I'm estimating the effect of wealth inequality on life expectancy at the region level from 2000-2015 (every 5 years) with 290 observations (78regionsx4). My data is balanced with gaps (there are some missing values, about 22). First, I declared the dataset as panel data using the code
Code:
xtset region year, delta(4)
.

Then I checked for endogeneity using the regression test by Wooldridge and found out it is wealth is endogenous. In my data, wealth and education are highly correlated (0.8) but I don't know yet how to test jointly if both are endogenous. Also, instead of using enrollment rate, I am using mean of household head's education as proxy variable. Then I have an interaction term where I interacted inequality with wealth (I did this manually multiply them
Code:
gen ginixwealth=gini*wealth
. I used 1 period lag of wealth as instrument

Then, I run my G2SLS IV random effects regression with and without year dummies. This is based on the Hausman fe vs re test.

Code:
. xtivreg lifeexp gini ginixwealth education urbanization doctordensity econbudget socialbudget (wealt
> h=lag_wealth1), re vce(robust)

G2SLS random-effects IV regression              Number of obs     =        290
Group variable: region1                       Number of groups  =         76

R-sq:                                           Obs per group:
     within  = 0.4902                                         min =          3
     between = 0.5725                                         avg =        3.8
     overall = 0.5438                                         max =          4


                                                Wald chi2(8)      =     396.18
corr(u_i, X)       = 0 (assumed)                Prob > chi2       =     0.0000

                             (Std. Err. adjusted for 76 clusters in province1)
------------------------------------------------------------------------------
             |               Robust
     lifeexp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      wealth |   9.02e-06   .0000274     0.33   0.742    -.0000447    .0000627
        gini |   -.093408   .0146482    -6.38   0.000     -.122118   -.0646979
 ginixwealth |  -6.24e-08   4.70e-07    -0.13   0.894    -9.84e-07    8.60e-07
        education |   .9834762   .2699046     3.64   0.000     .4544729     1.51248
       urbanization |  -.0147435   .0089642    -1.64   0.100     -.032313    .0028259
      doctordensity |  -17.16256   7.629362    -2.25   0.024    -32.11584    -2.20929
  econbudget |   .0151777   .0123215     1.23   0.218     -.008972    .0393275
socialbudget |    .019107    .010045     1.90   0.057    -.0005809    .0387948
       _cons |   64.00818   2.213286    28.92   0.000     59.67022    68.34614
-------------+----------------------------------------------------------------
     sigma_u |  2.3424085
     sigma_e |  2.5574487
         rho |  .45619732   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented:   wealth
Instruments:    gini ginixwealth educ urban doctor econbudget socialbudget
                lag_wealth1
------------------------------------------------------------------------------

. xtivreg lifeexp gini ginixwealth education urbanization doctordensity econbudget socialbudget (wealt
> h=lag_wealth1) i.year, re vce(robust)

G2SLS random-effects IV regression              Number of obs     =        290
Group variable: region1                       Number of groups  =         76

R-sq:                                           Obs per group:
     within  = 0.9623                                         min =          3
     between = 0.2282                                         avg =        3.8
     overall = 0.4021                                         max =          4


                                                Wald chi2(11)     =    3432.22
corr(u_i, X)       = 0 (assumed)                Prob > chi2       =     0.0000

                             (Std. Err. adjusted for 76 clusters in province1)
------------------------------------------------------------------------------
             |               Robust
     lifeexp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      wealth |  -6.87e-06   .0000187    -0.37   0.713    -.0000435    .0000297
        gini |   .0014845   .0069483     0.21   0.831    -.0121338    .0151029
 ginixwealth |   4.24e-07   2.53e-07     1.68   0.093    -7.08e-08    9.19e-07
        education |  -.0465661   .1583917    -0.29   0.769    -.3570081    .2638758
       urbanization |   .0038474    .002319     1.66   0.097    -.0006977    .0083925
      doctordensity |   1.494077   2.478137     0.60   0.547    -3.362981    6.351135
  econbudget |    .004155   .0037391     1.11   0.266    -.0031734    .0114834
socialbudget |   .0034093   .0030565     1.12   0.265    -.0025813       .0094
             |
        year |
       2008  |   1.906733     .07849    24.29   0.000     1.752895    2.060571
       2013  |   3.522017   .1118214    31.50   0.000     3.302851    3.741183
       2017  |    4.85928   .1687632    28.79   0.000      4.52851     5.19005
             |
       _cons |   66.51479   1.181323    56.31   0.000     64.19944    68.83014
-------------+----------------------------------------------------------------
     sigma_u |    2.51575
     sigma_e |  .62218199
         rho |   .9423609   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented:   wealth
Instruments:    gini ginixwealth education urbanization doctordensity econbudget socialbudget
                2008.year 2013.year 2017.year lag_wealth1
------------------------------------------------------------------------------

.
I don't understand what could be wrong. The year dummies seem to have absorbed most of the effects and coefficients became insignificant and some reversed in sign. My professor said it's not a good result. Am I estimating it wrong? He also suggested I should change to GMM estimation.