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# Re: st: problem with generated regressands and WLS

 From Stas Kolenikov <[email protected]> To [email protected] Subject Re: st: problem with generated regressands and WLS Date Wed, 13 Oct 2010 15:34:47 -0500

```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 <[email protected]>:
> 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
>
> Arka
>
> 2010/10/12 Arka Roy Chaudhuri <[email protected]>:
>> 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
>>
>> Arka
>>
>> 2010/10/12 Austin Nichols <[email protected]>:
>>> Arka Roy Chaudhuri <[email protected]>:
>>> 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?
>>>
>
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>

--
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.

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```