Large Panel Data Models with Cross-Sectional Dependence: A Survey

This paper provides an overview of the recent literature on estimation and inference in large panel data models with cross-sectional dependence. It reviews panel data models with strictly exogenous regressors as well as dynamic models with weakly exogenous regressors. The paper begins with a review of the concepts of weak and strong cross-sectional dependence, and discusses the exponent of cross-sectional dependence that characterizes the different degrees of cross-sectional dependence. It considers a number of alternative estimators for static and dynamic panel data models, distinguishing between factor and spatial models of cross-sectional dependence. The paper also provides an overview of tests of independence and weak cross-sectional dependence.

[1]  M. Pesaran,et al.  Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit , 2010, SSRN Electronic Journal.

[2]  J. Bai,et al.  Large Dimensional Factor Analysis , 2008 .

[3]  Z. Bai,et al.  On the limit of the largest eigenvalue of the large dimensional sample covariance matrix , 1988 .

[4]  J. Bai,et al.  Panel Data Models With Interactive Fixed Effects , 2009 .

[5]  Recursive mean adjustment in time-series inferences , 1999 .

[6]  Gary Chamberlain,et al.  FUNDS, FACTORS, AND DIVERSIFICATION IN ARBITRAGE PRICING MODELS , 1983 .

[7]  M. Hashem Pesaran,et al.  Testing Weak Cross-Sectional Dependence in Large Panels , 2012, SSRN Electronic Journal.

[8]  Elisa Tosetti,et al.  Large Panels with Common Factors and Spatial Correlations , 2007, SSRN Electronic Journal.

[9]  P. Loubaton,et al.  THE EMPIRICAL EIGENVALUE DISTRIBUTION OF A GRAM MATRIX: FROM INDEPENDENCE TO STATIONARITY , 2005 .

[10]  Serena Ng,et al.  Determining the Number of Primitive Shocks in Factor Models , 2007 .

[11]  James H. Stock,et al.  Dynamic Factor Models , 2011 .

[12]  A. Zellner.  An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[13]  P. Jensen,et al.  Testing for Cross-sectional Dependence in Regional Panel Data , 2011 .

[14]  D. Griffith.  Spatial Autocorrelation , 2020, Spatial Analysis Methods and Practice.

[15]  G. Kapetanios.  A New Method for Determining the Number of Factors in Factor Models with Large Datasets , 2004 .

[16]  Takashi Yamagata,et al.  A test of cross section dependence for a linear dynamic panel model with regressors , 2009 .

[17]  J. Bai,et al.  Determining the Number of Factors in Approximate Factor Models , 2000 .

[18]  J. Keith Ord,et al.  Spatial Processes Models and Applications , 1981 .

[19]  P. Whittle,et al.  Latent Variables in Socio‐Economic Models , 1978 .

[20]  M. Hallin,et al.  Determining the Number of Factors in the General Dynamic Factor Model , 2007 .

[21]  D. Mare,et al.  The Oxford Handbook of Economic Forecasting , 2015, J. Oper. Res. Soc..

[22]  Lung-fei Lee,et al.  Spatial Panel Data Models , 2015 .

[23]  J. LeSage.  Spatial Econometrics , 1998 .

[24]  L. Anselin.  Spatial Econometrics: Methods and Models , 1988 .

[25]  A. Chudik,et al.  Large Panel Data Models with Cross-Sectional Dependence , 2015 .

[26]  Geert Dhaene,et al.  Split-Panel Jackknife Estimation of Fixed-Effect Models , 2015 .

[27]  A. Ullah,et al.  A Bias-Adjusted LM Test of Error Cross-Section Independence , 2008 .

[28]  P. Whittle.  ON STATIONARY PROCESSES IN THE PLANE , 1954 .

[29]  K. Berk.  Consistent Autoregressive Spectral Estimates , 1974 .

[30]  Takashi Yamagata,et al.  Testing Slope Homogeneity in Large Panels , 2005, SSRN Electronic Journal.

[31]  Jörg Breitung,et al.  A Canonical Correlation Approach for Selecting the Number of Dynamic Factors , 2013 .

[32]  Badi H. Baltagi,et al.  Testing Panel Data Regression Models with Spatial Error Correlation , 2002 .

[33]  G. Kapetanios,et al.  Panels with Nonstationary Multifactor Error Structures , 2006, SSRN Electronic Journal.

[34]  Ronald Smith,et al.  A Principal Components Approach to Cross-Section Dependence in Panels , 2002 .

[35]  D. Dickey,et al.  Testing for unit roots in autoregressive-moving average models of unknown order , 1984 .

[36]  P. O'Connell.  The overvaluation of purchasing power parity , 1998 .

[37]  Badi H. Baltagi,et al.  A companion to theoretical econometrics , 2003 .

[38]  M. Pesaran,et al.  Large Panels with Common Factors and Spatial Correlation , 2011 .

[39]  J. Ord,et al.  Spatial Processes: Models and Applications , 1984 .

[40]  Marco Lippi,et al.  THE GENERALIZED DYNAMIC FACTOR MODEL: REPRESENTATION THEORY , 2001, Econometric Theory.

[41]  Donggyu Sul,et al.  Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence , 2003 .

[42]  Donggyu Sul,et al.  Dynamic Panel Estimation and Homogeneity Testing Under Cross Section Dependence , 2002 .

[43]  F. Moscone,et al.  A Review and Comparison of Tests of Cross-Section Independence in Panels , 2009 .

[44]  George Kapetanios,et al.  A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets , 2010 .

[45]  Tom Wansbeek,et al.  Cross-Sectional Dependence in Panel Data Analysis , 2012 .

[46]  George Kapetanios,et al.  Alternative Approaches to Estimation and Inference in Large Multifactor Panels: Small Sample Results with an Application to Modelling of Asset Returns , 2005, SSRN Electronic Journal.

[47]  Markku Rahiala,et al.  Panel Data , 2011, International Encyclopedia of Statistical Science.

[48]  Marco Lippi,et al.  The generalized dynamic factor model: consistency and rates , 2004 .

[49]  Adrian Pagan,et al.  The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics , 1980 .

[50]  Lung-fei Lee,et al.  Some recent developments in spatial panel data models , 2010 .

[51]  M. Weidner,et al.  Dynamic Linear Panel Regression Models with Interactive Fixed Effects , 2014 .

[52]  J. W. Silverstein,et al.  No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices , 1998 .

[53]  Ron Smith,et al.  Unobserved Heterogeneity in Panel Time Series Models , 2004, Comput. Stat. Data Anal..

[54]  Chihwa Kao,et al.  Testing for Sphericity in a Fixed Effects Panel Data Model , 2011 .

[55]  C. Granger.  Long memory relationships and the aggregation of dynamic models , 1980 .

[56]  Sean Holly,et al.  Spatial and Temporal Diffusion of House Prices in the UK , 2010, SSRN Electronic Journal.

[57]  Minkee Song,et al.  Asymptotic Theory for Dynamic Heterogeneous Panels with Cross-Sectional Dependence and Its Applications , 2012 .

[58]  Matthew Harding,et al.  Estimating the Number of Factors in Large Dimensional Factor Models 1 , 2013 .

[59]  P. Moran.  The Interpretation of Statistical Maps , 1948 .

[60]  Seung C. Ahn,et al.  Eigenvalue Ratio Test for the Number of Factors , 2013 .

[61]  M. Pesaran,et al.  Factor Models , 2021, Modern Equity Investing Strategies.

[62]  M. Pesaran.  General diagnostic tests for cross-sectional dependence in panels , 2004, Empirical Economics.

[63]  M. Pesaran,et al.  Common Correlated Effects Estimation of Heterogenous Dynamic Panel Data Models with Weakly Exogenous Regressors , 2013 .

[64]  Luc Anselin,et al.  Spatial Dependence in Linear Regression Models with an Introduction to Spatial Econometrics , 1995 .

[65]  D. Andrews,et al.  Cross-Section Regression with Common Shocks , 2003 .

[66]  A. Onatski.  Determining the Number of Factors from Empirical Distribution of Eigenvalues , 2010, The Review of Economics and Statistics.

[67]  Alexei Onatski,et al.  Asymptotics of the principal components estimator of large factor models with weakly influential factors , 2012 .

[68]  A. Ullah,et al.  Handbook of Applied Economic Statistics , 2000 .

[69]  M. Hallin,et al.  The Generalized Dynamic-Factor Model: Identification and Estimation , 2000, Review of Economics and Statistics.

[70]  Cross sectional averages or principal components , 2011 .

[71]  Thomas J. Sargent,et al.  Business cycle modeling without pretending to have too much a priori economic theory , 1976 .

[72]  Vasilis Sarafidis,et al.  On the Impact of Error Cross-Sectional Dependence in Short Dynamic Panel Estimation , 2009 .

[73]  Robert Haining,et al.  Spatial Data Analysis: Theory and Practice , 2003 .

[74]  Martin Weidner,et al.  Analysis of interactive fixed effects dynamic linear panel regression with measurement error , 2011 .

[75]  M. Pesaran,et al.  Weak and Strong Cross-Section Dependence and Estimation of Large Panels , 2009, SSRN Electronic Journal.

[76]  Jean-Marie Dufour,et al.  Exact Tests for Contemporaneous Correlation of Disturbances in Seemingly Unrelated Regressions * , 2022 .

[77]  Mark W. Watson,et al.  Consistent Estimation of the Number of Dynamic Factors in a Large N and T Panel , 2007 .

[78]  S. John.  Some optimal multivariate tests , 1971 .

[79]  Cheng Hsiao,et al.  Diagnostic Tests of Cross‐Section Independence for Limited Dependent Variable Panel Data Models* , 2012 .

[80]  A. Onatski.  TESTING HYPOTHESES ABOUT THE NUMBER OF FACTORS IN LARGE FACTOR MODELS , 2009 .

[81]  M. Pesaran,et al.  Estimating Long-Run Relationships From Dynamic Heterogeneous Panels , 1995 .

[82]  James R. Schott,et al.  Testing for complete independence in high dimensions , 2005 .

[83]  Serena Ng,et al.  Testing Cross-Section Correlation in Panel Data Using Spacings , 2006 .

[84]  Marc,et al.  The Generalized Dynamic Factor Model determining the number of factors ∗ , 2005 .

[85]  M. Pesaran.  Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure , 2004, SSRN Electronic Journal.

[86]  E. Frees.  Assessing cross-sectional correlation in panel data , 1995 .