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

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Wed, 13 Oct 2010 21:46:01 -0500 |

That's more or less the mainstream hierarchical linear model extensively used in education. You might want to check say Raudenbush & Bryk (2002) SAGE book. The methods described there do take into account the sampling variability for both individual and district-level estimates properly, and I already mentioned Stata commands that implement these methods. 2010/10/13 Arka Roy Chaudhuri <gabuisi@gmail.com>: > Thanks so much for the reply. I am not sure this is a hierarchical > model.Actually what I am trying to analyze is the effect of trade > reforms on the gender wage gap in a district over time.So my first > stage regression is at the level of the individual, y is log wages, > the z's are individual level factors like education,marital status and > the x's are interactions between the male dummy and district dummies.I > also have district dummies and a male dummy in the first stage. I take > the betas(the coefficients on the interactions between district > dummies and the male dummy) as estimates of the residual(i.e. the gap > after correcting for factors like education) gender wage gap within a > district. In the next step I regress this district level gender wage > gap(beta) on the district level tariffs(the variable q in the > equation) and estimate delta which is my main parameter of interest. I > could have done the whole analysis at the individual level but I would > like to get an estimate of the gender wage gap ie the betas.Thus my > question is since my dependent variable in the second stage is an > estimate and not taken directly from the data how should I correct for > this fact?Thanks > > Arka > > 2010/10/13 Stas Kolenikov <skolenik@gmail.com>: >> Is this a multilevel model with interactions between levels? If yes, >> you'd want to estimate it as such, probably in -gllamm- or -xtmixed-. >> If not, you can still run this is the reduced form with all the >> interactions spelled out as a regular regression, although you'd >> probably want to correct for heteroskedasticity and/or clustering. >> >> 2010/10/13 Arka Roy Chaudhuri <gabuisi@gmail.com>: >>> 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/ >>> >> >> >> >> -- >> Stas Kolenikov, also found at http://stas.kolenikov.name >> Small print: I use this email account for mailing lists only. >> >> * >> * 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/ >> > > * > * 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/ > -- Stas Kolenikov, also found at http://stas.kolenikov.name Small print: I use this email account for mailing lists only. * * 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:*Arka Roy Chaudhuri <gabuisi@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>

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

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

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

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