{"id":2345,"date":"2024-11-23T21:00:06","date_gmt":"2024-11-23T13:00:06","guid":{"rendered":"https:\/\/changjinyuan.com\/?p=2345"},"modified":"2025-07-07T13:15:06","modified_gmt":"2025-07-07T05:15:06","slug":"jinyuan-chang-shi-z-jia-zhang-2023-culling-the-herd-of-moments-with-penalized-empirical-likelihood-journal-of-business-economic-statistics-41-791-805","status":"publish","type":"post","link":"https:\/\/changjinyuan.com\/index.php\/en\/publications-en\/publications-all-en\/2345\/","title":{"rendered":"Chang, J., Shi, Z., &#038; Zhang, J. (2023). Culling the herd of moments with penalized empirical likelihood. Journal of Business &#038; Economic Statistics, 41, 791-805."},"content":{"rendered":"<p>Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in the meantime a few invalid ones may undermine consistency. This article investigates the empirical likelihood estimation of these moment-defined models in high-dimensional settings. We propose a penalized empirical likelihood (PEL) estimation and establish its oracle property with consistent detection of invalid moments. The PEL estimator is asymptotically normally distributed, and a projected PEL procedure further eliminates its asymptotic bias and provides more accurate normal approx- imation to the finite sample behavior. Simulation exercises demonstrate excellent numerical performance of these methods in estimation and inference.<\/p>\r\n\r\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" style=\"width: 100%; height: 600px;\" data=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2025\/07\/Culling-the-Herd-of-Moments-with-Penalized-Empirical-Likelihood.pdf\" width=\"300\" height=\"150\" aria-label=\"\u5d4c\u5165 &lt;strong&gt;&lt;mark style=&quot;background-color:rgba(0, 0, 0, 0)&quot; class=&quot;has-inline-color has-vivid-cyan-blue-color&quot;&gt;Culling the herd of moments with penalized empirical likelihood.pdf&lt;\/mark&gt;&lt;\/strong&gt;\"><\/object><a id=\"wp-block-file--media-c6a808ef-b708-420a-a523-a5be9487e6d4\" href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2025\/07\/Culling-the-Herd-of-Moments-with-Penalized-Empirical-Likelihood.pdf\"><strong><mark class=\"has-inline-color has-vivid-cyan-blue-color\" style=\"background-color: rgba(0, 0, 0, 0);\">Culling the herd of moments with penalized empirical likelihood.pdf<\/mark><\/strong><\/a><a class=\"wp-block-file__button wp-element-button\" href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2025\/07\/Culling-the-Herd-of-Moments-with-Penalized-Empirical-Likelihood.pdf\" download=\"\" aria-describedby=\"wp-block-file--media-c6a808ef-b708-420a-a523-a5be9487e6d4\">Download<\/a><\/div>","protected":false},"excerpt":{"rendered":"<p>Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in the meantime a few invalid ones may undermine consistency. This article investigates the empirical likelihood estimation of these moment-defined models in high-dimensional settings. We propose a penalized empirical likelihood (PEL) estimation and establish its oracle property with consistent detection of invalid moments. The PEL estimator is asymptotically normally distributed, and a projected PEL procedure further eliminates its asymptotic bias and provides more accurate normal approx- imation to the finite sample behavior. Simulation exercises demonstrate excellent numerical performance of these methods in estimation and inference.<\/p>\n","protected":false},"author":1,"featured_media":2342,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[21],"tags":[],"class_list":["post-2345","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-publications-all-en"],"acf":[],"lang":"en","translations":{"en":2345,"cn":2341},"pll_sync_post":[],"_links":{"self":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2345","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/comments?post=2345"}],"version-history":[{"count":7,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2345\/revisions"}],"predecessor-version":[{"id":5007,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2345\/revisions\/5007"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media\/2342"}],"wp:attachment":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media?parent=2345"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/categories?post=2345"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/tags?post=2345"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}