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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 Tue, 12 Oct 2010 21:20:52 -0700

```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?
>
> 2010/10/12 Arka Roy Chaudhuri <gabuisi@gmail.com>:
>> Hi,
>>
>>   I have a two-stage estimation strategy. In the first stage I
>> estimate a no of parameters β1.....βN. I use these parameters as my
>> dependent variable/regessand in the second stage equation.Now since my
>> regressands are generated I need to use the first stage
>> variance-covariance matrix of my variables as weights in the second
>> stage.To elaborate here is my first stage:
>>
>>  y= α + β1x1+ β2x2 +................. +βnxn+ ρ1z1 +  ρ2z2 + u
>>
>> Now I want to use the β's from the first stage as my second stage
>> regressands. My second stage looks like:
>>
>>  β= γ+ δx + ε
>>
>> Here in the second stage as my β's are estimates from the first stage
>> I believe I should use the variance-covariance matrix of the β's as
>> the weighing matrix in the second stage.
>> Could somebody please tell me if I am doing this correctly and how to
>> implement it in Stata?Thanks
>>
>> Arka
>>
>> --
>> Arka Roy Chaudhuri
>> PhD Student
>> University of British Columbia
>>
>
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```