{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T03:58:26Z","timestamp":1788321506812,"version":"build-2803163510"},"reference-count":50,"publisher":"The Econometric Society","issue":"3","license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/legalcode"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>In this paper, we study the asymptotic behavior of specification tests in conditional moment restriction models under first\u2010order local identification failure with dependent data. More specifically, we obtain conditions under which the conventional specification test for conditional moment restrictions retains its standard normal limit when first\u2010order local identification fails but global identification is still attainable. In the process, we derive some novel intermediate results that include extending the first\u2010 and second\u2010order local identification framework to models defined by conditional moment restrictions, establishing the rate of convergence of the GMM estimator and characterizing the asymptotic representation for degenerate<jats:italic>U<\/jats:italic>\u2010statistics under strong mixing dependence. Importantly, the specification test is robust to first\u2010order local identification failure regardless of the number of directions in which the Jacobian of the conditional moment restrictions is degenerate and remains valid even if the model is first\u2010order identified.<\/jats:p>","DOI":"10.3982\/qe2242","type":"journal-article","created":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T08:09:13Z","timestamp":1721894953000},"page":"849-891","source":"Crossref","is-referenced-by-count":6,"title":["Specification testing for conditional moment restrictions under local identification failure"],"prefix":"10.3982","volume":"15","author":[{"given":"Prosper","family":"Dovonon","sequence":"first","affiliation":[{"name":"Department of Economics, Concordia University"},{"name":"CIREQ"},{"name":"CIRANO"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nikolay","family":"Gospodinov","sequence":"additional","affiliation":[{"name":"Research Department, Federal Reserve Bank of 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