Dear Colleagues,

I am analyzing a panel data that collects information on children every two years since 2010, so the panel data has a total of five waves (2010,12,14,16,18). I want to know the association of family structure (especially parental absence) on child's mental health (whether child (age>=10) are depressed or not). I am using xtlogit command with either re / fe option to run random and fixed effect models.
Besides family structure variables, I have included child's age and its quadratic term as the independent variables, and both are significant.
However, when I included the panel indicator dummies (cfps_wave: panel year indicators 2012, 2014, 2016, 2018), the coefficients and significant levels for the age and the family structure variables changed considerably.

Code:
. xtlogit depress2cat ib1.race_han_x c.age_self_x##c.age_self_x ib3.tz_4cat i.region3cat, fe nolog or
PHP Code:
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              depress2cat | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
               race_han_x |
      minority ethnicity  |          1  (omitted)
               age_self_x |   .6243016   .0433709    -6.78   0.000     .5448294    .7153661
                          |
c.age_self_x#c.age_self_x |   1.011407   .0022313     5.14   0.000     1.007043    1.015789
                          |
                  tz_4cat |
       no parent at home  |   1.187886   .1047134     1.95   0.051      .999403    1.411917
       only mama at home  |   1.022447   .1331064     0.17   0.865     .7921873    1.319635
       only baba at home  |    .890598   .1651428    -0.62   0.532     .6192189    1.280912
                          |
               region3cat |
                 Central  |   .5709849   .2092956    -1.53   0.126     .2783652    1.171208
             West Region  |   1.141726   .3581595     0.42   0.673     .6173623    2.111465
------------------------------------------------------------------------------------------- 
PHP Code:
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              depress2cat | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
               race_han_x |
      minority ethnicity  |          1  (omitted)
               age_self_x |   .7124481   .0749088    -3.22   0.001     .5797696    .8754895
                          |
c.age_self_x#c.age_self_x |   1.010447   .0022359     4.70   0.000     1.006074    1.014839
                          |
                  tz_4cat |
       no parent at home  |    1.06177    .142238     0.45   0.655      .816584    1.380575
       only mama at home  |   1.028602   .1349585     0.21   0.830     .7953619     1.33024
       only baba at home  |   .8869098   .1651149    -0.64   0.519     .6157611    1.277458
                          |
                cfps_wave |
                    2012  |    .552281   .0923899    -3.55   0.000     .3978913    .7665769
                    2014  |   .4985043   .1642456    -2.11   0.035     .2613471    .9508676
                    2016  |   .4897406    .244647    -1.43   0.153     .1839727    1.303704
                    2018  |   .4146053   .2762311    -1.32   0.186     .1123365    1.530202
                          |
               region3cat |
                 Central  |   .5780685   .2126524    -1.49   0.136     .2810931    1.188799
             West Region  |   1.178924   .3724338     0.52   0.602     .6347208    2.189721
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My question is: should I include the panel year indicators in the model or not? I know that including time trend is important. As children get older, their mental health state will change. but since I have already included age, should I also need to include survey year indicators? Then the effect of survey year indicators may be spurious. I would be glad if you can give me some advice or references on this issue.