Interpretation formulas of Poisson regression coefficient formula for percentages and logs

[Helen Hickmann]

Dear Statalist members,

I have done a Poisson fixed effects panel regression (Stata 13) regressing the number of high skilled employees on different explanatory variables. I am a little confused as to interpret my coefficients, I had no problems with dummy variables (taking the example from Wooldridge (2016:546) using[ exp(b1)-1]*100), but have one variable that is a firms export share in percentage as total numbers (so 80 if the firms export share is 80%, not 0.8).

I have found a forum entry somewhere (I cannot find it anymore:/) that has told me to use the formula [exp(b1*10)-1]*100 to calculate the effect of a ten percentage point increase on the dependent variable but in the case of the regression below for a subsample, this would mean that a ten percent increase in the export share, e.g. from 40 to 50 per cent would result in a [exp(0.02191*10)-1]*100=24.5 per cent decrease in the expected number of high skilled employees, and that seems way too high. So I am wondering if this formula might be wrong. I have checked several books but could not find an example that matches mine.

For logged variables (as turnover below) I have found a formula suggesting that a ten percent increase in turnover results in a [exp(0.55537*ln(1.1)-1]*100=5.4 per cent increase in the expected number of high skilled employees. This number seems more reasonable but generally it does not make sense that an increase in export share has a so much larger effect than the same increase in turnover...

Does anyone have the correct formulas to interpret these two coefficients?

Best,
Helen

 Conditional fixed-effects Poisson regression    Number of obs     =      5,778
Group variable: idnum                           Number of groups  =      1,141

                                                Obs per group:
                                                              min =          2
                                                              avg =        5.1
                                                              max =         12

                                                Wald chi2(19)     =     124.27
Log pseudolikelihood  = -11946.676              Prob > chi2       =     0.0000

                                  (Std. Err. adjusted for clustering on idnum)
------------------------------------------------------------------------------
             |               Robust
   highskill |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   investict |   -0.00127    0.01990    -0.06   0.949     -0.04028     0.03774
product_inno |    0.00352    0.02504     0.14   0.888     -0.04556     0.05260
process_inno |   -0.00309    0.03642    -0.08   0.932     -0.07447     0.06830
  lnturnover |    0.55537    0.06823     8.14   0.000      0.42163     0.68910
   lnavwages |   -0.08005    0.04703    -1.70   0.089     -0.17223     0.01213
  collective |   -0.01919    0.02391    -0.80   0.422     -0.06606     0.02768
 exportshare |   -0.02191    0.01100    -1.99   0.046     -0.04346    -0.00035
  investment |   -0.00179    0.00110    -1.63   0.102     -0.00395     0.00036
             |
        year |
       2008  |   -0.03672    0.03296    -1.11   0.265     -0.10132     0.02789
       2009  |   -0.03015    0.03442    -0.88   0.381     -0.09762     0.03732
       2010  |   -0.03578    0.03690    -0.97   0.332     -0.10810     0.03654
       2011  |    0.00830    0.03712     0.22   0.823     -0.06446     0.08106
       2012  |    0.06552    0.04054     1.62   0.106     -0.01394     0.14497
       2013  |    0.03576    0.04118     0.87   0.385     -0.04495     0.11647
       2014  |    0.06289    0.05151     1.22   0.222     -0.03807     0.16386
       2015  |    0.08398    0.05862     1.43   0.152     -0.03091     0.19886
       2016  |    0.06948    0.05608     1.24   0.215     -0.04044     0.17939
       2017  |    0.09956    0.06558     1.52   0.129     -0.02897     0.22810
       2018  |    0.08761    0.06331     1.38   0.166     -0.03648     0.21169
------------------------------------------------------------------------------

[Jeff Wooldridge]

Helen: That is the correct calculation. I initially suspected exportshare is a proportion but you say clearly it's a percent. The estimate seems high, but there must be a literature to compare it with. Also, the confidence interval is very wide and almost includes zero.

By the way, to a first approximation you can take the change you're interested in and multiple it by the corresponding coefficient, and then multiply by 100 to get the percent change. So on export share, that would lead to a 22% decline -- which is pretty similar to the more precise calculation.

JW

[Helen Hickmann]

Dear Jeff,

Thank you very much for your reply. I am glad I have the right formula, even when the result is a little counter-intuitive. Export shares in the literature should generally have a positive effect on higher skilled people and a negative one for low skilled, so the sign of the coefficient is already strange. And then the magnitude is even more strange as that would mean that an increase in export share of lets say 30% would lead to a decrease in high skilled employees of over 100%... So I guess there is something wrong with the sub-sample, or maybe the model variables do not fit with the industry sub-sample (Education, Health and Social work).

Anyhow, I will mention it as puzzling and that should be ok
Thanks again,

Helen

[Carlo Lazzaro]

Helen:
as an aside, your -Prob>Chi2- is highly significant, whereas the greatest majority of your coefficents is not (and, as Jeff highlighted, the 95% are very wide): I would re-run the model with less predictors and see if the results still remain the same.

[Helen Hickmann]

Dear Carlo,

thank you very much for your input, I have chosen these predictors because they fit and are significant for my main model with the complete sample, while the example above ist just for a subsample (education and health industry) which is about 10% of my total sample of firms. To compare different industry groups I should use the same predictors, I have just mentioned in my thesis that these predictors do not seem to fit well for the subsample

best,
Helen

[Carlo Lazzaro]

Helen:
thanks for clarifying.