Testing for endogeneity panel data

[Francisco Nobre]

Hello!
I have run the command xtivreg2 y x1 x2 (x3=z) i.year, fe endog(x3)
It appeared the following error "factor variables not allowed".
I have taken out the variable "i.year" and could get now the results. Nevertheless, I need the dummy variable for the year to control for year effects.
How can I overcome this situation?

Thank you!

[Carlo Lazzaro]

Francisco:
the user-written programme -xtivreg2- does not support -fvvarlist- notation; hence, you have to prefix your code with -xi-.

xi: xtivreg2 y x1 x2 (x3=z) i.year, fe endog(x3)

Otherwise, you can consider using the built-in command -xtivreg-, which allows factor variables notation (I presume that you use Stata 15; otherwise, as per FAQ, you have to tell the list which Stata release supports your analyses):

use http://www.stata-press.com/data/r14/nlswork
. xtreg ln_w age c.age#c.age tenure i.not_smsa i.union i.south, fe

Fixed-effects (within) regression               Number of obs     =     19,007
Group variable: idcode                          Number of groups  =      4,134

R-sq:                                           Obs per group:
     within  = 0.1333                                         min =          1
     between = 0.2375                                         avg =        4.6
     overall = 0.2031                                         max =         12

                                                F(6,14867)        =     381.19
corr(u_i, Xb)  = 0.2074                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0311984   .0033902     9.20   0.000     .0245533    .0378436
             |
 c.age#c.age |  -.0003457   .0000543    -6.37   0.000    -.0004522   -.0002393
             |
      tenure |   .0176205   .0008099    21.76   0.000     .0160331    .0192079
  1.not_smsa |  -.0972535   .0125377    -7.76   0.000    -.1218289    -.072678
     1.union |   .0975672   .0069844    13.97   0.000     .0838769    .1112576
     1.south |  -.0620932    .013327    -4.66   0.000    -.0882158   -.0359706
       _cons |   1.091612   .0523126    20.87   0.000     .9890729    1.194151
-------------+----------------------------------------------------------------
     sigma_u |   .3910683
     sigma_e |  .25545969
         rho |  .70091004   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4133, 14867) = 8.31                 Prob > F = 0.0000

. xtivreg ln_w age c.age#c.age i.not_smsa (tenure = i.union i.south), fe

Fixed-effects (within) IV regression            Number of obs     =     19,007
Group variable: idcode                          Number of groups  =      4,134

R-sq:                                           Obs per group:
     within  =      .                                         min =          1
     between = 0.1304                                         avg =        4.6
     overall = 0.0897                                         max =         12

                                                Wald chi2(4)      =  147926.58
corr(u_i, Xb)  = -0.6843                        Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      tenure |   .2403531   .0373419     6.44   0.000     .1671643    .3135419
         age |   .0118437   .0090032     1.32   0.188    -.0058023    .0294897
             |
 c.age#c.age |  -.0012145   .0001968    -6.17   0.000    -.0016003   -.0008286
             |
  1.not_smsa |  -.0167178   .0339236    -0.49   0.622    -.0832069    .0497713
       _cons |   1.678287   .1626657    10.32   0.000     1.359468    1.997106
-------------+----------------------------------------------------------------
     sigma_u |  .70661941
     sigma_e |  .63029359
         rho |  .55690561   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F  test that all u_i=0:     F(4133,14869) =     1.44      Prob > F    = 0.0000
------------------------------------------------------------------------------
Instrumented:   tenure
Instruments:    age c.age#c.age 1.not_smsa 1.union 1.south
------------------------------------------------------------------------------

[Francisco Nobre]

Dear Carlo,
Thank you for your answer. I was able to get the results. However, I am having some doubts when interpreting the results.
It got this:
-------------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 8.506
Chi-sq(1) P-val = 0.0035
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 8.181
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: 0.365
Chi-sq(1) P-val = 0.5457
Regressors tested: unem
------------------------------------------------------------------------------
Instrumented: unem
Included instruments: materialdeprivation pop inc dens lprisoners _Iyear_2008
_Iyear_2009 _Iyear_2010 _Iyear_2011 _Iyear_2012
_Iyear_2013 _Iyear_2014 _Iyear_2015
Excluded instruments: bankrupt
------------------------------------------------------------------------------

Looking at this results, I think that the p-value obtained for the endogeneity test cannot reject the null hypothesis that the variable is exogenous.
But I don't know how to interpret the results regarding the weak identification test.

Thank you very much.

Best Regards,
Francisco Nobre

[Carlo Lazzaro]

Francisco:
the topics you're interested in are comprehensively covered under -ivregress postestimation- Example 3, Stata .pdf manual.

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