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Re: st: GMM minimization of regional errors imputed from hhd level model


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: GMM minimization of regional errors imputed from hhd level model
Date   Sun, 30 Jun 2013 23:37:08 -0400

Vladimír Hlásny <vhlasny@gmail.com>:
I can't see that in your code:
  , myrhs(x1) instruments(x1)
and myrhs gets multiplied by theta2, so it must be at the individual level.
Perhaps you should follow the usual advice, and illustrate your
problem using a publicly available dataset.

On Sun, Jun 30, 2013 at 11:18 PM, Vladimír Hlásny <vhlasny@gmail.com> wrote:
> Dear Austin:
> Thanks for the link to optimize(). I will check whether that could
> solve my 'region-level minimization' vs. 'household-level model'
> problem.
> Regarding your point:
> What you call 'x1' is a function of all incomes in a region, not
> income of a single household.
> Vladimir
>
>
> On Mon, Jul 1, 2013 at 11:10 AM, Austin Nichols <austinnichols@gmail.com> wrote:
>> Vladimír Hlásny <vhlasny@gmail.com>,
>>
>> If you're not familiar with optimize(), start with the help file. Or
>> just follow the link I sent.
>>
>> You don't seem to take my point about your trick; if you put all the
>> weight of optimization on one residual per group, and -gmm- is trying
>> to make that one residual orthogonal to an instrument x1=income, but
>> you (unluckily) have x1=0 in each of those cases, then how could -gmm-
>> possibly improve on residual times zero, equals zero? An unlucky case,
>> but possible, given your syntax, I think.
>>
>> On Sun, Jun 30, 2013 at 10:02 PM, Vladimír Hlásny <vhlasny@gmail.com> wrote:
>>> Dear Austin:
>>> I am computing the "one-per-region residuals" as the difference
>>> between regional actual population and predicted population (sum of
>>> household-inverse-probabilities). So my trick doesn't depend on luck -
>>> the residuals contain information on all households within a region.
>>>
>>> In the code that I pasted in my original email, notice the summation
>>> across households:
>>> egen double `pophat' = sum( (1+exp(b0+income*b1)) / exp(b0+income*b1))
>>> `if', by(`region')
>>> replace residual = (pop - `pophat') * oneiffirst
>>>
>>> The 'oneiffirst' is a binary indicator for one residual per region, my
>>> trick. By using that, I ensure that only one region-level residual is
>>> considered per region. Instead, I would have liked to use an 'if'
>>> statement (such as 'if oneiffirst'), so that Stata would know that
>>> there are only 2500 (region-level) observations. But Stata doesn't
>>> allow it. Is there another way to essentially restrict the sample
>>> inside of the function evaluator program - the sample in which the
>>> moments are evaluated - after GMM is called in a hhd-level dataset?
>>>
>>> I am not familiar with 'optimize()'. Will that let me declare samples
>>> so that I estimate a region-level regression in which moments are
>>> computed from a hhd-level equation?
>>> Thank you.
>>> Vladimir
>>>
>>> On Mon, Jul 1, 2013 at 1:17 AM, Austin Nichols <austinnichols@gmail.com> wrote:
>>>> Vladimír Hlásny <vhlasny@gmail.com>:
>>>> My question is: why try trick -gmm- into doing an optimization it's
>>>> not designed for? You are trying to make the first residual within
>>>> group orthogonal to income; what if you got unlucky and the first case
>>>> in each group had zero income--hard to see how you could improve the
>>>> objective function, right?
>>>>
>>>> Instead start with Mata's optimize() which can be used to roll your
>>>> own GMM and much else besides: see e.g.
>>>> http://www.stata.com/meeting/snasug08/nichols_gmm.pdf
>>>>
>>>> On Sat, Jun 29, 2013 at 10:10 PM, Vladimír Hlásny <vhlasny@gmail.com> wrote:
>>>>> Dear Austin:
>>>>> The model is definitely identified. Matlab runs the model well,
>>>>> because I can use household-level and region-level variables
>>>>> simultaneously. My trick in Stata also works, except that it produces
>>>>> imprecise results and occasionally fails to converge. (My current
>>>>> trick is to make Stata think that the model is at the household level,
>>>>> and manually setting all-but-one-per-region hhd-level residuals to
>>>>> zero.)
>>>>>
>>>>> Incomes of the responding households are my instrument.
>>>>> Essentially, because each region has a different survey-response-rate
>>>>> and different distribution of incomes of responding households, GMM
>>>>> estimates the relationship between households' response-probability
>>>>> and their income (subject to assumptions on representativeness of
>>>>> responding households).
>>>>>
>>>>> In sum:
>>>>> I need Stata to use region-level and household-level variables (or
>>>>> matrices) simultaneously. Specifically, Stata must minimize
>>>>> region-level residuals computed from a household-level logistic
>>>>> equation. E.g., if I feed household-level data into the GMM
>>>>> function-evaluator program, can I instruct the GMM to use only one
>>>>> residual per region?
>>>>>
>>>>> Vladimir
>>>>>
>>>>> On Sat, Jun 29, 2013 at 10:27 PM, Austin Nichols
>>>>> <austinnichols@gmail.com> wrote:
>>>>>> Vladimír Hlásny <vhlasny@gmail.com>:
>>>>>> I have not read the ref.  But you do not really have instruments. That
>>>>>> is, you are not setting E(Ze) to zero with e a residual from some
>>>>>> equation and Z your instrument; you do not have moments of that type.
>>>>>> Seems you should start with optimize() instead of -gmm-, as you are
>>>>>> just minimizing the sum of squared deviations from targets at the
>>>>>> region level. Or am I still misunderstanding this exercise?
>>>>>>
>>>>>> On Fri, Jun 28, 2013 at 10:08 PM, Vladimír Hlásny <vhlasny@gmail.com> wrote:
>>>>>>> Thanks for responding, Austin.
>>>>>>>
>>>>>>> The full reference is: Korinek, Mistiaen and Ravallion (2007), An
>>>>>>> econometric method of correcting for unit nonresponse bias in surveys,
>>>>>>> J. of Econometrics 136.
>>>>>>>
>>>>>>> My sample includes 12000 responding households. I know their income,
>>>>>>> and which of 2500 regions they come from. In addition, for each
>>>>>>> region, I know the number of non-responding households. I find the
>>>>>>> coefficient on income by fitting estimated regional population to
>>>>>>> actual population:
>>>>>>>
>>>>>>> P_i = logit f(income_i,theta)
>>>>>>> actual_j = responding_j + nonresponding_j
>>>>>>> theta = argmin {sum(1/P_i) - actual_j}
>>>>>>>
>>>>>>> Response probability may not be monotonic in income. The logit may be
>>>>>>> a non-monotonic function of income.
>>>>>>>
>>>>>>> Thanks for any thoughts on how to estimate this in Stata, or how to
>>>>>>> make my 'trick' (setting 12000-2500 hhd-level residuals manually to
>>>>>>> zero) work better.
>>>>>>>
>>>>>>> Vladimir
>>>>>>>
>>>>>>> On Sat, Jun 29, 2013 at 1:49 AM, Austin Nichols <austinnichols@gmail.com> wrote:
>>>>>>>> Vladimír Hlásny <vhlasny@gmail.com>:
>>>>>>>> As the FAQ hints, if you don't provide full references, don't expect
>>>>>>>> good answers.
>>>>>>>>
>>>>>>>> I don't understand your description--how are you running a logit of
>>>>>>>> response on income, when you only have income for responders?  Can you
>>>>>>>> give a sense of what the data looks like?
>>>>>>>>
>>>>>>>> On another topic, why would anyone expect response probability to be
>>>>>>>> monotonic in income?
>>>>>>>>
>>>>>>>> On Fri, Jun 28, 2013 at 10:05 AM, Vladimír Hlásny <vhlasny@gmail.com> wrote:
>>>>>>>>> Hi,
>>>>>>>>> I am using a method by Korinek, Mistiaen and Ravallion (2007) to
>>>>>>>>> correct for unit-nonresponse bias. That involves estimating
>>>>>>>>> response-probability for each household,  inferring regional
>>>>>>>>> population from these probabilities, and fitting against actual
>>>>>>>>> regional populations. I must use household-level data and region-level
>>>>>>>>> data simultaneously, because coefficients in the household-level model
>>>>>>>>> are adjusted based on fit of the regional-level populations.
>>>>>>>>>
>>>>>>>>> I used a trick - manually resetting residuals of all but
>>>>>>>>> one-per-region household - but this trick doesn't produce perfect
>>>>>>>>> results. Please find the details, remaining problems, as well as the
>>>>>>>>> Stata code described below. Any thoughts on this?
>>>>>>>>>
>>>>>>>>> Thank you for any suggestions!
>>>>>>>>>
>>>>>>>>> Vladimir Hlasny
>>>>>>>>> Ewha Womans University
>>>>>>>>> Seoul, Korea
>>>>>>>>>
>>>>>>>>> Details:
>>>>>>>>> I am estimating households' probability to respond to a survey as a
>>>>>>>>> function of their income. For each responding household (12000), I
>>>>>>>>> have data on income. Also, at the level of region (3000), I know the
>>>>>>>>> number of responding and non-responding households.
>>>>>>>>>
>>>>>>>>> I declare a logit equation of response-probability as a function of
>>>>>>>>> income, to estimate it for all responding households.
>>>>>>>>>
>>>>>>>>> The identification is provided by fitting of population in each
>>>>>>>>> region. For each responding household, I estimate their true mass as
>>>>>>>>> the inverse of their response probability. Then I sum the
>>>>>>>>> response-probabilities for all households in a region, and fit it
>>>>>>>>> against the true population.
>>>>>>>>>
>>>>>>>>> Stata problem:
>>>>>>>>> I am estimating GMM at the regional level. But, to obtain the
>>>>>>>>> population estimate in each region, I calculate response-probabilities
>>>>>>>>> at the household level and sum them up in a region. This region-level
>>>>>>>>> fitting and response-probability estimation occurs
>>>>>>>>> simultaneously/iteratively -- as logit-coefficients are adjusted to
>>>>>>>>> minimize region-level residuals, households response-probabilities
>>>>>>>>> change.

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