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Re: st: time-invariant regressors in xtdpdsys


From   Hewan Belay <hewan_belay@yahoo.com>
To   Stata List <statalist@hsphsun2.harvard.edu>
Subject   Re: st: time-invariant regressors in xtdpdsys
Date   Tue, 5 Aug 2008 09:02:22 -0700 (PDT)

--CORRECTION -- 

[Apologies, there was an important error in my question earlier. Below is the corrected version]

I want to add to my question below a more stata-oriented (as opposed to 
econometric) question but related to the same topic. I estimated a dynamic 
model including time-invariant regressors using -xtdpdsys-. Since -xtdpd- 
is a generalised version of the former, it should be possible to replicate 
this estimation in -xtdpd-, but I was not able to. Here is an example:

webuse abdata, clear
by id, s: egen avg_emp = mean(emp)
/* No. 1 */    xtdpdsys     n w k avg
/* No. 2 */    xtdpdsys     n w k
/* No. 3 */    xtdpd L(0/1).n w k avg, div(w k avg) dgmmiv(n) lgmmiv(n)

Equation 3 was an attempt to replicate the results of equation 1. Instead 
however, (3) produces results identical to (2) i.e. is not able to 
identify the time-invariant variable. I tried different ways of writing 
the -xtdpd- command to get the results of (1), to no avail. How can -xtdpd-
be made to replicate Blundell-Bond with time-invariant regressors, which 
it should be able to, since it is supposed to be able to accomodate 
estimations of Blundell-Bond as well as Arellano-Bond (or -xtdpdsys- and -
xtabond-)? Below please find the full results of the above stated commands.

Thanks in advance,
Hewan


.. webuse abdata, clear

.. by id, s: egen avg_emp = mean(emp)

.. /* No. 1 */    xtdpdsys         n w k avg
note: avg_emp dropped from div() because of collinearity

System 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 =     38               Wald chi2(4)          =   4550.53
                                             Prob > chi2           =    0.0000
One-step results
------------------------------------------------------------------------------
           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .5514304    .043601    12.65   0.000      .465974    .6368869
           w |  -.6130319   .0513926   -11.93   0.000    -.7137595   -.5123042
           k |   .3334923   .0239851    13.90   0.000     .2864823    .3805022
     avg_emp |  -.0032794   .0042283    -0.78   0.438    -.0115668    .0050079
       _cons |   2.541278   .1785823    14.23   0.000     2.191263    2.891293
------------------------------------------------------------------------------
Instruments for differenced equation
        GMM-type: L(2/.).n
        Standard: D.w D.k
Instruments for level equation
        GMM-type: LD.n
        Standard: _cons

.. /* No. 2 */    xtdpdsys         n w k

System 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 =     38               Wald chi2(3)          =   4601.24
                                             Prob > chi2           =    0.0000
One-step results
------------------------------------------------------------------------------
           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .5419106   .0416037    13.03   0.000     .4603688    .6234524
           w |  -.6152988   .0510225   -12.06   0.000     -.715301   -.5152965
           k |   .3306255   .0235661    14.03   0.000     .2844369    .3768142
       _cons |   2.531675   .1771563    14.29   0.000     2.184455    2.878895
------------------------------------------------------------------------------
Instruments for differenced equation
        GMM-type: L(2/.).n
        Standard: D.w D.k
Instruments for level equation
        GMM-type: LD.n
        Standard: _cons


.. /* No. 3 */    xtdpd L(0/1).n w k avg, div(w k avg) dgmmiv(n) lgmmiv(n)
note: avg_emp dropped from div() because of collinearity
note: D.avg_emp 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 =     38               Wald chi2(3)          =   4601.24
                                             Prob > chi2           =    0.0000
One-step results
------------------------------------------------------------------------------
           n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           n |
         L1. |   .5419106   .0416037    13.03   0.000     .4603688    .6234524
           w |  -.6152988   .0510225   -12.06   0.000     -.715301   -.5152965
           k |   .3306255   .0235661    14.03   0.000     .2844369    .3768142
       _cons |   2.531675   .1771563    14.29   0.000     2.184455    2.878895
------------------------------------------------------------------------------
Instruments for differenced equation
        GMM-type: L(2/.).n
        Standard: D.w D.k
Instruments for level equation
        GMM-type: LD.n
        Standard: _cons




> 
> From   Hewan Belay <hewan_belay@yahoo.com> 
> To   Stata List <statalist@hsphsun2.harvard.edu> 
> Subject   st: time-invariant regressors in xtdpdsys 
> Date   Mon, 4 Aug 2008 18:20:53 -0700 (PDT) 
> 
> -----------------------------------------------------------------------
> Dear List,
> 
> I have been trying to learn about the properties of the
> estimates of time-
> invariant regressors obtained when estimating a dynamic
> panel data model 
> with the Blundell-Bond method, using -xtdpdsys- or -xtdpd-
> , e.g. estimating the model
> 
> y_it = a + b*y_it-1 + c*x_it + d*z_i + u_i + e_it
> 
> so my question refers to the estimator d-hat. One of the 
> big attractions of using Arellano-Bover/Blundell-Bond (
> -xtdpdsys- ) 
> rather than Arellano-Bond ( -xtabond- ) is that parameters
> of time-
> invariant explanatory variables can be identified ... in
> addition to the 
> other attractions (consistency and greater precision when T
> is small, n is 
> small, and the true value of the parameter b (see above) is
> large in 
> absolute value).
> 
> But neither the stata manual's discussions of
> -xtdpdsys- and -xtdpd-, nor 
> for that matter the paper Blundell and Bond (1998), discuss
> the properties 
> of the estimates of time-fixed variables' parameters.
> The paper only 
> explores an AR(1) model, i.e. the RHS contains only the LDV
> plus the 
> errors, and then uses the usual UK data (see -webuse
> abdata- ) with time-
> varying regressors only. The stata manual accordingly only
> picks up on the 
> discussion based on the UK data results. Nor have I seen
> much discussion 
> on this in other articles. 
> 
> Any directions, or references, would be much appreciated!
> Hewan


      

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