Title

xtdynestimb dd -- Difference, System and Double-D GMM panel
estimators in the presence of structural breaks (Chowdhury & Russell 2017)

(part of xtdynestimb. See also csdgmm,
ablasso, postestimation.)

Syntax

xtdynestimb dd depvar [indepvars] [if] [in]
[, options]

Model
variant(type) moment-condition set: difference,
system, ddback, ddforward or full; default full

lags(#) autoregressive order p; default lags(1)

gmmlags(min max) lag window for the level instruments; default
gmmlags(2 .)

Estimator
twostep two-step efficient GMM (default)

onestep one-step GMM, robust variance

nowindmeijer no Windmeijer two-step correction

Reporting
compare estimate and tabulate all five variants together

graph coefficient plot (or variant comparison with compare)

graphname(name) name for the graph

notable suppress the output table

level(#) confidence level; default level(95)

Description

xtdynestimb dd implements the family of GMM estimators in Chowdhury &
Russell (2017) for the dynamic panel model when the fixed effects are subject to
structural (mean) breaks. Such breaks add a non-zero term to the usual
Arellano-Bond and Blundell-Bond moment conditions, biasing the difference and
system GMM estimators. The paper proposes additional moment conditions in which
both the instruments and the estimating equation are in first differences
(double-difference, hence "double-D"), which remain valid whether or not
there is a break and whether or not the break is common across units.

The lagged dependent variable(s) are generated automatically according to
lags(). Any indepvars are treated as strictly exogenous and enter the
equation and the instrument set in the appropriate transform.

Moment conditions and variants

The five variants correspond to Table 1 of Chowdhury & Russell (2017):

variant moment conditions used

difference (1) E[y_i,t-s · Dv_it] = 0 (Arellano-Bond)

system (1) + (2) E[Dy_i,t-1 · (v_it+eta_i)] = 0 (Blundell-Bond)

ddback (3) E[Dy_i,t-s · Dv_it] = 0, S>=2 (backward double-D)

ddforward (4) E[Dy_i,t+s · Dv_it] = 0, S>=2 (forward double-D)

full (1)+(2)+(3)+(4) (full system; most efficient)

Moment conditions (3) and (4) are the break-robust additions. full stacks
all four and, in the simulations of Chowdhury & Russell (2017), recovers the
true autoregressive parameter most accurately in the presence of breaks. When
persistence is low, the pure double-D variants can suffer weak-instrument bias;
use full or system in that case.

Options

variant(type) chooses the moment-condition set (see above).

lags(#) sets the autoregressive order p. With lags(2)
the model includes y_i,t-1 and y_i,t-2.

gmmlags(min max) limits the lag depth of the level (Arellano-Bond)
instruments to control instrument proliferation, exactly as the lag range does
in xtabond2. The minimum must be at least 2.

twostep, onestep, nowindmeijer control the GMM step and
the variance estimator. The default is two-step with the Windmeijer (2005)
correction. onestep reports a fully robust one-step variance.

compare re-estimates the model under all five variants and prints a
compact table of the first-lag (persistence) coefficient, its standard error and
the number of moments for each, so the break-sensitivity of difference/system
relative to the double-D variants is visible at a glance. It also returns
r(compare).

graph draws a coefficient plot; with compare it draws the
five-variant comparison of the persistence coefficient.

Stored results

In addition to the common e() results,
dd stores:

Scalars

e(j), e(j_df), e(j_p) Hansen J statistic, df, p-value

e(n_moments) number of moment conditions

Macros

e(variant) variant used

e(step), e(vce), e(gmmlags) estimator settings

With compare, r(compare) is a 5×5 matrix (rows = variants;
columns = b, se, z, p, moments).

Examples

. webuse abdata

. xtset id year

Full break-robust estimator

. xtdynestimb dd n, lags(1)

Compare all five variants and plot

. xtdynestimb dd n, lags(1) compare graph

AR(2) with capped instruments, one-step robust

. xtdynestimb dd n w, lags(2) gmmlags(2 4) variant(full) onestep

References

Chowdhury, R. A., and B. Russell. 2017. The Difference, System and
'Double-D' GMM panel estimators in the presence of structural breaks.
Scottish Journal of Political Economy 64(4): 373-395.

Windmeijer, F. 2005. A finite sample correction for the variance of
linear efficient two-step GMM estimators. Journal of Econometrics
126: 25-51.

Author

Dr Merwan Roudane

merwanroudane920@gmail.com

github.com/merwanroudane