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Testing for Regime Switching: A Comment

<!DOCTYPE html> <HTML lang="en"> <HEAD> <TITLE>Testing for Regime Switching: A Comment</TITLE> <meta charset="utf-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css" integrity="sha384-Gn5384xqQ1aoWXA+058RXPxPg6fy4IWvTNh0E263XmFcJlSAwiGgFAW/dAiS6JXm" crossorigin="anonymous"> <link rel="stylesheet" href="/css/font-awesome.min.css"> <!-- <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/fork-awesome@1.2.0/css/fork-awes ome.min.css" integrity="sha256-XoaMnoYC5TH6/+ihMEnospgm0J1PM/nioxbOUdnM8HY=" crossorigin="anonymous">--> <!-- <link rel="stylesheet" href="https://site-assets.fontawesome.com/releases/v6.2.0/css/all.css" />--> <link href="/css/normalnew.css" rel="stylesheet" type="text/css"/> <link href="/css/pushy.css" rel="stylesheet" type="text/css"/> <link rel="icon" type="image.jpg" href="/favicon.ico"> <!--[if lte IE 9]> <script src="/css/html5shiv.min.js"></script> <script src="/css/respond.min.js"></script> <![endif]--> <script type='text/javascript'> var captchaContainer = null; var loadCaptcha = function() { captchaContainer = grecaptcha.render('captcha_container', { 'sitekey' : '6LdQebIaAAAAACSKxvbloyrkQ_q-MqhOAGgD5PQV', 'callback' : function(response) { console.log(response); } }); }; </script> <META NAME="handle" CONTENT="RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1809-1812"><META NAME="DOI" CONTENT="ECTA9622"><META NAME="description" CONTENT="Downloadable (with restrictions)! In Cho and White (2007) &quot;Testing for Regime Switching&quot; the authors obtain the asymptotic null distribution of a quasi-likelihood ratio (QLR) statistic. The statistic is designed to test the null hypothesis of one regime against the alternative of Markov switching between two regimes. Likelihood ratio statistics are used because the test involves nuisance parameters that are not identified under the null hypothesis, together with other nonstandard features. Cho and White focus on a quasi-likelihood, which ignores certain serial correlation properties but allows for a tractable factorization of the likelihood. While the majority of their paper focuses on asymptotic behavior under the null hypothesis, Theorem 1(b) states that the quasi-maximum likelihood estimator (QMLE) is consistent under the alternative hypothesis. Consistency of the QMLE requires that the expected quasi-log-likelihood attain a global maximum at the population parameter values. This requirement holds for some Markov regime-switching processes but, as we show below, not for an autoregressive process as analyzed in Cho and White.<br><small>(This abstract was borrowed from another version of this item.)</small>"> <META NAME="keywords" CONTENT=""> <META NAME="jel_code" CONTENT=""> <META NAME="author" CONTENT="Andrew V. Carter & Douglas G. Steigerwald"> <META NAME="author_shortid" CONTENT="pst324"> <META NAME="title" CONTENT="Testing for Regime Switching: A Comment"> <META NAME="download" CONTENT="1"> <META NAME="freedownload" CONTENT="0"> <META NAME="date" CONTENT="2012-02-02"> <META NAME="citation_publication_date" CONTENT="2012"> <META NAME="citation_authors" content="Andrew V. Carter; Douglas G. 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Consistency of the QMLE requires that the expected quasi-log-likelihood attain a global maximum at the population parameter values. This requirement holds for some Markov regime-switching processes but, as we show below, not for an autoregressive process as analyzed in Cho and White.<br><small>(This abstract was borrowed from another version of this item.)</small>"> <META NAME="citation_publisher" content="Econometric Society"> <META NAME="citation_journal_title" content="Econometrica"> <META NAME="citation_keywords" content=""> <META NAME="citation_abstract_html_url" content="https://ideas.repec.org/a/ecm/emetrp/v80y2012i4p1809-1812.html"> <META NAME="citation_abstract_pdf_url" content="https://ideas.repec.org/a/ecm/emetrp/v80y2012i4p1809-1812.html"> <META NAME="redif-type" content="article"> <META NAME="citation_type" content="redif-article"> <META NAME="citation_year" content="2012"> <META NAME="citation_volume" content="80"> <META NAME="citation_issue" content="4"> <META NAME="citation_firstpage" content="1809"> <META NAME="citation_lastpage" content="1812"> <META NAME="twitter:card" content="summary_large_image"> <META NAME="twitter:site" content="@repec_org"> <META NAME="twitter:title" content="Testing for Regime Switching: A Comment, by Andrew V. 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The statistic is designed to test the null hypothesis of one regime against the alternative of Markov switching between two regimes. Likelihood ratio statistics are used because the test involves nuisance parameters that are not identified under the null hypothesis, together with other nonstandard features. Cho and White focus on a quasi-likelihood, which ignores certain serial correlation properties but allows for a tractable factorization of the likelihood. While the majority of their paper focuses on asymptotic behavior under the null hypothesis, Theorem 1(b) states that the quasi-maximum likelihood estimator (QMLE) is consistent under the alternative hypothesis. Consistency of the QMLE requires that the expected quasi-log-likelihood attain a global maximum at the population parameter values. 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id="cites-tab" data-toggle="tab" href="#cites" role="tab" aria-controls="cites" aria-selected="false">17 Citations</a> </li> <li class="nav-item"> <a class="nav-link" id="mrel-tab" data-toggle="tab" href="#mrel" role="tab" aria-controls="mrel" aria-selected="false">Most related</a> </li> <li class="nav-item"> <a class="nav-link" id="more-tab" data-toggle="tab" href="#more" role="tab" aria-controls="more" aria-selected="false">Related works & more</a> </li> <!-- Placeholder usernotes pill--> <li class="nav-item"> <a class="nav-link" id="correct-tab" data-toggle="tab" href="#correct" role="tab" aria-controls="correct" aria-selected="false">Corrections</a> </li> </ul> <div class="tab-content" id="myTabContent"> <div class="tab-pane fade show active" id="author-abstract" role="tabpanel" aria-labelledby="author-abstract-tab"> <h2>Author</h2> <div id="author-body"> <div id="authortable"> <div id="listed-authors">Listed: <ul id="authorlist"><li class="authorname">Andrew V. Carter</li> <li class="authorname">Douglas G. Steigerwald</li> </ul></div><div id="registered-authors"> <a href="https://authors.repec.org/">Registered:</a> <ul id="authorregistered"><li><a href="/f/pst324.html">Douglas Gardiner Steigerwald </A></li> </ul> </div> </div> </div> <h2 style="clear:left">Abstract</h2><div id="abstract-body">In Cho and White (2007) &quot;Testing for Regime Switching&quot; the authors obtain the asymptotic null distribution of a quasi-likelihood ratio (QLR) statistic. The statistic is designed to test the null hypothesis of one regime against the alternative of Markov switching between two regimes. Likelihood ratio statistics are used because the test involves nuisance parameters that are not identified under the null hypothesis, together with other nonstandard features. Cho and White focus on a quasi-likelihood, which ignores certain serial correlation properties but allows for a tractable factorization of the likelihood. While the majority of their paper focuses on asymptotic behavior under the null hypothesis, Theorem 1(b) states that the quasi-maximum likelihood estimator (QMLE) is consistent under the alternative hypothesis. Consistency of the QMLE requires that the expected quasi-log-likelihood attain a global maximum at the population parameter values. This requirement holds for some Markov regime-switching processes but, as we show below, not for an autoregressive process as analyzed in Cho and White.<br><small>(This abstract was borrowed from another version of this item.)</small></div> <h2>Suggested Citation</h2> <div id="biblio-body"> <LI class="list-group-item downgate"> Andrew V. Carter & Douglas G. Steigerwald, 2012. "<B><A HREF="/a/ecm/emetrp/v80y2012i4p1809-1812.html">Testing for Regime Switching: A Comment</A></B>," <A HREF="/s/ecm/emetrp.html">Econometrica</A>, Econometric Society, vol. 80(4), pages 1809-1812, July. </li> Handle: <i style="word-break:break-all">RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1809-1812</i> <br>DOI: ECTA9622 <form method="post" action="/cgi-bin/refs.cgi" enctype="multipart/form-data" target="refs" class="form-inline" role="form" style="margin-bottom: 10px;"> <input type="hidden" name="handle" value="RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1809-1812"> <div class="pull-left" style="padding-right: 2px;"> <input type="submit" class="btn btn-default fa" name="ref" value="Export reference &#xf08e;"> as </div> <div class="col-xs-8" style="padding-left: 0;"> <select name="output" size="1"> <option value="0">HTML</option> <option value="0.5">HTML with abstract</option> <option value="1">plain text</option> <option value="1.5">plain text with abstract</option> <option value="2">BibTeX</option> <option value="3">RIS (EndNote, RefMan, ProCite)</option> <option value="4">ReDIF</option> <option value="6">JSON</option> </select> </div> </form></div> </div> <div class="tab-pane fade" id="download" role="tabpanel" aria-labelledby="download-tab"> <h2>Download full text from publisher</h2><p></p> <FORM METHOD=GET ACTION="/cgi-bin/get_doc.pl" target="_blank"> <INPUT TYPE=HIDDEN NAME="urn" VALUE="RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1809-1812"><INPUT TYPE="radio" NAME="url" VALUE="http://hdl.handle.net/10.3982/ECTA9622" checked><B>File URL:</B> <span style="word-break:break-all">http://hdl.handle.net/10.3982/ECTA9622</span><BR><B>Download Restriction:</B> Access to full text is restricted to subscribers.<BR> <HR><INPUT TYPE="radio" NAME="url" VALUE="https://libkey.io/ECTA9622?utm_source=ideas"> <B>File URL:</B> <span style="word-break:break-all">https://libkey.io/ECTA9622?utm_source=ideas</span><BR> <B>LibKey link</B>: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item<BR> <font size="+2" color="red">---><INPUT TYPE="SUBMIT" class="btn fa" VALUE="Download the selected file &#xf08e;" style="color:white;background-color:#2d4e8b;"><---</font></FORM><P>As the access to this document is restricted, you may want to look for a different version below or <A HREF="/cgi-bin/htsearch2?q=%22Testing+for+Regime+Switching++A+Comment%22" rel="nofollow">search</A> for a different version of it. <h2>Other versions of this item:</h2> <div class="otherversion"><UL><LI class="list-group-item downfree"> Carter, Andrew V & Steigerwald, Douglas G, 2010. "<B><A HREF="https://ideas.repec.org/p/cdl/ucsbec/qt5079q9dc.html">Testing for Regime Switching: A Comment</A></B>," <A HREF="https://ideas.repec.org/s/cdl/ucsbec.html">University of California at Santa Barbara, Economics Working Paper Series</A> qt5079q9dc, Department of Economics, UC Santa Barbara. </UL></div> </div> <div class="tab-pane fade" id="refs" role="tabpanel" aria-labelledby="refs-tab"><h2>References listed on IDEAS</h2><form method="post" action="/cgi-bin/refs.cgi" enctype="multipart/form-data" target="refs" class="form-inline" role="form" style="margin-bottom: 10px;"> <input type="hidden" name="handle" value="repec:eee:econom:v:143:y:2008:i:2:p:263-273#repec:cla:uclawp:215#repec:cla:levarc:176#repec:eee:econom:v:23:y:1983:i:3:p:337-342#repec:oxp:obooks:9780198523543#repec:fip:fedlwp:2003-015#repec:oxp:obooks:9780199641178#repec:bro:econwp:2002-26"> <div class="pull-left" style="padding-right: 2px;"> <input type="submit" class="btn btn-default fa" name="ref" value="Export references &#xf08e;"> as </div> <div class="col-xs-8" style="padding-left: 0;"> <select name="output" size="1"> <option value="0">HTML</option> <option value="0.5">HTML with abstract</option> <option value="1">plain text</option> <option value="1.5">plain text with abstract</option> <option value="2">BibTeX</option> <option value="3">RIS (EndNote, RefMan, ProCite)</option> <option value="4">ReDIF</option> <option value="6">JSON</option> </select> </div> </form> <ol class="list-group"><LI class="list-group-item downgate"> Levine, David, 1983. "<B><A HREF="/a/eee/econom/v23y1983i3p337-342.html">A remark on serial correlation in maximum likelihood</A></B>," <A HREF="/s/eee/econom.html">Journal of Econometrics</A>, Elsevier, vol. 23(3), pages 337-342, December. <div class="otherversion"><UL> <LI class="list-group-item downfree"> David Levine, 1981. "<B><A HREF="/p/cla/uclawp/215.html">A Remark on Serial Correlation in Maximum Likelihood</A></B>," <A HREF="/s/cla/uclawp.html">UCLA Economics Working Papers</A> 215, UCLA Department of Economics. <LI class="list-group-item downfree"> David K. Levine, 1983. "<B><A HREF="/p/cla/levarc/176.html">A Remark on Serial Correlation in Maximum Likelihood</A></B>," <A HREF="/s/cla/levarc.html">Levine's Working Paper Archive</A> 176, David K. Levine. </UL></div> <LI class="list-group-item downnone"> Durbin, James & Koopman, Siem Jan, 2012. "<B><A HREF="/b/oxp/obooks/9780199641178.html">Time Series Analysis by State Space Methods</A></B>," <A HREF="/s/oxp/obooks.html">OUP Catalogue</A>, Oxford University Press, edition 2, number 9780199641178. <div class="publishedas"><UL> <LI class="list-group-item downnone"> Durbin, James & Koopman, Siem Jan, 2001. "<B><A HREF="/b/oxp/obooks/9780198523543.html">Time Series Analysis by State Space Methods</A></B>," <A HREF="/s/oxp/obooks.html">OUP Catalogue</A>, Oxford University Press, number 9780198523543. </UL></div> <div class="otherversion"><UL> <LI class="list-group-item downfree"> Tom Doan, "undated". "<B><A HREF="/c/boc/bocode/rts00251.html">SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM</A></B>," <A HREF="/s/boc/bocode.html">Statistical Software Components</A> RTS00251, Boston College Department of Economics. </UL></div> <LI class="downfree">Sean D. Campbell, 2002. 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"<B><A HREF="/p/fip/fedlwp/2003-015.html">Estimation of Markov regime-switching regression models with endogenous switching</A></B>," <A HREF="/s/fip/fedlwp.html">Working Papers</A> 2003-015, Federal Reserve Bank of St. Louis. </UL></div> </ol> <A TARGET="_blank" HREF="http://citec.repec.org/cgi-bin/get_data.pl?h=RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1809-1812&o=all"><B>Full references</B> <i class="fa fa-external-link"></i></A> (including those not matched with items on IDEAS)<P> </div> <div class="tab-pane fade" id="cites" role="tabpanel" aria-labelledby="cites-tab"> <H2>Citations</H2> Citations are extracted by the <A HREF="http://citec.repec.org/">CitEc Project</A>, subscribe to its <A HREF="http://citec.repec.org/cgi-bin/rss.pl?h=RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1809-1812">RSS feed</A> for this item. <form method="post" action="/cgi-bin/refs.cgi" enctype="multipart/form-data" target="refs" class="form-inline" role="form" style="margin-bottom: 10px;"> <input type="hidden" name="handle" value="repec:cdl:ucsbec:qt5rn986z6#repec:ipg:wpaper:2014-328#repec:arx:papers:1612.04932#repec:arx:papers:1801.06862#repec:igi:igierp:591#repec:cir:cirwor:2016s-63#repec:lvl:crrecr:1701#repec:nbr:nberwo:21863#repec:aoz:wpaper:234#repec:bca:bocawp:17-13#repec:spr:italej:v:1:y:2015:i:3:p:315-332#repec:bis:biswps:526#repec:bla:randje:v:47:y:2016:i:2:p:293-325#repec:bpj:jecome:v:2:y:2013:i:1:p:25-34:n:1#repec:mtl:montec:15-2016#repec:tsj:stataj:v:14:y:2014:i:3:p:481-498#repec:udt:wpecon:2021_07#repec:zbw:bubdps:432013#repec:udt:wpecon:2024_04#repec:cdl:ucsbrw:qt9245c5d1#repec:udt:wpecon:2023_01#repec:cdl:ucsbec:qt3685g3qr#repec:spr:empeco:v:54:y:2018:i:3:d:10.1007_s00181-017-1256-z#repec:wly:emetrp:v:90:y:2022:i:4:p:1681-1710#repec:cdl:ucsbrw:qt535178qf#repec:taf:emetrv:v:36:y:2017:i:6-9:p:713-727#repec:fip:fedbwp:12-14#repec:bos:wpaper:wp2015-004#repec:eea:boewps:wp2013-8#repec:taf:jnlbes:v:38:y:2020:i:2:p:285-302#repec:bde:wpaper:1748#repec:eee:macchp:v2-163"> <div class="pull-left" style="padding-right: 2px;"> <input type="submit" class="btn btn-default fa" name="ref" value="Export citations &#xf08e;"> as </div> <div class="col-xs-8" style="padding-left: 0;"> <select name="output" size="1"> <option value="0">HTML</option> <option value="0.5">HTML with abstract</option> <option value="1">plain text</option> <option value="1.5">plain text with abstract</option> <option value="2">BibTeX</option> <option value="3">RIS (EndNote, RefMan, ProCite)</option> <option value="4">ReDIF</option> <option value="6">JSON</option> </select> </div> </form><P> <BR><B>Cited by:</B><ol class="list-group"><LI class="list-group-item downgate"> Boris Blagov, 2018. 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"<B><A HREF="/a/tsj/stataj/v14y2014i3p481-498.html">Obtaining critical values for test of Markov regime switching</A></B>," <A HREF="/s/tsj/stataj.html">Stata Journal</A>, StataCorp LP, vol. 14(3), pages 481-498, September. <div class="otherversion"><UL> <LI class="list-group-item downfree"> Steigerwald, Douglas G & Bostwick, Valerie K, 2012. "<B><A HREF="/p/cdl/ucsbec/qt3685g3qr.html">Obtaining Critical Values for Test of Markov Regime Switching</A></B>," <A HREF="/s/cdl/ucsbec.html">University of California at Santa Barbara, Economics Working Paper Series</A> qt3685g3qr, Department of Economics, UC Santa Barbara. </UL></div> <LI class="list-group-item downgate"> Carter Andrew V. & Steigerwald Douglas G., 2013. 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"<B><A HREF="/a/gam/jecnmx/v4y2016i4p39-d80001.html">Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters</A></B>," <A HREF="/s/gam/jecnmx.html">Econometrics</A>, MDPI, vol. 4(4), pages 1-13, October. <LI class="list-group-item downfree"> Scott Brave & R. Andrew Butters & Alejandro Justiniano, 2016. "<B><A HREF="/p/fip/fedhwp/wp-2016-05.html">Forecasting Economic Activity with Mixed Frequency Bayesian VARs</A></B>," <A HREF="/s/fip/fedhwp.html">Working Paper Series</A> WP-2016-5, Federal Reserve Bank of Chicago. <LI class="list-group-item">repec:spo:wpmain:info:hdl:2441/1904 is not listed on IDEAS <LI class="list-group-item downgate"> H谩ri, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "<B><A HREF="/a/eee/insuma/v42y2008i2p492-504.html">Estimating the term structure of mortality</A></B>," <A HREF="/s/eee/insuma.html">Insurance: Mathematics and Economics</A>, Elsevier, vol. 42(2), pages 492-504, April. <LI class="list-group-item downgate"> Brave, Scott A. & Gascon, Charles & Kluender, William & Walstrum, Thomas, 2021. "<B><A HREF="/a/eee/intfor/v37y2021i3p1261-1275.html">Predicting benchmarked US state employment data in real time</A></B>," <A HREF="/s/eee/intfor.html">International Journal of Forecasting</A>, Elsevier, vol. 37(3), pages 1261-1275. <div class="otherversion"><UL> <LI class="list-group-item downfree"> Scott Brave & Charles S. Gascon & William Kluender & Thomas Walstrum, 2019. "<B><A HREF="/p/fip/fedhwp/87482.html">Predicting Benchmarked US State Employment Data in Realtime</A></B>," <A HREF="/s/fip/fedhwp.html">Working Paper Series</A> WP 2019-11, Federal Reserve Bank of Chicago. <LI class="list-group-item downfree"> Scott A. Brave & Charles S. Gascon & William Kluender & Thomas Walstrum, 2019. "<B><A HREF="/p/fip/fedlwp/86649.html">Predicting Benchmarked US State Employment Data in Real Time</A></B>," <A HREF="/s/fip/fedlwp.html">Working Papers</A> 2019-037, Federal Reserve Bank of St. Louis, revised 11 Mar 2021. </UL></div> <LI class="list-group-item downfree"> Alejandro Rodriguez & Esther Ruiz, 2009. "<B><A HREF="/a/bla/jtsera/v30y2009i2p167-178.html">Bootstrap prediction intervals in state鈥搒pace models</A></B>," <A HREF="/s/bla/jtsera.html">Journal of Time Series Analysis</A>, Wiley Blackwell, vol. 30(2), pages 167-178, March. <div class="otherversion"><UL> <LI class="list-group-item downfree"> Rodr铆guez, Alejandro, 2008. "<B><A HREF="/p/cte/wsrepe/ws081104.html">Bootstrap prediction intervals in State Space models</A></B>," <A HREF="/s/cte/wsrepe.html">DES - Working Papers. Statistics and Econometrics. WS</A> ws081104, Universidad Carlos III de Madrid. Departamento de Estad脙颅stica. </UL></div> <LI class="list-group-item downfree"> Parrini, Alessandro, 2013. "<B><A HREF="/p/pra/mprapa/103745.html">Importance Sampling for Portfolio Credit Risk in Factor Copula Models</A></B>," <A HREF="/s/pra/mprapa.html">MPRA Paper</A> 103745, University Library of Munich, Germany. <LI class="list-group-item downgate"> Marie Bessec, 2019. "<B><A HREF="/a/taf/emetrv/v38y2019i7p711-732.html">Revisiting the transitional dynamics of business cycle phases with mixed-frequency data</A></B>," <A HREF="/s/taf/emetrv.html">Econometric Reviews</A>, Taylor & Francis Journals, vol. 38(7), pages 711-732, August. <div class="otherversion"><UL> <LI class="list-group-item downfree"> Marie Bessec, 2016. "<B><A HREF="/p/hal/wpaper/hal-01358595.html">Revisiting the transitional dynamics of business-cycle phases with mixed frequency data</A></B>," <A HREF="/s/hal/wpaper.html">Working Papers</A> hal-01358595, HAL. <LI class="list-group-item downnone"> Marie Bessec, 2019. "<B><A HREF="/p/hal/journl/hal-02181552.html">Revisiting the transitional dynamics of business-cycle phases with mixed-frequency data</A></B>," <A HREF="/s/hal/journl.html">Post-Print</A> hal-02181552, HAL. </UL></div> </ol> </div> <div class="tab-pane fade" id="more" role="tabpanel" aria-labelledby="more-tab"> <H2> More about this item</H2><h3>Statistics</h3> <A HREF="http://logec.repec.org/scripts/paperstat.pl?h=RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1809-1812">Access and download statistics</A> </div> <!-- placeholder usernotes tab--> <div class="tab-pane fade" id="correct" role="tabpanel" aria-labelledby="correct-tab"> <h2>Corrections</H2> <P>All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: <I style="word-break:break-all;">RePEc:ecm:emetrp:v:80:y:2012:i:4:p:1809-1812</I>. 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