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# Re: st: discrepancy xtdpd vs xtabond2

 From Daniel Borowczyk Martins To statalist@hsphsun2.harvard.edu Subject Re: st: discrepancy xtdpd vs xtabond2 Date Sat, 18 Sep 2010 21:02:30 +0100

```I don't if this helps, but I find a discrepancy between xtdpd and
xtabond2 regarding the choice of instruments.

1. I generate an interaction between w and a dummy  "year above 1980".

2. I estimate the model "n w wx" with both commands using the second
lag of w as a gmm-style instrument. The results are exactly the same.

3. I include the interaction in the set of gmm-style instruments. In
theory, the number of instruments should not change. However, while
xtbond2 uses the same instrument set, xtdpd includes one more
instrument. The coefficient estimates differ.

use http://www.stata-press.com/data/r7/abdata.dta

. gen dum = 0

. replace dum=1 if year>1980

. gen wxdum = w*dum

. xtabond2 n w wxdum, gmm(w, l(2 2)) twostep robust nolevel
Favoring speed over space. To switch, type or click on mata: mata set
matafavor space, perm.

Dynamic panel-data estimation, two-step difference GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =       891
Time variable : year                            Number of groups   =       140
Number of instruments = 7                       Obs per group: min =         6
Wald chi2(2)  =     79.80                                      avg =      6.36
Prob > chi2   =     0.000                                      max =         8
------------------------------------------------------------------------------
|              Corrected
n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
w |  -2.353727   .3606461    -6.53   0.000    -3.060581   -1.646874
wxdum |  -.0129464   .0072152    -1.79   0.073    -.0270881    .0011952
------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.w
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -0.14  Pr > z =  0.888
Arellano-Bond test for AR(2) in first differences: z =   1.49  Pr > z =  0.137
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(5)    =   7.21  Prob > chi2 =  0.206
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(5)    =   8.31  Prob > chi2 =  0.140
(Robust, but can be weakened by many instruments.)

. xtdpd n w wxdum, dgmmiv(w, l(2 2)) twostep vce(robust) nocons

Dynamic panel-data estimation                Number of obs         =       891
Group variable: id                           Number of groups      =       140
Time variable: year
Obs per group:    min =         6
avg =  6.364286
max =         8

Number of instruments =      7               Wald chi2(2)          =     79.80
Prob > chi2           =    0.0000
Two-step results
------------------------------------------------------------------------------
|              WC-Robust
n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
w |  -2.353727   .3606461    -6.53   0.000    -3.060581   -1.646874
wxdum |  -.0129464   .0072152    -1.79   0.073    -.0270881    .0011952
------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/2).w

. xtabond2 n w wxdum, gmm(w wxdum, l(2 2)) twostep robust nolevel
Favoring speed over space. To switch, type or click on mata: mata set
matafavor space, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix
for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step difference GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =       891
Time variable : year                            Number of groups   =       140
Number of instruments = 7                       Obs per group: min =         6
Wald chi2(2)  =     79.80                                      avg =      6.36
Prob > chi2   =     0.000                                      max =         8
------------------------------------------------------------------------------
|              Corrected
n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
w |  -2.353727   .3606461    -6.53   0.000    -3.060581   -1.646874
wxdum |  -.0129464   .0072152    -1.79   0.073    -.0270881    .0011952
------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.(w wxdum)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -0.14  Pr > z =  0.888
Arellano-Bond test for AR(2) in first differences: z =   1.49  Pr > z =  0.137
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(5)    =   7.21  Prob > chi2 =  0.206
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(5)    =   8.31  Prob > chi2 =  0.140
(Robust, but can be weakened by many instruments.)

. xtdpd n w wxdum, dgmmiv(w wxdum, l(2 2)) twostep vce(robust) nocons

Dynamic panel-data estimation                Number of obs         =       891
Group variable: id                           Number of groups      =       140
Time variable: year
Obs per group:    min =         6
avg =  6.364286
max =         8

Number of instruments =      8               Wald chi2(2)          =     80.04
Prob > chi2           =    0.0000
Two-step results
------------------------------------------------------------------------------
|              WC-Robust
n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
w |  -2.351772   .3582057    -6.57   0.000    -3.053842   -1.649701
wxdum |  -.0129616   .0071573    -1.81   0.070    -.0269896    .0010663
------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/2).w L(2/2).wxdum

-----------------------------------------------------------------------------------------------------------------------------

On Sat, Sep 18, 2010 at 6:37 PM, David Roodman (droodman@cgdev.org)
<DRoodman@cgdev.org> wrote:
> I'm not sure what is causing the discrepancy. I stripped down Daniel's example to something simpler that still generates a discrepancy, and then ran the equivalent in DPD for Ox (Doornik, Arrelano, and Bond 2001). DPD agrees with xtabond2. However, the last time something like that happened (http://www.stata.com/statalist/archive/2010-01/msg00432.html), it turned out that the problem was DPD *and* xtabond2. (I used DPD as my benchmark in writing xtabond2.) Below are the runs from xtdpd, xtabond2, and DPD:
>
> . xtdpd n w, dgmmiv(w k, l(2 2)) nocons
>
> Dynamic panel-data estimation                Number of obs         =       891
> Group variable: id                           Number of groups      =       140
> Time variable: year
>                                             Obs per group:    min =         6
>                                                               avg =  6.364286
>                                                               max =         8
>
> Number of instruments =     14               Wald chi2(1)          =    323.67
>                                             Prob > chi2           =    0.0000
> One-step results
> ------------------------------------------------------------------------------
>           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           w |   -2.77159    .154056   -17.99   0.000    -3.073534   -2.469646
> ------------------------------------------------------------------------------
> Instruments for differenced equation
>        GMM-type: L(2/2).w L(2/2).k
>
> . xtabond2 n w, gmm(w k, l(2 2)) nolevel
> Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
>
> Dynamic panel-data estimation, one-step difference GMM
> ------------------------------------------------------------------------------
> Group variable: id                              Number of obs      =       891
> Time variable : year                            Number of groups   =       140
> Number of instruments = 14                      Obs per group: min =         6
> Wald chi2(1)  =    312.84                                      avg =      6.36
> Prob > chi2   =     0.000                                      max =         8
> ------------------------------------------------------------------------------
>           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           w |  -2.878515    .162745   -17.69   0.000    -3.197489   -2.559541
> ------------------------------------------------------------------------------
> Instruments for first differences equation
>  GMM-type (missing=0, separate instruments for each period unless collapsed)
>    L2.(w k)
> ------------------------------------------------------------------------------
> Arellano-Bond test for AR(1) in first differences: z =  -1.32  Pr > z =  0.186
> Arellano-Bond test for AR(2) in first differences: z =   0.64  Pr > z =  0.524
> ------------------------------------------------------------------------------
> Sargan test of overid. restrictions: chi2(13)   =  46.13  Prob > chi2 =  0.000
>  (Not robust, but not weakened by many instruments.)
>
>
>
> DPD code:
> #include <oxstd.h>
> #import <packages/dpd/dpd>
>
> main()
> {
>    decl dpd = new DPD(), time = timer(), x;
>
>
>        dpd.SetYear("YEAR");      // specify columns with years
>        dpd.SetGroup("IND");
>
>        dpd.Select(Y_VAR, {"n", 0, 0});      // formulate model
>        dpd.Select(X_VAR, {"w", 0, 0});      // formulate model
>    dpd.SetDummies(D_NONE); // specify dummies
>        dpd.SetOptions(FALSE, -1, -1, -1); // request classical standard errors
>    dpd.Gmm("w", 2, 2);            // GMM-type instruments
>    dpd.Gmm("k", 2, 2);            // GMM-type instruments
>
>    dpd.SetTest(1, 2); // specification,Sargan,AR 1-2 tests
>
>        dpd.SetMethod(M_1STEP);
>        dpd.Estimate();
>
>    delete dpd;                     // finished with object
> }
>
> DPD results:
> DPD package version 1.24, object created on 18-09-2010
>
> DPD( 1) Modelling n by 1-step (using abdata.in7)
>
>                  ----   1-step estimation using DPD ----
>                  Coefficient  Std.Error  t-value  t-prob
> Dw                   -2.87851     0.1628    -17.7   0.000
>
> sigma               0.2478555  sigma^2            0.06143233
> sigma levels        0.1752603
> no. of observations       891  no. of parameters           1
> Warning: standard errors not robust to heteroscedasticity
>
> Transformation used:      first differences
> Level instruments:        Gmm("w",2,2)  Gmm("k",2,2)
>
> constant:                  no  time dummies:               0
> number of individuals     140 (derived from year)
> longest time series         8 [1977 - 1984]
> shortest time series        6 (unbalanced panel)
>
> Wald (joint):    Chi^2(1) =     312.5 [0.000] **
> Sargan test:    Chi^2(13) =     46.08 [0.000] **
> AR(1) test:        N(0,1) =    -1.323 [0.186]
> AR(2) test:        N(0,1) =    0.6374 [0.524]
>
>
> -------------------------------------------------
>
> From      Daniel Borowczyk Martins <stata.danielbm@gmail.com>
> To        statalist@hsphsun2.harvard.edu
> Subject           st: discrepancy xtdpd vs xtabond2
> Date      Fri, 17 Sep 2010 09:55:50 +0100
>
> Dear Stata users,
>
> I believe stata's xtdpd and Roodman's xtabond2 produce different
> results when estimating a just-identified model.
>
> Below I present a set of estimations of the same model using
> alternatively xtabond2 and xtdpd and abdata.dta . All estimation
> generate the same coefficient estimates, except for the
> just-identified model (the last three tables below). I can't figure
> out what's going on. Do you have suggestion?
>
> . xtdpd n w k yr*, dgmmiv(w k, l(2 10)) div( yr*) vce(robust) twostep nocons
> note: yr1976 dropped from div() because of collinearity
> note: D.yr1976 dropped because of collinearity
>
> Dynamic panel-data estimation                Number of obs         =       891
> Group variable: id                           Number of groups      =       140
> Time variable: year
>                                             Obs per group:    min =         6
>                                                               avg =  6.364286
>                                                               max =         8
>
> Number of instruments =     64               Wald chi2(10)         =    263.63
>                                             Prob > chi2           =    0.0000
> Two-step results
> ------------------------------------------------------------------------------
>             |              WC-Robust
>           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           w |  -.5251849   .1867368    -2.81   0.005    -.8911822   -.1591875
>           k |   .6931066   .1156379     5.99   0.000     .4664605    .9197527
>      yr1977 |  -.0468811   .0224064    -2.09   0.036    -.0907969   -.0029653
>      yr1978 |   -.079391   .0260936    -3.04   0.002    -.1305336   -.0282485
>      yr1979 |  -.0908402   .0294539    -3.08   0.002    -.1485689   -.0331115
>      yr1980 |  -.1082455    .028502    -3.80   0.000    -.1641083   -.0523827
>      yr1981 |  -.1367655   .0256726    -5.33   0.000    -.1870828   -.0864482
>      yr1982 |  -.1329874   .0307649    -4.32   0.000    -.1932854   -.0726893
>      yr1983 |  -.1100415   .0381101    -2.89   0.004     -.184736    -.035347
>      yr1984 |  -.0741515   .0441612    -1.68   0.093    -.1607057    .0124028
> ------------------------------------------------------------------------------
> Instruments for differenced equation
>        GMM-type: L(2/10).w L(2/10).k
>        Standard: D.yr1977 D.yr1978 D.yr1979 D.yr1980 D.yr1981
> D.yr1982 D.yr1983 D.yr1984
>
> . drop _est_dpd _est_ab2
>
> . estimates store dpd
>
> . xtabond2 n w k yr*, gmm(w k, l(2 10)) iv(yr*) robust twostep nolevel
> Favoring speed over space. To switch, type or click on mata: mata set
> matafavor space, perm.
> yr1984 dropped due to collinearity
> Warning: Two-step estimated covariance matrix of moments is singular.
>  Using a generalized inverse to calculate optimal weighting matrix
> for two-step estimation.
>  Difference-in-Sargan/Hansen statistics may be negative.
>
> Dynamic panel-data estimation, two-step difference GMM
> ------------------------------------------------------------------------------
> Group variable: id                              Number of obs      =       891
> Time variable : year                            Number of groups   =       140
> Number of instruments = 64                      Obs per group: min =         6
> Wald chi2(10) =    263.63                                      avg =      6.36
> Prob > chi2   =     0.000                                      max =         8
> ------------------------------------------------------------------------------
>             |              Corrected
>           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           w |  -.5251849   .1867368    -2.81   0.005    -.8911822   -.1591875
>           k |   .6931066   .1156379     5.99   0.000     .4664605    .9197527
>      yr1976 |   .0741515   .0441612     1.68   0.093    -.0124028    .1607057
>      yr1977 |   .0272704    .046981     0.58   0.562    -.0648106    .1193514
>      yr1978 |  -.0052396   .0514405    -0.10   0.919    -.1060611     .095582
>      yr1979 |  -.0166887   .0541152    -0.31   0.758    -.1227526    .0893751
>      yr1980 |   -.034094   .0519545    -0.66   0.512     -.135923     .067735
>      yr1981 |  -.0626141     .03934    -1.59   0.111    -.1397191     .014491
>      yr1982 |  -.0588359   .0246208    -2.39   0.017    -.1070917   -.0105801
>      yr1983 |    -.03589   .0152096    -2.36   0.018    -.0657003   -.0060797
> ------------------------------------------------------------------------------
> Instruments for first differences equation
>  Standard
>    D.(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
>  GMM-type (missing=0, separate instruments for each period unless collapsed)
>    L(2/10).(w k)
> ------------------------------------------------------------------------------
> Arellano-Bond test for AR(1) in first differences: z =  -0.40  Pr > z =  0.689
> Arellano-Bond test for AR(2) in first differences: z =  -1.70  Pr > z =  0.088
> ------------------------------------------------------------------------------
> Sargan test of overid. restrictions: chi2(54)   = 100.69  Prob > chi2 =  0.000
>  (Not robust, but not weakened by many instruments.)
> Hansen test of overid. restrictions: chi2(54)   =  61.06  Prob > chi2 =  0.237
>  (Robust, but can be weakened by many instruments.)
>
> Difference-in-Hansen tests of exogeneity of instrument subsets:
>  iv(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
>    Hansen test excluding group:     chi2(46)   =  51.97  Prob > chi2 =  0.253
>    Difference (null H = exogenous): chi2(8)    =   9.09  Prob > chi2 =  0.335
>
> . estimates store ab2
>
> . esttab dpd ab2
>
> --------------------------------------------
>                      (1)             (2)
>                        n               n
> --------------------------------------------
> w                  -0.525**        -0.525**
>                  (-2.81)         (-2.81)
>
> k                   0.693***        0.693***
>                   (5.99)          (5.99)
>
> yr1977            -0.0469*         0.0273
>                  (-2.09)          (0.58)
>
> yr1978            -0.0794**      -0.00524
>                  (-3.04)         (-0.10)
>
> yr1979            -0.0908**       -0.0167
>                  (-3.08)         (-0.31)
>
> yr1980             -0.108***      -0.0341
>                  (-3.80)         (-0.66)
>
> yr1981             -0.137***      -0.0626
>                  (-5.33)         (-1.59)
>
> yr1982             -0.133***      -0.0588*
>                  (-4.32)         (-2.39)
>
> yr1983             -0.110**       -0.0359*
>                  (-2.89)         (-2.36)
>
> yr1984            -0.0742
>                  (-1.68)
>
> yr1976                             0.0742
>                                   (1.68)
> --------------------------------------------
> N                     891             891
> --------------------------------------------
> t statistics in parentheses
> * p<0.05, ** p<0.01, *** p<0.001
>
> . drop  _est_dpd _est_ab2
>
> . xtdpd n w k yr*, dgmmiv(w k, l(2 3)) div( yr*) vce(robust) twostep nocons
> note: yr1976 dropped from div() because of collinearity
> note: D.yr1976 dropped because of collinearity
>
> Dynamic panel-data estimation                Number of obs         =       891
> Group variable: id                           Number of groups      =       140
> Time variable: year
>                                             Obs per group:    min =         6
>                                                               avg =  6.364286
>                                                               max =         8
>
> Number of instruments =     34               Wald chi2(10)         =    345.89
>                                             Prob > chi2           =    0.0000
> Two-step results
> ------------------------------------------------------------------------------
>             |              WC-Robust
>           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           w |  -.3776668   .2218938    -1.70   0.089    -.8125707    .0572371
>           k |   .5092317   .1684431     3.02   0.003     .1790893    .8393742
>      yr1977 |  -.0312372   .0242268    -1.29   0.197     -.078721    .0162465
>      yr1978 |  -.0533206   .0304038    -1.75   0.079    -.1129109    .0062697
>      yr1979 |  -.0617977   .0331106    -1.87   0.062    -.1266932    .0030978
>      yr1980 |  -.0896192    .032657    -2.74   0.006    -.1536258   -.0256127
>      yr1981 |  -.1448843   .0292449    -4.95   0.000    -.2022033   -.0875652
>      yr1982 |  -.1697914   .0378177    -4.49   0.000    -.2439128   -.0956701
>      yr1983 |  -.1665457   .0492459    -3.38   0.001    -.2630659   -.0700256
>      yr1984 |  -.1511347   .0648747    -2.33   0.020    -.2782867   -.0239827
> ------------------------------------------------------------------------------
> Instruments for differenced equation
>        GMM-type: L(2/3).w L(2/3).k
>        Standard: D.yr1977 D.yr1978 D.yr1979 D.yr1980 D.yr1981
> D.yr1982 D.yr1983 D.yr1984
>
> . estimates store dpd
>
> . xtabond2 n w k yr*, gmm(w k, l(2 3)) iv(yr*) robust twostep nolevel
> Favoring speed over space. To switch, type or click on mata: mata set
> matafavor space, perm.
> yr1984 dropped due to collinearity
> Warning: Two-step estimated covariance matrix of moments is singular.
>  Using a generalized inverse to calculate optimal weighting matrix
> for two-step estimation.
>  Difference-in-Sargan/Hansen statistics may be negative.
>
> Dynamic panel-data estimation, two-step difference GMM
> ------------------------------------------------------------------------------
> Group variable: id                              Number of obs      =       891
> Time variable : year                            Number of groups   =       140
> Number of instruments = 34                      Obs per group: min =         6
> Wald chi2(10) =    345.89                                      avg =      6.36
> Prob > chi2   =     0.000                                      max =         8
> ------------------------------------------------------------------------------
>             |              Corrected
>           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           w |  -.3776668   .2218938    -1.70   0.089    -.8125707    .0572371
>           k |   .5092317   .1684431     3.02   0.003     .1790893    .8393742
>      yr1976 |   .1511347   .0648747     2.33   0.020     .0239827    .2782867
>      yr1977 |   .1198974   .0689463     1.74   0.082    -.0152348    .2550297
>      yr1978 |   .0978141   .0758716     1.29   0.197    -.0508914    .2465197
>      yr1979 |    .089337   .0789305     1.13   0.258     -.065364     .244038
>      yr1980 |   .0615155   .0736248     0.84   0.403    -.0827866    .2058175
>      yr1981 |   .0062504   .0554414     0.11   0.910    -.1024127    .1149135
>      yr1982 |  -.0186567   .0355157    -0.53   0.599    -.0882662    .0509527
>      yr1983 |   -.015411   .0205404    -0.75   0.453    -.0556695    .0248474
> ------------------------------------------------------------------------------
> Instruments for first differences equation
>  Standard
>    D.(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
>  GMM-type (missing=0, separate instruments for each period unless collapsed)
>    L(2/3).(w k)
> ------------------------------------------------------------------------------
> Arellano-Bond test for AR(1) in first differences: z =   0.44  Pr > z =  0.660
> Arellano-Bond test for AR(2) in first differences: z =  -0.86  Pr > z =  0.390
> ------------------------------------------------------------------------------
> Sargan test of overid. restrictions: chi2(24)   =  43.27  Prob > chi2 =  0.009
>  (Not robust, but not weakened by many instruments.)
> Hansen test of overid. restrictions: chi2(24)   =  25.01  Prob > chi2 =  0.405
>  (Robust, but can be weakened by many instruments.)
>
> Difference-in-Hansen tests of exogeneity of instrument subsets:
>  iv(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
>    Hansen test excluding group:     chi2(16)   =  16.30  Prob > chi2 =  0.432
>    Difference (null H = exogenous): chi2(8)    =   8.71  Prob > chi2 =  0.367
>
> . estimates store ab2
>
> . esttab dpd ab2
>
> --------------------------------------------
>                      (1)             (2)
>                        n               n
> --------------------------------------------
> w                  -0.378          -0.378
>                  (-1.70)         (-1.70)
>
> k                   0.509**         0.509**
>                   (3.02)          (3.02)
>
> yr1977            -0.0312           0.120
>                  (-1.29)          (1.74)
>
> yr1978            -0.0533          0.0978
>                  (-1.75)          (1.29)
>
> yr1979            -0.0618          0.0893
>                  (-1.87)          (1.13)
>
> yr1980            -0.0896**        0.0615
>                  (-2.74)          (0.84)
>
> yr1981             -0.145***      0.00625
>                  (-4.95)          (0.11)
>
> yr1982             -0.170***      -0.0187
>                  (-4.49)         (-0.53)
>
> yr1983             -0.167***      -0.0154
>                  (-3.38)         (-0.75)
>
> yr1984             -0.151*
>                  (-2.33)
>
> yr1976                              0.151*
>                                   (2.33)
> --------------------------------------------
> N                     891             891
> --------------------------------------------
> t statistics in parentheses
> * p<0.05, ** p<0.01, *** p<0.001
>
>
> . xtdpd n w k yr*, dgmmiv(w k, l(2 2)) div( yr*) vce(robust) twostep nocons
> note: yr1976 dropped from div() because of collinearity
> note: D.yr1976 dropped because of collinearity
>
> Dynamic panel-data estimation                Number of obs         =       891
> Group variable: id                           Number of groups      =       140
> Time variable: year
>                                             Obs per group:    min =         6
>                                                               avg =  6.364286
>                                                               max =         8
>
> Number of instruments =     22               Wald chi2(10)         =    282.19
>                                             Prob > chi2           =    0.0000
> Two-step results
> ------------------------------------------------------------------------------
>             |              WC-Robust
>           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           w |  -.5975386     .22683    -2.63   0.008    -1.042117     -.15296
>           k |   .8595294   .2587153     3.32   0.001     .3524567    1.366602
>      yr1977 |  -.0548315   .0248217    -2.21   0.027    -.1034811   -.0061819
>      yr1978 |  -.0999575   .0341455    -2.93   0.003    -.1668814   -.0330336
>      yr1979 |  -.1194597   .0385212    -3.10   0.002      -.19496   -.0439595
>      yr1980 |    -.12629   .0349355    -3.61   0.000    -.1947623   -.0578176
>      yr1981 |  -.1332924   .0315413    -4.23   0.000    -.1951123   -.0714726
>      yr1982 |  -.1101542   .0543083    -2.03   0.043    -.2165964   -.0037119
>      yr1983 |   -.073628   .0737858    -1.00   0.318    -.2182454    .0709895
>      yr1984 |   -.038052   .0967039    -0.39   0.694    -.2275881    .1514842
> ------------------------------------------------------------------------------
> Instruments for differenced equation
>        GMM-type: L(2/2).w L(2/2).k
>        Standard: D.yr1977 D.yr1978 D.yr1979 D.yr1980 D.yr1981
> D.yr1982 D.yr1983 D.yr1984
>
> . estimates store dpd
>
> . xtabond2 n w k yr*, gmm(w k, l(2 2)) iv(yr*) robust twostep nolevel
> Favoring speed over space. To switch, type or click on mata: mata set
> matafavor space, perm.
> yr1984 dropped due to collinearity
> Warning: Two-step estimated covariance matrix of moments is singular.
>  Using a generalized inverse to calculate optimal weighting matrix
> for two-step estimation.
>  Difference-in-Sargan/Hansen statistics may be negative.
>
> Dynamic panel-data estimation, two-step difference GMM
> ------------------------------------------------------------------------------
> Group variable: id                              Number of obs      =       891
> Time variable : year                            Number of groups   =       140
> Number of instruments = 22                      Obs per group: min =         6
> Wald chi2(10) =    265.24                                      avg =      6.36
> Prob > chi2   =     0.000                                      max =         8
> ------------------------------------------------------------------------------
>             |              Corrected
>           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>           w |  -.5482155   .1914433    -2.86   0.004    -.9234375   -.1729936
>           k |   .7211971   .3095853     2.33   0.020     .1144209    1.327973
>      yr1976 |   .0840834   .1057541     0.80   0.427    -.1231909    .2913577
>      yr1977 |   .0351314   .1117762     0.31   0.753    -.1839458    .2542087
>      yr1978 |  -.0016077   .1249189    -0.01   0.990    -.2464443    .2432289
>      yr1979 |   -.017301   .1322428    -0.13   0.896    -.2764921    .2418901
>      yr1980 |  -.0296638   .1200275    -0.25   0.805    -.2649135    .2055858
>      yr1981 |   -.051615     .08634    -0.60   0.550    -.2208382    .1176082
>      yr1982 |  -.0477458   .0482995    -0.99   0.323     -.142411    .0469194
>      yr1983 |   -.025815   .0244998    -1.05   0.292    -.0738337    .0222037
> ------------------------------------------------------------------------------
> Instruments for first differences equation
>  Standard
>    D.(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
>  GMM-type (missing=0, separate instruments for each period unless collapsed)
>    L2.(w k)
> ------------------------------------------------------------------------------
> Arellano-Bond test for AR(1) in first differences: z =  -0.48  Pr > z =  0.631
> Arellano-Bond test for AR(2) in first differences: z =  -1.36  Pr > z =  0.173
> ------------------------------------------------------------------------------
> Sargan test of overid. restrictions: chi2(12)   =  28.17  Prob > chi2 =  0.005
>  (Not robust, but not weakened by many instruments.)
> Hansen test of overid. restrictions: chi2(12)   =  14.79  Prob > chi2 =  0.253
>  (Robust, but can be weakened by many instruments.)
>
> Difference-in-Hansen tests of exogeneity of instrument subsets:
>  iv(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
>    Hansen test excluding group:     chi2(4)    =   5.46  Prob > chi2 =  0.243
>    Difference (null H = exogenous): chi2(8)    =   9.33  Prob > chi2 =  0.315
>
> . estimates store ab2
>
> . esttab dpd ab2
>
> --------------------------------------------
>                      (1)             (2)
>                        n               n
> --------------------------------------------
> w                  -0.598**        -0.548**
>                  (-2.63)         (-2.86)
>
> k                   0.860***        0.721*
>                   (3.32)          (2.33)
>
> yr1977            -0.0548*         0.0351
>                  (-2.21)          (0.31)
>
> yr1978            -0.1000**      -0.00161
>                  (-2.93)         (-0.01)
>
> yr1979             -0.119**       -0.0173
>                  (-3.10)         (-0.13)
>
> yr1980             -0.126***      -0.0297
>                  (-3.61)         (-0.25)
>
> yr1981             -0.133***      -0.0516
>                  (-4.23)         (-0.60)
>
> yr1982             -0.110*        -0.0477
>                  (-2.03)         (-0.99)
>
> yr1983            -0.0736         -0.0258
>                  (-1.00)         (-1.05)
>
> yr1984            -0.0381
>                  (-0.39)
>
> yr1976                             0.0841
>                                   (0.80)
> --------------------------------------------
> N                     891             891
> --------------------------------------------
> t statistics in parentheses
> * p<0.05, ** p<0.01, *** p<0.001
>
> Daniel
>
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

*
*   For searches and help try:
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```