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A Simple Panel Unit Root Test in the Presence of Cross Section Dependence
 JOURNAL OF APPLIED ECONOMETRICS
, 2006
"... 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 thi ..."
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Cited by 372 (16 self)
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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 ADF regressions are augmented with the cross section averages of lagged levels and firstdifferences of the individual series. New asymptotic results are obtained both for the individual cross sectionally augmented ADF (CADF) statistics, and 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.
Dynamic panel estimation and homogeneity testing under cross section dependence. Cowles Foundation Discussion Paper #1362,
, 2002
"... Summary This paper deals with cross section dependence, homogeneity restrictions and small sample bias issues in dynamic panel regressions. To address the bias problem we develop a panel approach to median unbiased estimation that takes account of cross section dependence. The estimators given here ..."
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Cited by 166 (8 self)
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Summary This paper deals with cross section dependence, homogeneity restrictions and small sample bias issues in dynamic panel regressions. To address the bias problem we develop a panel approach to median unbiased estimation that takes account of cross section dependence. The estimators given here considerably reduce the effects of bias and gain precision from estimating cross section error correlation. This paper also develops an asymptotic theory for tests of coefficient homogeneity under cross section dependence, and proposes a modified Hausman test to test for the presence of homogeneous unit roots. An orthogonalization procedure, based on iterated method of moments estimation, is developed to remove cross section dependence and permit the use of conventional and meta unit root tests with panel data. Some simulations investigating the finite sample performance of the estimation and test procedures are reported.
A PANIC Attack on Unit Roots and Cointegration
, 2003
"... This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC – a ‘Panel Analysis of Nonstationarity in Idiosyncratic and Common components’. PANIC consists of univariate and ..."
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Cited by 142 (3 self)
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This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC – a ‘Panel Analysis of Nonstationarity in Idiosyncratic and Common components’. PANIC consists of univariate and panel tests with a number of novel features. It can detect whether the nonstationarity is pervasive, or variablespecific, or both. It tests the components of the data instead of the observed series. Inference is therefore more accurate when the components have different orders of integration. PANIC also permits the construction of valid panel tests even when crosssection correlation invalidates pooling of statistics constructed using the observed data. The key to PANIC is consistent estimation of the components even when the regressions are individually spurious. We provide a rigorous theory for estimation and inference. In Monte Carlo simulations, the tests have very good size and power. PANIC is applied to a panel of inflation series.
Panel Data Models with Interactive Fixed Effects
, 2005
"... This paper considers large N and large T panel data models with unobservable multiple interactive effects. These models are useful for both micro and macro econometric modelings. In earnings studies, for example, workers ’ motivation, persistence, and diligence combined to influence the earnings in ..."
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Cited by 125 (6 self)
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This paper considers large N and large T panel data models with unobservable multiple interactive effects. These models are useful for both micro and macro econometric modelings. In earnings studies, for example, workers ’ motivation, persistence, and diligence combined to influence the earnings in addition to the usual argument of innate ability. In macroeconomics, the interactive effects represent unobservable common shocks and their heterogeneous responses over cross sections. Since the interactive effects are allowed to be correlated with the regressors, they are treated as fixed effects parameters to be estimated along with the common slope coefficients. The model is estimated by the least squares method, which provides the interactiveeffects counterpart of the within estimator. We first consider model identification, and then derive the rate of convergence and the limiting distribution of the interactiveeffects estimator of the common slope coefficients. The estimator is shown to be √ NT consistent. This rate is valid even in the presence of correlations and heteroskedasticities in both dimensions, a striking contrast with fixed T framework in which serial correlation and heteroskedasticity imply unidentification. The asymptotic distribution is not necessarily centered at zero. Biased corrected estimators are derived. We also derive the constrained estimator and its limiting distribution, imposing additivity coupled with interactive effects. The problem of testing additive versus interactive effects is also studied. We also derive identification conditions for models with grand mean, timeinvariant regressors, and common regressors. It is shown that there exists a set of necessary and sufficient identification conditions for those models. Given identification, the rate of convergence and limiting results continue to hold. Key words and phrases: incidental parameters, additive effects, interactive effects, factor
Cointegration Vector Estimation by Panel DOLS and LongRun Money Demand
 Oxford Bulletin of Economics and Statistics
, 2003
"... We study the panel dynamic ordinary least square (DOLS) estimator of a homogeneous cointegration vector for a balanced panel of N individuals observed over T time periods. Allowable heterogeneity across individuals include individualspecific time trends, individualspecific fixed effects and times ..."
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Cited by 92 (0 self)
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We study the panel dynamic ordinary least square (DOLS) estimator of a homogeneous cointegration vector for a balanced panel of N individuals observed over T time periods. Allowable heterogeneity across individuals include individualspecific time trends, individualspecific fixed effects and timespecific effects. The estimator is fully parametric, computationally convenient, and more precise than the single equation estimator. For fixed N as T fi 1, the estimator converges to a function of Brownian motions and the Wald statistic for testing a set of s linear constraints has a limiting v2(s) distribution. The estimator also has a Gaussian sequential limit distribution that is obtained first by letting T fi 1 and then letting N fi 1. In a series of MonteCarlo experiments, we find that the asymptotic distribution theory provides a reasonably close approximation to the exact finite sample distribution. We use panel DOLS to estimate coefficients of the longrun money demand function from a panel of 19 countries with annual observations that span from 1957 to 1996. The estimated income elasticity is 1.08 (asymptotic s.e. 0.26) and the estimated interest rate semielasticity is)0.02 (asymptotic s.e. 0.01). *This paper was previously circulated under the title ‘A Computationally Simple Cointegration
Testing for error correction in panel data
 Oxford Bulletin of Economics and Statistics
, 2007
"... This paper proposes new error correction based cointegration tests for panel data. The limiting distributions of the tests are derived and critical values are provided. Our simulation results suggest that the tests have good smallsample properties with small size distortions and high power relative ..."
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Cited by 90 (2 self)
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This paper proposes new error correction based cointegration tests for panel data. The limiting distributions of the tests are derived and critical values are provided. Our simulation results suggest that the tests have good smallsample properties with small size distortions and high power relative to other popular residualbased panel cointegration tests. In our empirical application, we present evidence suggesting that international health care expenditures and GDP are cointegrated once the possibility of an invalid common factor restriction has been accounted for.
Unit Roots and Cointegration in Panels
, 2007
"... This paper provides a review of the literature on unit roots and cointegration in panels where the time dimension (T), and the cross section dimension (N) are relatively large. It distinguishes between the first generation tests developed on the assumption of the cross section independence, and the ..."
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Cited by 54 (3 self)
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This paper provides a review of the literature on unit roots and cointegration in panels where the time dimension (T), and the cross section dimension (N) are relatively large. It distinguishes between the first generation tests developed on the assumption of the cross section independence, and the second generation tests that allow, in a variety of forms and degrees, the dependence that might prevail across the different units in the panel. In the analysis of cointegration the hypothesis testing and estimation problems are further complicated by the possibility of cross section cointegration which could arise if the unit roots in the different cross section units are due to common random walk components.
Large panels with common factors and spatial correlations
 IZA DISCUSSION PAPER
, 2007
"... This paper considers the statistical analysis of large panel data sets where even after conditioning on common observed effects the cross section units might remain dependently distributed. This could arise when the cross section units are subject to unobserved common effects and/or if there are spi ..."
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Cited by 52 (5 self)
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This paper considers the statistical analysis of large panel data sets where even after conditioning on common observed effects the cross section units might remain dependently distributed. This could arise when the cross section units are subject to unobserved common effects and/or if there are spill over effects due to spatial or other forms of local dependencies. The paper provides an overview of the literature on cross section dependence, introduces the concepts of timespecific weak and strong cross section dependence and shows that the commonly used spatial models are examples of weak cross section dependence. It is then established that the Common Correlated Effects (CCE) estimator of panel data model with a multifactor error structure, recently advanced by Pesaran (2006), continues to provide consistent estimates of the slope coefficient, even in the presence of spatial error processes. Small sample properties of the CCE estimator 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. We also explore the role of certain characteristics of spatial processes in determining the performance of CCE estimators, such as the form and intensity of spatial dependence, and the sparseness of the spatial weight matrix.
Estimation and inference in short panel vector autoregressions with unit roots and cointegration
, 2003
"... This paper considers estimation and inference in panel vector autoregressions (PVARs) where (i) the individual effects are either random or fixed, (ii) the timeseries properties of the model variables are unknown a priori and may feature unit roots and cointegrating relations, and (iii) the time di ..."
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Cited by 47 (1 self)
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This paper considers estimation and inference in panel vector autoregressions (PVARs) where (i) the individual effects are either random or fixed, (ii) the timeseries properties of the model variables are unknown a priori and may feature unit roots and cointegrating relations, and (iii) the time dimension of the panel is short and its crosssectional dimension is large. Generalized Method of Moments (GMM) and Quasi Maximum Likelihood (QML) estimators are obtained andthencomparedintermsoftheirasymptoticandfinite sample properties. It is shown that GMM estimators based only on standard orthogonality conditions break down if the underlying time series contain unit roots. Extended GMM estimators making use of further moment conditions are not subject to this problem. However, their finite sample performance is shown to deteriorate as a ratio of crosssection to timeseries variation is increased, while the performance of the fixed effects QML estimator is invariant to this ratio. The QML estimators also tend to outperform the various GMM estimators in finite sample. Overall, our findings favor the use of the fixed effects QML estimator, given that it does not impose any restrictions on the distribution generating the individual effects. The paper also shows how the fixed effects QML
Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence
, 2004
"... Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N →∞. The results extend earlier work by Nickell (1981) and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic t ..."
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Cited by 44 (8 self)
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Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N →∞. The results extend earlier work by Nickell (1981) and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic trends, predetermined and exogenous regressors, and errors that may be cross sectionally dependent. The asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient. Another finding of interest is that, when there is cross section error dependence, the probability limit of the dynamic panel regression estimator is a random variable rather than a constant, which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where N is very large. Some proposals for bias correction are suggested and finite sample performance is analyzed in simulations.