xtabond2 with forward value of dependent variable

[Marco Tacchi]

Hello,

I'm estimating a model with the independent variables lagged one year with respect to the dependent variable. In Stata, it can be done with the forward operator, f.y, instead of using lag operators for all independent variables.
xtreg f.y i.year x1 x2 x3, fe robust
That is identical to
xtreg y i.year l.(x1 x2 x3), fe robust

I was wondering if using the forward operator would work for xtabond2. For example, would this syntax
xtabond2 f.y y i.year x1 x2 x3, gmm(y x1 x2 x3, lag(1 .) collapse) iv(i.year) robust twostep
be equated to this one
xtabond2 y l.y i.year l.(x1 x2 x3), gmm(l.y l.(x1 x2 x3), lag(1 .) collapse) iv(i.year) robust twostep

I have checked on my dataset and the results slightly differ. The same size is the same, but not the effect sizes and their standard errors.

Would be grateful for any help with this.

[Andrew Musau]

xtabond2 is from SSC, as you are asked to explain in FAQ Advice #12. You are not lagging the year dummies, so the specifications are not equivalent. Factor variables and time-series operators cannot be combined, implying that you'd need to revert to the xi: prefix to replicate the regression with a lead dependent variable.

webuse abdata, clear
xtabond2 F.wage wage emp cap i.year, gmm(wage emp cap, lag(1 .)) iv(i.year) robust twostep
xi: xtabond2 wage L.(wage emp cap i.year), gmm(L.(wage emp cap), lag(1 .)) iv(L.(i.year)) robust twostep

Res.:

. xtabond2 F.wage wage emp cap i.year, gmm(wage emp cap, lag(1 .)) iv(i.year) robust twostep
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
1976b.year dropped due to collinearity
1984.year 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 system GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =       891
Time variable : year                            Number of groups   =       140
Number of instruments = 113                     Obs per group: min =         6
Wald chi2(10) =  48978.15                                      avg =      6.36
Prob > chi2   =     0.000                                      max =         8
------------------------------------------------------------------------------
             |              Corrected
      F.wage | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
        wage |    .730943   .0761746     9.60   0.000     .5816435    .8802424
         emp |  -.0303798   .0130557    -2.33   0.020    -.0559686   -.0047911
         cap |    .076475   .0237867     3.22   0.001     .0298541     .123096
             |
        year |
       1977  |   .9595188   .2715415     3.53   0.000     .4273072     1.49173
       1978  |   1.510568   .3094509     4.88   0.000     .9040551     2.11708
       1979  |   1.417334   .2842273     4.99   0.000     .8602588    1.974409
       1980  |   2.129389   .3125112     6.81   0.000     1.516878    2.741899
       1981  |   2.582254   .3037354     8.50   0.000     1.986944    3.177565
       1982  |   2.385963   .3188669     7.48   0.000     1.760995    3.010931
       1983  |   1.673695   .4314453     3.88   0.000     .8280777    2.519312
             |
       _cons |   4.879062   2.003949     2.43   0.015     .9513932     8.80673
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(1976b.year 1977.year 1978.year 1979.year 1980.year 1981.year 1982.year
    1983.year 1984.year)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/8).(wage emp cap)
Instruments for levels equation
  Standard
    1976b.year 1977.year 1978.year 1979.year 1980.year 1981.year 1982.year
    1983.year 1984.year
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(wage emp cap)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.00  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   0.82  Pr > z =  0.413
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(102)  = 268.32  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(102)  = 113.03  Prob > chi2 =  0.214
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(81)   = 101.52  Prob > chi2 =  0.061
    Difference (null H = exogenous): chi2(21)   =  11.51  Prob > chi2 =  0.952
  iv(1976b.year 1977.year 1978.year 1979.year 1980.year 1981.year 1982.year 1983.year 1984.year)
    Hansen test excluding group:     chi2(95)   = 104.46  Prob > chi2 =  0.238
    Difference (null H = exogenous): chi2(7)    =   8.57  Prob > chi2 =  0.285


.
. xi: xtabond2 wage L.(wage emp cap i.year), gmm(L.(wage emp cap), lag(1 .)) iv(L.(i.year)) robust twostep
i.year            _Iyear_1976-1984    (naturally coded; _Iyear_1976 omitted)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
L._Iyear_1984 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 system GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =       891
Time variable : year                            Number of groups   =       140
Number of instruments = 113                     Obs per group: min =         6
Wald chi2(10) =  48978.15                                      avg =      6.36
Prob > chi2   =     0.000                                      max =         8
------------------------------------------------------------------------------
             |              Corrected
        wage | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
        wage |
         L1. |    .730943   .0761746     9.60   0.000     .5816435    .8802424
             |
         emp |
         L1. |  -.0303798   .0130557    -2.33   0.020    -.0559686   -.0047911
             |
         cap |
         L1. |    .076475   .0237866     3.22   0.001     .0298541     .123096
             |
 _Iyear_1977 |
         L1. |   .9595188   .2715415     3.53   0.000     .4273072     1.49173
             |
 _Iyear_1978 |
         L1. |   1.510568   .3094509     4.88   0.000     .9040551     2.11708
             |
 _Iyear_1979 |
         L1. |   1.417334   .2842273     4.99   0.000     .8602588    1.974409
             |
 _Iyear_1980 |
         L1. |   2.129389   .3125112     6.81   0.000     1.516878    2.741899
             |
 _Iyear_1981 |
         L1. |   2.582254   .3037354     8.50   0.000     1.986944    3.177565
             |
 _Iyear_1982 |
         L1. |   2.385963   .3188669     7.48   0.000     1.760995    3.010931
             |
 _Iyear_1983 |
         L1. |   1.673695   .4314453     3.88   0.000     .8280777    2.519312
             |
       _cons |   4.879062   2.003949     2.43   0.015     .9513932     8.80673
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(L._Iyear_1977 L._Iyear_1978 L._Iyear_1979 L._Iyear_1980 L._Iyear_1981
    L._Iyear_1982 L._Iyear_1983 L._Iyear_1984)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/8).(L.wage L.emp L.cap)
Instruments for levels equation
  Standard
    L._Iyear_1977 L._Iyear_1978 L._Iyear_1979 L._Iyear_1980 L._Iyear_1981
    L._Iyear_1982 L._Iyear_1983 L._Iyear_1984
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(L.wage L.emp L.cap)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.00  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   0.82  Pr > z =  0.413
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(102)  = 268.32  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(102)  = 113.03  Prob > chi2 =  0.214
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(81)   = 101.52  Prob > chi2 =  0.061
    Difference (null H = exogenous): chi2(21)   =  11.51  Prob > chi2 =  0.952
  iv(L._Iyear_1977 L._Iyear_1978 L._Iyear_1979 L._Iyear_1980 L._Iyear_1981 L._Iyear_1982 L._Iyear_1983 L._Iyear_1984)
    Hansen test excluding group:     chi2(95)   = 104.46  Prob > chi2 =  0.238
    Difference (null H = exogenous): chi2(7)    =   8.57  Prob > chi2 =  0.285


.

[Marco Tacchi]

Thank you, Andrew! Understood and much appreciated.