I am currently working on my thesis on the impact of land title certificate on crop diversity index of individual household. I have a short panel data (T=
5 and N=1519). The survey periods are 2007, 2010,2013,2016,and 2017. The panel data is unbalanced, but because I use Fixed-Effect model at least I mitigate some attrition problem. Using an IV (village mean of land ownership with documents) and testing for the endogeneity of the main regressor, I found out that land certificate is indeed endogenous and the IV is not a weak instrument. Here is the result using -xtivreg,endog()- command

Code:
global y1 hh_simpson_crop_area
global y22 document
global x1 ln_cultivatedarea irrigation  ///
female_head age_head age2 dep_ratio  mean_education ///
tractor moto ///
assets ln_remit credit ///
phone hh_spo ///
envir_shock ///
made_road ln_distance villassets ///
ln_offfarm ln_selfemp ln_livestock ln_envir_inc
tab time, gen(t)
Code:
xtivreg2 $y1 ($y22=villdoc_excl) $x1 t1-t5, fe endog($y22)
Code:
--------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic):         312.274
                                                   Chi-sq(1) P-val =    0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):              335.118
Stock-Yogo weak ID test critical values: 10% maximal IV size             16.38
                                         15% maximal IV size              8.96
                                         20% maximal IV size              6.66
                                         25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments):           0.000
                                                 (equation exactly identified)
-endog- option:
Endogeneity test of endogenous regressors:                              10.963
                                                   Chi-sq(1) P-val =    0.0009
Comparing non-IV and IV fixed-effect estimate gives me this result
Code:
----------------------------------------------------
                              (1)             (2)   
                     Simpson Di~x    Simpson Di~x   
----------------------------------------------------
Share of Documente~d      -0.0141*        -0.0997***
                          (-1.92)         (-3.64)   

Constant                   0.0721           0.110   
                           (0.68)          (1.02)   
----------------------------------------------------
Observations                 5865            5863   
Instrument                     No             Yes   
Control Variables             Yes             Yes   
Time Control                  Yes             Yes   
Robust                         No              No   
----------------------------------------------------
t statistics in parentheses
* p<0.10, ** p<0.05, *** p<0.010
So I conclude that IV model gives a better estimation as non-IV model.

However, I have a problem with testing the assumption of the fixed-effect model. I am not sure whether there is a strict exogeneity between the variables. And the variance distribution could possibly be homoscedastic too. I cannot produce a postestimation using -xttest- command for -xtivreg- command. However, after using the option -vce(cluster var)- command I see moderate difference in the t-stat between the normal standard errors and the robust standard errors, the result looks like following

Code:

----------------------------------------------------
                              (1)             (2)   
                     Simpson Di~x    Simpson Di~x   
----------------------------------------------------
Share of Documente~d      -0.0997***      -0.0997**
                          (-3.64)         (-2.41)   

Constant                    0.110           0.110   
                           (1.02)          (0.81)   
----------------------------------------------------
Observations                 5863            5863   
Instrument                    Yes             Yes   
Control Variables             Yes             Yes   
Time Control                  Yes             Yes   
Robust                         No             Yes   
----------------------------------------------------
t statistics in parentheses
* p<0.10, ** p<0.05, *** p<0.010
My questions are:

1.Can I have a valid inference with the normal standard error or should I go with the clustered-robust standard error?
2.Since I cannot use the -vif- command for the estimation using-xtivreg- , should I do to test for the multicollinearity one by one?
3.Other than giving arguments for the exogeneity assumption of the IV, should I worry about other things for my IV estimation after seeing this result?


Thank you,
Raihan