Special Issue of Econometric Reviews
Dependence in Cross-section, Time-series and Panel
Data
Edited by
Badi H. Baltagi and Esfandiar Maasoumi
Contents:
An Overview of Dependence in Cross-section, Time-series and Panel Data
Badi H. Baltagi and Esfandiar Maasoumi
Lessons from a Decade of IPS and LLC
JoakimWesterlund and Jeorg Breitung
Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit
Alexander Chudik and M. Hashem Pesaran
A Nonparametric Poolability Test for Panel Data Models with Cross Section
Dependence
Sainan Jin and Liangjun Su
A Generalized Spatial Panel Data Model with Random E¤ects
Badi H. Baltagi, Peter Egger and Michael Pfa¤ermayr
On Two-step Estimation of a Spatial Autoregressive Model
with Autoregressive Disturbances and Endogenous Regressors
David M. Drukker, Peter Egger and Ingmar R. Prucha
Two Stage Least Squares Estimation of Spatial Autoregressive Models
with Endogenous Regressors and Many Instruments
Xiaodong Liu and Lung-fei Lee
Nonparametric Estimation in Large Panels with Cross Sectional Dependence
Xiao Huang
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An Overview of Dependence in Cross-section,
Time-series and Panel Data
Badi H. Baltagi and Esfandiar Maasoumi
In this overview we present a summary of the contents of a collection of latest
papers to deal with several aspects of dependence in time-series, cross-section
and panels. These papers are collected in this special issue of Econometric Reviews. They include spatial models which usually account for dependence across
geographic space as well as social interaction across individuals, see the papers
by Baltagi, Egger, and Pfa¤ermayr (2013), Liu and Lee (2013) and Drukker,
Egger and Prucha (2013). Also factor models, popular in macroeconomics to
account for dependence among countries, see the papers by Chudik and Pesaran
(2013) and Huang (2013).1 Additionally, a poolability test for large dimensional
semiparametric panel data models with cross-section dependence is proposed by
Jin and Su (2013), and a tour de force on what lessons one learns from panel unit
root tests and how deceptive inference can be under cross-section dependence
is reviewed by Westerlund and Breitung (2013).
Westerlund and Breitung (2013) focus on the analysis of panel unit roots
and in particular the two in‡uential tests by Levin, Lin and Chu (2002) and Im,
Peseran and Shin (2003). These are …rst-generation panel unit roots tests that
are appropriate when the cross-sectional units are independent of each other.
Westerlund and Breitung emphasize important facts some of them well known
and others ignored in this literature. These include the following: (1) The IPS
and LLC statistics are standard normally distributed as N ! 1 even if T is
…xed; (2) The LLC test can be more powerful than the IPS test; (3) Deterministic components need not be treated as in the Dickey and Fuller approach; (4)
Incidental trends reduce the local power of the LLC test; (5) The initial condition may a¤ect the asymptotic properties of the tests. (6) The GMM approach
can also be used in the unit root case; (7) Lag augmentation does not remove
the e¤ects of serial correlation; (8) The consistency of the LLC test depends on
the long-run variance estimator; (9) Cross-section dependence leads to deceptive
inference; (10) The IPS and LLC tests fail under cross-unit cointegration; (11)
Sequential limits need not imply joint limits. They warn the researcher not to
approach the panel unit root testing problem from a too narrow and stylized
perspective.
Chudik and Pesaran (2013) extend the analysis of in…nite dimensional vector
autoregressive (IVAR) models to the case where one of the cross section units in
the IVAR model is dominant or pervasive, in the sense that its direct or indirect
e¤ects on the rest of the system can lead to strong cross section dependence. An
important example in a multi-country analysis is the role of the US in the global
economy. The dominant unit in‡uences the rest of the variables in the IVAR
model both directly and indirectly, and its e¤ects do not vanish as the dimension
1 See
also the papers by Sara…dis and Wansbeek (2011) and Chudik, Pesaran and Tosetti
(2011) for important discussion of weak and strong dependence.
2
of the model (N) tends to in…nity. The dominant unit acts as a dynamic factor in
the regressions of the non-dominant units and yields an in…nite order distributed
lag relationship between the two types of units. Despite this it is shown that
the e¤ects of the dominant unit as well as those of the neighborhood units can
be consistently estimated by running augmented least squares regressions that
include distributed lag functions of the dominant unit and its neighbors (if any).
The asymptotic distribution of the estimators is derived and their small sample
properties investigated by means of Monte Carlo experiments.
Jin and Su (2013) propose a nonparametric poolability test for large dimensional semiparametric panel data models with cross-section dependence. The
test requires sieve estimation of the heterogeneous regression relationships under
the alternative. They establish the asymptotic normal distributions of their test
statistics under both the null hypothesis of poolability and a sequence of Pitman local alternatives. In addition, they prove the consistency of their test and
suggest a bootstrap method as an alternative way to obtain the critical values.
Using Monte Carlo simulations, they show that their test performs reasonably
well in …nite samples.
Baltagi, Egger, and Pfa¤ermayr (2013) propose a generalized panel data
model with random e¤ects and …rst-order spatially autocorrelated residuals that
encompasses two previously suggested speci…cations. The …rst speci…cation assumes that spatial correlation occurs only in the remainder error term, whereas
no spatial correlation takes place in the individual e¤ects (see Anselin, 1988,
and Baltagi, Song, and Koh, 2003; referred to as the Anselin model). Another
speci…cation assumes that the same spatial error process applies to both the
individual and remainder error components (see Kapoor, Kelejian, and Prucha,
2007; referred to as the KKP model). The encompassing speci…cation allows
the researcher to test for these models as restricted speci…cations using Lagrange Multiplier and Likelihood Ratio tests. Using Monte Carlo experiments,
they show that the suggested tests are powerful in testing for these restricted
speci…cations even in small and medium sized samples.
Drukker, Egger and Prucha (2013) consider a spatial-autoregressive model
with autoregressive disturbances, that allows for endogenous regressors. Extending earlier work by Kelejian and Prucha (1998, 1999), they propose a twostep generalized method of moments (GMM) and instrumental variable (IV)
estimation approach. They derive the joint limiting distribution of their GMM
estimator and the IV estimator for the regression parameters and prove consistency of their GMM estimator for the spatial-autoregressive parameter in
the disturbance process. They propose a joint test of zero spatial interactions
in the dependent variable, the exogenous variables and the disturbances. Using
Monte Carlo experiments, they study the performance of this estimator in small
samples.
Liu and Lee (2013) consider instrumental variable estimation of spatial autoregressive (SAR) models with endogenous regressors in the presence of many
instruments. They derive the asymptotic distribution of the 2SLS estimator
when the number of instruments grows with the sample size, and suggest a biascorrection procedure based on the leading-order many-instrument bias. The
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approximate MSE can be minimized to choose the instruments as in Donald
and Newey (2001). Using Monte-Carlo experiments, they …nd that, for the
case where some instruments are more important than others, the instrument
selection often leads to smaller bias, better precision and more reliable inference.
Huang (2013) proposes nonparametric estimation in panel data under cross
sectional dependence. The cross sectional dependence has a multifactor structure and the proposed method is an extension of Pesaran’s (2006) procedure
using nonparametric estimation. Both the number of cross sectional units (N)
and the time dimension of the panel (T) are assumed to be large. Local linear
regression is used to …lter the unobserved cross sectional factors and to estimate
the nonparametric conditional mean. Monte Carlo simulations show that the
proposed method has good …nite sample properties and that the e¢ ciency loss
of this nonparametric method decreases as sample size increases.
This small collection of papers represent state of art and signi…cant advances
in cross-sections, time series and panels with dependence structures. They well
represent the major advances that have been made in this area in the last few
years. In particular for spatial econometric models analyzing dependence, factor
models and IVAR models, nonparametric estimation and testing in panels with
dependence, as well as panel unit roots.
Badi H. Baltagi
Distinguished Professor of Economics
CPR Senior Research Associate
Center for Policy Research
426 Eggers Hall
Syracuse University Syracuse, NY 13244-1020
Email address: bbaltagi@maxwell.syr.edu
and
Esfandiar Maasoumi
Arts & Sciences Distinguished Professor,
Department of Economics
1602 Fishburne Drive
Emory University,
Atlanta, GA 30322
Email address: esfandiar.maasoumi@emory.edu
References
Anselin, L. (1988). Spatial econometrics: methods and models. Kluwer Academic Publishers, Dordrecht.
Baltagi, B.H., P. Egger and M. Pfa¤ermayr (2013),"A Generalized Spatial
Panel Data Model with Random E¤ects", Econometric Reviews, Issue 1, Vol
33.
Baltagi, B.H., S.H. Song, and W. Koh (2003). Testing panel data models with spatial
error correlation. Journal of Econometrics 117, 123-150.
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Chaudik, A. and M.H. Pesaran (2013),"Econometric Analysis of High Dimensional
VARs Featuring a Dominant Unit", Econometric Reviews, Issue 1, Vol 33.
Chudik, A., M. H. Pesaran, and E. Tosetti (2011). Weak and strong cross section dependence and estimation of large panels. Econometrics Journal 14, C45–C90.
Donald, S. G. and Newey, W. K. (2001). Choosing the number of instruments, Econometrica 69: 1161–1191.
Drukker, D.M, P. Egger and I. R. Prucha (2013),"On Two-step Estimation of
a Spatial Autoregressive Model with Autoregressive Disturbances and Endogenous
Regressors", Econometric Reviews, Issue 1, Vol 33.
Huang, X. (2013),"Nonparametric Estimation in Large Panels with Cross Sectional
Dependence", Econometric Reviews, Issue 1, Vol 33.
Im, K. S., M. H. Peseran and Y. Shin (2003). Testing for Unit Roots in Heterogeneous
Panels. Journal of Econometrics 115, 53–74.
Jin, S. and L. Su (2013),"A Nonparametric Poolability Test for Panel Data Models
with Cross Section Dependence", Economertric Reviews, Issue 1, Vol 33.
Kapoor, M., H.H. Kelejian, and I.R. Prucha (2007). Panel data models with spatially
correlated error components. Journal of Econometrics 140, 97-130.
Kelejian, H.H. and Prucha, I.R. (1998). A Generalized Spatial Two-Stage Least Squares
Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances.
Journal of Real Estate Finance and Economics 17, 99-121.
Kelejian, H.H. and Prucha, I.R. (1999). A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review 40, 509-533.
Levin, A., C. Lin, and C.-J. Chu (2002). Unit Root Tests in Panel Data: Asymptotic and
Finite-sample Properties. Journal of Econometrics 108, 1–24.
Liu, X. and L-F. Lee (2013),"Two Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments", Econometric Reviews, Issue 1, Vol 33.
Pesaran, M. H. (2006). Estimation and inference in large heterogeneous panels with a
multifactor error structure. Econometrica 74: 967-1012.
Pesaran, M. H. and E. Tosetti (2011). Large panels with common factors and spatial
correlations. Journal of Econometrics 161, 182–202.
Sara…dis, V. and T. Wansbeek (2012). Cross-sectional dependence in panel data analysis,
forthcoming in Econometric Reviews (to update later).
Westerlund, J. and J. Breitung (2013),"Lessons from a Decade of IPS and LLC",
Econometric Reviews, Issue 1, Vol 33.
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