[gov2001] Coefficients on "r1" and "year"

Hi Nino, The question is to interpret the sign of the coefficients on Z, and you have parameterized sigma^2 as exp(gamma*Z). On the other hand, mu is still parameterized as beta*X. As Gary mentioned in class, there most definitely ARE instances when you would be interested in the effect of certain covariates on the variance term. This problem is trying to get you through an instance where that might be the case. I hope that helps -- Maya On Sun, Feb 28, 2010 at 4:49 PM, Malekovic, Nino <nino_malekovic at hks11.harvard.edu> wrote: > Thanks Maya, > > I made my way through the problem 3. The tiny question that I still have is about the last part. > In modelling the sigma square as exp(gamma*Z_it), there was only a tiny reparameterization in the formula for likelihood. > However, when you ask us to examine the sign (positive or negative) on the coefficients for Z ("r1" and "year"), > do you refer to effect coefficients for those covariates coming from estimation of mu? > The reason I ask is, I never modeled variance/sigma square in the past, > so I guess if that model of sigma square was more sophisticated we could estimate > the coefficients for Z as they relate to estimation of sigma square. Perhaps we could even do it here, > but since our goal is to estimate the maximum likelihood, such coefficients would not really be important for the final result. > I may have misunderstood the question, so could you please confirm that the coefficients for Z that you refer to in the last part of problem 3 > ?are effect coeffients for "r1" and "year" covariates coming from estimation of mu? > > Your help is appreciated. > > Nino > > ________________________________________ > From: gov2001-l-bounces at lists.fas.harvard.edu [gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of gov2001-l-request at lists.fas.harvard.edu [gov2001-l-request at lists.fas.harvard.edu] > Sent: Sunday, February 28, 2010 4:14 PM > To: gov2001-l at lists.fas.harvard.edu > Subject: gov2001-l Digest, Vol 55, Issue 47 > > Send gov2001-l mailing list submissions to > ? ? ? ?gov2001-l at lists.fas.harvard.edu > > To subscribe or unsubscribe via the World Wide Web, visit > ? ? ? ?http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l > or, via email, send a message with subject or body 'help' to > ? ? ? ?gov2001-l-request at lists.fas.harvard.edu > > You can reach the person managing the list at > ? ? ? ?gov2001-l-owner at lists.fas.harvard.edu > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of gov2001-l digest..." > > > Today's Topics: > > ? 1. Re: gamma and Z_it (Maya Sen) > ? 2. Re: loading the data (Abigail Coplin) > ? 3. Re: loading the data (Maya Sen) > ? 4. Sigma? (Meryl Federman) > ? 5. Hessian Problems (Abigail Coplin) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sun, 28 Feb 2010 12:44:37 -0500 > From: Maya Sen <msen at fas.harvard.edu> > Subject: Re: [gov2001] gamma and Z_it > To: "Class List for Gov 2001/E-2001" <gov2001-l at lists.fas.harvard.edu> > Message-ID: > ? ? ? ?<16e0be401002280944u4a24a0e9o7f2eb7dad5db3c84 at mail.gmail.com> > Content-Type: text/plain; charset=UTF-8 > > Hey all, > > So Anil is right in that the bearded man wants you to test whether > sigma^2 should be modeled as functions of "r1" and "year". As for your > parameterization of mu, the problem says to use the parameterization > you used in problem one. So you should actually feel free to include > the entirety of the covariates (which is what you did in problem one). > > hope that helps -- > Maya > > Thanks Maya, > > I made my way through the problem 3. The tiny question that I still have is about the last part. > In modelling the sigma square as exp(gamma*Z_it), there was only a tiny reparameterization in the formula for likelihood. > However, when you ask us to examine the sign (positive or negative) on the coefficients for Z ("r1" and "year"), > do you refer to effect coefficients for those covariates coming from estimation of mu? > The reason I ask is, I never modeled variance/sigma square in the past, > so I guess if that model of sigma square was more sophisticated we could estimate > the coefficients for Z as they relate to estimation of sigma square. Perhaps we could even do it here, > but since our goal is to estimate the maximum likelihood, such coefficients would not really be important for the final result. > I may have misunderstood the question, so could you please confirm that the coefficients for Z that you refer to in the last part of problem 3 > ?are effect coeffients for "r1" and "year" covariates coming from estimation of mu? > > Your help is appreciated. > > Nino > > > > On Sun, Feb 28, 2010 at 11:38 AM, Doshi, Anil <adoshi at hbs.edu> wrote: >> Nino, >> I believe the "explanatory variables suggested" by the bearded man are in the intro paragraph of problem 3. Specifically, the year (year) and the South dummy (r1) are the explanatory variables for sigma_2. >> >> Whether you use dummies r1...r6 to explain the beta parameter will probably depend on your results from Problem Two. Did you think the bearded man was right? If you did, then it probably makes sense to continue with the model from Problem 2. If you disagreed (i.e. you did not reject the null hypothesis that the regional dummy variables were different than zero), then you will probably want to stick with the model from Problem 1 to estimate beta. >> >> I hope this helps. >> Anil >> >> >> Anil Doshi >> Doctoral Student | Technology and Operations Management >> Harvard Business School >> 302 Wyss Hall >> Boston, MA 02163 >> tel 646-244-5396 >> email adoshi at hbs.edu >> >> On Feb 28, 2010, at 4:00 AM, Malekovic, Nino wrote: >> >> Hi all, >> >> In the problem 3, "Z_it is a vector of the explanatory variables suggested by the bearded man". Are those the variables he suggested to leave out of the model, r1, r2, r3, r4, r5 and r6? The only sensible interpretation that I have is that we do not use these six explanatory variables for estimating ?_it. However, we use them for estimating ?_it^2 =e^(Z_it*?). Furthermore, the remaining explanatory variables (matrix X without r1, r2, r3, r4, r5, and r6) are to be used for estimating betas, as in the problem 2. >> >> I would not like to misinterpret the instruction, and will appreciate if someone confirmed that, or at least clarified it a bit. >> >> Best regards, >> Nino Malekovic >> MPA Candidate, Class 2011 >> Harvard Kennedy School >> ________________________________________ >> From: gov2001-l-bounces at lists.fas.harvard.edu [gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of gov2001-l-request at lists.fas.harvard.edu [gov2001-l-request at lists.fas.harvard.edu] >> Sent: Saturday, February 27, 2010 12:00 PM >> To: gov2001-l at lists.fas.harvard.edu >> Subject: gov2001-l Digest, Vol 55, Issue 45 >> >> Send gov2001-l mailing list submissions to >> ? ? ? gov2001-l at lists.fas.harvard.edu >> >> To subscribe or unsubscribe via the World Wide Web, visit >> ? ? ? http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l >> or, via email, send a message with subject or body 'help' to >> ? ? ? gov2001-l-request at lists.fas.harvard.edu >> >> You can reach the person managing the list at >> ? ? ? gov2001-l-owner at lists.fas.harvard.edu >> >> When replying, please edit your Subject line so it is more specific >> than "Re: Contents of gov2001-l digest..." >> >> >> Today's Topics: >> >> ?1. pset4 posted, due thurs (Maya Sen) >> ?2. error message (Chiara Superti) >> ?3. Re: error message (Iain Osgood) >> ?4. panel data in R (Chiara Superti) >> ?5. Re: panel data in R (Maya Sen) >> >> >> ---------------------------------------------------------------------- >> >> Message: 1 >> Date: Sat, 27 Feb 2010 09:29:06 -0500 >> From: Maya Sen <msen at fas.harvard.edu> >> Subject: [gov2001] pset4 posted, due thurs >> To: "Class List for Gov 2001/E-2001" <gov2001-l at lists.fas.harvard.edu> >> Message-ID: >> ? ? ? <16e0be401002270629o6fac0026y4cd3e47eba642041 at mail.gmail.com> >> Content-Type: text/plain; charset=ISO-8859-1 >> >> Hi all, >> >> Just a reminder -- pset 4 has been posted, and it's due Thursday >> before 6pm. If you are writing the replication paper, also "due" >> Thursday is an email from your group of co-authors with your intended >> paper and a few lines about why it's a good choice. >> >> Maya >> >> >> ------------------------------ >> >> Message: 2 >> Date: Sat, 27 Feb 2010 10:00:35 -0500 >> From: Chiara Superti <csuperti at fas.harvard.edu> >> Subject: [gov2001] error message >> To: Class List for Gov 2001/E-2001 <gov2001-l at lists.fas.harvard.edu> >> Message-ID: <D42F22A7-C271-4F24-ACB5-A2F4525F5539 at fas.harvard.edu> >> Content-Type: text/plain; charset=us-ascii >> >> Hi everyone, >> I am trying to use the optim function in ps4 and I am always getting the following error: >> Error in optim(par = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ?: >> (list) object cannot be coerced to type 'double' >> >> Could anyway tell me what I am doing wrong??? >> Thanks >> Chiara >> >> ------------------------------ >> >> Message: 3 >> Date: Sat, 27 Feb 2010 10:13:23 -0500 >> From: Iain Osgood <osgood2 at fas.harvard.edu> >> Subject: Re: [gov2001] error message >> To: "Class List for Gov 2001/E-2001" <gov2001-l at lists.fas.harvard.edu> >> Message-ID: >> ? ? ? <e7322f8f1002270713v40c2f442j262ca82799972319 at mail.gmail.com> >> Content-Type: text/plain; charset="iso-8859-1" >> >> Hi Chiara, >> Its hard to tell without the complete code, but frequently this error >> message involves attempts to convert a dataframe (which is of mode 'list' >> and class 'dataframe') into a matrix incorrectly. ?Perhaps in your function >> code do you have a line like as.numeric(data) when it should be >> as.matrix(data)? >> Iain >> >> On Sat, Feb 27, 2010 at 10:00 AM, Chiara Superti >> <csuperti at fas.harvard.edu>wrote: >> >>> Hi everyone, >>> I am trying to use the optim function in ps4 and I am always getting the >>> following error: >>> Error in optim(par = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ?: >>> (list) object cannot be coerced to type 'double' >>> >>> Could anyway tell me what I am doing wrong??? >>> Thanks >>> Chiara >>> _______________________________________________ >>> gov2001-l mailing list >>> gov2001-l at lists.fas.harvard.edu >>> http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l >>> >>> >>