xtabond vs. xtabond2: How to get the same results?

Sofie Laub

Join Date: Apr 2020

Posts: 7
#1

xtabond vs. xtabond2: How to get the same results?

24 Apr 2020, 03:53

Hello,

I am currently working with the Arellano Bond difference estimator and I'm not able to generate the same results for the commands xtabond and xtabond2.

I tried to replicate the results from the following xtabond command with the xtabond2 command (x1 and x2 are exogenous):

xtabond y x1 x2 i.year, twostep vce(robust)

xtabond2 y l.y x1 x2 i.year, gmm(l.y) iv(x1 x2 i.year) noleveleq twostep robust small

Why do the two options not generate the same results?

Also, I am wondering how variables are treated if they are listed before the comma, but not after the comma. For example, how is x2 being estimated in the following case?

xtabond2 y l.y x1 x2, gmm(l.y) iv(x1) noleveleq twostep robust

I also asked another question yesterday about the interaction of an endogenous and exogenous variable. Any responses would be really appreciated!

Thank you so much in advance.
Sofie
Tags: Arellano-Bond, gmm, panel data, xtabond, xtabond2
Andrew Musau

Join Date: Oct 2014

Posts: 10254
#2

24 Apr 2020, 05:17

Have you looked at the documentation for xtabond2 (from SSC) for equivalent syntax?

Code:

help xtabond2

Also, xtabond does not support factor variables, so you probably want

Code:

xi: xtabond y x1 x2 i.year, twostep vce(robust)
Comment
Eric de Souza

Join Date: Mar 2014

Posts: 587
#3

24 Apr 2020, 05:45

The Stata Journal article by David Roodman gives a detailed description of xtabond2. Also on page 42 there is an example with xtabond and xtabond2
Comment
Sofie Laub

Join Date: Apr 2020

Posts: 7
#4

24 Apr 2020, 06:14

Thank you for your help.

I actually did type xi before the commands. Sorry that I forgot to mention it.

I read the paper and the syntax in Stata, but apparently I do not understand it. Does anyone see my mistake in that particular case?

Last edited by Sofie Laub; 24 Apr 2020, 06:16.
Comment
Eric de Souza

Join Date: Mar 2014

Posts: 587
#5

24 Apr 2020, 07:01

You will a brief introduction to xtabond2 posted by me here:
https://www.statalist.org/forums/for...-me-for-coding
Note that your xtabond command does not contain a lagged y as dependent variable, but your xtabond2 does
Comment
Sofie Laub

Join Date: Apr 2020

Posts: 7
#6

24 Apr 2020, 08:24

Thank you Eric. I did not list l.y in the xtabond command, because this command automatically includes the lagged dependent variable in the estimation. This is because the command tells Stata that I have a dynamic panel data model.
Comment

Andrew Musau

Join Date: Oct 2014
Posts: 10254

24 Apr 2020, 08:33

I read the paper and the syntax in Stata, but apparently I do not understand it. Does anyone see my mistake in that particular case?

In addition to the fact that you need to explicitly specify the lagged dependent variable in xtabond2, you need to look at the instrument set for the level and differenced equations when translating the syntax. So here is your xtabond command:

xtabond y x1 x2 i.year, twostep vce(robust)

We can make a reproducible example using Stata's abdata dataset and see the results

Code:

webuse abdata, clear
xi: xtabond wage emp cap i.year, twostep vce(robust)

Res.:

Code:

. xi: xtabond wage emp cap i.year, twostep vce(robust)
i.year            _Iyear_1976-1984    (naturally coded; _Iyear_1976 omitted)
note: _Iyear_1984 dropped because of collinearity

Arellano-Bond dynamic panel-data estimation     Number of obs     =        751
Group variable: id                              Number of groups  =        140
Time variable: year
                                                Obs per group:
                                                              min =          5
                                                              avg =   5.364286
                                                              max =          7

Number of instruments =     38                  Wald chi2(10)     =     189.18
                                                Prob > chi2       =     0.0000
Two-step results
                                     (Std. Err. adjusted for clustering on id)
------------------------------------------------------------------------------
             |              WC-Robust
        wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        wage |
         L1. |     .22362   .7350978     0.30   0.761    -1.217145    1.664385
             |
         emp |  -.0652363   .0399532    -1.63   0.103    -.1435432    .0130707
         cap |    .174836    .062315     2.81   0.005     .0527008    .2969711
 _Iyear_1977 |  -2.580239   .5124058    -5.04   0.000    -3.584536   -1.575942
 _Iyear_1978 |  -2.369046    1.49994    -1.58   0.114    -5.308874    .5707818
 _Iyear_1979 |  -2.086565   1.735373    -1.20   0.229    -5.487834    1.314704
 _Iyear_1980 |   -2.07073   1.629248    -1.27   0.204    -5.263998    1.122538
 _Iyear_1981 |  -1.396799   1.890739    -0.74   0.460     -5.10258    2.308981
 _Iyear_1982 |  -.4331267   1.487038    -0.29   0.771    -3.347668    2.481414
 _Iyear_1983 |   .0409424   .3901312     0.10   0.916    -.7237007    .8055855
       _cons |   19.89907    19.4321     1.02   0.306    -18.18714    57.98528
------------------------------------------------------------------------------
Instruments for differenced equation
        GMM-type: L(2/.).wage
        Standard: D.emp D.cap D._Iyear_1977 D._Iyear_1978 D._Iyear_1979
                  D._Iyear_1980 D._Iyear_1981 D._Iyear_1982 D._Iyear_1983
                  D._Iyear_1984
Instruments for level equation
        Standard: _cons

GMM type instruments for the differenced equation are the lags of the dependent variable (starting from the second). Standard instruments are the differenced independent variables. No instruments for the level equation. So let's explicitly include the lagged dependent variable and these instruments and see how we fair.

Code:

 xtabond2 wage L.wage emp cap i.year, gmm(L.wage, eq(d)) iv(emp cap i.year, eq(d)) robust twostep

Res.:

Code:

. xtabond2 wage L.wage emp cap i.year, gmm(L.wage, eq(d)) iv(emp cap i.year, eq(d)) robust twostep
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, 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      =       891
Time variable : year                            Number of groups   =       140
Number of instruments = 38                      Obs per group: min =         6
Wald chi2(12) =    202.48                                      avg =      6.36
Prob > chi2   =     0.000                                      max =         8
------------------------------------------------------------------------------
             |              Corrected
        wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        wage |
         L1. |     .22362   .1058023     2.11   0.035     .0162514    .4309887
             |
         emp |  -.0652363   .0331144    -1.97   0.049    -.1301393   -.0003332
         cap |    .174836   .0401353     4.36   0.000     .0961722    .2534997
             |
        year |
       1976  |          0  (empty)
       1977  |  -2.580239   .4375939    -5.90   0.000    -3.437907   -1.722571
       1978  |  -2.369046   .5340449    -4.44   0.000    -3.415755   -1.322338
       1979  |  -2.086565   .5805174    -3.59   0.000    -3.224358   -.9487722
       1980  |   -2.07073   .5552539    -3.73   0.000    -3.159008   -.9824523
       1981  |  -1.396799    .602433    -2.32   0.020    -2.577546   -.2160524
       1982  |  -.4331267   .4871627    -0.89   0.374    -1.387948    .5216946
       1983  |   .0409424   .3763874     0.11   0.913    -.6967635    .7786482
       1984  |          0  (omitted)
             |
       _cons |   19.89907   2.964961     6.71   0.000     14.08785    25.71028
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(emp cap 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).L.wage
Instruments for levels equation
  Standard
    _cons
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.87  Pr > z =  0.004
Arellano-Bond test for AR(2) in first differences: z =  -0.43  Pr > z =  0.668
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(25)   =  80.43  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(25)   =  53.74  Prob > chi2 =  0.001
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  iv(emp cap 1976b.year 1977.year 1978.year 1979.year 1980.year 1981.year 1982.year 1983.year 1984.year, eq(diff))
    Hansen test excluding group:     chi2(16)   =  25.60  Prob > chi2 =  0.060
    Difference (null H = exogenous): chi2(9)    =  28.14  Prob > chi2 =  0.001

So, we got it right!

Comment

Sofie Laub

Join Date: Apr 2020

Posts: 7
#8

24 Apr 2020, 08:53

Thank you so much Andew!

So I shall use "eq(d)" instead of "noleveleq".

This solves my problem.
1 like
Comment
Sebastian Kripfganz

Join Date: May 2014

Posts: 2601
#9

24 Apr 2020, 09:08

As an aside, there are several problems with xtabond2. For example, in your case with omitted time dummy coefficients, the degrees of freedoms for the Sargan/Hansen test are computed incorrectly, and therefore also the respective p-values. For more information about this and other issues and the xtdpdgmm command as a potential alternative, see my presentation at last year's London Stata Conference:
Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

https://www.kripfganz.de/stata/
1 like
Comment

Sandy Lovejoy

Join Date: Aug 2020
Posts: 9

#10

05 Aug 2020, 21:34

Originally posted by Andrew Musau View Post

Code:

webuse abdata, clear
xi: xtabond wage emp cap i.year, twostep vce(robust)

Res.:

Code:

. xi: xtabond wage emp cap i.year, twostep vce(robust)
i.year _Iyear_1976-1984 (naturally coded; _Iyear_1976 omitted)
note: _Iyear_1984 dropped because of collinearity

Arellano-Bond dynamic panel-data estimation Number of obs = 751
Group variable: id Number of groups = 140
Time variable: year
Obs per group:
min = 5
avg = 5.364286
max = 7

Number of instruments = 38 Wald chi2(10) = 189.18
Prob > chi2 = 0.0000
Two-step results
(Std. Err. adjusted for clustering on id)
------------------------------------------------------------------------------
| WC-Robust
wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
wage |
L1. | .22362 .7350978 0.30 0.761 -1.217145 1.664385
|
emp | -.0652363 .0399532 -1.63 0.103 -.1435432 .0130707
cap | .174836 .062315 2.81 0.005 .0527008 .2969711
_Iyear_1977 | -2.580239 .5124058 -5.04 0.000 -3.584536 -1.575942
_Iyear_1978 | -2.369046 1.49994 -1.58 0.114 -5.308874 .5707818
_Iyear_1979 | -2.086565 1.735373 -1.20 0.229 -5.487834 1.314704
_Iyear_1980 | -2.07073 1.629248 -1.27 0.204 -5.263998 1.122538
_Iyear_1981 | -1.396799 1.890739 -0.74 0.460 -5.10258 2.308981
_Iyear_1982 | -.4331267 1.487038 -0.29 0.771 -3.347668 2.481414
_Iyear_1983 | .0409424 .3901312 0.10 0.916 -.7237007 .8055855
_cons | 19.89907 19.4321 1.02 0.306 -18.18714 57.98528
------------------------------------------------------------------------------
Instruments for differenced equation
 GMM-type: L(2/.).wage
Standard: D.emp D.cap D._Iyear_1977 D._Iyear_1978 D._Iyear_1979
D._Iyear_1980 D._Iyear_1981 D._Iyear_1982 D._Iyear_1983
D._Iyear_1984
Instruments for level equation
 Standard: _cons

Code:

xtabond2 wage L.wage emp cap i.year, gmm(L.wage, eq(d)) iv(emp cap i.year, eq(d)) robust twostep

Res.:

Code:

. xtabond2 wage L.wage emp cap i.year, gmm(L.wage, eq(d)) iv(emp cap i.year, eq(d)) robust twostep
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, 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 = 891
Time variable : year Number of groups = 140
Number of instruments = 38 Obs per group: min = 6
Wald chi2(12) = 202.48 avg = 6.36
Prob > chi2 = 0.000 max = 8
------------------------------------------------------------------------------
| Corrected
wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
wage |
L1. | .22362 .1058023 2.11 0.035 .0162514 .4309887
|
emp | -.0652363 .0331144 -1.97 0.049 -.1301393 -.0003332
cap | .174836 .0401353 4.36 0.000 .0961722 .2534997
|
year |
1976 | 0 (empty)
1977 | -2.580239 .4375939 -5.90 0.000 -3.437907 -1.722571
1978 | -2.369046 .5340449 -4.44 0.000 -3.415755 -1.322338
1979 | -2.086565 .5805174 -3.59 0.000 -3.224358 -.9487722
1980 | -2.07073 .5552539 -3.73 0.000 -3.159008 -.9824523
1981 | -1.396799 .602433 -2.32 0.020 -2.577546 -.2160524
1982 | -.4331267 .4871627 -0.89 0.374 -1.387948 .5216946
1983 | .0409424 .3763874 0.11 0.913 -.6967635 .7786482
1984 | 0 (omitted)
|
_cons | 19.89907 2.964961 6.71 0.000 14.08785 25.71028
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(emp cap 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).L.wage
Instruments for levels equation
Standard
_cons
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.87 Pr > z = 0.004
Arellano-Bond test for AR(2) in first differences: z = -0.43 Pr > z = 0.668
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(25) = 80.43 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(25) = 53.74 Prob > chi2 = 0.001
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(emp cap 1976b.year 1977.year 1978.year 1979.year 1980.year 1981.year 1982.year 1983.year 1984.year, eq(diff))
Hansen test excluding group: chi2(16) = 25.60 Prob > chi2 = 0.060
Difference (null H = exogenous): chi2(9) = 28.14 Prob > chi2 = 0.001

So, we got it right!

Hi, I wanted to thank you for this, because it was the clearest explanation I have seen on Statalist for how to use xtabond to help you set up xtabond2. Your analysis with the colors really made everything click!

(next, I have to figure out how to translate xtabond2 syntax to xtdpdgmm)

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