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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 22:10:43 -0400 |

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. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: GMM minimization of regional errors imputed from hhd level model***From:*Vladimír Hlásny <vhlasny@gmail.com>

**References**:**st: GMM minimization of regional errors imputed from hhd level model***From:*Vladimír Hlásny <vhlasny@gmail.com>

**Re: st: GMM minimization of regional errors imputed from hhd level model***From:*Austin Nichols <austinnichols@gmail.com>

**Re: st: GMM minimization of regional errors imputed from hhd level model***From:*Vladimír Hlásny <vhlasny@gmail.com>

**Re: st: GMM minimization of regional errors imputed from hhd level model***From:*Austin Nichols <austinnichols@gmail.com>

**Re: st: GMM minimization of regional errors imputed from hhd level model***From:*Vladimír Hlásny <vhlasny@gmail.com>

**Re: st: GMM minimization of regional errors imputed from hhd level model***From:*Austin Nichols <austinnichols@gmail.com>

**Re: st: GMM minimization of regional errors imputed from hhd level model***From:*Vladimír Hlásny <vhlasny@gmail.com>

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