Yves Croissant, Professor of Economics, CEMOI, Faculté de Droit et d'Economie, Université de La Réunion, France Giovanni Millo, Senior Economist, Group Insurance Research, Assicurazioni Generali S.p.A., Trieste, Italy

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• Preface xiiiAcknowledgments xviiAbout the CompanionWebsite xix1 Introduction 11.1 Panel Data Econometrics: A Gentle Introduction 11.1.1 Eliminating Unobserved Components 21.1.1.1 Differencing Methods 21.1.1.2 LSDV Methods 21.1.1.3 Fixed Effects Methods 21.2 R for Econometric Computing 61.2.1 The Modus Operandi of R 71.2.2 Data Management 81.2.2.1 Outsourcing to Other Software 81.2.2.2 Data ManagementThrough Formulae 81.3 plm for the Casual R User 81.3.1 R for the Matrix Language User 91.3.2 R for the User of Econometric Packages 101.4 plm for the Proficient R User 111.4.1 Reproducible EconometricWork 121.4.2 Object-orientation for the User 131.5 plm for the R Developer 131.5.1 Object-orientation for Development 141.6 Notations 171.6.1 General Notation 181.6.2 Maximum Likelihood Notations 181.6.3 Index 181.6.4 The Two-way Error Component Model 181.6.5 Transformation for the One-way Error Component Model 191.6.6 Transformation for the Two-ways Error Component Model 201.6.7 Groups and Nested Models 201.6.8 Instrumental Variables 201.6.9 Systems of Equations 201.6.10 Time Series 211.6.11 Limited Dependent and Count Variables 211.6.12 Spatial Panels 212 The Error Component Model 232.1 Notations and Hypotheses 232.1.1 Notations 232.1.2 Some Useful Transformations 242.1.3 Hypotheses Concerning the Errors 252.2 Ordinary Least Squares Estimators 272.2.1 Ordinary Least Squares on the Raw Data: The Pooling Model 272.2.2 The between Estimator 282.2.3 The within Estimator 292.3 The Generalized Least Squares Estimator 332.3.1 Presentation of the GLS Estimator 342.3.2 Estimation of the Variances of the Components of the Error 352.4 Comparison of the Estimators 392.4.1 Relations between the Estimators 392.4.2 Comparison of the Variances 402.4.3 Fixed vs Random Effects 402.4.4 Some Simple Linear Model Examples 422.5 The Two-ways Error Components Model 472.5.1 Error Components in the Two-ways Model 472.5.2 Fixed and Random Effects Models 482.6 Estimation of a Wage Equation 493 Advanced Error Components Models 533.1 Unbalanced Panels 533.1.1 Individual Effects Model 533.1.2 Two-ways Error Component Model 543.1.2.1 Fixed Effects Model 553.1.2.2 Random Effects Model 563.1.3 Estimation of the Components of the Error Variance 573.2 Seemingly Unrelated Regression 643.2.1 Introduction 643.2.2 Constrained Least Squares 653.2.3 Inter-equations Correlation 663.2.4 SUR With Panel Data 673.3 The Maximum Likelihood Estimator 713.3.1 Derivation of the Likelihood Function 713.3.2 Computation of the Estimator 733.4 The Nested Error Components Model 743.4.1 Presentation of the Model 743.4.2 Estimation of the Variance of the Error Components 754 Tests on Error Component Models 834.1 Tests on Individual and/or Time Effects 834.1.1 F Tests 844.1.2 Breusch-Pagan Tests 844.2 Tests for Correlated Effects 884.2.1 The Mundlak Approach 894.2.2 Hausman Test 904.2.3 Chamberlain’s Approach 904.2.3.1 Unconstrained Estimator 914.2.3.2 Constrained Estimator 934.2.3.3 Fixed Effects Models 934.3 Tests for Serial Correlation 954.3.1 Unobserved Effects Test 954.3.2 Score Test of Serial Correlation and/or Individual Effects 964.3.3 Likelihood Ratio Tests for AR(1) and Individual Effects 994.3.4 Applying Traditional Serial Correlation Tests to Panel Data 1014.3.5 Wald Tests for Serial Correlation using within and First-differenced Estimators 1024.3.5.1 Wooldridge’s within-based Test 1024.3.5.2 Wooldridge’s First-difference-based Test 1034.4 Tests for Cross-sectional Dependence 1044.4.1 Pairwise Correlation Coefficients 1044.4.2 CD-type Tests for Cross-sectional Dependence 1054.4.3 Testing Cross-sectional Dependence in a pseries 1075 Robust Inference and Estimation for Non-spherical Errors 1095.1 Robust Inference 1095.1.1 Robust Covariance Estimators 1095.1.1.1 Cluster-robust Estimation in a Panel Setting 1105.1.1.2 Double Clustering 1155.1.1.3 Panel Newey-west and SCC 1165.1.2 Generic Sandwich Estimators and Panel Models 1205.1.2.1 Panel Corrected Standard Errors 1225.1.3 Robust Testing of Linear Hypotheses 1235.1.3.1 An Application: Robust Hausman Testing 1255.2 Unrestricted Generalized Least Squares 1275.2.1 General Feasible Generalized Least Squares 1285.2.1.1 Pooled GGLS 1295.2.1.2 Fixed Effects GLS 1305.2.1.3 First Difference GLS 1325.2.2 Applied Examples 1336 Endogeneity 1396.1 Introduction 1396.2 The Instrumental Variables Estimator 1406.2.1 Generalities about the Instrumental Variables Estimator 1406.2.2 The within Instrumental Variables Estimator 1416.3 Error Components Instrumental Variables Estimator 1436.3.1 The General Model 1436.3.2 Special Cases of the General Model 1456.3.2.1 The within Model 1456.3.2.2 Error Components Two Stage Least Squares 1466.3.2.3 The Hausman and Taylor Model 1466.3.2.4 The Amemiya-Macurdy Estimator 1476.3.2.5 The Breusch, Mizon and Schmidt’s Estimator 1476.3.2.6 Balestra and Varadharajan-Krishnakumar Estimator 1476.4 Estimation of a System of Equations 1546.4.1 TheThree Stage Least Squares Estimator 1556.4.2 The Error Components Three Stage Least Squares Estimator 1566.5 More Empirical Examples 1587 Estimation of a Dynamic Model 1617.1 Dynamic Model and Endogeneity 1637.1.1 The Bias of the ols Estimator 1637.1.2 The within Estimator 1647.1.3 Consistent Estimation Methods for Dynamic Models 1657.2 GMM Estimation of the Differenced Model 1687.2.1 Instrumental Variables and Generalized Method of Moments 1687.2.2 One-step Estimator 1697.2.3 Two-steps Estimator 1717.2.4 The Proliferation of Instruments in the Generalized Method of Moments Difference Estimator 1727.3 Generalized Method of Moments Estimator in Differences and Levels 1747.3.1 Weak Instruments 1747.3.2 Moment Conditions on the Levels Model 1757.3.3 The System GMM Estimator 1777.4 Inference 1787.4.1 Robust Estimation of the Coefficients’ Covariance 1787.4.2 Overidentification Tests 1797.4.3 Error Serial Correlation Test 1817.5 More Empirical Examples 1828 Panel Time Series 1858.1 Introduction 1858.2 Heterogeneous Coefficients 1868.2.1 Fixed Coefficients 1868.2.2 Random Coefficients 1878.2.2.1 The Swamy Estimator 1878.2.2.2 The Mean Groups Estimator 1908.2.3 Testing for Poolability 1928.3 Cross-sectional Dependence and Common Factors 1948.3.1 The Common Factor Model 1958.3.2 Common Correlated Effects Augmentation 1968.3.2.1 cce Mean Groups vs. cce Pooled 1988.3.2.2 Computing the ccep Variance 1998.4 Nonstationarity and Cointegration 2008.4.1 Unit Root Testing: Generalities 2018.4.2 First Generation Unit Root Testing 2048.4.2.1 Preliminary Results 2048.4.2.2 Levin-Lin-Chu Test 2058.4.2.3 Im, Pesaran and Shin Test 2058.4.2.4 The Maddala and Wu Test 2068.4.3 Second Generation Unit Root Testing 2079 Count Data and Limited Dependent Variables 2119.1 Binomial and Ordinal Models 2139.1.1 Introduction 2139.1.1.1 The Binomial Model 2139.1.1.2 Ordered Models 2149.1.2 The Random Effects Model 2149.1.2.1 The Binomial Model 2149.1.2.2 Ordered Models 2179.1.3 The Conditional Logit Model 2199.2 Censored or Truncated Dependent Variable 2239.2.1 Introduction 2239.2.2 The Ordinary Least Squares Estimator 2239.2.3 The Symmetrical Trimmed Estimator 2259.2.3.1 Truncated Sample 2259.2.3.2 Censored Sample 2269.2.4 The Maximum Likelihood Estimator 2269.2.4.1 Truncated Sample 2269.2.4.2 Censored Sample 2279.2.5 Fixed Effects Model 2279.2.5.1 Truncated Sample 2279.2.5.2 Censored Sample 2299.2.6 The Random Effects Model 2339.2.6.1 Truncated Sample 2339.2.6.2 Censored Sample 2349.3 Count Data 2369.3.1 Introduction 2369.3.1.1 The Poisson Model 2369.3.1.2 The NegBin Model 2379.3.2 Fixed Effects Model 2379.3.2.1 The Poisson Model 2379.3.2.2 Negbin Model 2399.3.3 Random Effects Models 2399.3.3.1 The Poisson Model 2399.3.3.2 The NegBin Model 2409.4 More Empirical Examples 24310 Spatial Panels 24510.1 Spatial Correlation 24510.1.1 Visual Assessment 24510.1.2 Testing for Spatial Dependence 24610.1.2.1 CD p Tests for Local Cross-sectional Dependence 24710.1.2.2 The Randomized W Test 24710.2 Spatial Lags 25010.2.1 Spatially Lagged Regressors 25110.2.2 Spatially Lagged Dependent Variables 25310.2.2.1 Spatial OLS 25410.2.2.2 ML Estimation of the sar Model 25410.2.3 Spatially Correlated Errors 25510.3 Individual Heterogeneity in Spatial Panels 25810.3.1 Random versus Fixed Effects 25810.3.2 Spatial Panel Models with Error Components 26010.3.2.1 Spatial Panels with Independent Random Effects 26010.3.2.2 Spatially Correlated Random Effects 26110.3.3 Estimation 26110.3.3.1 Spatial Models with a General Error Covariance 26210.3.3.2 General Maximum Likelihood Framework 26310.3.3.3 Generalized Moments Estimation 26710.3.4 Testing 26910.3.4.1 LM Tests for Random Effects and Spatial Errors 26910.3.4.2 Testing for Spatial Lag vs Error 27210.4 Serial and Spatial Correlation 27710.4.1 Maximum Likelihood Estimation 27710.4.1.1 Serial and Spatial Correlation in the Random Effects Model 27710.4.1.2 Serial and Spatial Correlation with KKP-Type Effects 27810.4.2 Testing 28110.4.2.1 Tests for Random Effects, Spatial, and Serial Error Correlation 28110.4.2.2 Spatial Lag vs Error in the Serially Correlated Model 284Bibliography 285Index 297

Yves Croissant, Professor of Economics, CEMOI, Faculté de Droit et d'Economie, Université de La Réunion, France Giovanni Millo, Senior Economist, Group Insurance Research, Assicurazioni Generali S.p.A., Trieste, Italy

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• Preface xiiiAcknowledgments xviiAbout the CompanionWebsite xix1 Introduction 11.1 Panel Data Econometrics: A Gentle Introduction 11.1.1 Eliminating Unobserved Components 21.1.1.1 Differencing Methods 21.1.1.2 LSDV Methods 21.1.1.3 Fixed Effects Methods 21.2 R for Econometric Computing 61.2.1 The Modus Operandi of R 71.2.2 Data Management 81.2.2.1 Outsourcing to Other Software 81.2.2.2 Data ManagementThrough Formulae 81.3 plm for the Casual R User 81.3.1 R for the Matrix Language User 91.3.2 R for the User of Econometric Packages 101.4 plm for the Proficient R User 111.4.1 Reproducible EconometricWork 121.4.2 Object-orientation for the User 131.5 plm for the R Developer 131.5.1 Object-orientation for Development 141.6 Notations 171.6.1 General Notation 181.6.2 Maximum Likelihood Notations 181.6.3 Index 181.6.4 The Two-way Error Component Model 181.6.5 Transformation for the One-way Error Component Model 191.6.6 Transformation for the Two-ways Error Component Model 201.6.7 Groups and Nested Models 201.6.8 Instrumental Variables 201.6.9 Systems of Equations 201.6.10 Time Series 211.6.11 Limited Dependent and Count Variables 211.6.12 Spatial Panels 212 The Error Component Model 232.1 Notations and Hypotheses 232.1.1 Notations 232.1.2 Some Useful Transformations 242.1.3 Hypotheses Concerning the Errors 252.2 Ordinary Least Squares Estimators 272.2.1 Ordinary Least Squares on the Raw Data: The Pooling Model 272.2.2 The between Estimator 282.2.3 The within Estimator 292.3 The Generalized Least Squares Estimator 332.3.1 Presentation of the GLS Estimator 342.3.2 Estimation of the Variances of the Components of the Error 352.4 Comparison of the Estimators 392.4.1 Relations between the Estimators 392.4.2 Comparison of the Variances 402.4.3 Fixed vs Random Effects 402.4.4 Some Simple Linear Model Examples 422.5 The Two-ways Error Components Model 472.5.1 Error Components in the Two-ways Model 472.5.2 Fixed and Random Effects Models 482.6 Estimation of a Wage Equation 493 Advanced Error Components Models 533.1 Unbalanced Panels 533.1.1 Individual Effects Model 533.1.2 Two-ways Error Component Model 543.1.2.1 Fixed Effects Model 553.1.2.2 Random Effects Model 563.1.3 Estimation of the Components of the Error Variance 573.2 Seemingly Unrelated Regression 643.2.1 Introduction 643.2.2 Constrained Least Squares 653.2.3 Inter-equations Correlation 663.2.4 SUR With Panel Data 673.3 The Maximum Likelihood Estimator 713.3.1 Derivation of the Likelihood Function 713.3.2 Computation of the Estimator 733.4 The Nested Error Components Model 743.4.1 Presentation of the Model 743.4.2 Estimation of the Variance of the Error Components 754 Tests on Error Component Models 834.1 Tests on Individual and/or Time Effects 834.1.1 F Tests 844.1.2 Breusch-Pagan Tests 844.2 Tests for Correlated Effects 884.2.1 The Mundlak Approach 894.2.2 Hausman Test 904.2.3 Chamberlain’s Approach 904.2.3.1 Unconstrained Estimator 914.2.3.2 Constrained Estimator 934.2.3.3 Fixed Effects Models 934.3 Tests for Serial Correlation 954.3.1 Unobserved Effects Test 954.3.2 Score Test of Serial Correlation and/or Individual Effects 964.3.3 Likelihood Ratio Tests for AR(1) and Individual Effects 994.3.4 Applying Traditional Serial Correlation Tests to Panel Data 1014.3.5 Wald Tests for Serial Correlation using within and First-differenced Estimators 1024.3.5.1 Wooldridge’s within-based Test 1024.3.5.2 Wooldridge’s First-difference-based Test 1034.4 Tests for Cross-sectional Dependence 1044.4.1 Pairwise Correlation Coefficients 1044.4.2 CD-type Tests for Cross-sectional Dependence 1054.4.3 Testing Cross-sectional Dependence in a pseries 1075 Robust Inference and Estimation for Non-spherical Errors 1095.1 Robust Inference 1095.1.1 Robust Covariance Estimators 1095.1.1.1 Cluster-robust Estimation in a Panel Setting 1105.1.1.2 Double Clustering 1155.1.1.3 Panel Newey-west and SCC 1165.1.2 Generic Sandwich Estimators and Panel Models 1205.1.2.1 Panel Corrected Standard Errors 1225.1.3 Robust Testing of Linear Hypotheses 1235.1.3.1 An Application: Robust Hausman Testing 1255.2 Unrestricted Generalized Least Squares 1275.2.1 General Feasible Generalized Least Squares 1285.2.1.1 Pooled GGLS 1295.2.1.2 Fixed Effects GLS 1305.2.1.3 First Difference GLS 1325.2.2 Applied Examples 1336 Endogeneity 1396.1 Introduction 1396.2 The Instrumental Variables Estimator 1406.2.1 Generalities about the Instrumental Variables Estimator 1406.2.2 The within Instrumental Variables Estimator 1416.3 Error Components Instrumental Variables Estimator 1436.3.1 The General Model 1436.3.2 Special Cases of the General Model 1456.3.2.1 The within Model 1456.3.2.2 Error Components Two Stage Least Squares 1466.3.2.3 The Hausman and Taylor Model 1466.3.2.4 The Amemiya-Macurdy Estimator 1476.3.2.5 The Breusch, Mizon and Schmidt’s Estimator 1476.3.2.6 Balestra and Varadharajan-Krishnakumar Estimator 1476.4 Estimation of a System of Equations 1546.4.1 TheThree Stage Least Squares Estimator 1556.4.2 The Error Components Three Stage Least Squares Estimator 1566.5 More Empirical Examples 1587 Estimation of a Dynamic Model 1617.1 Dynamic Model and Endogeneity 1637.1.1 The Bias of the ols Estimator 1637.1.2 The within Estimator 1647.1.3 Consistent Estimation Methods for Dynamic Models 1657.2 GMM Estimation of the Differenced Model 1687.2.1 Instrumental Variables and Generalized Method of Moments 1687.2.2 One-step Estimator 1697.2.3 Two-steps Estimator 1717.2.4 The Proliferation of Instruments in the Generalized Method of Moments Difference Estimator 1727.3 Generalized Method of Moments Estimator in Differences and Levels 1747.3.1 Weak Instruments 1747.3.2 Moment Conditions on the Levels Model 1757.3.3 The System GMM Estimator 1777.4 Inference 1787.4.1 Robust Estimation of the Coefficients’ Covariance 1787.4.2 Overidentification Tests 1797.4.3 Error Serial Correlation Test 1817.5 More Empirical Examples 1828 Panel Time Series 1858.1 Introduction 1858.2 Heterogeneous Coefficients 1868.2.1 Fixed Coefficients 1868.2.2 Random Coefficients 1878.2.2.1 The Swamy Estimator 1878.2.2.2 The Mean Groups Estimator 1908.2.3 Testing for Poolability 1928.3 Cross-sectional Dependence and Common Factors 1948.3.1 The Common Factor Model 1958.3.2 Common Correlated Effects Augmentation 1968.3.2.1 cce Mean Groups vs. cce Pooled 1988.3.2.2 Computing the ccep Variance 1998.4 Nonstationarity and Cointegration 2008.4.1 Unit Root Testing: Generalities 2018.4.2 First Generation Unit Root Testing 2048.4.2.1 Preliminary Results 2048.4.2.2 Levin-Lin-Chu Test 2058.4.2.3 Im, Pesaran and Shin Test 2058.4.2.4 The Maddala and Wu Test 2068.4.3 Second Generation Unit Root Testing 2079 Count Data and Limited Dependent Variables 2119.1 Binomial and Ordinal Models 2139.1.1 Introduction 2139.1.1.1 The Binomial Model 2139.1.1.2 Ordered Models 2149.1.2 The Random Effects Model 2149.1.2.1 The Binomial Model 2149.1.2.2 Ordered Models 2179.1.3 The Conditional Logit Model 2199.2 Censored or Truncated Dependent Variable 2239.2.1 Introduction 2239.2.2 The Ordinary Least Squares Estimator 2239.2.3 The Symmetrical Trimmed Estimator 2259.2.3.1 Truncated Sample 2259.2.3.2 Censored Sample 2269.2.4 The Maximum Likelihood Estimator 2269.2.4.1 Truncated Sample 2269.2.4.2 Censored Sample 2279.2.5 Fixed Effects Model 2279.2.5.1 Truncated Sample 2279.2.5.2 Censored Sample 2299.2.6 The Random Effects Model 2339.2.6.1 Truncated Sample 2339.2.6.2 Censored Sample 2349.3 Count Data 2369.3.1 Introduction 2369.3.1.1 The Poisson Model 2369.3.1.2 The NegBin Model 2379.3.2 Fixed Effects Model 2379.3.2.1 The Poisson Model 2379.3.2.2 Negbin Model 2399.3.3 Random Effects Models 2399.3.3.1 The Poisson Model 2399.3.3.2 The NegBin Model 2409.4 More Empirical Examples 24310 Spatial Panels 24510.1 Spatial Correlation 24510.1.1 Visual Assessment 24510.1.2 Testing for Spatial Dependence 24610.1.2.1 CD p Tests for Local Cross-sectional Dependence 24710.1.2.2 The Randomized W Test 24710.2 Spatial Lags 25010.2.1 Spatially Lagged Regressors 25110.2.2 Spatially Lagged Dependent Variables 25310.2.2.1 Spatial OLS 25410.2.2.2 ML Estimation of the sar Model 25410.2.3 Spatially Correlated Errors 25510.3 Individual Heterogeneity in Spatial Panels 25810.3.1 Random versus Fixed Effects 25810.3.2 Spatial Panel Models with Error Components 26010.3.2.1 Spatial Panels with Independent Random Effects 26010.3.2.2 Spatially Correlated Random Effects 26110.3.3 Estimation 26110.3.3.1 Spatial Models with a General Error Covariance 26210.3.3.2 General Maximum Likelihood Framework 26310.3.3.3 Generalized Moments Estimation 26710.3.4 Testing 26910.3.4.1 LM Tests for Random Effects and Spatial Errors 26910.3.4.2 Testing for Spatial Lag vs Error 27210.4 Serial and Spatial Correlation 27710.4.1 Maximum Likelihood Estimation 27710.4.1.1 Serial and Spatial Correlation in the Random Effects Model 27710.4.1.2 Serial and Spatial Correlation with KKP-Type Effects 27810.4.2 Testing 28110.4.2.1 Tests for Random Effects, Spatial, and Serial Error Correlation 28110.4.2.2 Spatial Lag vs Error in the Serially Correlated Model 284Bibliography 285Index 297

Yves Croissant, Professor of Economics, CEMOI, Faculté de Droit et d'Economie, Université de La Réunion, France Giovanni Millo, Senior Economist, Group Insurance Research, Assicurazioni Generali S.p.A., Trieste, Italy

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• Preface xiiiAcknowledgments xviiAbout the CompanionWebsite xix1 Introduction 11.1 Panel Data Econometrics: A Gentle Introduction 11.1.1 Eliminating Unobserved Components 21.1.1.1 Differencing Methods 21.1.1.2 LSDV Methods 21.1.1.3 Fixed Effects Methods 21.2 R for Econometric Computing 61.2.1 The Modus Operandi of R 71.2.2 Data Management 81.2.2.1 Outsourcing to Other Software 81.2.2.2 Data ManagementThrough Formulae 81.3 plm for the Casual R User 81.3.1 R for the Matrix Language User 91.3.2 R for the User of Econometric Packages 101.4 plm for the Proficient R User 111.4.1 Reproducible EconometricWork 121.4.2 Object-orientation for the User 131.5 plm for the R Developer 131.5.1 Object-orientation for Development 141.6 Notations 171.6.1 General Notation 181.6.2 Maximum Likelihood Notations 181.6.3 Index 181.6.4 The Two-way Error Component Model 181.6.5 Transformation for the One-way Error Component Model 191.6.6 Transformation for the Two-ways Error Component Model 201.6.7 Groups and Nested Models 201.6.8 Instrumental Variables 201.6.9 Systems of Equations 201.6.10 Time Series 211.6.11 Limited Dependent and Count Variables 211.6.12 Spatial Panels 212 The Error Component Model 232.1 Notations and Hypotheses 232.1.1 Notations 232.1.2 Some Useful Transformations 242.1.3 Hypotheses Concerning the Errors 252.2 Ordinary Least Squares Estimators 272.2.1 Ordinary Least Squares on the Raw Data: The Pooling Model 272.2.2 The between Estimator 282.2.3 The within Estimator 292.3 The Generalized Least Squares Estimator 332.3.1 Presentation of the GLS Estimator 342.3.2 Estimation of the Variances of the Components of the Error 352.4 Comparison of the Estimators 392.4.1 Relations between the Estimators 392.4.2 Comparison of the Variances 402.4.3 Fixed vs Random Effects 402.4.4 Some Simple Linear Model Examples 422.5 The Two-ways Error Components Model 472.5.1 Error Components in the Two-ways Model 472.5.2 Fixed and Random Effects Models 482.6 Estimation of a Wage Equation 493 Advanced Error Components Models 533.1 Unbalanced Panels 533.1.1 Individual Effects Model 533.1.2 Two-ways Error Component Model 543.1.2.1 Fixed Effects Model 553.1.2.2 Random Effects Model 563.1.3 Estimation of the Components of the Error Variance 573.2 Seemingly Unrelated Regression 643.2.1 Introduction 643.2.2 Constrained Least Squares 653.2.3 Inter-equations Correlation 663.2.4 SUR With Panel Data 673.3 The Maximum Likelihood Estimator 713.3.1 Derivation of the Likelihood Function 713.3.2 Computation of the Estimator 733.4 The Nested Error Components Model 743.4.1 Presentation of the Model 743.4.2 Estimation of the Variance of the Error Components 754 Tests on Error Component Models 834.1 Tests on Individual and/or Time Effects 834.1.1 F Tests 844.1.2 Breusch-Pagan Tests 844.2 Tests for Correlated Effects 884.2.1 The Mundlak Approach 894.2.2 Hausman Test 904.2.3 Chamberlain’s Approach 904.2.3.1 Unconstrained Estimator 914.2.3.2 Constrained Estimator 934.2.3.3 Fixed Effects Models 934.3 Tests for Serial Correlation 954.3.1 Unobserved Effects Test 954.3.2 Score Test of Serial Correlation and/or Individual Effects 964.3.3 Likelihood Ratio Tests for AR(1) and Individual Effects 994.3.4 Applying Traditional Serial Correlation Tests to Panel Data 1014.3.5 Wald Tests for Serial Correlation using within and First-differenced Estimators 1024.3.5.1 Wooldridge’s within-based Test 1024.3.5.2 Wooldridge’s First-difference-based Test 1034.4 Tests for Cross-sectional Dependence 1044.4.1 Pairwise Correlation Coefficients 1044.4.2 CD-type Tests for Cross-sectional Dependence 1054.4.3 Testing Cross-sectional Dependence in a pseries 1075 Robust Inference and Estimation for Non-spherical Errors 1095.1 Robust Inference 1095.1.1 Robust Covariance Estimators 1095.1.1.1 Cluster-robust Estimation in a Panel Setting 1105.1.1.2 Double Clustering 1155.1.1.3 Panel Newey-west and SCC 1165.1.2 Generic Sandwich Estimators and Panel Models 1205.1.2.1 Panel Corrected Standard Errors 1225.1.3 Robust Testing of Linear Hypotheses 1235.1.3.1 An Application: Robust Hausman Testing 1255.2 Unrestricted Generalized Least Squares 1275.2.1 General Feasible Generalized Least Squares 1285.2.1.1 Pooled GGLS 1295.2.1.2 Fixed Effects GLS 1305.2.1.3 First Difference GLS 1325.2.2 Applied Examples 1336 Endogeneity 1396.1 Introduction 1396.2 The Instrumental Variables Estimator 1406.2.1 Generalities about the Instrumental Variables Estimator 1406.2.2 The within Instrumental Variables Estimator 1416.3 Error Components Instrumental Variables Estimator 1436.3.1 The General Model 1436.3.2 Special Cases of the General Model 1456.3.2.1 The within Model 1456.3.2.2 Error Components Two Stage Least Squares 1466.3.2.3 The Hausman and Taylor Model 1466.3.2.4 The Amemiya-Macurdy Estimator 1476.3.2.5 The Breusch, Mizon and Schmidt’s Estimator 1476.3.2.6 Balestra and Varadharajan-Krishnakumar Estimator 1476.4 Estimation of a System of Equations 1546.4.1 TheThree Stage Least Squares Estimator 1556.4.2 The Error Components Three Stage Least Squares Estimator 1566.5 More Empirical Examples 1587 Estimation of a Dynamic Model 1617.1 Dynamic Model and Endogeneity 1637.1.1 The Bias of the ols Estimator 1637.1.2 The within Estimator 1647.1.3 Consistent Estimation Methods for Dynamic Models 1657.2 GMM Estimation of the Differenced Model 1687.2.1 Instrumental Variables and Generalized Method of Moments 1687.2.2 One-step Estimator 1697.2.3 Two-steps Estimator 1717.2.4 The Proliferation of Instruments in the Generalized Method of Moments Difference Estimator 1727.3 Generalized Method of Moments Estimator in Differences and Levels 1747.3.1 Weak Instruments 1747.3.2 Moment Conditions on the Levels Model 1757.3.3 The System GMM Estimator 1777.4 Inference 1787.4.1 Robust Estimation of the Coefficients’ Covariance 1787.4.2 Overidentification Tests 1797.4.3 Error Serial Correlation Test 1817.5 More Empirical Examples 1828 Panel Time Series 1858.1 Introduction 1858.2 Heterogeneous Coefficients 1868.2.1 Fixed Coefficients 1868.2.2 Random Coefficients 1878.2.2.1 The Swamy Estimator 1878.2.2.2 The Mean Groups Estimator 1908.2.3 Testing for Poolability 1928.3 Cross-sectional Dependence and Common Factors 1948.3.1 The Common Factor Model 1958.3.2 Common Correlated Effects Augmentation 1968.3.2.1 cce Mean Groups vs. cce Pooled 1988.3.2.2 Computing the ccep Variance 1998.4 Nonstationarity and Cointegration 2008.4.1 Unit Root Testing: Generalities 2018.4.2 First Generation Unit Root Testing 2048.4.2.1 Preliminary Results 2048.4.2.2 Levin-Lin-Chu Test 2058.4.2.3 Im, Pesaran and Shin Test 2058.4.2.4 The Maddala and Wu Test 2068.4.3 Second Generation Unit Root Testing 2079 Count Data and Limited Dependent Variables 2119.1 Binomial and Ordinal Models 2139.1.1 Introduction 2139.1.1.1 The Binomial Model 2139.1.1.2 Ordered Models 2149.1.2 The Random Effects Model 2149.1.2.1 The Binomial Model 2149.1.2.2 Ordered Models 2179.1.3 The Conditional Logit Model 2199.2 Censored or Truncated Dependent Variable 2239.2.1 Introduction 2239.2.2 The Ordinary Least Squares Estimator 2239.2.3 The Symmetrical Trimmed Estimator 2259.2.3.1 Truncated Sample 2259.2.3.2 Censored Sample 2269.2.4 The Maximum Likelihood Estimator 2269.2.4.1 Truncated Sample 2269.2.4.2 Censored Sample 2279.2.5 Fixed Effects Model 2279.2.5.1 Truncated Sample 2279.2.5.2 Censored Sample 2299.2.6 The Random Effects Model 2339.2.6.1 Truncated Sample 2339.2.6.2 Censored Sample 2349.3 Count Data 2369.3.1 Introduction 2369.3.1.1 The Poisson Model 2369.3.1.2 The NegBin Model 2379.3.2 Fixed Effects Model 2379.3.2.1 The Poisson Model 2379.3.2.2 Negbin Model 2399.3.3 Random Effects Models 2399.3.3.1 The Poisson Model 2399.3.3.2 The NegBin Model 2409.4 More Empirical Examples 24310 Spatial Panels 24510.1 Spatial Correlation 24510.1.1 Visual Assessment 24510.1.2 Testing for Spatial Dependence 24610.1.2.1 CD p Tests for Local Cross-sectional Dependence 24710.1.2.2 The Randomized W Test 24710.2 Spatial Lags 25010.2.1 Spatially Lagged Regressors 25110.2.2 Spatially Lagged Dependent Variables 25310.2.2.1 Spatial OLS 25410.2.2.2 ML Estimation of the sar Model 25410.2.3 Spatially Correlated Errors 25510.3 Individual Heterogeneity in Spatial Panels 25810.3.1 Random versus Fixed Effects 25810.3.2 Spatial Panel Models with Error Components 26010.3.2.1 Spatial Panels with Independent Random Effects 26010.3.2.2 Spatially Correlated Random Effects 26110.3.3 Estimation 26110.3.3.1 Spatial Models with a General Error Covariance 26210.3.3.2 General Maximum Likelihood Framework 26310.3.3.3 Generalized Moments Estimation 26710.3.4 Testing 26910.3.4.1 LM Tests for Random Effects and Spatial Errors 26910.3.4.2 Testing for Spatial Lag vs Error 27210.4 Serial and Spatial Correlation 27710.4.1 Maximum Likelihood Estimation 27710.4.1.1 Serial and Spatial Correlation in the Random Effects Model 27710.4.1.2 Serial and Spatial Correlation with KKP-Type Effects 27810.4.2 Testing 28110.4.2.1 Tests for Random Effects, Spatial, and Serial Error Correlation 28110.4.2.2 Spatial Lag vs Error in the Serially Correlated Model 284Bibliography 285Index 297