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PART ONE PANEL DATA AS A MULTIVARIATE TIME SERIES BY STATES
1 Data Analysis Based on a Single Time Series by States
1.1 Introduction 3
1.2 Multivariate Growth Models 3
1.2.1 Continuous Growth Models 3
1.2.2 Discontinuous Growth Models 8
1.3 Alternative Multivariate Growth Models 10
1.3.1 A Generalization of MAR(p)_GM 10
1.3.2 Multivariate Lagged Variables Growth Models 11
1.3.3 Multivariate Lagged-Variable Autoregressive Growth Models 13
1.3.4 Bounded MLVAR(p;q)_GM 13
1.3.5 Special Notes 13
1.4 Various Models Based on Correlated States 14
1.4.1 Seemingly Causal Models with Trend 15
1.4.2 The Application of the Object “VAR” 18
1.4.3 The Application of the Instrumental Variables Models 20
1.5 Seemingly Causal Models with Time-Related Effects 21
1.5.1 SCM Based on the Path Diagram in Figure 1.10(a) 21
1.5.2 SCM Based on the Path Diagram in Figure 1.10(b) 22
1.6 The Application of the Object POOL 23
1.6.1 What is a Fixed-Effect Model? 23
1.6.2 What is a Random Effect Model? 25
1.6.3 Special Notes 27
1.7 Growth Models of Sample Statistics 29
1.8 Special Notes on Time-State Observations 32
1.9 Growth Models with an Environmental Variable 32
1.9.1 The Simplest Possible Model 33
1.9.2 The Application of VAR and VEC Models 34
1.9.3 Application of ARCH Model 37
1.9.4 The Application of Instrumental Variables Models 38
1.10 Models with an Environmental Multivariate 40
1.10.1 Bivariate Correlation and Simple Linear Regressions 40
1.10.2 Simple Models with an Environmental Multivariate 42
1.10.3 The VAR Models 43
1.11 Special Piece-Wise Models 49
1.11.1 The Application of Growth Models 49
1.11.2 Equality Tests by Classifications 53
2 Data Analysis Based on Bivariate Time Series by States 55
2.1 Introduction 55
2.2 Models Based on Independent States 56
2.2.1 MAR(p) Growth Model with an Exogenous Variable 56
2.2.2 A General MAR(p) Model with an Exogenous Variable 56
2.3 Time-Series Models Based on Two Correlated States 60
2.3.1 Analysis using the Object System 61
2.3.2 Two-SLS Instrumental Variables Models 65
2.3.3 Three-SLS Instrumental Variables Models 69
2.3.4 Analysis using the Object “VAR” 70
2.4 Time-Series Models Based on Multiple Correlated States 72
2.4.1 Extension of the Path Diagram in Figure 2.6 72
2.4.2 SCMs as VAR Models 74
2.5 Time-Series Models with an Environmental Variable Zt, Based on
Independent States 78
2.5.1 The Simplest Possible Model 78
2.5.2 Interaction Models Based on Two Independent States 81
2.6 Models Based on Correlated States 82
2.6.1 MLV(1) Interaction Model with Trend 83
2.6.2 Simultaneous SCMs with Trend 83
2.7 Piece-Wise Time-Series Models 86
3 Data Analysis Based on Multivariate Time Series by States 87
3.1 Introduction 87
3.2 Models Based on (X_i,Y_i,Z_i) for Independent States 88
3.2.1 MLVAR(p; q) Model with Trend Based on (X_i,Y_i,Z_i) 88
3.3 Models Based on (X_i, Y_i,Z_i) for Correlated States 90
3.3.1 MLV(1) Interaction Model with Trend 91
3.3.2 MLV(1) Interaction Model with Time-Related Effects 93
3.4 Simultaneous SCMs with Trend 96
3.4.1 The Basic Simultaneous SCMs with Trend 96
3.4.2 Alternative Time Series Models 98
3.5 Models Based on (X1_i,X2_i,X3_i, Y1_i,Y2_i) for Independent States 100
3.5.1 Lagged Endogenous Variables: First Autoregressive Model with Exogenous Variables and Trend 100
3.5.2 A Mixed Lagged Variables First Autoregressive Model with Trend 101
3.5.3 Lagged Endogenous Variables: First Autoregressive Model with Exogenous Variables and Time-Related Effects 102
3.5.4 Various Interaction Models 103
3.6 Models Based on (X_i,Y_i) for Correlated States 103
3.6.1 Additive Models 103
3.6.2 Interaction Models 104
3.6.3 Alternative Models for Two Correlated States 105
3.7 Discontinuous Time-Series Models 106
3.8 Additional Examples for Correlated States 107
3.9 Special Notes and Comments 109
3.9.1 Extended Models 109
3.9.2 Not-Recommended Models 109
3.9.3 Problems with Data Analysis 110
4 Applications of Seemingly Causal Models 111
4.1 Introduction 111
4.1.1 Deleting Time t from Models 111
4.1.2 Replacing Time t with an Environmental Variable 111
4.2 SCMs Based on a Single Time Series Y_it 112
4.3 SCMs Based on Bivariate Time Series (X_it,Y_it) 118
4.3.1 Additive SCM 119
4.3.2 ATwo-Way Interaction Standard SCM 119
4.3.3 AThree-Way Interaction Standard SCM 120
4.4 SCMs Based on a Trivariate (X1_i,X2_i,Y1_i) 120
4.4.1 Simple SCMs for Two Correlated States 120
4.4.2 Various Time-Series Models 121
4.5 SCMs Based on a Trivariate (X_it,Y1_it,Y2_it) 126
4.6 SCMs Based on Multivariate Endogenous and Exogenous Variables 127
4.6.1 Simple Additive SCM 127
4.6.2 ATwo-Way Interaction SCM 128
4.6.3 AThree-Way Interaction SCM 128
4.6.4 Special Notes and Comments 128
4.6.5 Various Alternative SCMs 129
4.7 Fixed- and Random Effects Models 133
4.7.1 A Fixed-Effect Model and a MANCOVA Model 133
4.7.2 A Random Effect Model and a Single Regression 135
4.8 Models with Cross-Section Specific Coefficients 138
4.8.1 MAR(p) Model with Cross-Section Specific Coefficients 138
4.8.2 Advanced PLS Estimation Methods 139
4.8.3 Instrumental Variables Model 142
4.8.4 Special Notes and Comments 143
4.9 Cases in Industry 146
4.9.1 Dummy Variables Models 146
PART TWO POOL PANEL DATA ANALYSIS 149
5 Evaluation Analysis 151
5.1 Introduction 151
5.2 Preliminary Evaluation Analysis 152
5.3 The Application of the Object “Descriptive Statistics and Tests” 153
5.3.1 Analysis Using the Option “Stats by Classification. . .” 153
5.3.2 Analysis Using the Option “Equality Tests by Classification. . .” 156
5.3.3 Analysis Using the Option “N-Way Tabulation. . .” 157
5.4 Analysis Based on Ordinal Problem Indicators 158
5.5 Multiple Association between Categorical Variables 161
5.5.1 Applications of N-Way Tabulation 161
5.5.2 Application of Kendall’s Tau 164
6 General Choice Models 165
6.1 Introduction 165
6.2 Multi-Factorial Binary Choice Models 165
6.2.1 One-Way Binary Choice Model 165
6.2.2 Two-Way Binary Choice Model 168
6.2.3 Multi-Factorial Binary Choice Model 171
6.3 Binary Logit Model of Yit on a Numerical Variable Xit 175
6.3.1 A Comparative Study 175
6.3.2 General Binary Logit Model with a Single Numerical Variable X 177
6.3.3 Special Notes and Comments 182
6.4 Binary Logit Model of a Zero-One Indicator Yit on (X1it,X2it) 182
6.4.1 The Simplest Possible Function 182
6.4.2 Functions for Binary Logit Translog Models 185
6.5 Binary Choice Model of a Zero-One Indicator Yit on (X1it,X2it,X3it) 187
6.5.1 The Linear Effect of X3 on Y Depends on X1 and X2 188
6.5.2 Alternative Effects of X3 on Y Depends on X1 and X2 190
6.6 Binary Choice Model of a Zero-One Indicator Yit on (X1it,. . ., Xhit,. . .) 190
6.7 Special Notes and Comments 190
7 Advanced General Choice Models 192
7.1 Introduction 192
7.2 Categorical Data Analyses 193
7.2.1 Multi-Factorial Binary Choice Models 193
7.2.2 Ordered Choice Models 200
7.2.3 Not-Recommended Models 201
7.2.4 Application of N-Way Tabulation 202
7.2.5 Applications of Ordinal-Ordinal Association 205
7.3 Multi-Factorial Choice Models with a Numerical Independent Variable 207
7.3.1 Nonparametric Estimation Methods 209
7.3.2 Parametric Estimation Methods 209
7.3.3 Polynomial-Effect BCM with Three Numerical Exogenous Variables 212
7.3.4 A Study of Li, et al. (2010) 213
7.3.5 A Study of Hameed, et al. (2010) 214
7.3.6 A Study of Francis and Martin (2010) 215
8 Univariate General Linear Models 216
8.1 Introduction 216
8.2 ANOVA and Quantile Models 216
8.3 Continuous Linear-Effect Models 221
8.3.1 Bivariate Correlation Analysis 222
8.3.2 STEPLS Regressions 224
8.4 Piece-Wise Autoregressive Linear Models by Time Points 227
8.4.1 The Simplest Linear-Effect Models Based on (Xit,Yit) by Time Points 228
8.4.2 General Linear-Effect Model Based on (Xit,Yit) by Time Points 229
8.4.3 Linear-Effect Model Based on (X1it, X2it,Yit) by Time Points 235
8.4.4 Linear Models Based on (X1it, X2it, X3it,Yit) by Time Points 239
8.5 ANCOVA Models 241
9 Fixed-Effects Models and Alternatives 244
9.1 Introduction 244
9.2 Cross-Section Fixed-Effects Models 245
9.2.1 Individual Fixed-Effects Models 245
9.2.2 Group Fixed-Effects Models 250
9.3 Time-Fixed-Effects Models 251
9.4 Two-Way Fixed-Effects Models 254
9.4.1 Two-Way Fixed-Effects Models 254
9.4.2 Interaction FEMs 258
9.5 Extended Fixed-Effects Models 265
9.5.1 Least Square FEMs 265
9.5.2 Alternative FEMs 266
9.6 Selected Fixed-Effects Models from the Journal of Finance, 2011 274
9.6.1 Additive FEM Applied by Hendershott, et al. (2011) 274
9.6.2 FEM Applied by Engelberg and Parsons (2011) 276
9.6.3 Special FEMs Applied by Benmelech and Bergman (2011) 277
9.7 Heterogeneous Regression Models 278
9.7.1 Heterogeneous Regressions by Individuals 278
9.7.2 Heterogeneous Classical Growth Models by Individuals or Groups 279
9.7.3 Piece-Wise Heterogeneous Regressions 281
9.7.4 Heterogeneous Regressions with Trend by Individuals or Groups 281
9.7.5 Heterogeneous Regressions with Time-Related Effects by Individuals or Groups 283
10 Special Notes on Selected Problems 286
10.1 Introduction 286
10.2 Problems with Dummy Variables 286
10.2.1 A Dummy of the Return Rate Rit 286
10.2.2 Other Types of Dummy Variables 287
10.3 Problems with the Numerical Variable Rit 288
10.3.1 Problem with Outliers 288
10.3.2 Problem with the Models of Rit with its Dummy DRit 289
10.4 Problems with the First Difference Variable 294
10.5 Problems with Ratio Variables 295
10.6 The CAPM and its Extensions or Modifications 298
10.6.1 Generalized CAPM 298
10.6.2 GCAPM with Exogenous Variables 299
10.6.3 Advanced Models of Rit by Firms or Asset i 299
10.6.4 Illustrative Data Analysis to Generate Betas 300
10.7 Selected Heterogeneous Regressions from International Journals 305
10.7.1 Heterogeneous Regressions of Naes, Skjeltrop and Odegaard (2011) 305
10.7.2 LV(1) Heterogeneous Regressions Models 305
10.7.3 Alternative Models 306
10.7.4 Extended Models 307
10.7.5 Sets of the Simplest LV(p) Heterogeneous Regressions 308
10.8 Models without the Time-Independent Variable 308
10.8.1 Interaction Models 308
10.8.2 Additive Models 310
10.9 Models with Time Dummy Variables 311
10.9.1 Interaction Models 311
10.9.2 Models with Additive Time Dummy Variables 311
10.9.3 Models with Additive Time and Group Dummy Variables 311
10.9.4 Models with Time as a Numerical Independent Variable 312
10.10 Final Remarks 312
10.10.1 Remarks on the Interaction or Additive Models 312
10.10.2 Remarks on Linear or Nonlinear Effects Models 313
10.10.3 Remarks on the True Population Model 313
11 Seemingly Causal Models 314
11.1 Introduction 314
11.2 MANOVA Models 314
11.3 Multivariate Heterogeneous Regressions by Group and Time 315
11.3.1 The Simplest MHR with an Exogenous Numerical Variable X 316
11.3.2 MHR with Two Exogenous Numerical Variables 317
11.4 MANCOVA Models 318
11.5 Discontinuous and Continuous MGLM by Time 319
11.6 Illustrative Linear-Effect Models by Times 319
11.6.1 Multivariate Linear-Effect Models (LEMs) by Time 320
11.7 Illustrative SCMs by Group and Time 331
11.7.1 Linear-Effect Models by Group and Time 331
11.7.2 Nonlinear-Effect Models 332
11.7.3 Bounded SCM by Group and Time 334
PART THREE BALANCED PANEL DATA AS NATURAL EXPERIMENTAL DATA 337
12 Univariate Lagged Variables Autoregressive Models 339
12.1 Introduction 339
12.2 Developing Special Balanced Pool Data 339
12.3 Natural Experimental Data Analysis 341
12.3.1 Developing Group-Based Variables 342
12.3.2 Alternative Models Applied 342
12.4 The Simplest Heterogeneous Regressions 343
12.4.1 Sets of the Simplest Models by Time 343
12.4.2 The Simplest Heterogeneous Regressions by Group and Time 343
12.4.3 The Simplest Heterogeneous Regressions by Group with Trends 343
12.4.4 The Simplest Heterogeneous Regressions by Group with Time-Related Effects 344
12.4.5 Not-Recommended or the Worst Model 344
12.5 LVAR(1,1) Heterogeneous Regressions 344
12.5.1 LVAR(1,1) Heterogeneous Regressions by Group and Time Period 344
12.5.2 LVAR(1,1) Heterogeneous Regressions by Group with Trend 345
12.5.3 LVAR(1,1) Heterogeneous Regressions by Group with Trend-Related Effects 345
12.5.4 Applications of LV(p,q) Models 346
12.5.5 Special Selected LV(p) or AR(q) Models 355
12.6 Manual Stepwise Selection for General Linear LV(1) Model 362
12.7 Manual Stepwise Selection for Binary Choice LV(1) Models 369
12.8 Manual Stepwise Selection for Ordered Choice Models 378
12.9 Bounded Models by Group and Time 387
12.9.1 Bounded Polynomial LV(1) Model by Group and Time 387
12.9.2 Bounded Models by Group with the Time Numerical Variable 393
13 Multivariate Lagged Variables Autoregressive Models 396
13.1 Introduction 396
13.2 Seemingly Causal Models 396
13.2.1 Specific Characteristics of the Model (13.1) 398
13.2.2 Alternative or Modified Models 399
13.3 Alternative Data Analyses 400
13.3.1 Regression Analysis Based on Each Yg 400
13.3.2 Multivariate Data Analysis Based on Each Sub-Sample 401
13.4 SCMs Based on (Y1,Y2) 401
13.4.1 SCMs by CF and the Time t Based on Figure 13.1(a) 402
13.4.2 SCMs by CF and the Time t Based on Figure 13.1(b) 403
13.4.3 SCMs by CF and the Time t Based on Figure 13.1(c) 404
13.4.4 Empirical Results Based on the Models of (Y1,Y2) 405
13.4.5 SCM with the Time Numerical Independent Variable 417
13.5 Advanced Autoregressive SCMs 421
13.5.1 SCMs Based on (Y1,Y2,Y3) 421
13.6 SCMs Based on (Y1,Y2) with Exogenous Variables 430
13.6.1 SCMs Based on (X1,Y1,Y2) 430
13.6.2 Illustrative Data Analyses 432
14 Applications of GLS Regressions 441
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