This paper proposes simple tests of error cross-sectional dependence which are applicable to a variety of panel data models, including stationary and unit root dynamic heterogeneous panels with short
...T
and large
N
. The proposed tests are based on the average of pair-wise correlation coefficients of the OLS residuals from the individual regressions in the panel and can be used to test for cross-sectional dependence of any fixed order
p
, as well as the case where no a priori ordering of the cross-sectional units is assumed, referred to as
CD
(
p
)
and
CD
tests, respectively. Asymptotic distribution of these tests is derived and their power function analyzed under different alternatives. It is shown that these tests are correctly centred for fixed
N
and
T
and are robust to single or multiple breaks in the slope coefficients and/or error variances. The small sample properties of the tests are investigated and compared to the Lagrange multiplier test of Breusch and Pagan using Monte Carlo experiments. It is shown that the tests have the correct size in very small samples and satisfactory power, and, as predicted by the theory, they are quite robust to the presence of unit roots and structural breaks. The use of the
CD
test is illustrated by applying it to study the degree of dependence in per capita output innovations across countries within a given region and across countries in different regions. The results show significant evidence of cross-dependence in output innovations across many countries and regions in the World.
This paper proposes a standardized version of Swamy's test of slope homogeneity for panel data models where the cross section dimension (
N
) could be large relative to the time series dimension (
T
...). The proposed test, denoted by
Δ
˜
, exploits the cross section dispersion of individual slopes weighted by their relative precision. In the case of models with strictly exogenous regressors, but with non-normally distributed errors, the test is shown to have a standard normal distribution as
(
N
,
T
)
→
j
∞
such that
N
/
T
2
→
0
. When the errors are normally distributed, a mean-variance bias adjusted version of the test is shown to be normally distributed irrespective of the relative expansion rates of
N
and
T
. The test is also applied to stationary dynamic models, and shown to be valid asymptotically so long as
N
/
T
→
κ
, as
(
N
,
T
)
→
j
∞
, where
0
⩽
κ
<
∞
. Using Monte Carlo experiments, it is shown that the test has the correct size and satisfactory power in panels with strictly exogenous regressors for various combinations of
N
and
T
. Similar results are also obtained for dynamic panels, but only if the autoregressive coefficient is not too close to unity and so long as
T
⩾
N
.
This paper extends the Common Correlated Effects (CCE) approach developed by Pesaran (2006) to heterogeneous panel data models with lagged dependent variables and/or weakly exogenous regressors. We ...show that the CCE mean group estimator continues to be valid but the following two conditions must be satisfied to deal with the dynamics: a sufficient number of lags of cross section averages must be included in individual equations of the panel, and the number of cross section averages must be at least as large as the number of unobserved common factors. We establish consistency rates, derive the asymptotic distribution, suggest using covariates to deal with the effects of multiple unobserved common factors, and consider jackknife and recursive de-meaning bias correction procedures to mitigate the small sample time series bias. Theoretical findings are accompanied by extensive Monte Carlo experiments, which show that the proposed estimators perform well so long as the time series dimension of the panel is sufficiently large.
This article considers testing the hypothesis that errors in a panel data model are weakly cross-sectionally dependent, using the exponent of cross-sectional dependence α, introduced recently in ...Bailey, Kapetanios, and Pesaran (2012). It is shown that the implicit null of the cross-sectional dependence (CD) test depends on the relative expansion rates of N and T. When T = O(N
ε
), for some 0 < ε ≤1, then the implicit null of the CD test is given by 0 ≤ α < (2 − ε)/4, which gives 0 ≤ α <1/4, when N and T tend to infinity at the same rate such that T/N → κ, with κ being a finite positive constant. It is argued that in the case of large N panels, the null of weak dependence is more appropriate than the null of independence which could be quite restrictive for large panels. Using Monte Carlo experiments, it is shown that the CD test has the correct size for values of α in the range 0, 1/4, for all combinations of N and T, and irrespective of whether the panel contains lagged values of the dependent variables, so long as there are no major asymmetries in the error distribution.
This paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure. The unobserved factors and the individual-specific errors are allowed ...to follow arbitrary stationary processes, and the number of unobserved factors need not be estimated. The basic idea is to filter the individual-specific regressors by means of cross-section averages such that asymptotically as the cross-section dimension (N) tends to infinity, the differential effects of unobserved common factors are eliminated. The estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross-sectional averages of the dependent variable and the individual-specific regressors. A number of estimators (referred to as common correlated effects (CCE) estimators) are proposed and their asymptotic distributions are derived. The small sample properties of mean group and pooled CCE estimators are investigated by Monte Carlo experiments, showing that the CCE estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics, and for relatively small values of N and T.
This paper provides a characterisation of the degree of cross-sectional dependence in a two dimensional array, {xit, i = 1, 2, ...N; t = 1, 2, ..., T} in terms of the rate at which the variance of ...the cross-sectional average of the observed data varies with N. Under certain conditions this is equivalent to the rate at which the largest eigenvalue of the covariance matrix of xt
= (x
1t
, x
2t
, ..., xNt
)′ rises with N. We represent the degree of cross-sectional dependence by α, which we refer to as the ‘exponent of cross-sectional dependence’, and define it by the standard deviation, Std(x̄t
) = O (N
α–1), where x̄t
is a simple cross-sectional average of xit
. We propose bias corrected estimators, derive their asymptotic properties for α > 1/2 and consider a number of extensions. We include a detailed Monte Carlo simulation study supporting the theoretical results. We also provide a number of empirical applications investigating the degree of inter-linkages of real and financial variables in the global economy.
This paper considers methods for estimating the slope coefficients in large panel data models that are robust to the presence of various forms of error cross-section dependence. It introduces a ...general framework where error cross-section dependence may arise because of unobserved common effects and/or error spill-over effects due to spatial or other forms of local dependencies. Initially, this paper focuses on a panel regression model where the idiosyncratic errors are spatially dependent and possibly serially correlated, and derives the asymptotic distributions of the mean group and pooled estimators under heterogeneous and homogeneous slope coefficients, and for these estimators proposes non-parametric variance matrix estimators. The paper then considers the more general case of a panel data model with a multifactor error structure and spatial error correlations. Under this framework, the Common Correlated Effects (CCE) estimator, recently advanced by
Pesaran (2006), continues to yield estimates of the slope coefficients that are consistent and asymptotically normal. Small sample properties of the estimators under various patterns of cross-section dependence, including spatial forms, are investigated by Monte Carlo experiments. Results show that the CCE approach works well in the presence of weak and/or strong cross-sectionally correlated errors.
This paper proposes a pair-wise approach to testing for output convergence that considers all
N
(
N
-
1
)
/
2
possible pairs of log per-capita output gaps across
N economies. A general probabilistic ...definition of output convergence is also proposed, which suggests that all such output gap pairs must be stationary with a constant mean. The approach is compatible with individual output series having unit roots, or other non-stationary common components and does not involve the choice of a reference country in computation of output gaps. It is also applicable when
N is large relative to
T (the time dimension of the panel). After providing some encouraging Monte Carlo evidence on the small sample properties of the pair-wise test, the test is applied to output series in the Penn World Tables over 1950–2000. Overall, the results do not support output convergence, and suggest that the findings of convergence clubs in the literature might be spurious. However, significant evidence of growth convergence is found, a result which is reasonably robust to the choice of the sample period and country groupings. Non-convergence of log per-capita outputs combined with growth convergence suggests that while common technological progress seems to have been diffusing reasonably widely across economies, there are nevertheless important country-specific factors that render output gaps highly persistent, such that we cannot be sure that the probability for the output gaps to lie within a fixed range will be non-zero.
This paper studies the relationship between public debt expansion and economic growth and investigates whether the debt-growth relation varies with the level of indebtedness. We contribute ...theoretically by developing tests for threshold effects in the context of dynamic heterogeneous panel data models with cross-sectionally dependent errors. In the empirical application, using data on a sample of forty countries over the 1965–2010 period, we find no evidence for a universally applicable threshold effect in the relationship between public debt and economic growth. Regardless of the threshold, however, we find significant negative effects of public debt buildup on output growth.
A number of panel unit root tests that allow for cross-section dependence have been proposed in the literature that use orthogonalization type procedures to asymptotically eliminate the ...cross-dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative where the standard augmented Dickey-Fuller (ADF) regressions are augmented with the cross-section averages of lagged levels and first-differences of the individual series. New asymptotic results are obtained both for the individual cross-sectionally augmented ADF (CADF) statistics and for their simple averages. It is shown that the individual CADF statistics are asymptotically similar and do not depend on the factor loadings. The limit distribution of the average CADF statistic is shown to exist and its critical values are tabulated. Small sample properties of the proposed test are investigated by Monte Carlo experiments. The proposed test is applied to a panel of 17 OECD real exchange rate series as well as to log real earnings of households in the PSID data.
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