--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 <[email protected]>
> To Stata List <[email protected]>
> 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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