Fixed Effect Model Insignificant p-values

[Konstantinos Babalis]

Hi Satalist Users,

I currently working on an applied project for my BSc.I am trying to estimate the effects of smoking on wages, using Longitudinal Data. As this is my first time using Stata and Im relatively new to econometric analysis, I would appreciate your help some help to get in the right direction.

Specifically I am using ln(hourly_wage) as a dependent variable and the following independet variables:
age and dummies on Smoking (Current_Smoker), Marriage (Married), Education (Education) and whether an individual lives in London (London_Region). Based on relevant literature I am expecting a negative coefficient on smoking and positive coeffecients on the rest.

Using the hausman test, I have to use a Fixed Effects model. However, in running both an RE and a FE, while I am getting the expected sings, the p-values are significant under RE but insignificant under FE. Any ideas as to why is that/Alternatives to proceed with.

Below is an example of the data I am using and the FE/RE model.

Thanks for reading and apologies if this question is too elementary.

Best,
Konstantinos

* Example generated by -dataex-. To install: ssc install dataex
clear
input float ln_hourly_wage int age float(Current_Smoker Educated Married London_Region)
         . 40 0 0 0 0
         . 41 0 0 0 0
-1.5998685 27 . 1 0 1
  1.938442 31 0 0 0 0
 1.4868356 32 0 0 0 0
  2.187459 34 0 0 0 0
 -1.466337 32 1 0 0 0
         . 43 . 0 0 0
         . 44 0 0 0 0
         . 45 0 0 0 0
         . 46 0 0 0 0
         . 26 0 0 0 0
  2.135531 43 0 0 0 1
 2.3328905 44 0 0 0 1
 2.2285895 48 0 0 0 0
 2.0928645 49 0 0 0 0
 2.7593434 50 0 0 0 0
 2.5510464 51 0 0 0 0
 2.0794415 52 0 0 0 0
 -1.466337 25 0 1 0 0
  1.634014 26 0 1 0 0
  2.012822 36 1 0 1 0
  1.941505 38 1 0 1 0
  1.974081 39 1 0 1 0
         . 34 0 0 0 0
         . 35 0 0 0 0
         . 36 0 0 0 0
 2.6621404 35 0 1 0 0
 2.8668995 37 0 1 0 0
         . 57 . 1 1 0
         . 58 0 1 1 0
         . 59 0 1 1 0
         . 60 0 1 1 0
  2.815501 30 0 1 1 0
 3.0727496 32 0 1 1 0
 3.0908585 33 0 1 1 0
  3.142028 34 0 1 1 0
  2.618958 45 1 1 1 0
 2.6634095 46 1 1 1 0
   2.86012 47 1 1 1 0
 2.5700946 35 1 0 1 0
  2.588787 37 0 0 1 0
  2.610766 38 1 0 1 0
   2.70206 39 0 0 1 0
  2.717156 40 0 0 1 0
   3.02489 39 0 1 0 0
   3.08373 40 0 1 0 0
  2.862104 43 0 1 0 0
  3.024423 30 0 1 1 0
  3.111434 31 0 1 1 0
 3.0202274 33 0 1 1 0
-1.5998685 44 0 1 1 0
-1.5998685 44 0 1 1 0
-1.5998685 45 0 1 1 0
 -1.466337 46 1 1 1 0
  2.540996 52 0 0 1 0
         . 53 0 0 1 0
 2.6597795 47 0 1 1 0
 -1.466337 48 0 1 1 0
 1.9348603 49 0 1 1 0
 2.3611286 50 0 1 1 0
   2.81445 44 0 1 1 0
  2.572438 45 0 1 1 0
  2.647983 46 0 1 1 0
  2.705969 48 0 1 1 0
   2.97104 28 0 1 1 0
 2.8081336 30 0 1 1 0
 3.3866694 32 0 1 0 0
  3.465736 33 0 1 1 0
 3.5352485 34 0 1 1 0
  3.491053 35 0 1 1 0
 3.5352485 36 0 1 1 0
  2.946461 39 0 1 1 0
 3.0608716 40 0 1 1 0
 3.0334725 42 0 1 1 0
  3.129784 44 0 1 1 0
 3.1297834 43 0 1 1 0
  3.182203 44 0 1 1 0
 3.1891665 45 0 1 1 0
  2.993651 46 0 1 1 0
   3.19914 47 0 1 1 0
  2.307622 59 0 1 0 0
  2.600979 60 0 1 0 0
 2.6227384 53 0 1 1 0
  2.664375 54 0 1 1 0
  2.729984 55 0 1 1 0
 -1.466337 56 0 1 1 0
 -1.466337 57 0 1 1 0
  3.075173 42 0 1 1 0
         . 55 0 1 1 0
         . 56 0 1 1 0
   3.50858 57 0 1 1 0
   3.62263 52 0 1 1 0
         . 53 0 1 1 0
 3.3449435 54 0 1 1 0
   3.61207 55 0 1 1 0
 3.3211546 56 0 1 1 0
 2.1594841 50 1 1 1 0
         . 51 1 1 1 0
 1.7361553 52 1 1 1 0
end
label values age i_age_dv

[Carlo Lazzaro]

Konstantinos:
-your data excerpt makes impossible to replicate your analysis (both -panelid- and -timevar- are missing);
-as per FAQ, you're kindly requested not to post screenshots but share what you typed and what Stata gave you back via CODE delimiters.
All that said, I woud check whether:
- your model is correctly specified. Just out of cusriosity: have you checked whether the relationship between age and the regressand is quadratic rather than linear?
- have you checked that your model does not suffer for reverse causation (if smoking might affect hourly wage the other way around is theoretically possible, due to the share of disosable income that can be allotted to that unhealthy habit that I gave up 30 years ago).

[Phil Bromiley]

There is a different way to view this. The Hausman operates under the assumption that within panel changes in variables have the same parameters as between panel variation. Under this assumption, an significant Hausman suggests bias in estimating the between effect. However, it may be that the true within and between effects legitimately they differ. If you look at explained variation, all the variation is between panels. What this might mean is that stable differences matter, but year-to-year variation doesn't matter much.

Think about housing costs if you own a house. The stable (between/panel level) differences are things like mortgage and taxes, and within things like heating and cooling variation with weather. Very different factors can drive within and between effects.

For example, your educated variable seems like a dummy so you're dividing at some point between educated and not educated. The within only picks up the effect for individuals who moved from uneducated to educated in the panel (so, they got another year of education?) but the between picks up the general differences. Adding a year of education this year or last year may not make much difference in my income immediately, but might in the long run. Note also, the within effect does not include folks who are always uneducated or always educated which means the highly educated or very poorly educated cannot contribute to the within effect even if they really differ a lot. Likewise, the within estimate on married only applies to those who change status in your sample - newly married or newly divorced. The effects of being married may not occur that quickly. Longer-term effects would appear in the panel-level differences between married and unmarried.

You might look at the between estimates as well as the within.

I should note that my position on this is not necessarily shared by others.