The difference, system and ‘Double‐D’ GMM panel estimators in the presence of structural breaks
| Date | 01 July 2018 |
| Published date | 01 July 2018 |
| Author | Rosen Azad Chowdhury,Bill Russell |
| DOI | http://doi.org/10.1111/sjpe.12142 |
THE DIFFERENCE, SYSTEM AND
‘DOUBLE-D’ GMM PANEL ESTIMATORS
IN THE PRESENCE OF STRUCTURAL
BREAKS
Rosen Azad Chowdhury* and Bill Russell**
ABSTRACT
The effects of structural breaks in dynamic panels are more complicated than in
time series models as the bias can be either negative or positive. This paper
focuses on the effects of mean shifts in otherwise stationary processes within an
instrumental variable panel estimation framework. We show the sources of the
bias and a Monte Carlo analysis calibrated on United States bank lending data
demonstrates the size of the bias for a range of auto-regressive parameters. We
also propose additional moment conditions that can be used to reduce the biases
caused by shifts in the mean of the data.
II
NTRODUCTION
Instrumental variable panel estimators are used in almost all fields of eco-
nomics and are usually consistent and efficient when applied to mean station-
ary data. However, econometricians have noted that in some cases, like in the
presence of heteroscedasticity or highly persistent data, instrumental variables
estimators can perform poorly. Furthermore, Carrion i-Silvestre et al. (2005)
and Bai and Carrion-i- Silvestre (2009) demonstrate that unaccounted struc-
tural breaks bias the least squares estimates in standard auto-regressive panels
when the data are exogenous. In this paper we add another dimension to this
existing literature by showing how structural breaks in the mean of the vari-
ables can result in severely biased estimates in dynamic panels when the data
are endogenous. We also propose two new moment conditions for the general-
ized method of moments (GMM) estimator that reduces the bias substantially
when the dynamic panels contain structural breaks.
The effects of structural breaks in dynamic panels that incorporate endoge-
nous variables are complicated. Arellano and Bover (1995) and Blundell and
Bond (1998) show that applying the difference GMM estimator to highly
*Swansea University
**University of Dundee School of Business
Scottish Journal of Political Economy, DOI: 10.1111/sjpe.12142, Vol. 65, No. 3, July 2018
©2017 Scottish Economic Society.
271
persistent data in dynamic models leads to invalid instruments which in turn
causes a downward bias (in absolute terms) to the estimated coefficient on the
lagged dependent variable. The usual way to overcome the problem of highly
persistent data as suggested by these papers is to assume that the persistence
has some economic rationale and estimate the model using the systems GMM
estimator where the instruments are included as first differences. However, if
the data looks persistent only because of structural breaks then this solution
to ‘imagined’ persistence in the data leads to biased estimates and possibly
incorrect inference. Consequently, unaccounted structural breaks in mean
introduce an ‘endogeneity’ bias in difference and system GMM estimators
which is over and above the biases outlined in Carrion i-Silvestre et al. (2005)
and Bai and Carrion-i- Silvestre (2009) when the variables are strictly exoge-
nous. This paper seeks to identify the ‘endogeneity’ bias in the difference and
system panel estimators before proposing two new moment conditions which
can be used to reduce the ‘endogeneity’ bias.
In the next section we begin by demonstrating the moment conditions for
the difference and system (which is the combination of difference and level)
GMM estimators are not zero in the presence of structural breaks. We there-
fore suggest two moment conditions that are zero in the presence of structural
breaks and term the associated GMM estimator the ‘double-D’ GMM estima-
tor.
1
Section 3 uses a Monte Carlo analysis calibrated on United States bank
lending data to examine the difference, system and double-D GMM estima-
tors both without and with structural breaks in the data. We find that when
there are structural breaks in the data then for panels where the length of the
data is short the double-D estimator out performs the difference and system
GMM estimators for low levels of persistence (i.e., when the autoregressive
coefficients are less than 0.6) and the difference and system GMM estimators
perform marginally better than the double-D estimator when persistence is
high with the autoregressive coefficients greater than 0.6. However, with
longer length panels the double-D GMM estimator outperforms both the dif-
ference and system estimators even when the data are highly persistent. A
panel data model of the bank lending channel is then estimated in Section 4
to demonstrate the advantage of the double-D GMM estimator when estimat-
ing models in the presence of structural breaks.
II STRUCTURAL BREAKS AND THEIR IMPACT ON THE GMM PANEL
ESTIMATORS
Structural breaks and the difference GMM estimator
Consider the following AR(1) process before the break in period T
B
;
yit ¼ayit1þgiþvit ;t\TBð1Þ
where ‘i’ represents the panel entity, g
i
is an entity specific fixed effect and vit
is a random error term.
1
The name of the estimator will become evident later in the paper.
272 R. A. CHOWDHURY AND B. RUSSELL
Scottish Journal of Political Economy
©2017 Scottish Economic Society
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