{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T12:51:50Z","timestamp":1787662310848,"version":"build-2736575974"},"reference-count":54,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T00:00:00Z","timestamp":1614038400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p>Researchers often trim observations with small values of the denominator <jats:italic>A<\/jats:italic> when they estimate moments of the form \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000025_inline1.png\"\/><jats:tex-math>\n$\\mathbb {E}[B\/A]$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Large trimming is common in practice to reduce variance, but it incurs a large bias. This paper provides a novel method of correcting the large trimming bias. If a researcher is willing to assume that the joint distribution between <jats:italic>A<\/jats:italic> and <jats:italic>B<\/jats:italic> is smooth, then the trimming bias may be estimated well. Along with the proposed bias correction method, we also develop an inference method. Practical advantages of the proposed method are demonstrated through simulation studies, where the data generating process entails a heavy-tailed distribution of \n<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466621000025_inline2.png\"\/><jats:tex-math>\n$B\/A$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Applying the proposed method to the Compustat database, we analyze the history of external financial dependence of U.S. manufacturing firms for years 2000\u20132010.<\/jats:p>","DOI":"10.1017\/s0266466621000025","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T07:29:25Z","timestamp":1614065365000},"page":"66-112","source":"Crossref","is-referenced-by-count":20,"title":["ESTIMATION AND INFERENCE FOR MOMENTS OF RATIOS WITH ROBUSTNESS AGAINST LARGE TRIMMING BIAS"],"prefix":"10.1017","volume":"38","author":[{"given":"Yuya","family":"Sasaki","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takuya","family":"Ura","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2021,2,23]]},"reference":[{"key":"S0266466621000025_r13","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA10771"},{"key":"S0266466621000025_r23","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2010.00315.x"},{"key":"S0266466621000025_r18","unstructured":"Dunbar, G. , Lewbel, A. , & Pendakur, K. 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