I am having some issues replicating some -xtdpd- results with
-gmm-. First, -gmm- generates a puzzling error when I specify
analytic derivatives and use instruments with a higher lag
limit. Second, even when I don't specify the analytic
derivatives, -gmm- generates different results from -xtdpd-.
Here I repeat David Drukker's example with one change: I
increase the lag limit for both the level and differenced
equation by 1. Stata reports a conformability error and I
don't understand why:
. webuse abdata, clear
.
. gmm (n - {rho}*L.n - {c}) (D.n - {rho}*LD.n ),
xtinstruments(1: D.n, lags(2/2)) xtinstruments(2:n, lags(3/.))
instrume
> nts(2:, noconstant) deriv(1/rho = -1*L.n) deriv(1/c=-1)
deriv(2/rho = -1*LD.n) winitial(xt LD) onestep vce(unadjusted)
> variables(L.n ) nocommonesample
Step 1
*: 3200 conformability error
gmm_deriv(): - function returned error
criterion_gnr(): - function returned error
opt__calluser1_q(): - function returned error
opt__eval_gn_q1(): - function returned error
opt__eval(): - function returned error
opt__looputil_iter0_gn(): - function returned error
opt__loop_gn(): - function returned error
optimize(): - function returned error
mymin(): - function returned error
_gmm_wrk(): - function returned error
<istmt>: - function returned error
r(3200);
If I don't specify the analytic derivatives then -gmm- will
produce an estimate (see output below). I can't seem to
replicate its results when I use what I think would be the
equivalent -xtdpd- command, however:
. gmm (n - {rho}*L.n - {c}) (D.n - {rho}*LD.n ),
xtinstruments(1: D.n, lags(2/2)) xtinstruments(2:n,
lags(3/.)) instrume
> nts(2:, noconstant) winitial(xt LD) onestep vce(unadjusted)
variables(L.n ) nocommonesample
Step 1
Iteration 0: GMM criterion Q(b) = .08204623
Iteration 1: GMM criterion Q(b) = .00013918
Iteration 2: GMM criterion Q(b) = .00013918
GMM estimation
Number of parameters = 2
Number of moments = 29
Initial weight matrix: XT LD Number
of obs = *
Coef. Std. Err. z P>z [95% Conf. Interval]
/rho 1.073292 .0239215 44.87 0.000 1.026407
1.120177
/c -.1340523 .0259783 -5.16 0.000 -.1849688
-.0831359
* Number of observations for equation 1: 891
Number of observations for equation 2: 751
Instruments for equation 1:
XT-style: L2D.n
Standard: _cons
Instruments for equation 2:
XT-style: L(3/.).n
.
. xtdpd n L.n, dgmm(n, lagrange(3 .)) lgmm(n, lag(2))
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 = 28 Wald chi2(1)
= 2059.36
Prob > chi2 = 0.0000
One-step results
n Coef. Std. Err. z P>z [95% Conf. Interval]
n
L1. 1.080427 .0238084 45.38 0.000 1.033764
1.127091
_cons -.1309317 .0261323 -5.01 0.000 -.1821502
-.0797133
Instruments for differenced equation
GMM-type: L(3/.).n
Instruments for level equation
GMM-type: L2D.n
Standard: _cons
-- Julian
---- Original message ----
>Date: Wed, 13 Jan 2010 18:29:11 -0600 (CST)
>From: "David M. Drukker" <[email protected]>
>Subject: Re: st: RE: xtdpd vs. xtabond2 discrepancy
>To: [email protected]
>Cc: [email protected], David Roodman <[email protected]>
>
>There has been some discussion about a difference in the
standard errors
>reported by -xtdpd- and -xtabond2-.
>
>The discussion began with question about how to get the point
estimates to
>match.
>
>Julian <[email protected]> noted that
>
>> You need to add an h(2) option to -xtabond2-. The following
>> will produce the same point estimates:
>>
>> webuse abdata, clear
>> xtabond2 n L.n, gmm(n, laglimits(2 .)) small h(2)
>> xtdpd n L.n, dgmm(n, lagrange(2 .)) lgmm(n, lag(1))
>
>Julian continued that
>> The standard errors are still different though.
>
>David Roodman <[email protected]> noted that
>
>> I think the remaining discrepency between xtdpd in xtabond2
in the
>> standard errors only occurs if you do one-step, non-robust
estimation,
>> which is rare.
>
>David went to verify that -xtabond2- is able replicate a
version of DPD in
>OX that has a known bug, but I do not understand how this
resolves anything.
>
>I cannot speak to what -xtabond2- does, so I will not say
anything about it.
>
>Below I illustrate that -xtdpd- produces the same point
estimates and
>standard errors as produced by the -gmm- command in Stata. I
conclude that
>the point estimates and standard errors produced by -xtdpd-
are correct,
>because I can reproduce them using another Stata command that
is independent
>of -xtdpd-.
>
>I begin by loading the data and estimating the paramters
using -xtdpd-.
>
>. webuse abdata, clear
>
>.
>. xtdpd n L.n, dgmm(n, lagrange(2 .)) lgmm(n, lag(1))
>
>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 = 36 Wald chi2(1)
= 1724.98
> Prob > chi2
= 0.0000
>One-step results
>------------------------------------------------------------------------------
> n | Coef. Std. Err. z P>|z|
[95% Conf. Interval]
>-------------+----------------------------------------------------------------
> n |
> L1. | 1.170374 .0281795 41.53 0.000
1.115144 1.225605
> |
> _cons | -.228391 .0308445 -7.40 0.000
-.2888452 -.1679369
>------------------------------------------------------------------------------
>Instruments for differenced equation
> GMM-type: L(2/.).n
>Instruments for level equation
> GMM-type: LD.n
> Standard: _cons
>
>Now I estimate the parameters using the -gmm- command.
>
>. gmm (n - {rho}*L.n - {c}) ///
>> (D.n - {rho}*LD.n ), ///
>> xtinstruments(1:D.n, lags(1/1))
///
>> xtinstruments(2:n, lags(2/.))
///
>> instruments(2: , noconstant)
///
>> deriv(1/rho = -1*L.n)
///
>> deriv(1/c = -1)
///
>> deriv(2/rho = -1*LD.n)
///
>> winitial(xt LD) onestep vce(unadjusted)
///
>> variables(L.n )
///
>> nocommonesample
>
>Step 1
>Iteration 0: GMM criterion Q(b) = .10163841
>Iteration 1: GMM criterion Q(b) = .00035315
>Iteration 2: GMM criterion Q(b) = .00035315
>
>GMM estimation
>
>Number of parameters = 2
>Number of moments = 37
>Initial weight matrix: XT LD Number
of obs = *
>
>------------------------------------------------------------------------------
> | Coef. Std. Err. z P>|z|
[95% Conf. Interval]
>-------------+----------------------------------------------------------------
> /rho | 1.170374 .0281795 41.53 0.000
1.115144 1.225605
> /c | -.228391 .0308445 -7.40 0.000
-.2888452 -.1679369
>------------------------------------------------------------------------------
>* Number of observations for equation 1: 891
> Number of observations for equation 2: 751
>------------------------------------------------------------------------------
>Instruments for equation 1:
> XT-style: LD.n
> Standard: _cons
>Instruments for equation 2:
> XT-style: L(2/.).n
>
>The two commands produce the same point estimates and the
same standard
>errors.
>
>The syntax for -gmm- is a little involved. This example is a
stripped down
>version of the example on page 612 of the Stata Reference
manual [R] A-H. I
>recommend looking there for details about how the -gmm-
syntax works.
>
>I conclude that the point estimates and the standard errors
produced by
>-xtdpd- are correct.
>
> --David
> [email protected]
>
>
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