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# Re: st: problem with generated regressands and WLS

 From Arka Roy Chaudhuri To statalist@hsphsun2.harvard.edu Subject Re: st: problem with generated regressands and WLS Date Wed, 13 Oct 2010 16:14:56 -0700

```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
>>
>> 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
>>>
>>> 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?
>>>>
>>
>> *
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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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>

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```