Hausman test with xtpoisson

[Jana Schue]

Hello everyone,

I am using a xtpoisson model, because I have a dependent count variable.
I want to do the hausman test to identify weather random or fixed effects are appropriate.

But when I run the command I get this error:

Command:

    local controls "fs lev rdi log_cum_ccount_l"
    xtpoisson ccit cvc `controls' i.fyear, fe  
    estimates store FE
    xtpoisson ccit cvc `controls' i.fyear, re 
    estimates store RE
    hausman FE RE

Error:

 hausman FE RE

Note: the rank of the differenced variance matrix (1) does not equal the number of coefficients being
        tested (14); be sure this is what you expect, or there may be problems computing the test.
        Examine the output of your estimators for anything unexpected and possibly consider scaling
        your variables so that the coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       FE           RE         Difference       Std. err.
-------------+----------------------------------------------------------------
         cvc |    .0098339     .0098898        -.000056        .0000255
          fs |    .5974155      .591949        .0054666        .0029526
         lev |    .0085263     .0084293         .000097               .
         rdi |    3.827848     3.940803       -.1129551        .0349159
log_cum_cc~l |    .1256671     .1270406       -.0013735        .0011273
       fyear |
       2011  |    .1952878     .1953048        -.000017         .000372
       2012  |   -.2026703     -.202584       -.0000863        .0005866
       2013  |   -.8893611    -.8897147        .0003537        .0008752
       2014  |   -1.281236    -1.281293        .0000569        .0010654
       2015  |   -1.940362    -1.940815        .0004539        .0012211
       2016  |   -3.151556    -3.151121       -.0004347        .0015606
       2017  |   -5.001195    -4.999619       -.0015762        .0021698
       2018  |    -8.85359    -8.851459       -.0021309        .0135448
       2019  |   -23.20433    -26.05828         2.85395               .
------------------------------------------------------------------------------
                      b = Consistent under H0 and Ha; obtained from xtpoisson.
       B = Inconsistent under Ha, efficient under H0; obtained from xtpoisson.

Test of H0: Difference in coefficients not systematic

chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
        = -0.00

Warning: chi2 < 0 ==> model fitted on these data
         fails to meet the asymptotic assumptions
         of the Hausman test; see suest for a
         generalized test.

Could anyone give me an advice what to do now?
Or is it simply okay to run this test with -xtreg-?


Kind regards,
Jana

[Joao Santos Silva]

Dear Jana Schue,

Poisson regression with RE is really not attractive because it does not have any of the robustness properties of Poisson regression with FE or even plain Poisson regression. So, just forget about the test and use the FE estimator.

Best wishes,

Joao

[Jana Schue]

Dear Joao,

thanks for your answer!
Could you explain me a bit more why the poisson RE does not have any of the robusness properties?

And are the tests for autocorrelation (Wooldrigde, 2002), Heteroskedasticity, Mulitcollinearity (VIF) and time-fixed effects relevant in the case of a -xtpoission- analysis?

Thanks in advance.

Best regards,
Jana

[Joao Santos Silva]

Dear Jana Schue,

In non-linear models, RE estimators need additional assumptions about the distribution of the random effects; these are difficult to justify. Also, check Wooldridge's (1999) paper of the robustness of the Poisson FE estimator. If you cluster the standard errors you do not have to worry about autocorrelation; Poisson regression is always heteroskedastic, so there is no need to worry about that either; multicollinearity is not something to test for (not only in this context), and it is up to you to decide on time-fixed effects. Anyway, you should read about these models and estimators before using them.

Best wishes,

Joao