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From |
Arka Roy Chaudhuri <gabuisi@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: problem with generated regressands and WLS |

Date |
Wed, 13 Oct 2010 12:18:09 -0700 |

I shall repost my earlier mail(using full names for the Greek characters) as I just learnt that many might not be able to see the Greek characters.I am extremely sorry for my mistake and the inconvenience caused. I wrote: Thanks for the response. Sorry for not making my notation clearer- I had used x for the independent variables in both the first and second stage.Revising my notation: 1st stage: y = alpha + beta1x1+ beta2x2 +................. +betanxn+ rho1z1 + rho2z2 + u 2nd stage: beta= p + deltaq + error In the first stage y is the dependent variable and x1...xn, z1,z2 are the independent variables, beta1-betan and rho1-rho2 are the parameters.alpha and p are the intercepts in the first and second stage respectively. The beta's(beta1.....betan) from the first stage constitute my dependent variable in the second stage-since there are n of them I have n observations for my dependent variable in the second stage. q is the independent variable in the second stage and delta is the parameter to be estimated. I also have n observations of q. Yes I do want to improve efficiency although I am not sure how. Should I use the entire variance-covariance matrix of the beta's from the first stage as the weighing matrix in the second stage?Or should I just use the variance(from the first stage) of the betas as analytic weights in the second stage?If I use the second method should not non-zero covariances across the observations(beta's) affect my results?Also if I am to use the entire variance-covariance matrix as the weighing matrix how should I implement it in Stata?Please advice.Thanks Arka 2010/10/12 Arka Roy Chaudhuri <gabuisi@gmail.com>: > Thanks for the response. Sorry for not making my notation clearer- I > had used x for the independent variables in both the first and second > stage.Revising my notation: > 1st stage: > y = α + β1x1+ β2x2 +................. +βnxn+ ρ1z1 + ρ2z2 + u > > 2nd stage: > β= p + δq + ε > > In the first stage y is the dependent variable and x1...xn, z1,z2 are > the independent variables.α and p are the intercepts in the first and > second stage respectively. > The β's(β1, β2,......βn) from the first stage constitute my dependent > variable in the second stage-since there are n of them I have n > observations for my dependent variable in the second stage. q is the > independent variable in the second stage. I also have n observations > of them. > Yes I do want to improve efficiency although I am not sure how. > Should I use the entire variance-covariance matrix of the β's from the > first stage as the weighing matrix in the second stage?Or should I > just use the variance(from the first stage) of the betas as analytic > weights in the second stage?If I use the second method shouldn't > non-zero covariances across the observations(β's) affect my > results?Also if I am to use the entire variance-covariance matrix as > the weighing matrix how should I implement it in Stata?Please > advice.Thanks > > Arka > > 2010/10/12 Austin Nichols <austinnichols@gmail.com>: >> Arka Roy Chaudhuri <gabuisi@gmail.com>: >> If you think beta is measured with an independent error, i.e. no >> endogeneity or other endemic problems, you can ignore the fact that it >> is generated; measurement error in the depvar is usually not a >> problem. But perhaps you are looking for improved efficiency, and you >> want to use the squared SE on beta as a measure of the error >> variance--but it does not vary by observation--see the manual entry on >> -vwls- for example. Is your "second stage" in matrix form using the >> same y and x and so forth, or have you reused notation? >> * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: problem with generated regressands and WLS***From:*Stas Kolenikov <skolenik@gmail.com>

**References**:**st: problem with generated regressands and WLS***From:*Arka Roy Chaudhuri <gabuisi@gmail.com>

**Re: st: problem with generated regressands and WLS***From:*Austin Nichols <austinnichols@gmail.com>

**Re: st: problem with generated regressands and WLS***From:*Arka Roy Chaudhuri <gabuisi@gmail.com>

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