instrumental variable with panel data

[Enrico Azzini]

Goodmorning, I have a doubt about the interpretation of results.
I typed

 xtivreg depvar 1var 2var (endogenousvar= iv1 iv2), fe first

However when the results are dysplayed I red among the instruments variables also the independet variables.
In my case:

. xtivreg EmpRat IntRt1 L.IMFlending FrtRt LifeExp MoneyExp SendEnrl Inf InflowForgnInvLag ForgnInvOutLag GovConsLag GrTrade PolStab (IMFintervLag=Un
> scLag UnscLag2 L3.Unsc) Lyp_all, fe first

First-stage within regression

Fixed-effects (within) regression               Number of obs     =        406
Group variable: Countryid                       Number of groups  =         39

R-sq:                                           Obs per group:
     within  = 0.1707                                         min =          2
     between = 0.5889                                         avg =       10.4
     overall = 0.3581                                         max =         15

                                                F(16,351)         =       4.51
corr(u_i, Xb)  = -0.6382                        Prob > F          =     0.0000

-----------------------------------------------------------------------------------
     IMFintervLag |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
           IntRt1 |   4.06e-20   8.18e-20     0.50   0.620    -1.20e-19    2.01e-19
                  |
       IMFlending |
              L1. |   .0003112   .0000552     5.63   0.000     .0002026    .0004198
                  |
            FrtRt |   .2780529   .1224215     2.27   0.024     .0372809    .5188249
          LifeExp |  -3.91e-18   5.59e-18    -0.70   0.485    -1.49e-17    7.09e-18
         MoneyExp |  -1.01e-17   5.47e-18    -1.85   0.065    -2.09e-17    6.42e-19
         SendEnrl |  -5.92e-19   5.11e-18    -0.12   0.908    -1.06e-17    9.45e-18
              Inf |  -7.60e-19   9.59e-18    -0.08   0.937    -1.96e-17    1.81e-17
InflowForgnInvLag |   .0041211   .0059112     0.70   0.486    -.0075048    .0157469
   ForgnInvOutLag |  -.0073391    .006467    -1.13   0.257     -.020058    .0053798
       GovConsLag |  -.0010917   .0022934    -0.48   0.634    -.0056022    .0034188
          GrTrade |   .3313871   .1641654     2.02   0.044     .0085154    .6542587
          PolStab |   .0028417   .0592084     0.05   0.962    -.1136062    .1192897
          Lyp_all |   .0462816     .01259     3.68   0.000     .0215203    .0710428
          UnscLag |   .0553762   .0770477     0.72   0.473    -.0961571    .2069095
         UnscLag2 |   .0932983    .079729     1.17   0.243    -.0635083     .250105
                  |
             Unsc |
              L3. |    .087662   .0738128     1.19   0.236    -.0575089    .2328329
                  |
            _cons |  -.5603178   .3502308    -1.60   0.111    -1.249133    .1284971
------------------+----------------------------------------------------------------
          sigma_u |  .29805667
          sigma_e |  .30855754
              rho |  .48269456   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------
F test that all u_i=0: F(38, 351) = 2.48                     Prob > F = 0.0000

Fixed-effects (within) IV regression            Number of obs     =        406
Group variable: Countryid                       Number of groups  =         39

R-sq:                                           Obs per group:
     within  = 0.1564                                         min =          2
     between = 0.1225                                         avg =       10.4
     overall = 0.1538                                         max =         15

                                                Wald chi2(14)     =  107811.97
corr(u_i, Xb)  = -0.1297                        Prob > chi2       =     0.0000

-----------------------------------------------------------------------------------
           EmpRat |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
     IMFintervLag |  -2.036931   2.095433    -0.97   0.331    -6.143904    2.070042
           IntRt1 |  -6.73e-19   4.53e-19    -1.49   0.137    -1.56e-18    2.15e-19
                  |
       IMFlending |
              L1. |  -.0005973   .0007468    -0.80   0.424     -.002061    .0008664
                  |
            FrtRt |   3.847822   .8421164     4.57   0.000     2.197305     5.49834
          LifeExp |   5.11e-19   3.15e-17     0.02   0.987    -6.13e-17    6.23e-17
         MoneyExp |   7.52e-17   3.71e-17     2.03   0.042     2.55e-18    1.48e-16
         SendEnrl |  -1.64e-18   2.81e-17    -0.06   0.954    -5.68e-17    5.35e-17
              Inf |  -3.89e-17   5.28e-17    -0.74   0.461    -1.42e-16    6.46e-17
InflowForgnInvLag |   .0803051   .0336882     2.38   0.017     .0142774    .1463327
   ForgnInvOutLag |   -.067039   .0391689    -1.71   0.087    -.1438088    .0097307
       GovConsLag |   .0013152   .0128427     0.10   0.918     -.023856    .0264864
          GrTrade |   .6603426   1.150045     0.57   0.566    -1.593704    2.914389
          PolStab |  -.0886509   .3265736    -0.27   0.786    -.7287234    .5514216
          Lyp_all |   .5510124   .1188344     4.64   0.000     .3181012    .7839235
            _cons |   46.06358   2.129946    21.63   0.000     41.88897     50.2382
------------------+----------------------------------------------------------------
          sigma_u |  10.303229
          sigma_e |  1.7010581
              rho |  .97346542   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------
F  test that all u_i=0:     F(38,353) =   295.98          Prob > F    = 0.0000
-----------------------------------------------------------------------------------
Instrumented:   IMFintervLag
Instruments:    IntRt1 L.IMFlending FrtRt LifeExp MoneyExp SendEnrl Inf
                InflowForgnInvLag ForgnInvOutLag GovConsLag GrTrade PolStab Lyp_all
                UnscLag UnscLag2 L3.Unsc
-----------------------------------------------------------------------------------

Honestly I don't understand what stata does. Does it uses as instruments all variables or only the ones that I have imposed? Why in the first stage there are coefficient for all the variables and why in the second stage, amog the instruments variables I read the name of all variable?
thax for your help. I hope I would be clear.

[Carlo Lazzaro]

Enrico:
see -ivreg- entry in Stata .pdf manual for clarifications.

[Enrico Azzini]

Hi Carlo thanx for your answer. I've already search help xtivreg on stata but it remain not clear for me.

[Carlo Lazzaro]

Enrico:
1) the first stage option reports the result of the endogenous variable regressed onto all the exogenous predictors (instruments included);
2) in the second stage regression are reported the results that follow from instrumenting the endogenous regressor. Despite Stata gathers together all the exogenous regressors under -Instruments-, the endogenous regressor is actually instrumented according to your instruction :

(endogenousvar= iv1 iv2)

As you have an overidentified model (2 instruments vs 1 endogenous regressor), test of overidentifying restrictions should follow.

[Carlo Lazzaro]

Enrico:
as you can see in the folowing toy-example with -ivregress-, the footnote after the second stage outcome tables is identical (but the way the listed variables are ordered differs, as instruments of the endogenous regressor are reported at the end of the list) regadless of the number of instruments:

. use "C:\Program Files\Stata16\ado\base\a\auto.dta"
(1978 Automobile Data)

. ivregress 2sls price (mpg = trunk) length i.foreign, first

First-stage regressions
-----------------------

                                                Number of obs     =         74
                                                F(   3,     70)   =      41.24
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6387
                                                Adj R-squared     =     0.6232
                                                Root MSE          =     3.5515

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      length |  -.2206762   .0310106    -7.12   0.000    -.2825249   -.1588276
             |
     foreign |
    Foreign  |  -1.127666    1.10474    -1.02   0.311    -3.331001    1.075669
       trunk |   .0044306   .1421115     0.03   0.975    -.2790018     .287863
       _cons |   63.04382   4.927405    12.79   0.000     53.21642    72.87122
------------------------------------------------------------------------------


Instrumental variables (2SLS) regression          Number of obs   =         74
                                                  Wald chi2(3)    =       0.29
                                                  Prob > chi2     =     0.9628
                                                  R-squared       =          .
                                                  Root MSE        =      26546

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -7793.364   239748.1    -0.03   0.974      -477691    462104.3
      length |  -1624.471   52749.26    -0.03   0.975    -105011.1    101762.2
             |
     foreign |
    Foreign  |  -5961.074   269678.3    -0.02   0.982    -534520.9    522598.7
       _cons |   479205.8   1.51e+07     0.03   0.975    -2.91e+07    3.01e+07
------------------------------------------------------------------------------
Instrumented:  mpg
Instruments:   length 1.foreign trunk

. ivregress 2sls price (mpg = trunk length) i.foreign, first

First-stage regressions
-----------------------

                                                Number of obs     =         74
                                                F(   3,     70)   =      41.24
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6387
                                                Adj R-squared     =     0.6232
                                                Root MSE          =     3.5515

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |  -1.127666    1.10474    -1.02   0.311    -3.331001    1.075669
       trunk |   .0044306   .1421115     0.03   0.975    -.2790018     .287863
      length |  -.2206762   .0310106    -7.12   0.000    -.2825249   -.1588276
       _cons |   63.04382   4.927405    12.79   0.000     53.21642    72.87122
------------------------------------------------------------------------------


Instrumental variables (2SLS) regression          Number of obs   =         74
                                                  Wald chi2(2)    =      30.73
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.2402
                                                  Root MSE        =     2553.6

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -410.0987   74.26281    -5.52   0.000    -555.6511   -264.5462
             |
     foreign |
    Foreign  |   2340.526   746.1295     3.14   0.002     878.1395    3802.913
       _cons |   14203.42   1514.389     9.38   0.000     11235.27    17171.56
------------------------------------------------------------------------------
Instrumented:  mpg
Instruments:   1.foreign trunk length

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