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Re: st: Interpretation of interaction term in log linear (non linear) model


From   Suryadipta Roy <sroy2138@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpretation of interaction term in log linear (non linear) model
Date   Fri, 14 Jun 2013 09:59:57 -0400

Dear David,
Thank you for the suggestions! I have cross country time series data
(unbalanced panel) where the dependent variable is zero for about 15%
of the observations. Many papers have recorded more zero-s, e.g. the
paper by Silva and Tenreryo that I mentioned in the previous email
reports about 50% of zero observations for the dependent variable
(Bilateral Import/Export). I started with a fixed effects log-linear
model (more traditional in the trade literature) and moved on to fixed
effects Poisson (following Bill Gould's Stata Blog suggestions and the
Stata meeting presentation by Austin Nichols :
http://www.stata.com/meeting/boston10/boston10_nichols.pdf , as well
as some other papers in the literature). I have indeed tried Negative
Binomial and might report the results in the paper (but Stata does not
have a true fixed effects NB model since the coefficients of the time
invariant explanatory variables are reported (Paul Allison, "Fixed
effects regression models", Sage, 2009, and some other issues
discussed here: Guimarães, P., (2008), The fixed effects negative
binomial model revisited, Economics Letters, 99, pp63–66), and the
bootstrap standard errors in NB is taking forever to run with my data.
Based on the theoretical development in the literature, I must control
for fixed effects in my regressions. I have also tried -zip- and
-zinb- but there is no conditional fixed effects model in Stata. I did
not venture to introduce about 5000 fixed effects in my regressions
with -zip- / -zinb- ; most likely these would take forever to run
(with more 100,000 observations) , will not converge, and suffer from
incidental parameters problem. I have also looked into hurdle models,
but the question is if the zero-s are due to non-reporting of data or
if countries are not able to trade for some other reasons- there is a
huge literature in this area which have argued in favor of Poisson.
Thank you very much for all the comments and helpful suggestions!

Best regards,
Suryadipta.



On Thu, Jun 13, 2013 at 4:58 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
> Dear Suryadipta,
>
> Thank you for the additional details.
>
> In many analyses of non-negative counts, where a Poisson distribution
> is plausible, the presence of a substantial number of zero counts
> leads to consideration of alternative models.  Sometimes a negative
> binomial distribution is satisfactory.  If the number of zero counts
> is large enough, further alternatives include zero-inflated models and
> hurdle models.  Cameron and Trivedi (2013) have an extensive
> discussion of various alternatives.  I have not seen your data, but
> your mention of "many zeros" raises a warning flag.
>
> "Following tradition" is sometimes a very weak justification for
> choosing a particular approach to analysis.  It is essential to
> understand whether the data are compatible with the "traditional
> approach."  If not, the "traditional approach" is not valid, no matter
> how popular it may be in the literature.
>
> When I get a chance, I will try to look at the two papers that you mentioned.
>
> Regards,
>
> David Hoaglin
>
> A. C. Cameron and P. K. Trivedi (2013).  Regression Analysis of Count
> Data, second edition.  Cambridge University Press.
>
> On Thu, Jun 13, 2013 at 3:23 PM, Suryadipta Roy <sroy2138@gmail.com> wrote:
>> Dear David,
>> Thank you very much for the wonderful suggestions! In the literature
>> that I am working on, some of the important papers have already being
>> applying Poisson maximum likelihood estimator to explain bilateral
>> import (to deal with the problem of zero trade in the whole sample),
>> and I am just following the tradition by applying it for my research
>> question here (with some interesting differences in the results
>> compared to the log-linear model). A couple of important works from
>> the ones that I have come across are, e.g. "The log of gravity" by
>> Santos Silva and Tenreryo (Review of Economics and Statistics, 2006),
>> and "Estimating the gravity model with gravity using panel data" by
>> Westerlund and Wilhelmsson (Applied Economics, 2011).
>>
>> Best regards,
>> Suryadipta.
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