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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: The use of pweights with regress |

Date |
Mon, 8 Nov 2004 13:45:40 -0500 |

> This is another way to remember the difference bewteen aweights and > pweights. aweights can be used to remove, so to speak, > heteroskedasticity. pweights are supposed to help you reduce > sampling biases in the coefficient estimates, but their use may > actually introduce heteroskedasticity, and hence automatic use of the > robust covariance estimator is triggered. (I hope I got this right!) Sandwich covariance estimator is in fact a fundamental estimator: even you have b = (X'X)^{-1} X'Y, and you are not willing to assume much about the distribution of Y's conditional on X, then you are led to Var[b] = Var[ (X'X)^{-1} X'Y ] = (X'X)^{-1} X' Var[Y] X' (X'X)^{-1} which is the sandwich (or robust, which I think is a not very happy choice of the name) variance estimator. Another, and may be more appropriate, way to derive it is through the estimating equations approach (which economists would call "moment conditions"): the normal equations for b are X'e = 0, and the variance of the estimators obtained from estimating equations / moment conditions is (E[derivative of the estimating equations])^{-1} times E[outer product of estimating equations] times (E[derivative of the estimating equations])^{-1}, which again leads to the robust / White / you name it formula. Now, in computing those expectations, it is important to use the sampling weights (pweights). So I'd say it has nothing to do with heteroskedasticity, although it is one of the most common model misspecifications with which people tend to deal with this sandwich estimator, at least within econometrics (survey statisticicans would raise a brow if you'd say that the sandwich estimator is only good to deal with heteroskedasticity). Rather, this is a generic variance estimation problem, and a general approach to solve it. -- Stas Kolenikov http://stas.kolenikov.name * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: The use of pweights with regress***From:*rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp)

**Re: st: The use of pweights with regress***From:*"Mark Schaffer" <M.E.Schaffer@hw.ac.uk>

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