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From |
DE SOUZA Eric <eric.de_souza@coleurope.eu> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: Multicollinearity Problem in Stata |

Date |
Wed, 31 Jul 2013 10:53:54 +0200 |

If you subtract 8.080053 from 1.929168 (regression without a constant) you get -6.150886 (coefficient of r_ow in the regression with a constant. Eric de Souza College of Europe Brugge (Bruges), Belgium http://www.coleurope.eu -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of FU Youyan Sent: 30 July 2013 16:41 To: statalist@hsphsun2.harvard.edu Subject: RE: st: Multicollinearity Problem in Stata I have double checked my data. I am sure that r_ew+r_ow equals a constant (0.2407656). The coefficients of lnnc and n1_ln in these two regressions are same indeed, but the coefficients of r_ow dose change. We can also see that the t-value and p-value of the constant in the first regression are exactly same as the t-value and p-value of r_ew in the second regression, which is consistent with your explanation about the omitted variable. Therefore, I am still confused about the coefficient change of r_ow and wonder which result is more reliable. ________________________________________ From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Yuval Arbel [yuval.arbel@gmail.com] Sent: 30 July 2013 14:04 To: statalist Subject: Re: st: Multicollinearity Problem in Stata See the example below on wage and gender. The fact that these variables are continous rather than dummies are irrelevant here. If indeed r_ew+r_ow equals a constant - the coefficients should be the same in both regressions On Mon, Jul 29, 2013 at 1:14 PM, FU Youyan <s1150901@sms.ed.ac.uk> wrote: > Dear Yuval, > > Thank you very much for this answer, it is quite helpful. I have a followed up question: > The r_ew and r_ow are two types of investment return in my research ( they are continuous variable rather than dummy), what I want to test is the impact of these two returns on investors' future behavior. In other words, I want to know how investors weight these two types of return. Therefore, I have to include both of the returns into my regression. In the regression with constant but omitting r_ew, the coefficient of r_ow is significantly negative (t-value=-3.30). However, in the regression without constant but including r_ew, the coefficient of r_ow is significantly positive (t-value=2.20). So, I would like to know which result is more reliable? > > Best wishes, > Youyan > ________________________________________ > From: owner-statalist@hsphsun2.harvard.edu > [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Yuval Arbel > [yuval.arbel@gmail.com] > Sent: 29 July 2013 17:58 > To: statalist > Subject: Re: st: Multicollinearity Problem in Stata > > Dear FU, > > This outcome is not strange at all. I believe what you encountered is > known in econometrics as "the dummy variable trap": > > I believe that r_ew+r_ow=constant. Consequently - when you run the > model with a constant - you get a perfect colinearity with the > constant term. But when you omit the constant - the problem is solved. > > In fact you can make use of these two specifications. Consider the > following exercise. Lets say that w is the wage male=0 for female and > 1 for male, and female=1 for female and 0 for male. if the average > wage is 1200 for male and 1000 for female - and you run the model > without the constant, you will get: > > w(hat)=1200*male+1000*female > > But if you omit male and use constant (in order to avoid the dummy > variable trap), you get > > w(hat)=1200-200*female > > The second specification is more common because it permits you to test > whether wage differences across gender are significant > > On Mon, Jul 29, 2013 at 9:10 AM, FU Youyan <s1150901@sms.ed.ac.uk> wrote: >> Dear Statalist users, >> >> I am encountering a strange multicollinearity problem when I conduct regression using Stata. The problem is illustrated below. I will VERY appreciate if any of you can answer my question. >> >> >> ********************************************************************* >> ******************************** >> note: r_ew omitted because of collinearity >> >> Linear regression Number of obs = 159 >> F( 3, 155) = 73.74 >> Prob > F = 0.0000 >> R-squared = 0.4900 >> Root MSE = .88944 >> >> ------------------------------------------------------------------------------ >> | Robust >> n2_ln | Coef. Std. Err. t P>|t| [95% Conf. Interval] >> -------------+------------------------------------------------------- >> -------------+--------- >> r_ow | -6.150886 1.861984 -3.30 0.001 -9.829026 -2.472746 >> r_ew | 0 (omitted) >> lnnc | .1853104 .0502188 3.69 0.000 .0861089 .2845119 >> n1_ln | .2328174 .0912362 2.55 0.012 .0525905 .4130443 >> _cons | 1.945399 .5489629 3.54 0.001 .8609843 3.029813 >> --------------------------------------------------------------------- >> --------- >> >> In the above regression table, r_ew is omitted due to the perfectly negative collinearity between r_ow and r_ew. >> >> (Correlation table is showed below). The relationship between these two variables is r_ow+r_ew=0.2407656,so there exists perfect collinearity. >> >> >> | n2_ln r_ow r_ew lnnc n1_ln >> -------------+--------------------------------------------- >> n2_ln | 1.0000 >> r_ow | -0.6565 1.0000 >> r_ew | 0.6565 -1.0000 1.0000 >> lnnc | 0.4587 -0.4285 0.4285 1.0000 >> n1_ln | 0.6419 -0.8468 0.8468 0.4103 1.0000 >> >> However, the variable of r_ew is not omitted when I run the exactly same regression but without intercept. >> >> >> Linear regression Number of obs = 159 >> F( 4, 155) = 441.13 >> Prob > F = 0.0000 >> R-squared = 0.8909 >> Root MSE = .88944 >> >> ------------------------------------------------------------------------------ >> | Robust >> n2_ln | Coef. Std. Err. t P>|t| [95% Conf. Interval] >> -------------+------------------------------------------------------- >> -------------+--------- >> r_ow | 1.929168 .8763971 2.20 0.029 .1979442 3.660391 >> r_ew | 8.080053 2.280073 3.54 0.001 3.576027 12.58408 >> lnnc | .1853104 .0502188 3.69 0.000 .0861089 .2845119 >> n1_ln | .2328174 .0912363 2.55 0.012 .0525905 .4130443 >> --------------------------------------------------------------------- >> --------- >> >> My question is why Stata does not omit r_ew when intercept term is excluded? And whether the regression result without intercept is valid? >> >> >> Thanks for your help. >> Youyan >> >> -- >> The University of Edinburgh is a charitable body, registered in >> Scotland, with registration number SC005336. >> >> >> * >> * For searches and help try: >> * http://www.stata.com/help.cgi?search >> * http://www.stata.com/support/faqs/resources/statalist-faq/ >> * http://www.ats.ucla.edu/stat/stata/ > > > > -- > Dr. Yuval Arbel > School of Business > Carmel Academic Center > 4 Shaar Palmer Street, > Haifa 33031, Israel > e-mail1: yuval.arbel@carmel.ac.il > e-mail2: yuval.arbel@gmail.com > You can access my latest paper on SSRN at: > http://ssrn.com/abstract=2263398 You can access previous papers on > SSRN at: http://ssrn.com/author=1313670 > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ > -- > The University of Edinburgh is a charitable body, registered in > Scotland, with registration number SC005336. > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ -- Dr. Yuval Arbel School of Business Carmel Academic Center 4 Shaar Palmer Street, Haifa 33031, Israel e-mail1: yuval.arbel@carmel.ac.il e-mail2: yuval.arbel@gmail.com You can access my latest paper on SSRN at: http://ssrn.com/abstract=2263398 You can access previous papers on SSRN at: http://ssrn.com/author=1313670 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/ -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Multicollinearity Problem in Stata***From:*FU Youyan <s1150901@sms.ed.ac.uk>

**Re: st: Multicollinearity Problem in Stata***From:*Yuval Arbel <yuval.arbel@gmail.com>

**RE: st: Multicollinearity Problem in Stata***From:*FU Youyan <s1150901@sms.ed.ac.uk>

**Re: st: Multicollinearity Problem in Stata***From:*Yuval Arbel <yuval.arbel@gmail.com>

**RE: st: Multicollinearity Problem in Stata***From:*FU Youyan <s1150901@sms.ed.ac.uk>

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