Problems with Poisson Postestimation

[Imran Khan]

Hi,

I am struggling with truly understanding my postestimation results following a poisson regression.
I have a panel dataset of 50 countries over 10 years. The dependant variable is a count i.e., the average number of World Bank conditions a country receives in a year. I proceeded in the following steps:

Step 1: Running Poisson regression

xtset country year
egen t= group(Year)
xtpoisson AvConditions ForeignAid GDP Inflation Investment t, vce(cluster recid)

I include a time trend to control for structural changes in conditionality over time.
I also assume that the errors are not independent within recipient countries, and therefore cluster the standard errors by recipient country in order to control for heteroscedasticity.

Step 2: Checking Goodness of Fit:

poisgof 
last estimates for poisson not found
r(301);

I couldn't perform the above test with ‘xtpoisson’.

Q1) What are the alternatives of checking goodness of fit of the model other than the above command and graphical representation?

One option was to perform LR chi-square test by estimating both the poisson and negative binomial (although a formal test didn’t find any evidence of overdispersion):

xtpoisson AvConditions ForeignAid GDP Inflation Investment t, vce(cluster recid
est store poisson
xtnbreg AvConditions ForeignAid GDP Inflation Investment t, vce(cluster recid
est store nbreg
lrtest poisson nbreg, stats force

However, I couldn't perform the above test because vcetype 'cluster’ is not allowed with xtnbreg.


Q2) In a previous post I was suggested to use ‘REST’, however; I have the following concerns related to REST:

• 2A) Is RESET only valid after poisson or is it only appropriate for 'OLS’?
• 2B) As I cant specify ‘vce cluster (country)’ and ‘fe/re’ with REST, can I still rely on it?

https://www.statalist.org/forums/for...ative-binomial

Step 3: Choosing b/w Fixed vs Random Effects:

Next, I wanted to perform Hausman test for comparing between fixed and random effects as follows:

xtpoisson AvConditions ForeignAid GDP Inflation Investment t, fe
est store fe
xtpoisson AvConditions ForeignAid GDP Inflation Investment t, re
est store fe
hausman fe re

According to the Hausman results, the data fails to meet the asymptotic assumptions of the Hausman test.

Upon reading the previous posts related to my problem, some alternatives discussed were using ‘suest’, ‘sigmamore’ which I cant do with poisson. In one of the previous posts, Joas Santos Silva suggested

The Poisson regression you are using is based on a non-linear model and in this context the random effects estimator will have to be based on unreasonable assumptions about the distribution of the errors. So, I would just stick to the FE regression.

https://www.statalist.org/forums/for...-for-xtpoisson

However, a key author in my research field has used poisson regression with random effects after performing Hausman test. There are numerous other studies using random effects with poisson. So, I got confused reading it.

Q3) Is there any other alternative to Hausman test for poisson regressions?
Q4) I also couldnt include vce(cluster recid) while performing Hausman. Is that OK to exclude it for the sake of Hausman test only?

Some of the problems might be solved by using ‘poisson/nbreg’ instead of ‘xtpoisson/xtnbreg’ but it also comes with some limitations for instance, the option of ‘fe/re’ is not allowed with ‘poisson’. I wonder the rationale behind two different command for the same purpose.

Apologies if I am not able to put the problems clearly.
I look forward to your guidance.

Best regards,
Imran Khan.

[Joao Santos Silva]

Dear Imran,

Sorry for the late reply. Here are some answers.

1) The FE Poisson regression is very robust and valid under very mild conditions. Also, in conditioning out the fixed effects, the estimator does not exactly model the probability of the counts but a related probability that depends on the same parameters. So, the goodness-of-fit test you mention is not really relevant in this context, an I am not aware of any graphic tool that would help here. Performing the LR test or comparing with the NB model are also not good choices because the result of the test would depend on the validity of the Poisson assumption, that is not needed in this context. By now you should be guessing that my recommendation is that you check the model with the RESET test; more on this below.

2) The RESET is appropriate in any model where the regressors enter the model in a linear index, so it is valid under very general conditions. You should do the RESET using clustered standard errors, and that is possible with the FE Poisson estimator.

3) The validity of the RE Poisson depends on very strong (and, for me, not believable) distributional assumptions. Therefore, unless in very special cases where we need to model probabilities of events, I would not consider the FE approach and would not try to perform such test.

4) Not sure if I understand this one, by my answer to 3 still applies.

Finally, xtpoisson and poisson have very different purposes although indeed they have some overlap. In contrast, I believe that xtnbreg and nbreg do not ovelap; for example, you cannot estimate a FE NB model by running nbreg with dummies.

Best wishes,

Joao

[Imran Khan]

Dear Joao,

Many thanks for your detailed reply.

What I have understood so far from your reply is as follows:

1) FE Poisson (i.e., xtpoisson, fe) is a safe option as it does not require the strict assumptions to be met. I can ignore the other post-estimation tests and can rely only on RESET. I am wondering if you could bring some literature references to my attention so that I can argue about it and understand it fully?

2) I performed the RESET using clustered standard errors and fe; however, it returned with the following error:

reset DV IV,  vce (cluster country)
option vce() not allowed

reset DV IV, fe 
option fe not allowed

I even can't use clustered standard errors with FE Poisson estimator:

xtpoisson DV IV, fe vce (cluster country)
option cluster not allowed

So, could you please elaborate your point a bit more as I am not able to use -fe and -vce together with -xtpoisson and -RESET?

You should do the RESET using clustered standard errors, and that is possible with the FE Poisson estimator.

3) I didn’t get why you would not consider the FE approach in the following statement? As far as I understand, you suggested to use FE in the first point.

Therefore, unless in very special cases where we need to model probabilities of events, I would not consider the FE approach and would not try to perform such test.

Looking forward to your assistance.

Best regards,
Imran Khan.

[Joao Santos Silva]

Dear Imran,

1) The key reference is

Wooldridge, J. M. (1999), “Distribution-Free Estimation of Some Nonlinear Panel Data Models,” Journal of Econometrics, 90, 77–97.

This paper shows that the FE Poisson regression is consistent under very mild conditions. Essentially the estimator is valid as long as the conditional mean is correctly specified and therefore the meaningful tests are tests for functional form misspecification.

2) You cannot perform the RESET like that; you have to do it "by hand"; see an example here. The command xtpoisson now allows clustered standard errors; if you are using an old version of Stata you can install xtpqml form SSC.

3) I am very sorry, that was a bad typo. I would not consider the RE approach!

Best wishes,

Joao