Contents
1. Basic Structure of Panel Data
1.1 Meaning of Fixed Effect
1.1.1 Fixed Effects with Non-Trended Data
1.1.2 Fixed Effects with Trended Panel Data
1.2 Meaning of Common Components
1.2.1 Aggregation or Macro Factor
1.2.2 Source of Cross Sectional
Dependence
1.2.3 Central Location Parameter
1.3 Meaning of Idiosyncratic Components
2 Statistical Models for Cross Sectional Dependence
2.1 Spatial Dependence
2.2 Gravity Model
2.3 Common Factor Approach
2.4 Other Variations
2.4.1 Dynamic Factor Model .
2.4.2 Hierarchical Factor Model
3 Factor Number Identification
3.1 A Step by Step Procedure for Determining the
Factor Number
3.2 Information Criteria and Alternative Methods
3.3 Standardization and Prewhitening
3.4 Practice: Factor Number Estimation
3.4.1 STATA Practice with Crime Rates
3.4.2 STATA Practice with Price Indexes
3.4.3 Practice with GAUSS
3.4.4 Practice with MATLAB
4 Decomposition of Panel: Estimation of Common and Idiosyncratic
Components
4.1 Measurement of Accuracy: Order in Probability
4.2 Estimation of the Common Factors
4.2.1 Cross Sectional Average (CSA) Approach
4.2.2 Principal Component Estimator
4.2.3 Comparison between Two Estimators for the
Common Factors
4.3 Estimation of the Idiosyncratic Components
4.4 Variance Decomposition
4.5 Cross Sectional Dependence and Level of
Aggregation
4.5.1 General Static Factor Structure
4.5.2 Hierarchical Factor Structure
4.6 Practice: Common Factors Estimation
4.6.1 GAUSS Practice I: Principal Component
Estimation
4.6.2 GAUSS Practice II: Standardization and
Estimation of PC Factors
4.6.3 MATLAB Practice
4.6.4 STATA Practice
5 Identification of Common Factors
5.1 Difference between Statistical and Latent
Factors
5.2 Asymptotically Weak Factors Approach
5.2.1 Single Factor Case
5.2.2 Multi-Factor Case
5.2.3 Some Tips to Identify Latent Factors
5.2.4 Application: Testing Homogeneity of Factor
Loadings
5.3 Residual Based Approach
5.4 Empirical Example: Exchange Rates
5.5 Practice: Identifying Common Factors
5.5.1 MATLAB Practice I: Leadership Model
5.5.2 MATLAB Practice II: Multiple Variables as
Single Factor
5.5.3 Practice with GAUSS
5.5.4 Practice with STATA
6 Static and Dynamic Relationships
6.1 Static and Dynamic Relationship under Cross
Sectional Independence
6.1.1 Spurious Cross Sectional
Regression
6.1.2 Spurious Pooled OLS Estimator
6.1.3 Time Series and Panel Fixed Effect
Regressions
6.1.4 Between Group Estimator
6.2 Static and Dynamic Relationship under Cross
Sectional Dependence
6.2.1 Homogeneous Factor Loadings
6.2.2 Heterogeneous Factor Loadings: Factor
Augmented Panel Regression
6.2.3 Cross Sectional Regressions with
Nonstationary Common Factors
6.3 Practice: Factor Augmented and Aggregation
Regressions
6.3.1 Practice with GAUSS I: Common-Dynamic
Relationship
6.3.2 Practice with GAUSS II: Idio-Dynamic
Relationship
6.3.3 Practice with MATLAB
6.3.4 Practice with STATA
6.4 Appendix: Modified Between Group Estimators
and An Econometric Application
6.4.1 Appendix A: Relationships Between the Five
Estimators
6.4.2 Appendix B: Estimation of Static
Relationships
6.4.3 Appendix C: Econometric Application
7 Convergence
7.1 Beta-Convergence: Pitfalls of Cross Country Regressions
7.2 Relative Convergence
7.2.1 Notion of Relative Convergence
7.2.2 How to Test: logt Regression
7.2.3 Clustering Algorithm .
7.2.4 Pitfalls of the logt
Regression and Alternative Solutions
7.3 Sigma-Convergence .
7.4 Empirical Example I: Household Expenditure
Data from KLIPS
7.5 Practice: Convergence Tests
7.5.1 Practice with MATLAB I: Weak Sigma
Convergence Test
7.5.2 Practice with MATLAB II: Relative
Convergence Test
7.5.3 Practice with GAUSS
7.5.4 Practice with STATA .
8 Appendix: Basic Panel Regressions
8.1 Standard Two-Way Fixed Effects Estimation
8.1.1 POLS Estimation .
8.1.2 One-Way Fixed Effect Estimation
8.1.3 Two-Way Fixed Effect Estimation
8.2 Valid Test Statistics .
8.2.1 Basic Inference Theory .
8.2.2 Cross Sectional Dependence
.
8.2.3 Solution: Use Two-Way Fixed Effect
8.2.4 Serial Dependent Panel: Use Panel Robust Covariance