<html><head><style type='text/css'>p { margin: 0; }</style></head><body><div style='font-family: Times New Roman; font-size: 12pt; color: #000000'><P>Dear colleagues,<BR></P>
<P><BR>The Department of Decision Sciences (DEC) of Bocconi University is pleased to invite you to the seminar:</P>
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<DIV style="FONT-SIZE: 10pt; COLOR: #000000; FONT-FAMILY: Arial"><SPAN style="FONT-STYLE: italic">DEC Seminar</SPAN><SPAN style="FONT-STYLE: italic"><BR>Università Bocconi, </SPAN><BR style="FONT-STYLE: italic"><SPAN style="FONT-STYLE: italic">Room 3-E4-SR03</SPAN><BR style="FONT-STYLE: italic"><SPAN style="FONT-STYLE: italic">Via Rontgen 1 - 3rd floor<BR></SPAN><SPAN style="FONT-STYLE: italic">Time: 12:30pm<BR></SPAN><SPAN style="FONT-STYLE: italic"><BR></SPAN><BR>The DEC seminar schedule is available at <SPAN class=Object id=OBJ_PREFIX_DWT2388><SPAN class=Object id=OBJ_PREFIX_DWT1495><SPAN class=Object id=OBJ_PREFIX_DWT6887><SPAN class=Object id=OBJ_PREFIX_DWT1407><A href="http://www.unibocconi.eu/statseminar" target=_blank>http://www.unibocconi.eu/statseminar</A></SPAN></SPAN></SPAN></SPAN> <BR><BR><SPAN style="FONT-WEIGHT: bold; TEXT-DECORATION: underline">Thursday, November 18th<BR><BR></SPAN>Eric Gautier<BR>(CREST – ENSAE)<BR><BR><SPAN style="FONT-WEIGHT: bold">"The IV selector: estimation and selection of the variables when the number of variables and instruments can be much larger than the sample size"</SPAN><BR><BR>We introduce and analyse a new instrumental variables estimation procedure<BR>for linear models containing endogenous regressors. It can handle<BR>a small sample size n and a large number of regressors, and even larger<BR>number of instruments L. Distributional assumptions on the error term<BR>or the distribution of the instruments and regressors are very mild. Under<BR>proper assumptions on the action of a matrix, relating the variables of the<BR>structural model and the instruments, on sparse vectors, and the assumption<BR>that the vector of coefficients in the structural model is sparse (or<BR>approximately sparse), it is possible to estimate the vector of coefficients<BR>even in cases where L is much larger than n. The procedure is a variation<BR>on the Dantzig selector of Candµes and Tao (2007). We obtain nonasymptotic<BR>upper bounds on the estimation of the vector of coefficients in<BR>lp-norms that hold with probability close to 1. The price that is paid<BR>in the upper bound, for not knowing which coordinates are non zero, is a<BR>power of log(L). Under proper assumptions, a thresholded<BR>version of the IV-selector is able to simultaneously select the right nonzero<BR>coefficients with a probability close to 1. The estimation reduces to simple<BR>linear programming. The method is completely robust to weak instruments and<BR>there is no real issue in selecting instruments with the IV -selector.<BR>Taking all possible exogenous instruments (up to an exponential in the sample size!)<BR>Still leads to tight bounds around the true vector of parameters. Adding an<BR>instrument which is irrelevant incurs a loss of log(L)-log(L-1) in the<BR>constant multiplying the parametric rate. This is totally negligible compared<BR>to the potential gain in adding an instrument with some power. It is also robust to heteroscedastic errors.<BR><BR>==============================================================================
<DIV style="FONT-SIZE: 10pt; COLOR: #000000; FONT-FAMILY: Arial"> </DIV>
<DIV style="FONT-SIZE: 10pt; COLOR: #000000; FONT-FAMILY: Arial">Sincerely,</DIV>
<DIV style="FONT-SIZE: 10pt; COLOR: #000000; FONT-FAMILY: Arial">Anna Simoni</DIV>
<P><BR><BR>---------------------------<BR>Anna Simoni </P>
<DIV style="FONT-SIZE: 10pt; COLOR: #000000; FONT-FAMILY: Arial">Assistant Professor<BR>Department of Decision Sciences<BR>Università Bocconi<BR>via Roentgen, 1<BR>20136 Milano - Italy</DIV>
<DIV style="FONT-SIZE: 10pt; COLOR: #000000; FONT-FAMILY: Arial">Email:<FONT color=#00008b><SPAN class=Object id=OBJ_PREFIX_DWT121><SPAN class=Object id=OBJ_PREFIX_DWT178><SPAN class=Object id=OBJ_PREFIX_DWT340><SPAN class=Object id=OBJ_PREFIX_DWT1700>anna.simoni@unibocconi.it</SPAN></SPAN></SPAN></SPAN><BR></FONT>Webpage: <SPAN class=Object id=OBJ_PREFIX_DWT122><SPAN class=Object id=OBJ_PREFIX_DWT179><SPAN class=Object id=OBJ_PREFIX_DWT341><SPAN class=Object id=OBJ_PREFIX_DWT1701><A href="http://faculty.unibocconi.eu/annasimoni/" target=_blank><FONT color=#00008b>http://faculty.unibocconi.eu/annasimoni/</FONT></A></SPAN></SPAN></SPAN></SPAN></DIV><BR></DIV></div></body></html>