ivreg2 commands and GMM problems

[Boldeanu Teodor]

Dear all,

Sorry for not asking a very hard question, but I am in a bit of a jam. I am trying to regress GDP/capita in the European Union from 1990 to 2014. I have 45 variables (investment, gov. expenditure, fdi) and some dummy variables.I posted a message some days ago that I did not undestand why I could not use country dummy variables for my panel data (i have dummy vars - East Europe,West Europe, North Europe, South Europe and West Asia (Cyprus is not included) 5-1=4 dummies to use). If I use a simple regression the dummies are not dropped but in first difference they are all omitted.

Code:

regress D.y D.x67 D.x68 D.x69 D.x70
note: _delete omitted because of collinearity
note: _delete omitted because of collinearity
note: _delete omitted because of collinearity
note: _delete omitted because of collinearity

      Source |       SS       df       MS              Number of obs =     658
-------------+------------------------------           F(  0,   657) =    0.00
       Model |           0     0           .           Prob > F      =       .
    Residual |  7.68248688   657  .011693283           R-squared     =  0.0000
-------------+------------------------------           Adj R-squared =  0.0000
       Total |  7.68248688   657  .011693283           Root MSE      =  .10814

------------------------------------------------------------------------------
         D.y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         x67 |
         D1. |          0  (omitted)
             |
         x68 |
         D1. |          0  (omitted)
             |
         x69 |
         D1. |          0  (omitted)
             |
         x70 |
         D1. |          0  (omitted)
             |
       _cons |   .0573657   .0042156    13.61   0.000     .0490881    .0656433

If I can not use the dummies is not a problem.

The main issue now is the GMM and system GMM. I am using xtabond2, but i do not now how to separate the endogenous and exogenous indep vars. If I understand correctly i can use ivreg2 to somehow separate the exogenous and endogenous vars. I have read Christopher F. Baum, Mark E. Schaffer (2007) and a lot of other articles. I followed this code in Baum ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6)

I wrote the following code in Stata 12, but I do not think is the right one.

 
 ivreg2 y l.y x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55 x56 x59 x61 x62 x63 x64 x65 x66 (x2= x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55 x56 x59 x61 x62 x63 x64 x65 x66)

. ivreg2 y l.y x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x
> 25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55 x56 x59 x61 x
> 62 x63 x64 x65 x66 (x2= x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x
> 22 x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55 x56 x
> 59 x61 x62 x63 x64 x65 x66)
Warning - duplicate variables detected
Duplicates:    x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22
               x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52
               x53 x54 x55 x56 x59 x61 x62 x63 x64 x65 x66
Warning - collinearities detected
Vars dropped:  x61

Ordinary Least Squares (OLS) regression
---------------------------------------

                                                      Number of obs =      294
                                                      F( 45,   248) =  1623.82
                                                      Prob > F      =   0.0000
Total (centered) SS     =  139.3348399                Centered R2   =   0.9966
Total (uncentered) SS   =  28420.33926                Uncentered R2 =   1.0000
Residual SS             =  .4712928801                Root MSE      =   .04004

I would not run the ivreg2 if the GMM regression did not have some problems. I tried a GMM code for my model - xtabond2 y l.y x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55 x56 x59 x61 x62 x63 x64 x65 x66, gmm (y x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55 x56 x59 x61 x62 x63 x64 x65 x66 , lag (2 2)) iv(x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55 x56 x59 x61 x62 x63 x64 x65 x66) nolevel small robust

The tests for the GMM (Arellano-Bond test for AR(1)/AR(2), Sargan are not to high). I think the others are good because are above 10%. If I undestand correctly the indep vars have to be separated in gmm(...., lag (22)) and iv (...)

 xtabond2 y l.y x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23
>  x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55 x56 x59 x61
>  x62 x63 x64 x65 x66, gmm (y x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x
> 20 x21 x22 x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x
> 55 x56 x59 x61 x62 x63 x64 x65 x66 , lag (2 2)) iv(x2 x3 x6 x7 x8 x9 x10 x11 x12 x14
>  x15 x16 x17 x18 x19 x20 x21 x22 x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48
>  x49 x51 x52 x53 x54 x55 x56 x59 x61 x62 x63 x64 x65 x66) nolevel small robust
Favoring speed over space. To switch, type or click on mata: mata set matafavor space,
>  perm.
x61 dropped due to collinearity
Warning: Number of instruments may be large relative to number of observations.
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate robust weighting matrix for Hansen test.
  Difference-in-Sargan statistics may be negative.

Dynamic panel-data estimation, one-step difference GMM
------------------------------------------------------------------------------
Group variable: Tara                            Number of obs      =       269
Time variable : An                              Number of groups   =        25
Number of instruments = 269                     Obs per group: min =         5
F(45, 25)     =     16.22                                      avg =     10.76
Prob > F      =     0.000                                      max =        18
------------------------------------------------------------------------------
             |               Robust
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           y |
         L1. |   .6444742   .0535591    12.03   0.000     .5341672    .7547812
             |
          x2 |   .3267434    .850656     0.38   0.704    -1.425215    2.078702
          x3 |   1.784339   .9669409     1.85   0.077    -.2071135    3.775791
          x6 |   .0820405   .0447111     1.83   0.078    -.0100438    .1741248
          x7 |   .0822454   .0779264     1.06   0.301    -.0782469    .2427378
          x8 |   .0080527   .0035589     2.26   0.033      .000723    .0153823
          x9 |   .0521821   .0473045     1.10   0.280    -.0452433    .1496075
         x10 |   .0717508   .0284243     2.52   0.018       .01321    .1302917
         x11 |  -.0134604   .0123682    -1.09   0.287    -.0389332    .0120125
         x12 |  -.0359401   .0292178    -1.23   0.230    -.0961153    .0242352
         x14 |  -.0576314   .0368055    -1.57   0.130    -.1334338     .018171
         x15 |   .0330871   .0456771     0.72   0.476    -.0609867    .1271609
         x16 |   .0896389   .0609492     1.47   0.154    -.0358883     .215166
         x17 |   -.033444   .0141182    -2.37   0.026     -.062521    -.004367
         x18 |  -.0165842   .0284531    -0.58   0.565    -.0751845     .042016
         x19 |  -.0667013   .0494731    -1.35   0.190     -.168593    .0351903
         x20 |  -.1462139   .0494067    -2.96   0.007    -.2479688   -.0444589
         x21 |    .058025   .0705351     0.82   0.418    -.0872446    .2032947
         x22 |  -.0490903   .0801029    -0.61   0.546    -.2140653    .1158846
         x23 |  -.0016426   .0565918    -0.03   0.977    -.1181956    .1149104
         x25 |  -.0028426   .0057779    -0.49   0.627    -.0147423    .0090572
         x30 |  -.1411703   .1712684    -0.82   0.418    -.4939042    .2115635
         x31 |   -.146848   .1586111    -0.93   0.363    -.4735137    .1798177
         x37 |  -.0821773   .0293899    -2.80   0.010     -.142707   -.0216476
         x39 |   .5071685   .1038441     4.88   0.000     .2932975    .7210395
         x40 |   .0643937   .0459269     1.40   0.173    -.0301945    .1589819
         x41 |   .0670588   .0425339     1.58   0.127    -.0205415     .154659
         x42 |   .0346284   .0318792     1.09   0.288    -.0310281    .1002848
         x44 |  -.0007494   .0024163    -0.31   0.759     -.005726    .0042271
         x45 |   .0216748    .110421     0.20   0.846    -.2057414     .249091
         x47 |  -.1881008   .1707786    -1.10   0.281    -.5398258    .1636243
         x48 |     .06257   .0961805     0.65   0.521    -.1355175    .2606574
         x49 |    .042767   .1191612     0.36   0.723    -.2026501    .2881841
         x51 |   .1317306   .1559247     0.84   0.406    -.1894023    .4528635
         x52 |    .047584   .1013505     0.47   0.643    -.1611513    .2563194
         x53 |  -.2797819   .9026986    -0.31   0.759    -2.138924    1.579361
         x54 |  -.0417117   .9903789    -0.04   0.967    -2.081435    1.998012
         x55 |   .4625591   1.898061     0.24   0.809     -3.44657    4.371688
         x56 |   -.021143    .021437    -0.99   0.333    -.0652933    .0230073
         x59 |   .4616406   .2365719     1.95   0.062    -.0255884    .9488696
         x62 |  -.0186189   .0228488    -0.81   0.423    -.0656769     .028439
         x63 |  -.0232095   .0317936    -0.73   0.472    -.0886897    .0422708
         x64 |   -.067938   .0270667    -2.51   0.019    -.1236829   -.0121931
         x65 |   .0468854   .0922582     0.51   0.616     -.143124    .2368947
         x66 |   .0167629   .0220209     0.76   0.454    -.0285899    .0621157
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23
    x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55
    x56 x59 x61 x62 x63 x64 x65 x66)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L2.(y x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22
    x23 x25 x30 x31 x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54
    x55 x56 x59 x61 x62 x63 x64 x65 x66)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.64  Pr > z =  0.008
Arellano-Bond test for AR(2) in first differences: z =  -1.72  Pr > z =  0.085
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(224)  = 299.66  Prob > chi2 =  0.001
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(224)  =   0.00  Prob > chi2 =  1.000
  (Robust, but can be weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  iv(x2 x3 x6 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x25 x30 x31
>  x37 x39 x40 x41 x42 x44 x45 x47 x48 x49 x51 x52 x53 x54 x55 x56 x59 x61 x62 x63 x64
>  x65 x66)
    Hansen test excluding group:     chi2(208)  =   0.00  Prob > chi2 =  1.000
    Difference (null H = exogenous): chi2(16)   =   0.00  Prob > chi2 =  1.000

Thank you all for your help and sorry for posting to many codes.

Best regards,
Teodor

[William Lisowski]

I cannot assist with your more substantive problems, but the first difference of variable that does not depend on time - for instance your country dummies - will be a constant zero - it will either be 1 minus 1 or 0 minus 0.

Differencing should be reserved for those variables that change over time. You should include undifferenced dummies in your differenced model.

[Boldeanu Teodor]

William - I think you are onto something with the first difference of dummy vars. I searched the forums and some researchers said that there is no problem in first differencing dummy vars. And now i just manually first differenced my dummy vars and saw that the country dummy vars are all 0 in first difference and the ones for corruption - have some 1s and -1s, so they are not dropped in my model. But i have lost alot of observations by doing so. So for x67 x68 x69 x79 (country dummies) i think i should not difference them in my model and the corruption ones also x61 x62 x63 x64 x65 x66. Or should I ???

Quot from a post of Mr. Wooldridge :
"Several comments:

1. Why are you including a lagged dependent variable? If you really want to do this, you should use xtabond or xtabond2.
2. Dummy variables are treated as all other variables. If you believe the equation written above, just use the differencing operator on the entire equation. Everything gets differenced. (I remain to this day puzzled as to why researchers think there is a problem differencing dummy variables.)

Here is what I would do, assuming no lagged dependent variables:"

If someone has a solution for ivreg2 and gmm i will be very grateful.

Best regards,
Teodor