Interpreting coefficients of a fixed-effects Poisson QMLE model

[Ashani Abayasekara]

Hi all,

I have a question about interpreting coefficients from a Poisson QMLE model. The dependent variable is perceived chances of losing one's job, ranging from 0-100%, and the independent variable is the unemployment rate. I use Poisson QMLE since there is a bunching of values at 0. The coefficient I obtain is 0.031. Is it correct to interpret this as follows: if the unemployment rate increased by one percentage point, the difference in logs of expected counts of perceived job loss is expected to increase by 0.03 percentage points (or should it be percent)?

I'm not really sure of the true meaning of "expected counts of perceived job loss" in this instance.

When I estimate this relationship using a linear fixed-effects regression model, I get a coefficient of 0.35. Would this be interpreted as a 1 percentage point increase in the unemployment rate leading to a 0.35 percentage point increase in the perceived chance of job loss?

Thank you,
Ashani

[Jeff Wooldridge]

An exponential functional form is probably not ideal for a variable with an upper bound. If you turn Y into a proportion, you could use fractional logit.

You have properly interpreted the linear model coefficient -- assuming Y and the unemployment rate are both measured in percentages (as opposed to, say, one being measured as a proportion). For the Poisson FE -- where the key is the exponential mean function -- it is 3.1 percent. This assumes the U rate is measured as a percent and not a proportion. And this has nothing to do with "counts." You are measuring a percent effect on the expected perceived chance of job loss.

Generally, it's a good idea to show an excerpt of your data set so there is no ambiguity.

If you redefine Y and U to be in the range [0,1], you can use fracreg logit and obtain the average marginal effect.

[Ashani Abayasekara]

Dear Prof. Wooldridge,

Thank you very much for the explanation. In this case, both variables are in percentages (perceived chance of job loss and the UR). But I have two other cases where the dependent variable is a cardinal measure, ranging from 0-10 (job security satisfaction) and 1-7 (extent of worry about the future of one's job). The UR is the same percentage measure. How would I interpret coefficients from linear fixed-effects models in these two cases? (I obtain coefficients of 0.031 and 0.039 for the two cases, respectively).

Here is an excerpt of my data:

* Example generated by -dataex-. For more info, type help dataex
clear
input long id float(year unemp_av6) byte(job_sec_sat job_worry) int job_lose
100014 2001  9.333334  7 2  2
100014 2002  9.666666  7 1 20
100014 2003       5.8  9 1  2
100014 2004  5.716667  7 2  2
100014 2005  5.183333  7 1  3
100014 2006  3.866667  8 1  2
100014 2007 3.8166666  6 1  5
100014 2008 3.9333334  7 1 20
100014 2009       6.8  0 .  .
100014 2010 4.7333336  . .  .
100014 2011  3.766667  . .  .
100014 2012  2.866667  . .  .
100014 2013  5.316667  . .  .
100014 2014  7.566667  . .  .
100014 2015 11.416667  . .  .
100014 2016  5.066667  . .  .
100014 2018       6.1  . .  .
100014 2019  5.666667  . .  .
100015 2001  9.333334  7 2  0
100015 2002  9.666666  2 7 20
100015 2003       5.8  8 2  0
100015 2004  5.716667  9 2  0
100015 2005  5.183333 10 3  0
100015 2006  3.866667  9 1  0
100015 2007 3.8166666  9 1  0
100015 2009       6.8 10 2  0
100015 2010 4.7333336 10 2  0
100015 2011  3.766667 10 3  0
100015 2012  2.866667  9 3  0
100015 2013  5.316667  8 3  0
100015 2015 11.416667  9 2  0
100015 2016  5.066667 10 1  0
100015 2017       4.8  8 5 20
100015 2018  6.166667  8 6  0
100015 2019  5.383333  8 6  0
100016 2007      4.85 10 1  0
100016 2008 4.7166667  9 1  2
100016 2009 4.7166667  9 2  2
100016 2010       4.5  9 2  0
100016 2011  4.116667  9 2 95
100016 2012      5.85  9 2  1
100016 2013  6.333333  9 2  1
100016 2014       6.7  9 6  0
100016 2015  6.766666  9 2  0
100016 2016      5.85  9 2  5
100016 2017  5.633333 10 1  0
100016 2018  6.033333 10 1  2
100016 2019  4.366667 10 1  0
100018 2001  7.133333  . .  .
100018 2002  5.516666  . .  .
100018 2003  6.766666  . .  .
100018 2004       5.3  . .  .
100018 2005      4.85  . .  .
100018 2006 2.8166666  2 2  0
100018 2007  2.966667  2 2  0
100018 2008 3.6666665  3 2  0
100018 2009      5.45  4 4 50
100018 2010  5.433333  5 4  0
100018 2011 4.4333334  6 5  0
100018 2012  4.133333  8 5  0
100018 2013  5.266666  7 5 50
100018 2014  5.516666  8 5  0
100018 2015       5.7  8 5  0
100018 2016  6.316667  7 3  0
100018 2018  6.883333  7 5  0
100018 2019  7.016666  9 5 10
100019 2001  7.133333  4 6 35
100019 2002  5.516666  3 6 15
100019 2003  6.766666  . .  .
100019 2004       5.3  4 6 10
100019 2005      4.85  6 6  5
100019 2006 2.8166666  6 6  0
100019 2007  2.966667  7 6  0
100019 2008 3.6666665  6 6  0
100019 2009      5.45  7 5 10
100019 2010  5.433333  7 5  0
100019 2011 4.4333334  6 5  0
100019 2012  4.133333  4 6  0
100019 2013  5.266666  7 6  0
100019 2014  5.516666  8 6  0
100019 2015       5.7  8 4  0
100019 2016  6.316667  3 6  0
100019 2017  6.133333  3 6  0
100019 2018  6.233334  8 6 10
100019 2019  4.266667  9 5  5
100020 2013  5.266666  8 4  0
100020 2014  5.516666  8 2  0
100020 2015       5.7  8 2  0
100020 2016  6.316667  9 5  0
100020 2017  6.133333  8 5  0
100020 2019  7.016666  9 5  5
100023 2001  5.666667 10 1  .
100023 2002 4.3166666 10 1  0
100023 2003  6.433333 10 1  0
100023 2004  4.733333  . .  .
100023 2005      4.75 10 1  .
100023 2006  4.633333  7 2  .
100023 2007 2.3833332 10 1  .
100023 2008  3.416667 10 1  .
100023 2009  3.016667 10 1  .
end
label values job_sec_sat AJBMS
label def AJBMS 0 "[0] Totally dissatisfied", modify
label def AJBMS 10 "[10] Totally satisfied", modify
label values job_worry AAGREE
label def AAGREE 1 "[1] Strongly disagree", modify
label def AAGREE 7 "[7] Strongly agree", modify
label values job_lose AJBMPLE