Statistically significant coefficient of zero in Poisson panel regression

[Helen Hickmann]

Hello Statalist members,

i am analysing a firm panel where I am regressing the number of high skilled employees on three dummies and some control variables. One of them is investment (in Euros). I am using a Poisson fixed effects regression and Stata 13. The coefficient for investment is 9.60e-11, which is basically zero (0.000 when I round coefficient to three decimals, same for the confidence interval and standard error) and I am wondering what this means and how to interpret it? If there is no relationship between the variables it should not be statistically significant or am I mistaken?

 xtpoisson highskill investict product_inno process_inno lnturnover lnavwages collective lnexportshare investment i.year, fe vce(robust)
note: 224 groups (224 obs) dropped because of only one obs per group
note: 10180 groups (49161 obs) dropped because of all zero outcomes

Iteration 0:   log pseudolikelihood =  -120765.5  
Iteration 1:   log pseudolikelihood = -108313.47  
Iteration 2:   log pseudolikelihood = -108273.22  
Iteration 3:   log pseudolikelihood = -108273.22  

Conditional fixed-effects Poisson regression    Number of obs     =     53,130
Group variable: idnum                           Number of groups  =      9,405

                                                Obs per group:
                                                              min =          2
                                                              avg =        5.6
                                                              max =         12

                                                Wald chi2(18)     =     161.63
Log pseudolikelihood  = -108273.22              Prob > chi2       =     0.0000

                                   (Std. Err. adjusted for clustering on idnum)
-------------------------------------------------------------------------------
              |               Robust
    highskill |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
    investict |   .0256531    .010968     2.34   0.019     .0041561      .04715
 product_inno |  -.0059202   .0283482    -0.21   0.835    -.0614816    .0496412
 process_inno |    .035324   .0168719     2.09   0.036     .0022557    .0683923
   lnturnover |   .2225503    .038659     5.76   0.000     .1467802    .2983205
    lnavwages |   .0048915   .0269775     0.18   0.856    -.0479835    .0577664
   collective |  -.0064905   .0217641    -0.30   0.766    -.0491475    .0361664
lnexportshare |   .0113623   .0076189     1.49   0.136    -.0035705    .0262951
   investment |   9.60e-11   2.14e-11     4.50   0.000     5.42e-11    1.38e-10
              |
         year |
        2008  |   .0124656   .0145073     0.86   0.390    -.0159682    .0408995
        2009  |   .0502652   .0342328     1.47   0.142    -.0168299    .1173603
        2010  |   .0917918   .0202746     4.53   0.000     .0520543    .1315292
        2011  |    .156842   .0540877     2.90   0.004     .0508321    .2628518
        2012  |   .2284362   .0607472     3.76   0.000     .1093738    .3474985
        2013  |   .2258726   .0640781     3.52   0.000     .1002819    .3514634
        2014  |    .271107    .067284     4.03   0.000     .1392328    .4029813
        2015  |   .2600914   .0546444     4.76   0.000     .1529904    .3671923
        2016  |   .2684858   .0528786     5.08   0.000     .1648456    .3721261
        2017  |   .3187303   .0638673     4.99   0.000     .1935527     .443908
        2018  |   .3404339   .0668107     5.10   0.000     .2094874    .4713804
-------------------------------------------------------------------------------

If anyone can tell me how to interpret the zero coefficient this would be of great help, I have tried research online as well as econometrics books but I have never found an example case like this with a coefficient being zero.

Thanks,

Helen

[William Lisowski]

Do you understand that if you measured investment in billions of euros (by dividing investment by 1,000,000,000), your coefficient would be 9,60e-2 = 0.0960, the standard error would be 0.0214, and the t statistic would remain 4.50?

The estimated coefficient is only near zero because the effect of an additional euro of investment is near zero. But if you add up a billion euros of effect, now you're talking real money and it has a noticeable effect.

In effect, you are confused about the meaning of statistical significance. While the estimate is very near zero, the standard error is even smaller, and this is telling us that for this estimate to have resulted from an actual zero effect would be an unlikely event.

[Leonardo Guizzetti]

The issue here is one of units and scale. I'm reasonably certain that investment is measured in single €, and firm investment is on the order of millions €. Try to rescale your investment variable into a more meaningful unit of currency and rerun the regression. Otherwise there isn't anything special about the interpretation. It's not that your coefficient is zero, it's that's it's a very small number to be multiplied by a very large number, on average. Also, one should always keep significant digits as is reported by Stata, not arbitrary numbers of decimal points. An added benefit of rescaling is that, at this scale, floating-point arithmetic is possible to bite you and result in some unnecessary precision errors.

Edit: crossed with #2.

[Helen Hickmann]

Hello,

thank you both very much, I was overlooking the effect of scales, this makes sense of course

[Jeff Wooldridge]

You might also try using log of investment if it’s never zero. That’s free of units of measurement.