Statalist


[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

Re: st: xtabond: different results in Stata 10


From   "David M. Drukker" <ddrukker@stata.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: xtabond: different results in Stata 10
Date   Tue, 11 Sep 2007 09:42:42 -0500 (CDT)

Thomas Blake Pepinsky <Thomas.Pepinsky@Colorado.EDU> asked about how the
constant term changed in -xtabond- between Stata 9 and Stata 10

Here is the short answer.  In Stata 9, -xtabond- reported the estimates of
the parameters of the first differenced model, so the reported constant
estimate was an estimate of the coefficient on a time trend in the model.
In Stata 10, -xtabond- reports estimates of the parameters of the level
model, so the reported constant estimate is an estimate of the constant in
the level model.  In Stata 10, -xtabond- can estimate both a time-trend and
a constant.

Here is a more detailed answer.

I begin with a simple example using the version 9 -xtabond- applied to the
familiar Arellano-Bond data.  What the variables measure is not important
except that this is yearly data so year is a time-trend.

. webuse abdata

. version 9: xtabond n w k year, noconstant

Arellano-Bond dynamic panel-data estimation     Number of obs      =       751
Group variable: id                              Number of groups   =       140

                                                Wald chi2(.)       =         .

Time variable: year                             Obs per group: min =         5
                                                               avg =  5.364286
                                                               max =         7

One-step results
------------------------------------------------------------------------------
         D.n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         LD. |   .2206198   .0621776     3.55   0.000      .098754    .3424856
           w |
         D1. |  -.4588164   .0493884    -9.29   0.000    -.5556158   -.3620169
           k |
         D1. |   .3516235   .0277573    12.67   0.000     .2972202    .4060267
        year |
         D1. |  -.0239647   .0025211    -9.51   0.000    -.0289059   -.0190234
------------------------------------------------------------------------------
Sargan test of over-identifying restrictions:
         chi2(27) =   119.42      Prob > chi2 = 0.0000

Arellano-Bond test that average autocovariance in residuals of order 1 is 0:
         H0: no autocorrelation   z =  -1.82   Pr > z = 0.0688
Arellano-Bond test that average autocovariance in residuals of order 2 is 0:
         H0: no autocorrelation   z =  -0.86   Pr > z = 0.3922

The variables in the estimates table are in first differences because the
estimated parameters are from the first-differenced model.
First-differencing causes the year variable to be collinear with the
constant, I specified the -noconstant- option.

Now, I will issue a similar command in Stata 10, allowing for a constant in
the model.

.  xtabond n w k year

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 =     32               Wald chi2(4)          =   1974.00
                                             Prob > chi2           =    0.0000
One-step results
------------------------------------------------------------------------------
           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .2206198   .0622192     3.55   0.000     .0986724    .3425673
           w |  -.4588164   .0494215    -9.28   0.000    -.5556807   -.3619521
           k |   .3516235   .0277759    12.66   0.000     .2971838    .4060632
        year |  -.0239647   .0025228    -9.50   0.000    -.0289092   -.0190201
       _cons |   49.85197   4.982592    10.01   0.000     40.08627    59.61767
------------------------------------------------------------------------------
Instruments for differenced equation
        GMM-type: L(2/.).n
        Standard: D.w D.k D.year
Instruments for level equation
        Standard: _cons


The estimates table is in levels. The estimated coefficient on year is an
estimate of the coefficient on the time-trend year and the estimated _cons
is an estimate of the constant term in the level model.

When comparing the two sets of results, I see that the estimated
coefficients on D.year and year are the same, as expected.  Similarly, we
also have equality of the estimates for the coefficients on LD.n and L.n,
D.w and w, and D.k and k.  There is no constant in the differenced model
because it would be collinear with D.year.  The estimated constant in the
Stata 10 output is for the constant in the level model.  The difference in
the standard errors is caused the additional parameter that is estimated in
the Stata 10 -xtabond.

The constant term for the level model is estimated by including a level
moment condition.  Technically, this moment condition is from an
Arellano-Bover/Blundell-Bond estimator, however including only the constant
in an Arellano-Bond estimator leaves the other parameters unchanged.

The estimated constant for the level model is useful when predicting levels
of the dependent variable.

The following example illustrates that dropping the constant from the model
does not change the remaining estimated parameters.  I also point out that
the standard errors now match those from the Stata 9 output, because the
number of parameters is the same.

. xtabond n w k year, noconstant

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 =     31               Wald chi2(4)          =   1976.65
                                             Prob > chi2           =    0.0000
One-step results
------------------------------------------------------------------------------
           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .2206198   .0621776     3.55   0.000      .098754    .3424856
           w |  -.4588164   .0493884    -9.29   0.000    -.5556158   -.3620169
           k |   .3516235   .0277573    12.67   0.000     .2972202    .4060267
        year |  -.0239647   .0025211    -9.51   0.000    -.0289059   -.0190234
------------------------------------------------------------------------------
Instruments for differenced equation
        GMM-type: L(2/.).n
        Standard: D.w D.k D.year

Reiterating the main points,

        1) in the Stata 9 -xtabond-, the output table was for the parameters
        in the differenced model;

        2) in the Stata 9 -xtabond-, the estimated constant is an estimate of the
	coefficient on a time trend;

        3) in the Stata 10 -xtabond-, the output table is for the parameters
        of the level model;

        4) in the Stata 10 -xtabond-, the estimated constant is an estimate
        of the constant in the level model; and

	5) including a constant in the Stata 10 -xtabond- does not affect any of the
	other parameter estimates.

I hope that this helps.

        David
	<ddrukker@stata.com>

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/



© Copyright 1996–2014 StataCorp LP   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index