I am trying to estimate the effect of a range of bank specific variables like Size, Risk leverage, Assets quality, Provision Coverage Ratio, NIM, non-Interest Income, Contingent Liabilities and Operating Efficiency on Stress level of banks. I have included GDP growth Rate, G-sec Yield, Call Money Rate, Stability, Inflation and USD-INR Exchange Rate as my macroeconomic control variables. My panel consists of 18 years from 2005-2022 and has got 39 banks. Hausman test indicates RE model to be appropriate.

I want to investigate whether, my dependent variable, i.e. Stress score follows any linear or quadratic time trend, by including c.year and then c.year##c.year, respectively. With linear time trend, the coefficient of timevar turned out to be insignificant. However, with quadratic time trend, the variable c.year##c.year was omitted citing multicollinearity as reason.


Code:
. xtreg STRESS_SCORE LN_ASSETS RISK_LEV GNPA PCR NIM NONINT_INC CONT_LIAB OP_EFF GDP_GR GSEC_YLD WTAVG_CMR STABILITY C
> P_INFL USDINR_EXC c.Year##c.Year , re
note: c.Year#c.Year omitted because of collinearity.

Random-effects GLS regression                   Number of obs     =        681
Group variable: BankID                          Number of groups  =         39

R-squared:                                      Obs per group:
     Within  = 0.5699                                         min =         15
     Between = 0.6987                                         avg =       17.5
     Overall = 0.6530                                         max =         18

                                                Wald chi2(15)     =     920.17
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

-------------------------------------------------------------------------------
 STRESS_SCORE | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
    LN_ASSETS |   852.2561   170.0258     5.01   0.000     519.0116    1185.501
     RISK_LEV |    27.7547   19.36566     1.43   0.152    -10.20129    65.71068
         GNPA |   12.03832   18.77313     0.64   0.521    -24.75635    48.83298
          PCR |  -4.035505   4.591998    -0.88   0.380    -13.03566    4.964646
          NIM |  -906.5539   215.4158    -4.21   0.000    -1328.761   -484.3466
   NONINT_INC |  -748.1694   245.9966    -3.04   0.002    -1230.314   -266.0249
    CONT_LIAB |   .0054839   .0003396    16.15   0.000     .0048183    .0061496
       OP_EFF |   479.4029   237.4127     2.02   0.043     14.08257    944.7232
       GDP_GR |  -64.94529   24.15464    -2.69   0.007    -112.2875   -17.60307
     GSEC_YLD |   115.9559   260.1435     0.45   0.656    -393.9159    625.8278
    WTAVG_CMR |   6.902367   116.1757     0.06   0.953    -220.7978    234.6026
    STABILITY |   .5993533   3.522829     0.17   0.865    -6.305264    7.503971
      CP_INFL |  -2.546553   49.51693    -0.05   0.959    -99.59795    94.50484
   USDINR_EXC |   57.17443   26.12808     2.19   0.029     5.964339    108.3845
         Year |  -113.7963   62.55224    -1.82   0.069    -236.3965    8.803796
              |
c.Year#c.Year |          0  (omitted)
              |
        _cons |   219487.2   123282.9     1.78   0.075    -22142.84    461117.2
--------------+----------------------------------------------------------------
      sigma_u |  1586.1843
      sigma_e |  1520.6156
          rho |   .5210955   (fraction of variance due to u_i)
-------------------------------------------------------------------------------
i) My first question is, why is this happening and should the outcome be interpreted as being "no quadratic trend in the dependent variable?"

Afterwards, I came across posts which mentioned, "if you don't expect a time trend so much as just haphazard shocks to outcome from year to year, then add i.time to the list of dependent variables". Further, in field like Finance, most of the time the shock is haphazard rather than following a time trend. Both these statements are attributed to Clyde Schechter. Assuming, my dependent variable, banking stress to be the outcome haphazard shocks to bank-specific and macroeconomic parameters, I re-ran my model by including i.year as one of the independent variable, as follows.

Code:
. xtreg STRESS_SCORE LN_ASSETS RISK_LEV GNPA PCR NIM NONINT_INC CONT_LIAB OP_EFF GDP_GR GSEC_YLD WTAVG_CMR STABILITY C
> P_INFL USDINR_EXC i.Year, re
note: 2017.Year omitted because of collinearity.
note: 2018.Year omitted because of collinearity.
note: 2019.Year omitted because of collinearity.
note: 2020.Year omitted because of collinearity.
note: 2021.Year omitted because of collinearity.
note: 2022.Year omitted because of collinearity.

Random-effects GLS regression                   Number of obs     =        681
Group variable: BankID                          Number of groups  =         39

R-squared:                                      Obs per group:
     Within  = 0.5756                                         min =         15
     Between = 0.6998                                         avg =       17.5
     Overall = 0.6552                                         max =         18

                                                Wald chi2(25)     =     925.79
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
STRESS_SCORE | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   LN_ASSETS |   824.5139   171.8609     4.80   0.000     487.6728    1161.355
    RISK_LEV |   34.37259    19.7128     1.74   0.081    -4.263789    73.00897
        GNPA |   2.299177   20.09347     0.11   0.909    -37.08329    41.68165
         PCR |  -1.816186   4.874106    -0.37   0.709    -11.36926    7.736886
         NIM |   -915.265   228.8066    -4.00   0.000    -1363.718   -466.8124
  NONINT_INC |  -696.9691   251.4479    -2.77   0.006    -1189.798   -204.1403
   CONT_LIAB |   .0055769   .0003431    16.25   0.000     .0049043    .0062494
      OP_EFF |   426.0327    246.092     1.73   0.083    -56.29879    908.3643
      GDP_GR |  -82.44671    31.5042    -2.62   0.009    -144.1938   -20.69962
    GSEC_YLD |   335.9414   884.0082     0.38   0.704    -1396.683    2068.566
   WTAVG_CMR |   204.2107   270.3801     0.76   0.450    -325.7246     734.146
   STABILITY |   15.96176   34.55709     0.46   0.644    -51.76889    83.69242
     CP_INFL |   265.7651   459.0772     0.58   0.563    -634.0097     1165.54
  USDINR_EXC |  -42.01288   48.95287    -0.86   0.391    -137.9587    53.93299
             |
        Year |
       2006  |  -584.4236   930.4732    -0.63   0.530    -2408.118     1239.27
       2007  |  -2037.475   2191.599    -0.93   0.353    -6332.929     2257.98
       2008  |  -2400.557   2484.468    -0.97   0.334    -7270.025    2468.911
       2009  |  -4409.829    4150.43    -1.06   0.288    -12544.52    3724.864
       2010  |  -3285.549   4798.677    -0.68   0.494    -12690.78    6119.686
       2011  |  -3744.712   4577.124    -0.82   0.413    -12715.71    5226.287
       2012  |  -5108.068   5756.694    -0.89   0.375    -16390.98    6174.845
       2013  |  -4399.575   4948.135    -0.89   0.374    -14097.74    5298.591
       2014  |  -3247.508   3938.395    -0.82   0.410    -10966.62    4471.604
       2015  |  -1828.772   2342.686    -0.78   0.435    -6420.353    2762.809
       2016  |  -706.4356   979.0437    -0.72   0.471    -2625.326    1212.455
       2017  |          0  (omitted)
       2018  |          0  (omitted)
       2019  |          0  (omitted)
       2020  |          0  (omitted)
       2021  |          0  (omitted)
       2022  |          0  (omitted)
             |
       _cons |   -7901.26   5665.685    -1.39   0.163     -19005.8    3203.279
-------------+----------------------------------------------------------------
     sigma_u |  1586.0957
     sigma_e |  1522.2238
         rho |  .52054002   (fraction of variance due to u_i)
------------------------------------------------------------------------------
ii) For the years retained in the outcome, the corresponding p-values demonstrate insignificant coefficients. Further, certain omitted years have been omitted owing to collinearity. In this regard, what should I infer from this outcome?
iii) Even though my time period begins from 2005, why it is not included in the result ?

Any help/ insight would be sincerely appreciated.

Warm regards
pankaj