reg3- Can the same exogenous variables appear more than once in the system?

[Hakan Gunduz]

Hi all,

I'm working on a 3SLS regression where I have three endogenous variables and a set of exogenous variables. Some of the exogenous variables have been shown to affect more than one endogenous variable. Is it OK to use the same exogenous variables in more than one equation? Here is my code and the output:

reg3 (winv wndf wdiv wcf wsize wcage wtang wmtb l.winv) (wndf winv wdiv wcf wsize wtang wol wmtb) (wdiv wndf winv wcur wtang wgrsales wsize wcf wrete wmtb), 3sls

Three-stage least-squares regression
--------------------------------------------------------------------------
Equation             Obs   Parms        RMSE    "R-sq"       chi2        P
--------------------------------------------------------------------------
winv              97,858       8     .084249    0.1450   41494.70   0.0000
wndf              97,858       7    .1062015   -0.4337    1721.02   0.0000
wdiv              97,858       9    .0251478   -0.2200   30011.62   0.0000
--------------------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
winv         |
        wndf |   .2695801   .0237924    11.33   0.000     .2229478    .3162124
        wdiv |  -2.439654   .1663055   -14.67   0.000    -2.765607   -2.113702
         wcf |   .2208368   .0115671    19.09   0.000     .1981657    .2435079
       wsize |   .0000653   .0001831     0.36   0.721    -.0002936    .0004242
       wcage |  -.0006201   .0004012    -1.55   0.122    -.0014064    .0001663
       wtang |   .0224688   .0013176    17.05   0.000     .0198865    .0250512
        wmtb |   .0281417   .0011543    24.38   0.000     .0258793    .0304041
             |
        winv |
         L1. |    .433095   .0033712   128.47   0.000     .4264874    .4397025
             |
       _cons |   .0122752   .0033467     3.67   0.000     .0057158    .0188345
-------------+----------------------------------------------------------------
wndf         |
        winv |   .1195631   .0093235    12.82   0.000     .1012894    .1378367
        wdiv |  -3.018776   .1875403   -16.10   0.000    -3.386348   -2.651203
         wcf |   .2196735   .0130419    16.84   0.000     .1941118    .2452351
       wsize |   .0033995   .0002015    16.87   0.000     .0030045    .0037944
       wtang |  -.0088237   .0017321    -5.09   0.000    -.0122185   -.0054288
         wol |  -.0033056   .0005753    -5.75   0.000    -.0044332   -.0021779
        wmtb |   .0194993   .0013735    14.20   0.000     .0168073    .0221913
       _cons |  -.0625745   .0041587   -15.05   0.000    -.0707254   -.0544236
-------------+----------------------------------------------------------------
wdiv         |
        wndf |  -.1677976   .0201453    -8.33   0.000    -.2072817   -.1283135
        winv |   .0180941   .0030847     5.87   0.000     .0120482    .0241401
        wcur |  -.0000704   .0000476    -1.48   0.139    -.0001636    .0000228
       wtang |  -.0022834   .0004652    -4.91   0.000    -.0031951   -.0013716
    wgrsales |  -.0054459   .0010195    -5.34   0.000    -.0074441   -.0034477
       wsize |   .0008075   .0000649    12.44   0.000     .0006803    .0009347
         wcf |   .0705199   .0008834    79.83   0.000     .0687885    .0722513
       wrete |   .0001201   .0000343     3.50   0.000     .0000529    .0001874
        wmtb |   .0066609   .0001025    65.00   0.000       .00646    .0068617
       _cons |  -.0186823   .0010157   -18.39   0.000    -.0206731   -.0166916
------------------------------------------------------------------------------
Endogenous variables:  winv wndf wdiv 
Exogenous variables:   wcf wsize wcage wtang wmtb L.winv wol wcur wgrsales 
     wrete

wcf, wsize, wtang and wmtb enter all equations in the system, while the rest of the exogenous variables are equation-specific. I have seen some studies using only equation-specific exogenous variables but I am not sure if this is the correct approach while setting a system of equations. I would appreciate your help.

Thanks.

[Phil Bromiley]

Absolutely. There is no problem with having a variable appear in more than one equation. Identification depends on having variables that doesn't appear in the other equations, but there is no limit on the number of variables that it can appear in all the equations or 2 of them or whatever..