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# Re: st: Symmetry Test

 From Ana To statalist@hsphsun2.harvard.edu Subject Re: st: Symmetry Test Date Thu, 12 May 2011 12:18:39 -0300

```Dear Alex (and Statalisters),

I will try to make myself clear know.

My plan is to estimate a Seven Demand Equations using Quiads Model
(based on nlsurquaids.ado routine by Brian Poi (2008))
My main goal is to test one hypothesis based on Browning & Chiappori
model (reference: Efficient Intra-Household Allocations: A general
Characterization and Empirical Tests, Econometrica, vol.66, no.6
(Nov.,1998), pp 1241-1278).

Based on the nslurquaids.ado routine (Brian Poi (2008)), without the
symmetry restriction and based on the originally demand for four goods
(and three share equations) generated by the author, I am trying to
implement this Browning and Chiappori test. If I am well suceeded, I
will extend this routine to "my" model (with more goods...).

Based on the following routine of the nlsurquaids.ado,

nlsur quaids @ w1 w2 w3 lnp1-lnp4 lnm, ifgnls nequations(3) param(a1
a2 a3 b1 b2 b3 g11 g12 g13 g21 g22 g23 g31 g32 g33 l1 l2 l3) nolog

the test I would like to carry out is something like:

(g31 - g13) = (g12 - g21)*(g23 - g32) & (g21 - g12) = (g31 - g13)*(g23 - g32)

The problem is that when I execute the command:

testnl (([eq1]_b[/g31] - [eq1]_b[/g13]) = ...*[eq2]_b[/g23] -
[eq3]_b[/g32])) (([eq2]_b[/g21] - [eq1]_b[/g12]) = ...*[eq2]_b[/g23] -
[eq3]_b[/g32]))

My guess is that I'm making a syntax error or that I am "forgetting"
to include a program or a command to name equations, parameters inside
the nlsurquaids.ado. Anyway, I'd appreciate if you can help me.

Thank you very much in advance.
Very best regards,
Ana.

2011/5/11 Alex Olssen <alex.olssen@gmail.com>:
> Dear Ana,
>
> I don't really understand what you are asking.
>
> "Based on your routine below, how could I distinguish the parameters fo
> interst for the symmetry test (g12 g21 g31 g13...) from the other
> parameters of the model?"
>
> What do you mean by "distinguish"?
>
> "Still, sometimes (for other exercises I'm planning to do), I'd like to
> keep only some parameters from the model and make some test."
>
> some parameters?
> You should be able to do this by removing the parameters you want to
> exclude from the
>
> scalar `name' = `at'[1,x]
>
> list, and delete the parameter and its associated variable from the
>
> replace w`i' = ...
>
> list.
>
> How can I "view "and "use" the some parameters from the model?
> In the case of ther symmetry test (if I only use the unrestricted
> model), I tried to use something like [eq_1]g12 = [eq_2]g2, but stata
> (actually, me!) always complain with something about: "equation [1]
>
> I don't understand what you are asking?  Do you want to test the
> single symmetry constraint g12 = g21 on its own?  That doesn't seem
> very sensible.
>
> If you want to test whether symmetry holds overall this should be
> simple.  In your second email you presented estimates from the
> constrained model, I presume you have the estimates for the
> unconstrained model - all you need to do to see if symmetry can be
> rejected for your data and model is to look at the likelihood ratio
> statistics.
>
> Kind regards,
>
> Alex
>
>
>
> On 12 May 2011 05:22, Ana <analunhb@gmail.com> wrote:
>> Dear Alex,
>> Thank you very much for your prompt response and for your help.
>> I'm still with a silly question about the symmetry test.
>> Based on your routine below, how could I distinguish the parameters fo
>> interst for the symmetry test (g12 g21 g31 g13...) from the other
>> parameters of the model?
>>
>> Still, sometimes (for other exercises I'm planning to do), I'd like to
>> keep only some parameters from the model and make some test.
>> How can I "view "and "use" the some parameters from the model?
>> In the case of ther symmetry test (if I only use the unrestricted
>> model), I tried to use something like [eq_1]g12 = [eq_2]g2, but stata
>> (actually, me!) always complain with something about: "equation [1]
>> Here is the estimates/results I can get from using nlsur quaids based
>> on my data:
>>
>> FGNLS regression
>>
>> Equation        Obs  Parms       RMSE   R-sq     Constant
>>
>> 1           w1      26784      .   .4765981     0.7898*      (none)
>> 2           w2      26784      .   .5114466     0.3840*      (none)
>> 3           w3      26784      .   .4442428     0.3384*      (none)
>>
>> * Uncentered R-sq
>>
>>
>> Coef.   Std. Err.      z        P>z     [95% Conf. Interval]
>>
>> /a1    1.461867   .0214499    68.15     0.000     1.419826    1.503908
>> /a2     .316065   .0206387    15.31     0.000     .2756139    .3565162
>> /a3     .292436   .0186566    15.67     0.000     .2558698    .3290022
>> /b1   -.6577555   .0084112   -78.20     0.000    -.6742412   -.6412698
>> /b2   -.0759965    .007929    -9.58     0.000     -.091537    -.060456
>> /b3   -.1354168   .0072402   -18.70     0.000    -.1496074   -.1212263
>> /g11   -1.520055    .045084   -33.72    0.000    -1.608418   -1.431692
>> /g12   -.0109163   .0207699    -0.53    0.599    -.0516245     .029792
>> /g13    -.399293   .0196141   -20.36    0.000    -.4377359   -.3608502
>> /g22   -.0250661   .0151875    -1.65    0.099     -.054833    .0047007
>> /g23   -.0521908     .01053    -4.96    0.000    -.0728293   -.0315523
>> /g33   -.0643672   .0144734    -4.45    0.000    -.0927346   -.0359998
>> /l1    .0855152   .0007695   111.13     0.000      .084007    .0870233
>> /l2    .0143847   .0007215    19.94     0.000     .0129705    .0157989
>> /l3     .021068   .0006599    31.93     0.000     .0197747    .0223613
>>
>>
>> .
>> end of do-file
>>
>>
>> Thanks a lot in advance.Again.
>> Best regards,
>> Ana.
>>
>> 2011/5/10 Alex Olssen <alex.olssen@gmail.com>:
>>> Dear Ana,
>>>
>>> I presume you removed the symmetry restriction by adjusting the
>>> variables `gij' = `gji' in the nlsurquaids.ado file.
>>>
>>> To test the symmetry restrictions you could,
>>>
>>> 1) rename the program without symmetry as nlsurquaids2.ado
>>>
>>> 2) run the program without symmetry and obtain the log likelihood
>>>
>>> scalar llnosymmetry = e(ll)
>>>
>>> 3) run the program with symmetry (the original nlsurquaids) and obtain
>>> the log likelihood
>>>
>>> scalar llsymmetry = e(ll)
>>>
>>> 4) implement the likelihood ratio test
>>>
>>> the statistic is given by 2*(llnosymmetry - llsymmetry)
>>> which follows a chi-squared distribution with the number of
>>> restrictions as the degrees of freedom.
>>>
>>> Kind regards,
>>>
>>> Alex Olssen
>>>
>>> On 11 May 2011 11:37, Ana <analunhb@gmail.com> wrote:
>>>> Dear Statalisters,
>>>>
>>>> I'm using Brian Pois nlsurquaids.ado to estimate a Four Demand Equations.
>>>> I've excluded the symmetry restriction from this program in order to
>>>> test this restriction.
>>>>
>>>> My model has the form:
>>>> nlsur quaids @ w1 w2 w3 lnp1-lnp4 lnm, ifgnls nequations(3) param(a1
>>>> a2 a3 b1 b2 b3 g11 g12 g13 g21 g22 g23 g31 g32 g33 l1 l2 l3) nolog
>>>>
>>>>
>>>> Does anybody know how to test the symmetry restriction?
>>>> I want to test if: g12=g21 g13=g31 g23=g32!
>>>>
>>>> Thanks a lot in advance.
>>>> Best regards,
>>>> Ana.
>>>> *
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>>>> *   http://www.ats.ucla.edu/stat/stata/
>>>>
>>>
>>> *
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>>>
>>
>> *
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>>
>
> *
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```