xtabond2: change in results when dropping the first two periods

[Nicolas Van de Sijpe]

Hi everyone,

I am using xtabond2 to run difference and system GMM regressions. I'm working in Stata version 15.1, and I'm using, as far as I can tell, the most recent version of xtabond2 (3.6.3 30 September 2015).

I was hoping someone would be able to help me understand why results change when I run a system GMM regression and drop the first 2 periods in the data. In the example below I use twice lagged levels as instruments for the differenced equations, and once lagged differences as instruments for the equations in levels. Since constructing these instruments requires observations in t-2, I assumed that excluding the first two periods would not affect results. However, the example below, based on Arellano and Bond’s data, seems to suggest otherwise. This is an annual dataset of firms for the period 1976-1984. As you can see, excluding years 1976 and 1977 changes results.

. clear all
. webuse abdata
. xtabond2 n L.n w k, gmm(n w k, laglimits(2 2) collapse) twostep robust small svmat
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.

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 = 7                       Obs per group: min =         6
F(3, 139)     =    196.28                                      avg =      6.36
Prob > F      =     0.000                                      max =         8
------------------------------------------------------------------------------
             |              Corrected
           n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .6422413   .2478509     2.59   0.011     .1521961    1.132286
             |
           w |  -1.031833    .402151    -2.57   0.011    -1.826957   -.2367086
           k |   .2615404   .0976378     2.68   0.008     .0684931    .4545878
       _cons |   3.701805   1.545091     2.40   0.018     .6468852    6.756725
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L2.(n w k) collapsed
Instruments for levels equation
  Standard
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(n w k) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.66  Pr > z =  0.008
Arellano-Bond test for AR(2) in first differences: z =  -1.35  Pr > z =  0.176
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(3)    =   6.86  Prob > chi2 =  0.077
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(3)    =   2.40  Prob > chi2 =  0.494
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(3)    =   2.40  Prob > chi2 =  0.494

* MODEL WITH FIRST TWO PERIODS EXCLUDED
. xtabond2 n L.n w k if year > 1977, gmm(n w k, laglimits(2 2) collapse) twostep robust small svmat
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =       811
Time variable : year                            Number of groups   =       140
Number of instruments = 7                       Obs per group: min =         5
F(3, 139)     =    214.70                                      avg =      5.79
Prob > F      =     0.000                                      max =         7
------------------------------------------------------------------------------
             |              Corrected
           n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .6765348   .2384935     2.84   0.005     .2049907    1.148079
             |
           w |  -.9759851   .3861351    -2.53   0.013    -1.739443   -.2125274
           k |   .2468775   .0970336     2.54   0.012     .0550248    .4387303
       _cons |   3.476404   1.482807     2.34   0.020     .5446311    6.408178
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L2.(n w k) collapsed
Instruments for levels equation
  Standard
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(n w k) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.73  Pr > z =  0.006
Arellano-Bond test for AR(2) in first differences: z =  -1.40  Pr > z =  0.161
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(3)    =   8.12  Prob > chi2 =  0.044
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(3)    =   2.95  Prob > chi2 =  0.399
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(3)    =   2.95  Prob > chi2 =  0.399

I looked at the instrument matrix e(Z) in both cases. When the first two years are not dropped, the constant shows up as an instrument for the equation in levels in 1977 (_cons has a value of 1) while all the other instruments are "zeroed out". When the first two years are dropped, _cons takes on a value of 0 for the equation in levels in 1977, as do the other instruments. I paste an extract of the instrument matrices below, for the firm with id = 5 (as this is a firm with data going back to 1976). I highlight the discrepancy in red.

First estimation:

                          Diff eq:    Diff eq:    Diff eq:  Levels eq:  Levels eq:  Levels eq:
                               L2.         L2.         L2.         LD.         LD.         LD.
                _cons           n           w           k           n           w           k
  5, 1976           0           0           0           0           0           0           0
  5, 1977           0           0           0           0           0           0           0
  5, 1978           0   4.4621887   3.0268579   3.1081855           0           0           0
  5, 1979           0   4.4670568    2.905709   3.1032538           0           0           0
  5, 1980           0   4.4659081   2.8979485   3.2255337           0           0           0
  5, 1981           0   4.5042443   2.9008501   3.2328379           0           0           0
  5, 1982           0    4.490881   2.9595506   3.3407183           0           0           0
  5, 1983           0           0           0           0           0           0           0
  5, 1984           0           0           0           0           0           0           0
  5, 1976           0           0           0           0           0           0           0
  5, 1977           1           0           0           0           0           0           0
  5, 1978           1           0           0           0   .00486803  -.12114882  -.00493169
  5, 1979           1           0           0           0   -.0011487  -.00776052   .12227988
  5, 1980           1           0           0           0   .03833628   .00290155   .00730419
  5, 1981           1           0           0           0  -.01336336   .05870056   .10788035
  5, 1982           1           0           0           0  -.07566118   .02735281  -.09050274
  5, 1983           0           0           0           0           0           0           0
  5, 1984           0           0           0           0           0           0           0

Now with the first two periods excluded (second estimation):

                          Diff eq:    Diff eq:    Diff eq:  Levels eq:  Levels eq:  Levels eq:
                               L2.         L2.         L2.         LD.         LD.         LD.
                _cons           n           w           k           n           w           k
  5, 1976           0           0           0           0           0           0           0
  5, 1977           0           0           0           0           0           0           0
  5, 1978           0   4.4621887   3.0268579   3.1081855           0           0           0
  5, 1979           0   4.4670568    2.905709   3.1032538           0           0           0
  5, 1980           0   4.4659081   2.8979485   3.2255337           0           0           0
  5, 1981           0   4.5042443   2.9008501   3.2328379           0           0           0
  5, 1982           0    4.490881   2.9595506   3.3407183           0           0           0
  5, 1983           0           0           0           0           0           0           0
  5, 1984           0           0           0           0           0           0           0
  5, 1976           0           0           0           0           0           0           0
  5, 1977           0           0           0           0           0           0           0
  5, 1978           1           0           0           0   .00486803  -.12114882  -.00493169
  5, 1979           1           0           0           0   -.0011487  -.00776052   .12227988
  5, 1980           1           0           0           0   .03833628   .00290155   .00730419
  5, 1981           1           0           0           0  -.01336336   .05870056   .10788035
  5, 1982           1           0           0           0  -.07566118   .02735281  -.09050274
  5, 1983           0           0           0           0           0           0           0
  5, 1984           0           0           0           0           0           0           0

How should I interpret what is happening? I realise that GMM "zeroes out" missing values for the instruments but I thought this left the moment conditions, and hence results, unaffected? Or does this only leave results unchanged asymptotically? I was not expecting the zeroeing out to bring an extra year of data into play; it seems as if the equation in levels for 1977 is used as part of the estimation, using only the constant as an instrument? Here, the effect on results is small, but I have other examples where the changes in results are more substantial (e.g. a static version of the above model).

For difference GMM excluding the first two years makes no difference to results. Of course, when I use xtabond2 to estimate only the equation in levels then again results change when I drop the first two periods.

Perhaps this is also relevant: using xtabond2 to estimate a static model with system GMM on only the first two years in the dataset returns some results:

. xtabond2 n w k if year < 1978, gmm(w k, laglimits(2 2) collapse) twostep robust small svmat
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 system GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =       218
Time variable : year                            Number of groups   =       138
Number of instruments = 1                       Obs per group: min =         1
F(2, 137)     =     47.72                                      avg =      1.58
Prob > F      =     0.000                                      max =         2
------------------------------------------------------------------------------
             |              Corrected
           n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           w |     .37529   .0384159     9.77   0.000     .2993251    .4512549
           k |          0  (omitted)
       _cons |          0  (omitted)
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L2.(w k) collapsed
Instruments for levels equation
  Standard
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(w k) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =      .  Pr > z =      .
Arellano-Bond test for AR(2) in first differences: z =      .  Pr > z =      .
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(-2)   =   0.00  Prob > chi2 =      .
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(-2)   =   0.00  Prob > chi2 =      .
  (Robust, but weakened by many instruments.)

Here, the only available instrument is the constant for the equations in levels in 1976 and 1977 -- see this extract from the instrument matrix e(Z) (again for the firm with id = 5):

                          Diff eq:    Diff eq:  Levels eq:  Levels eq:
                               L2.         L2.         LD.         LD.
                _cons           w           k           w           k
  5, 1976           0           0           0           0           0
  5, 1977           0           0           0           0           0
  5, 1978           0           0           0           0           0
  5, 1979           0           0           0           0           0
  5, 1980           0           0           0           0           0
  5, 1981           0           0           0           0           0
  5, 1982           0           0           0           0           0
  5, 1983           0           0           0           0           0
  5, 1984           0           0           0           0           0
  5, 1976           1           0           0           0           0
  5, 1977           1           0           0           0           0
  5, 1978           0           0           0           0           0
  5, 1979           0           0           0           0           0
  5, 1980           0           0           0           0           0
  5, 1981           0           0           0           0           0
  5, 1982           0           0           0           0           0
  5, 1983           0           0           0           0           0
  5, 1984           0           0           0           0           0

I would be grateful for any comments/answers that can help me understand this issue better.

Best,

Nicolas

[Sven-Kristjan Bormann]

Hi,
your question has nothing to do with the -xtabond2- command.
You probably misunderstand how lagged values work in estimations.
The information of the lagged value is definitely needed in your example and it is not thrown away. It just means that it is not possible to estimate a model at time t-2 and t-1, because that would require the information from t-3 and t-4, which you don't have.
So why do you want to exclude the first two years from your data? These data points are needed as lagged values for the third year. If you drop them, then you just move the starting point for the "real" estimation two periods further and you lose information from these two years.

Since constructing these instruments requires observations in t-2, I assumed that excluding the first two periods would not affect results.

For me, it looks like you want to throw away the information for these instruments. Thereby you reduce your dataset and then you are surprised that your results change?
Why should the results stay the same if the dataset changes?

In your example, the years 1975 and 1976 are not dropped but used to construct the instruments and thereby included in the estimation sample. If you drop them, the years 1977 and 1978 are used to construct the instruments. Following your logic, you would drop them also, because you believe that these two years don't affect the results until your left only with the year 1984.

I hope that you understand where the problem lies in your argument about dropping the years.

[Nicolas Van de Sijpe]

Hi,

this answer is not correct, I'm afraid.

If your answer was correct then dropping the first two periods would also affect difference GMM estimation with xtabond2, since here I'm using the levels of variables in t-2 as instruments for the differenced equation in t. But, as I mentioned in my post, excluding the first two periods does not affect difference GMM results; it only affects estimation involving the equations in levels. Likewise, if I manually construct the instruments and add them as "ivstyle" instruments in xtabond2 then dropping the first two periods does not affect results even in estimation involving the equations in levels. The same is true when I use ivreg2 with the same set of instruments. So this is not a general issue to do with how lagged values work.

Also, as can be seen from the instrument matrices I posted, adding "if year > 1977" does not affect any of the instruments apart from the constant. Hence, it is not correct to say that this if restriction makes the observations from these periods unavailable as instruments to estimate the equations in later periods: you can see that the same instruments are listed for all equations from 1978 onwards with or without the if restriction; the only difference is in the constant.

Why should the results stay the same if the dataset changes?

These panel data GMM estimators use information in the data from two periods ago. In periods t=1 and t=2 this information is not available. Hence why I found it surprising that dropping these two periods would affect the results (as I explained above, dropping these two periods does not change results with IV estimation, either using xtabond2 with the ivstyle option or using ivreg2). When people write down the moment conditions for these estimators they tend to say these apply "for T>=3", since for earlier periods the moment conditions (under the assumptions I used in my example) are not available (see for instance Arellano and Bond's 1991 ReStud paper). As a result this if restriction is not throwing away any information or reducing the dataset, not in the way you suggest at least.

Best,

Nicolas

[Sebastian Kripfganz]

The misunderstanding lies in how the if-condition works. The if-condition restricts the estimation sample for the variables specified as depvar and indepvars but it does not have any effect on the instruments. As you have one lag of the dependent variable in your model, you lose one observation in your initial estimation sample without the if-condition. If you then exclude the first two years, the estimation sample is smaller. This is obvious when you compare the number of observations per group in the estimation header.

With the difference GMM estimator, you already lose two observations without the if-condition, one because of the lagged dependent variable and one because of the differencing. (The system GMM estimator retains this second observation as it remains useful in the levels equation.) Hence, excluding the first two observations with an if-condition does not affect the results here.

A related fact: Things become different if you actually drop the first observations from the data set (drop if year < 1978) because now these first two observations are no longer available to form the instruments. When you just use an if-condition instead, these first two observations are still available and will be used to construct the instruments. Hence, the estimations differ.

[Nicolas Van de Sijpe]

Thanks for your reply Sebastian. I agree with what you write, but I'm still somewhat unsure as to which is the "correct" approach, if that makes sense. In other words, is it valid that the equation in levels for t=2 is used (or even in t=1 for a static model), even though the only non-zero instrument available for this equation is the constant? My understanding is that:
- this doesn't imply a different set of moment conditions, yet it changes results.
- the motivation for using the equation in levels in t=2 (or even t=1, if the model is static) is that this is a better approach in the sense that it uses additional information/data to identify the constant, which then has ramifications for the other coefficients.

Does this sound correct to you? If so, then I'm still slightly puzzled as to why results sometimes change quite drastically when excluding the first two periods (I'd imagine any change would be expected to be quite minimal). Here's an example for a static model, using the same Arrelano-Bond dataset:

. xtabond2 n w k yr*, gmm(w k, laglimits(2 2) collapse) iv(yr*, eq(level)) twostep robust small svmat
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
yr1978 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      =      1031
Time variable : year                            Number of groups   =       140
Number of instruments = 13                      Obs per group: min =         7
F(10, 139)    =     18.85                                      avg =      7.36
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
             |              Corrected
           n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           w |   .8059706   .6852795     1.18   0.242    -.5489488     2.16089
           k |   .5744416   .1165374     4.93   0.000     .3440265    .8048566
      yr1976 |  -.0774801   .0808325    -0.96   0.339    -.2373003    .0823401
      yr1977 |  -.0039351   .0198999    -0.20   0.844    -.0432807    .0354105
      yr1979 |  -.0184471   .0100241    -1.84   0.068    -.0382666    .0013723
      yr1980 |   -.037578   .0153432    -2.45   0.016    -.0679142   -.0072418
      yr1981 |  -.1242844   .0382819    -3.25   0.001    -.1999744   -.0485943
      yr1982 |  -.1854961   .0733822    -2.53   0.013    -.3305858   -.0404064
      yr1983 |   -.204342   .1058369    -1.93   0.056    -.4136004    .0049164
      yr1984 |  -.3512506   .1438808    -2.44   0.016    -.6357286   -.0667726
       _cons |  -1.138611   2.152153    -0.53   0.598    -5.393799    3.116578
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L2.(w k) collapsed
Instruments for levels equation
  Standard
    yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(w k) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.05  Pr > z =  0.293
Arellano-Bond test for AR(2) in first differences: z =  -1.31  Pr > z =  0.192
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(2)    =  22.35  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(2)    =   2.19  Prob > chi2 =  0.335
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(0)    =   0.00  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(2)    =   2.19  Prob > chi2 =  0.335


. xtabond2 n w k yr* if year > 1977, gmm(w k, laglimits(2 2) collapse) iv(yr*, eq(level)) twostep robust small svmat
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 system GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =       813
Time variable : year                            Number of groups   =       140
Number of instruments = 11                      Obs per group: min =         5
F(11, 139)    =     22.56                                      avg =      5.81
Prob > F      =     0.000                                      max =         7
------------------------------------------------------------------------------
             |              Corrected
           n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           w |   3.063095    4.97983     0.62   0.539    -6.782914     12.9091
           k |   .6401778   .1988856     3.22   0.002     .2469456     1.03341
      yr1976 |          0  (omitted)
      yr1977 |   .4752611   .6111821     0.78   0.438    -.7331546    1.683677
      yr1978 |   .2918185   .2174364     1.34   0.182    -.1380918    .7217289
      yr1979 |    .256266   .1826989     1.40   0.163    -.1049621    .6174941
      yr1980 |   .2356764   .1847002     1.28   0.204    -.1295087    .6008616
      yr1981 |   .0801087    .070567     1.14   0.258    -.0594148    .2196323
      yr1982 |  -.0610829   .1850691    -0.33   0.742    -.4269975    .3048316
      yr1983 |          0  (omitted)
      yr1984 |   -.024781   .3599033    -0.07   0.945    -.7363737    .6868117
       _cons |  -8.431845   15.65676    -0.54   0.591    -39.38805    22.52436
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L2.(w k) collapsed
Instruments for levels equation
  Standard
    yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(w k) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -0.69  Pr > z =  0.487
Arellano-Bond test for AR(2) in first differences: z =  -0.49  Pr > z =  0.621
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(-1)   =  19.54  Prob > chi2 =      .
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(-1)   =   1.84  Prob > chi2 =      .
  (Robust, but weakened by many instruments.)

For the levels equation, the use of the first two periods also breaks the equivalence between IV and GMM estimation of a just-identified model:

. xtabond2 n L.n w k, gmm(n w k, laglimits(1 1) collapse eq(level)) twostep robust small svmat
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.

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 = 4                       Obs per group: min =         6
F(3, 139)     =     92.27                                      avg =      6.36
Prob > F      =     0.000                                      max =         8
------------------------------------------------------------------------------
             |              Corrected
           n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .6011746   .6566814     0.92   0.362    -.6972011     1.89955
             |
           w |  -.6677898   .5853053    -1.14   0.256    -1.825042    .4894628
           k |   .3007044   .3115794     0.97   0.336    -.3153433    .9167522
       _cons |   2.618725   2.403247     1.09   0.278    -2.132922    7.370371
------------------------------------------------------------------------------
Instruments for levels equation
  Standard
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(n w k) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -0.91  Pr > z =  0.362
Arellano-Bond test for AR(2) in first differences: z =  -0.50  Pr > z =  0.617
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(0)    =   0.00  Prob > chi2 =      .
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(0)    =   0.00  Prob > chi2 =      .
  (Robust, but weakened by many instruments.)


. xtabond2 n L.n w k, iv(dL.n dL.w dL.k, eq(level)) twostep robust small svmat
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: id                              Number of obs      =       751
Time variable : year                            Number of groups   =       140
Number of instruments = 4                       Obs per group: min =         5
F(3, 139)     =    102.12                                      avg =      5.36
Prob > F      =     0.000                                      max =         7
------------------------------------------------------------------------------
             |              Corrected
           n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .6157058   .6225919     0.99   0.324    -.6152689    1.846681
             |
           w |  -.5616312   .5536499    -1.01   0.312    -1.656296    .5330331
           k |   .2951719    .295429     1.00   0.319    -.2889437    .8792876
       _cons |   2.257568   2.219958     1.02   0.311    -2.131683    6.646819
------------------------------------------------------------------------------
Instruments for levels equation
  Standard
    LD.n LD.w LD.k
    _cons
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.00  Pr > z =  0.318
Arellano-Bond test for AR(2) in first differences: z =  -0.46  Pr > z =  0.647
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(0)    =   0.00  Prob > chi2 =      .
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(0)    =   0.00  Prob > chi2 =      .
  (Robust, but weakened by many instruments.)


. ivreg2 n (L.n w k = dL.n dL.w dL.k), cluster(id) small

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on id

Number of clusters (id) =          140                Number of obs =      751
                                                      F(  3,   139) =   102.12
                                                      Prob > F      =   0.0000
Total (centered) SS     =  1350.891752                Centered R2   =   0.9683
Total (uncentered) SS   =  2122.555626                Uncentered R2 =   0.9798
Residual SS             =  42.81902289                Root MSE      =    .2394

------------------------------------------------------------------------------
             |               Robust
           n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .6157058   .6225918     0.99   0.324    -.6152689    1.846681
             |
           w |  -.5616312   .5536499    -1.01   0.312    -1.656295    .5330331
           k |   .2951719    .295429     1.00   0.319    -.2889437    .8792876
       _cons |   2.257568   2.219958     1.02   0.311    -2.131683    6.646819
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic):              0.506
                                                   Chi-sq(1) P-val =    0.4769
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):                0.108
                         (Kleibergen-Paap rk Wald F statistic):          0.177
Stock-Yogo weak ID test critical values:                       <not available>
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments):         0.000
                                                 (equation exactly identified)
------------------------------------------------------------------------------
Instrumented:         L.n w k
Excluded instruments: LD.n LD.w LD.k
------------------------------------------------------------------------------

Again, thanks for responding.

[Sebastian Kripfganz]

Well, it does change the moment condition for the intercept. Without the if-condition, the moment condition is that the expected value of the sum of the errors over all periods (in the static model case) shall be zero. With the if-condition, it is only the expected value of the sum of the errors over the periods excluding the first two periods. This moment condition does not only affect the estimate of the intercept but of all coefficients.

Regarding your just-identified model, the difference arises because the iv() option does not automatically replace missings with zeros unless you specify the mz suboption:

xtabond2 n L.n w k, iv(dL.n dL.w dL.k, eq(level) mz) twostep robust small svmat

These missing values are handled differently by different commands. The ivreg2 command apparently does not replace the missing values. In contrast, my own xtdpdgmm command always replaces missing values (in the instruments) by zeros.

[Nicolas Van de Sijpe]

Thanks, that makes sense. It's been very helpful to discuss this with you.