Heteroskedasticity or other problem with regression?

[Julia Smith]

Hello everyone, so I run a pooled OLS regression on panel data of log real monthly wage on education, age, sex, marital status, job sector, and more and got a pretty high R squared of 0.45, F-value of 43.19 and significant P-value, however with "hettest", heteroskedasticity was detected. I plotted the residual vs fitted values, and found them to look like this:

Since a lot of values are far from zero, what does this mean? Should I just reconsider the regression predictors, or is there something wrong with the data?It does have a lot of missing values but those get eliminated. Sorry but I'm pretty new.
Here is a clip of the data:

* Example generated by -dataex-. To install: ssc install dataex
clear
input int age byte(education sex region maritalstatus urban) long mainjobcode float Year
33 16 2 2 1 0 6 2009
18  . 2 4 5 1 . 2009
34  . 2 4 5 1 . 2009
19  . 1 1 4 0 . 2009
28  . 2 2 1 0 6 2009
19  . 1 4 5 1 . 2009
32 14 2 4 1 0 6 2009
14  . 1 4 5 0 6 2009
17  . 1 4 5 0 6 2009
28 61 1 2 5 1 5 2009
.  . 2 2 . 1 . 2009
.  . 1 4 . 0 . 2009
30 61 1 1 5 1 . 2009
26  . 1 3 5 1 . 2009
14  . 2 2 5 0 . 2009
28  . 1 1 3 0 7 2009
50  . 1 2 1 1 9 2009
42  . 2 1 1 1 . 2009
.  . 2 1 . 1 . 2009
33 51 1 3 1 1 3 2009
30 31 1 1 1 0 9 2009
29 41 1 4 5 1 7 2009
32 14 2 2 1 0 6 2009
16  . 1 2 5 0 6 2009
14  . 2 2 5 0 . 2009
29  . 1 4 5 0 9 2009
23 15 1 3 5 0 6 2009
20 14 1 1 5 1 . 2009
30 31 2 1 1 1 6 2009
21 17 2 4 3 0 9 2009
.  . 1 3 . 0 . 2009
59 12 1 3 1 0 9 2009
21  . 2 1 4 0 . 2009
.  . 2 2 . 0 . 2009
40  . 2 1 1 0 6 2009
24  . 2 2 1 0 . 2009
50  . 2 1 4 0 5 2009
18  . 1 2 5 1 . 2009
.  . 1 4 . 0 . 2009
25  . 2 2 5 1 . 2009
.  . 2 2 . 0 . 2009
21 11 2 4 1 0 6 2009
.  . 2 2 . 0 . 2009
46 17 2 3 4 0 7 2009
28  . 1 2 5 1 5 2009
47 17 1 3 1 0 9 2009
21 13 2 1 3 1 . 2009
21  . 2 3 5 0 . 2009
14  . 2 2 5 0 6 2009
17  . 2 4 5 0 6 2009
43 12 2 2 1 0 6 2009
23 16 2 3 1 0 5 2009
58 15 2 1 3 0 6 2009
23  . 1 1 5 0 . 2009
28 17 2 2 1 0 6 2009
48  . 1 4 1 0 6 2009
41  . 2 2 1 0 6 2009
43  . 2 3 1 1 . 2009
36 17 1 4 1 0 6 2009
15  . 2 3 5 0 6 2009
15  . 2 1 5 0 . 2009
38  . 2 2 1 0 6 2009
15  . 1 1 5 0 . 2009
56 17 1 1 1 0 6 2009
22  . 1 3 5 1 . 2009
63 11 1 1 2 0 6 2009
44  . 2 4 4 0 6 2009
18 15 2 2 1 0 6 2009
27 17 1 4 1 0 6 2009
18  . 1 3 5 0 6 2009
46  . 1 2 1 0 6 2009
52 15 1 4 4 0 6 2009
16  . 1 2 5 0 . 2009
26  . 2 2 1 0 . 2009
.  . 2 2 . 0 . 2009
61  . 2 1 4 0 6 2009
15  . 1 1 5 1 . 2009
47 33 1 2 2 0 . 2009
35 13 2 3 2 0 6 2009
25  . 2 1 1 1 6 2009
16 14 2 1 5 0 6 2009
21  . 1 3 5 0 6 2009
21 17 1 1 5 0 . 2009
.  . 2 1 . 1 . 2009
45 14 1 3 1 1 5 2009
31  . 2 3 2 0 6 2009
14  . 1 1 5 0 6 2009
14  . 1 3 5 1 . 2009
15  . 1 4 5 0 6 2009
38 34 2 3 1 0 6 2009
17  . 2 4 5 1 . 2009
18 14 2 4 5 0 6 2009
29 41 1 4 1 0 9 2009
56 14 2 4 1 0 6 2009
41  . 2 4 1 0 6 2009
30 16 1 1 1 1 8 2009
61 33 2 1 1 0 6 2009
63 16 1 2 1 0 6 2009
16  . 1 2 5 0 6 2009
17  . 1 3 5 1 . 2009
end
label values education h4q7
label def h4q7 11 "Completed P.1", modify
label def h4q7 12 "Completed P.2", modify
label def h4q7 13 "Completed P.3", modify
label def h4q7 14 "Completed P.4", modify
label def h4q7 15 "Completed P.5", modify
label def h4q7 16 "Completed P.6", modify
label def h4q7 17 "Completed P.7", modify
label def h4q7 31 "Completed S.1", modify
label def h4q7 33 "Completed S.3", modify
label def h4q7 34 "Completed S.4", modify
label def h4q7 41 "Completed Post primary Specialized training or Certificate", modify
label def h4q7 51 "Completed Post secondary Specialized training or diploma", modify
label def h4q7 61 "Completed Degree and above", modify
label values sex h2q3
label def h2q3 1 "Male", modify
label def h2q3 2 "Female", modify
label values region region
label def region 1 "Central", modify
label def region 2 "Eastern", modify
label def region 3 "Northern", modify
label def region 4 "Western", modify
label values maritalstatus h2q10
label def h2q10 1 "Married monogamously", modify
label def h2q10 2 "Married polygamously", modify
label def h2q10 3 "Divorced / Separated", modify
label def h2q10 4 "Widow/Widower", modify
label def h2q10 5 "Never married", modify
label values urban urban
label def urban 0 "Rural", modify
label def urban 1 "Urban", modify
label values mainjobcode mainjobcode
label def mainjobcode 3 "Technicians and Associate Professionals", modify
label def mainjobcode 5 "Services and Sales Workers", modify
label def mainjobcode 6 "Skilled Agricultural, Forestry and Fishery Workers", modify
label def mainjobcode 7 "Craft and Related Trades Workers", modify
label def mainjobcode 8 "Plant and Machine Operators and Assemblers", modify
label def mainjobcode 9 "Elementary Occupations", modify

[Carlo Lazzaro]

Julia:
1) unfortunately, your data excerpt does not help, as it misses both the regressand and the -paneid-;
2) why starting off with a pooled OLS when Stata offers you -xtreg-?
3) Is your residual distribution heteroskedastic? Just impose robustified standard errors.
4) Your model may suffer form endogeneity, as individual ability does not seem to appear among the set of predictors. On average, others things being equal, smarter people achieve better edication degress and negotiate better wages.

[Julia Smith]

Hello Carlo!
Thank you very much for your response.. I have included the panel ids and the log wages. It is unbalanced.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(pid logrealmwage) int age byte(education sex region maritalstatus urban) long mainjobcode float Year
 1         . 44 13 2 1 3 0 5 2009
 1         . 45 13 2 1 3 0 5 2010
 1         . 46 12 2 1 3 0 5 2011
 1         . 48 13 2 1 3 0 9 2013
 2         . 28 34 2 1 3 0 5 2009
 2 11.266673 29 34 2 1 3 0 5 2010
 2 11.147357 29 13 2 1 3 0 9 2011
 3         . 17 16 1 1 5 0 . 2009
 3  10.16806 18 17 1 1 5 0 9 2010
 3         . 18  . 1 1 . 0 . 2011
 7         . 18  . 2 1 3 0 . 2010
 7         . 18  . 2 1 . 0 . 2011
 8         . 43  . 2 1 2 0 6 2011
 8         . 46  . 2 1 3 0 6 2013
11         . 34 15 1 1 1 0 6 2009
11         . 34  . 1 1 1 0 6 2010
11         . 35 16 1 1 1 0 6 2011
11         . 39 16 1 1 1 1 6 2013
12         . 32 16 2 1 1 0 . 2009
12         . 32  . 2 1 1 0 . 2010
12         . 33 14 2 1 1 0 . 2011
12         . 37 34 2 1 1 1 5 2013
16         . 29 14 1 1 1 1 9 2009
16         . 31 15 1 1 1 1 5 2010
16         . 32 15 1 1 1 0 9 2011
17         .  .  . 1 1 . 1 . 2009
17         . 23  . 1 1 5 1 . 2010
17         . 24 34 1 1 5 0 7 2011
18 12.542545 24 32 1 1 5 1 5 2010
18 11.945865 25 33 1 1 5 0 9 2011
19         . 38 17 1 1 3 0 6 2009
19         . 39 17 1 1 3 0 6 2011
19         . 41 17 1 1 4 0 . 2013
29         . 28  . 2 1 1 1 . 2009
29         . 29  . 2 1 1 0 5 2011
30         . 35 17 1 1 1 1 . 2009
30         .  .  . 1 1 1 0 . 2011
35  12.96571 39 36 1 1 1 1 3 2009
35         . 40  . 1 1 1 1 . 2010
35         . 41 34 1 1 1 1 7 2011
36         . 37 34 2 1 1 1 . 2009
36         . 38 34 2 1 1 1 . 2010
36         . 39 34 2 1 1 1 . 2011
39 10.596635 19 31 2 1 5 1 9 2009
39         .  .  . 2 1 . 1 . 2010
39         .  .  . 2 1 . 1 . 2011
40         . 19 34 2 1 5 1 . 2009
40         .  .  . 2 1 . 1 . 2010
40         .  .  . 2 1 . 1 . 2011
41         . 20 17 2 1 5 1 5 2010
41 12.169008 19 31 2 1 5 1 9 2011
44         . 59 17 2 1 1 1 5 2009
44         . 60 22 2 1 1 1 5 2010
44         . 61 17 2 1 1 1 5 2011
44         . 64 17 2 1 1 1 5 2013
45         . 25 61 2 1 5 1 . 2009
45         . 25 61 2 1 5 1 . 2010
45         . 27  . 2 1 5 1 . 2011
46         . 23 36 1 1 5 1 . 2009
46         . 23  . 1 1 5 1 . 2010
46         . 25  . 1 1 5 1 . 2011
46 10.817887 28 36 1 1 5 1 5 2013
47         . 20  . 1 1 5 1 . 2009
47         . 20  . 1 1 5 1 . 2010
47         . 22 34 1 1 5 1 . 2011
47         . 25 51 1 1 5 1 5 2013
48         . 17  . 2 1 5 1 . 2009
48         . 17  . 2 1 5 1 . 2010
48         . 19  . 2 1 5 1 . 2011
48         . 21  . 2 1 5 1 6 2013
49 12.206073 39 17 2 1 3 1 9 2009
49 12.824818 41 17 2 1 3 1 4 2010
49  12.25127 43 17 2 1 3 1 9 2013
50         . 22 16 2 1 3 1 5 2009
50         .  .  . 2 1 1 1 . 2010
51         . 16  . 2 1 5 1 . 2009
51         . 17  . 2 1 5 1 . 2010
51         . 20  . 2 1 5 1 . 2013
53         . 19  . 1 1 5 1 . 2009
53  11.01536 20  . 1 1 5 1 5 2010
53         . 23  . 1 1 5 1 . 2013
63  11.98293 47  . 1 1 3 1 2 2009
63 13.353476 48 61 1 1 3 1 1 2010
63         . 49  . 1 1 3 1 3 2011
63         . 50  . 1 1 3 1 2 2013
64         . 17  . 2 1 5 1 . 2009
64         . 18  . 2 1 5 1 . 2010
64         . 19  . 2 1 5 1 . 2011
65         . 15  . 1 1 5 1 . 2009
65         . 17  . 1 1 5 1 . 2010
65         . 17  . 1 1 5 1 . 2011
65         . 19  . 1 1 5 1 . 2013
66         . 14  . 1 1 5 1 . 2010
66         . 15  . 1 1 5 1 . 2011
66         . 17  . 1 1 5 1 . 2013
67         .  .  . 2 1 . 1 . 2010
67         .  .  . 2 1 . 1 . 2011
68         . 25 51 1 1 5 1 9 2009
68         . 22 51 1 1 5 1 . 2010
68 11.252717 22 51 1 1 5 1 9 2011
end
label values education h4q7
label def h4q7 12 "Completed P.2", modify
label def h4q7 13 "Completed P.3", modify
label def h4q7 14 "Completed P.4", modify
label def h4q7 15 "Completed P.5", modify
label def h4q7 16 "Completed P.6", modify
label def h4q7 17 "Completed P.7", modify
label def h4q7 22 "Completed J.2", modify
label def h4q7 31 "Completed S.1", modify
label def h4q7 32 "Completed S.2", modify
label def h4q7 33 "Completed S.3", modify
label def h4q7 34 "Completed S.4", modify
label def h4q7 36 "Completed S.6", modify
label def h4q7 51 "Completed Post secondary Specialized training or diploma", modify
label def h4q7 61 "Completed Degree and above", modify
label values sex h2q3
label def h2q3 1 "Male", modify
label def h2q3 2 "Female", modify
label values region region
label def region 1 "Central", modify
label values maritalstatus h2q10
label def h2q10 1 "Married monogamously", modify
label def h2q10 2 "Married polygamously", modify
label def h2q10 3 "Divorced / Separated", modify
label def h2q10 4 "Widow/Widower", modify
label def h2q10 5 "Never married", modify
label values urban urban
label def urban 0 "Rural", modify
label def urban 1 "Urban", modify
label values mainjobcode mainjobcode
label def mainjobcode 1 "Managers", modify
label def mainjobcode 2 "Professionals", modify
label def mainjobcode 3 "Technicians and Associate Professionals", modify
label def mainjobcode 4 "Clerical Support Workers", modify
label def mainjobcode 5 "Services and Sales Workers", modify
label def mainjobcode 6 "Skilled Agricultural, Forestry and Fishery Workers", modify
label def mainjobcode 7 "Craft and Related Trades Workers", modify
label def mainjobcode 9 "Elementary Occupations", modify

I did try the fixed effects model and a lot of variables were insignificant with unexpected signs. Particularly education, and job sector.However, the random effects model worked well. I thought I could try to do some diagnostic tests with the pooled OLS model because its easier for me to understand and then after respecifying the model if necessary repeat the fixed and random effects models.
That's a very good observation. Do you know what I could use as a variable for ability?

[Carlo Lazzaro]

Julia:
I'm sortry again, but what I got from your excerpt is what follows:

. xtset pid Year
       panel variable:  pid (unbalanced)
        time variable:  Year, 2009 to 2013, but with gaps
                delta:  1 unit

. xtreg logrealmwage age i.education i.sex i.region i.maritalstatus i.urban i.mainjobcode i.Year, fe
note: 17.education omitted because of collinearity
note: 31.education omitted because of collinearity
note: 33.education omitted because of collinearity
note: 36.education omitted because of collinearity
note: 51.education omitted because of collinearity
note: 61.education omitted because of collinearity
note: 2.sex omitted because of collinearity
note: 1.region omitted because of collinearity
note: 3.maritalstatus omitted because of collinearity
note: 5.maritalstatus omitted because of collinearity
note: 1.urban omitted because of collinearity
note: 3.mainjobcode omitted because of collinearity
note: 5.mainjobcode omitted because of collinearity
note: 9.mainjobcode omitted because of collinearity
note: 2010.Year omitted because of collinearity
note: 2011.Year omitted because of collinearity
note: 2013.Year omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =         14
Group variable: pid                             Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 1.0000                                         min =          1
     between = 0.5028                                         avg =        1.4
     overall = 0.3955                                         max =          3

                                                F(4,0)            =          .
corr(u_i, Xb)  = 0.4247                         Prob > F          =          .

---------------------------------------------------------------------------------------------------------------------------
                                             logrealmwage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------------------------------------------+----------------------------------------------------------------
                                                      age |   .0112994          .        .       .            .           .
                                                          |
                                                education |
                                           Completed P.7  |          0  (omitted)
                                           Completed S.1  |          0  (omitted)
                                           Completed S.2  |     .60798          .        .       .            .           .
                                           Completed S.3  |          0  (omitted)
                                           Completed S.4  |   .1193161          .        .       .            .           .
                                           Completed S.6  |          0  (omitted)
Completed Post secondary Specialized training or diploma  |          0  (omitted)
                              Completed Degree and above  |          0  (omitted)
                                                          |
                                                      sex |
                                                  Female  |          0  (omitted)
                                                          |
                                                   region |
                                                 Central  |          0  (omitted)
                                                          |
                                            maritalstatus |
                                    Divorced / Separated  |          0  (omitted)
                                           Never married  |          0  (omitted)
                                                          |
                                                    urban |
                                                   Urban  |          0  (omitted)
                                                          |
                                              mainjobcode |
                 Technicians and Associate Professionals  |          0  (omitted)
                                Clerical Support Workers  |   .5961461          .        .       .            .           .
                              Services and Sales Workers  |          0  (omitted)
                                  Elementary Occupations  |          0  (omitted)
                                                          |
                                                     Year |
                                                    2010  |          0  (omitted)
                                                    2011  |          0  (omitted)
                                                    2013  |          0  (omitted)
                                                          |
                                                    _cons |   11.38607          .        .       .            .           .
----------------------------------------------------------+----------------------------------------------------------------
                                                  sigma_u |  .95028601
                                                  sigma_e |          .
                                                      rho |          .   (fraction of variance due to u_i)
---------------------------------------------------------------------------------------------------------------------------
F test that all u_i=0: F(9, 0) = .                           Prob > F =      .

. xtreg logrealmwage age i.education i.sex i.region i.maritalstatus i.urban i.mainjobcode i.Year, re
note: 1.region omitted because of collinearity
note: 3.maritalstatus omitted because of collinearity
note: 1.urban omitted because of collinearity
note: 3.mainjobcode omitted because of collinearity
note: 5.mainjobcode omitted because of collinearity
note: 9.mainjobcode omitted because of collinearity
note: 2010.Year omitted because of collinearity
note: 2011.Year omitted because of collinearity
note: 2013.Year omitted because of collinearity
insufficient observations
r(2001);

.

That said, some comments on your query:
1) as expected, the -fe- estimator wipes out any time-invariant predictors (due to demeaning);
2) you can perform post estimation tests after -xtreg-, too, even though they're not ready to use as after -regress-.
You can visually check heteroskedasticity of the epsilon component of the composite error, just like you did in your previous post.
More important, you can test whether the functional form of your panel data regression is misspecified just tweaking a bit the procedure reported in the -linktest. entry, Stata .pdf manual.
3) as far as an instrument for individual ability, Cameron & Trivedi suggest proximity to college (see pages 177-179 of the valuable https://www.stata.com/bookstore/micr...metrics-stata/).

[Julia Smith]

Thank you very much. Does this imply that over the time period of four years, many people do not acquire new education?

[Carlo Lazzaro]

Julia:
unfortunately, as per the results obtained from your excerpt, there's nothing I can say about that.
Can you please post what Stata gave you back if your run -xtreg,fe- and -xtreg,re- on your full dataset? Thanks.

[Marcos Almeida]

If possible, please present the results of the - hettest - in #1 as well.

[Julia Smith]

Marcos Almeida here are the hettest results. It does display heteroskedasticity but I use the robust option in all regressions as well.

[Julia Smith]

Carlo Lazzaro I am sorry about the improper formatting..but here they are. The significance and signs on important variables change but when I run the Hausman test, it suggests that I use a fixed effects model instead of a random effects model.

Fixed effects model:

Random effects model:

[Carlo Lazzaro]

Julia:
how could you have run -hausman- with non-default standard errors?

[Julia Smith]

Hello, sorry I run it without the robust option. Does it mean the test isnt meaningful then?

[Carlo Lazzaro]

The issue is that it is not methodologically correct to add non-default standard errors after -hausman- outcome, because heteroskedasticity and/or autocorrellation should be investigated in both -fe- and -re- specifications before running -hausman-.
That said, you should switch to the community-contributed command -xtoverid- that supports non-default standard errors, but, being a bit old-fashioned, does not allow -fvvarlist- notation (just prefix your -re- code with -xi:-, then).
In addition, you need only the -re- specification to make -xtoverid- run properly.
Hence, you should run your -re- code prefixed by -xi:- (unfortunately, as you posted a screenshot instead of using CODE delimiters, I cannot copy and elaborate on your -re- code myself; that's why the FAQ wisely remind listers not to share screenshots of their Stata sessions) and then run -xtoverid-.
If the -xtoverid-outcome rejects the null, go -fe-; otherwise, stick with the -re- specification.

[Phil Bromiley]

There is a theoretical issue that might be important here. A significant hausman test means the estimated within parameters differ from the estimated between parameters. The estimated between effects could differ from within because the true between parameters differ from the true within or because the between is estimated inconsistently.

Your fixed effects only uses the within person variation in education. Depending on how long your time series is, that might be relatively small relative to the between person variation in education. A three year or four year panel might easily have large panel level/between effects that differ from the within effects. Note also that your within is only estimated on individuals whose level of education varies within the panel. I don't know what your data look like, but it is possible that many of your individuals have finished their education and so have no variance within panel. Here, folks who finished their education and so have no variance will not influence the within estimates, but will influence the between estimate. It is quite likely that the situation and employment conditions of individuals still in school differs from the situation employment conditions of individuals who finished school.

Almost all of the tests and analysis about fixed versus random effects assume that the true within parameters do not differ from the true between parameters. This assumption is a matter of substance and theory, not econometrics. There are certainly many cases where the between should differ from the within, and even where they use the same variables where the meaning of between would be different from the meaning of within. Consider, for example, housing costs. Between would largely look at things like mortgage payments and taxes which are set well in advance, well within would look at month-to-month variation in heating and repair costs. If one had a model using the local level of the economy, the between would differentiate wealthy from poor while the within would essentially be a business cycle effect. If one looked at the scale of production facilities based on plant output, the between variation in output would look like the actual design scale while the within would largely reflect month-to-month variation in demand or down time.

While the estimate of the within effect from fixed effects has greater robustness than the random effects or between estimates since it controls fully for unobserved panel level omitted variables, that is not a good reason to use it if the between effects are theoretically important.

[Julia Smith]

Phil Bromiley I just saw your comment and i am so grateful for your analysis. Yes my panel is really short and I was doubting the fixed effects coefficients and yet the hausman test suggested I should use FE. I will use the random effects regression then i think. Thank you again