with other variables in the model. Monte Carlo studies suggest that my test controls size well, has good power, and is fairly robust to the tuning parameter choice.<\/jats:p>","DOI":"10.1002\/jae.70039","type":"journal-article","created":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T09:35:37Z","timestamp":1768037737000},"page":"240-252","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Consistent Heteroskedasticity\u2010Robust LM\u2010Type Specification Test for Semiparametric Models"],"prefix":"10.1002","volume":"41","author":[{"given":"Ivan","family":"Korolev","sequence":"first","affiliation":[{"name":"Department of Economics Binghamton University  Binghamton New York USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,1,10]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(82)90105-1"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/2938323"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511811241"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466610000502"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1573-4412(07)06076-X"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA10771"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA13830"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.08.003"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600008239"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(03)00118-0"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-96-2822-3"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1257\/jel.20241696"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1986.10478274"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011210"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.2001.2058"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.780"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2017.11.008"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466622000445"},{"key":"e_1_2_11_20_1","unstructured":"Gupta A. 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