Longitudinal and Panel Data : Analysis and Applications in the Social Sciences

This focuses on models and data that arise from repeated observations of a cross-section of individuals, households or companies. These models have found important applications within business, economics, education, political science and other social science disciplines. The author introduces the foundations of longitudinal and panel data analysis at a level suitable for quantitatively oriented graduate social science students as well as individual researchers. He emphasizes mathematical and statistical fundamentals but also describes substantive applications from across the social sciences, showing the breadth and scope that these models enjoy. The applications are enhanced by real-world data sets and software programs in SAS and Stata. (A cura dell'editore) Cover......Page 1 Half-title......Page 3 Title......Page 5 Copyright......Page 6 Contents......Page 7 Intended Audience and Level......Page 11 Organization......Page 12 Statistical Software......Page 15 Approach......Page 16 Acknowledgments......Page 18 Statistical Modeling......Page 19 Defining Longitudinal and Panel Data......Page 20 Some Notation......Page 21 Prevalence of Longitudinal and Panel Data Analysis......Page 22 Dynamic Relationships......Page 23 Historical Approach......Page 24 Longitudinal Data as Repeated Cross-Sectional Studies......Page 25 Heterogeneity......Page 26 Omitted Variables......Page 27 Efficiency of Estimators......Page 28 Drawbacks: Attrition......Page 29 Types of Inference......Page 30 Social Science Statistical Modeling......Page 31 Modeling Issues......Page 32 1.4 Historical Notes......Page 33 Data......Page 36 Basic Models......Page 37 Parameters of Interest......Page 40 Subject and Time Heterogeneity......Page 41 Data Exploration Techniques......Page 42 Basic Added-Variable Plot......Page 43 Trellis Plot......Page 48 Least-Squares Estimation......Page 49 ANOVA Table and Standard Errors......Page 51 Large-Sample Properties of Estimators......Page 55 2.4.1 Pooling Test......Page 56 Correlations and Added-Variable Plots......Page 58 2.4.3 Influence Diagnostics......Page 59 2.4.4 Cross-Sectional Correlation......Page 60 Calibration of Cross-Sectional Correlation Test Statistics......Page 61 2.4.5 Heteroscedasticity......Page 63 2.5.1 Serial Correlation......Page 64 Temporal Covariance Matrix......Page 65 2.5.2 Subject-Specific Slopes......Page 67 Sampling and Model Assumptions......Page 68 2.5.3 Robust Estimation of Standard Errors......Page 69 Further Reading......Page 70 2A.1 Basic Fixed-Effects Model: Ordinary Least-Squares Estimation......Page 71 2A.2 Fixed-Effects Models: Generalized Least-Squares Estimation......Page 72 Observation-Level Diagnostic Statistic......Page 73 2A.4 Cross-Sectional Correlation: Shortcut Calculations......Page 74 Section 2.1......Page 75 Section 2.3......Page 76 Section 2.4......Page 79 Section 2.5......Page 81 Empirical Exercises......Page 83 Sampling and Inference......Page 90 Traditional ANOVA Setup......Page 91 Sampling and Model Assumptions......Page 93 Time-Constant Variables......Page 95 Generalized Least-Squares Estimation......Page 96 Feasible GLS Estimator......Page 97 Pooling Test......Page 98 3.2 Example: Income Tax Payments......Page 99 3.3.1 Linear Mixed-Effects Model......Page 104 Repeated Measures Design......Page 106 Random-Coefficients Model......Page 107 Variations of the Random-Coefficients Model......Page 108 Group Effects......Page 109 3.3.2 Mixed Linear Models......Page 110 3.4 Inference for Regression Coefficients......Page 112 Matrix Inversion Formula......Page 113 Maximum Likelihood Estimation......Page 114 Robust Estimation of Standard Errors......Page 115 Testing Hypotheses......Page 116 3.5.1 Maximum Likelihood Estimation......Page 118 3.5.2 Restricted Maximum Likelihood......Page 119 Starting Values......Page 121 3.5.3 MIVQUEs......Page 123 Further Reading......Page 124 3A.1 Independence of Residuals and Least-Squares Estimators......Page 125 3A.2 Restricted Likelihoods......Page 126 Special Case: Testing the Importance of a Subset of Regression Coefficients......Page 128 Section 3.1......Page 131 Section 3.4......Page 135 Section 3.5......Page 138 Empirical Exercises......Page 139 4.1 Estimators versus Predictors......Page 143 Shrinkage Estimator......Page 144 Types of Predictors......Page 146 4.3 Best Linear Unbiased Predictors......Page 147 BLUPs as Predictors......Page 148 4.4.1 Linear Mixed-Effects Model......Page 151 4.4.2 Linear Combinations of Global Parameters and Subject-Specific Effects......Page 152 4.4.3 BLUP Residuals......Page 153 4.4.4 Predicting Future Observations......Page 154 4.5.1 Sources and Characteristics of Data......Page 156 4.5.2 In-Sample Model Specification......Page 161 4.5.3 Out-of-Sample Model Specification......Page 162 4.5.4 Forecasts......Page 164 4.6 Bayesian Inference......Page 165 4.7 Credibility Theory......Page 170 4.7.1 Credibility Theory Models......Page 171 4.7.2 Credibility Rate-Making......Page 172 Further Reading......Page 174 4A.2 Best Linear Unbiased Predictor......Page 175 4A.3 BLUP Variance......Page 176 Section 4.2......Page 177 Section 4.4......Page 178 Empirical Exercises......Page 181 5.1 Cross-Sectional Multilevel Models......Page 184 5.1.1 Two-Level Models......Page 185 Extended Two-Level Models......Page 187 Motivation for Multilevel Models......Page 189 5.1.2 Multiple-Level Models......Page 190 5.1.3 Multilevel Modeling in Other Fields......Page 191 5.2.1 Two-Level Models......Page 192 Growth-Curve Models......Page 193 5.2.2 Multiple-Level Models......Page 197 5.3 Prediction......Page 198 Two-Level Models......Page 199 Multiple-Level Models......Page 200 5.4 Testing Variance Components......Page 202 Appendix 5A High-Order Multilevel Models......Page 205 Section 5.3......Page 209 Section 5.4......Page 211 Empirical Exercise......Page 213 Appendix 5A......Page 216 6.1 Stochastic Regressors in Nonlongitudinal Settings......Page 217 6.1.1 Endogenous Stochastic Regressors......Page 218 6.1.2 Weak and Strong Exogeneity......Page 220 6.1.3 Causal Effects......Page 222 6.1.4 Instrumental Variable Estimation......Page 223 6.2.1 Longitudinal Data Models without Heterogeneity Terms......Page 226 6.2.2 Longitudinal Data Models with Heterogeneity Terms and Strictly Exogenous Regressors......Page 227 Fixed-Effects Estimation......Page 230 6.3 Longitudinal Data Models with Heterogeneity Terms and Sequentially Exogenous Regressors......Page 231 Estimation Difficulties......Page 232 6.4 Multivariate Responses......Page 239 6.4.1 Multivariate Regression......Page 240 6.4.2 Seemingly Unrelated Regressions......Page 241 6.4.3 Simultaneous-Equations Models......Page 243 Seemingly Unrelated Regression Models with Error Components......Page 246 Simultaneous-Equations Models with Error Components......Page 247 6.5.1 Cross-Sectional Models......Page 249 Mean Parameters......Page 250 Identification Issues......Page 251 Estimation Techniques......Page 252 6.5.2 Longitudinal Data Applications......Page 254 Growth-Curve Models......Page 256 Appendix 6A Linear Projections......Page 258 7.1 Heterogeneity......Page 260 Two Approaches to Modeling Heterogeneity......Page 261 Theoretical Identification with Heterogeneity May Be Impossible......Page 262 Estimation of Regression Coefficients without Complete Identification Is Possible......Page 263 7.2 Comparing Fixed- and Random-Effects Estimators......Page 265 7.2.1 A Special Case......Page 268 7.2.2 General Case......Page 270 Correlated-Effects Model......Page 272 7.3 Omitted Variables......Page 274 7.3.1 Models of Omitted Variables......Page 276 7.3.2 Augmented Regression Estimation......Page 279 7.4.1 Incomplete and Rotating Panels......Page 281 Missing-Data Models......Page 283 7.4.3 Nonignorable Missing Data......Page 286 Heckman Two-Stage Procedure......Page 287 Hausman and Wise Procedure......Page 288 EM Algorithm......Page 289 Section 7.2......Page 290 8.1 Introduction......Page 295 8.2.1 Covariance Structures......Page 298 8.2.2 Nonstationary Structures......Page 299 8.2.3 Continuous-Time Correlation Models......Page 301 8.3 Cross-Sectional Correlations and Time-Series Cross-Section Models......Page 304 8.4.1 The Model......Page 306 8.4.2 Estimation......Page 308 8.4.3 Forecasting......Page 310 8.5 Kalman Filter Approach......Page 313 8.5.1 Transition Equations......Page 314 8.5.2 Observation Set......Page 315 8.5.3 Measurement Equations......Page 316 8.5.4 Initial Conditions......Page 317 8.5.5 The Kalman Filter Algorithm......Page 318 Likelihood Equations......Page 319 8.6 Example: Capital Asset Pricing Model......Page 320 8A.2 Estimation......Page 330 Likelihood Equations......Page 331 8A.3 Prediction......Page 332 Forecasting......Page 334 Linear Probability Models......Page 336 Using Nonlinear Functions of Explanatory Variables......Page 337 Threshold Interpretation......Page 338 Random-Utility Interpretation......Page 339 Logistic Regression......Page 340 Logistic Regression Parameter Interpretation......Page 341 9.1.2 Inference for Logistic and Probit Regression Models Parameter Estimation......Page 342 9.1.3 Example: Income Tax Payments and Tax Preparers......Page 344 9.2 Random-Effects Models......Page 347 Random-Effects Likelihood......Page 348 Multilevel Model Extensions......Page 350 Maximum Likelihood Estimation......Page 353 Conditional Maximum Likelihood Estimation......Page 355 Conditional Likelihood Estimation......Page 356 GEE Estimators for the Random-Effects Binary Dependent-Variable Model......Page 357 GEE Estimation Procedure......Page 358 Further Reading......Page 361 9A.1 Consistency of Likelihood Estimators......Page 362 Computing the Distribution of Sums of Nonidentically, Independently Distributed Bernoulli Random Variables......Page 363 Computing the Conditional Maximum Likelihood Estimator......Page 364 Section 9.1......Page 365 10.1 Homogeneous Models......Page 368 10.1.1 Linear Exponential Families of Distributions......Page 369 10.1.2 Link Functions......Page 370 Maximum Likelihood Estimation for Canonical Links......Page 371 Maximum Likelihood Estimation for General Links......Page 372 Overdispersion......Page 373 10.2 Example: Tort Filings......Page 374 Marginal Models......Page 378 Generalized Estimating Equations......Page 380 GEEs with Unknown Variance Components......Page 381 Robust Estimation of Standard Errors......Page 382 10.4 Random-Effects Models......Page 384 Random-Effects Likelihood......Page 385 Serial Correlation and Overdispersion......Page 386 Computational Considerations......Page 388 10.5.1 Maximum Likelihood Estimation for Canonical Links......Page 389 10.5.2 Conditional Maximum Likelihood Estimation for Canonical Links......Page 391 10.5.3 Poisson Distribution......Page 392 10.6 Bayesian Inference......Page 394 10A.1 Moment-Generating Function......Page 398 10A.2 Sufficiency......Page 400 10A.3 Conjugate Distributions......Page 401 10A.4 Marginal Distributions......Page 402 Exercises and Extensions......Page 404 11.1 Homogeneous Models......Page 405 11.1.1 Statistical Inference......Page 406 Parameter Interpretations......Page 407 11.1.3 Multinomial (Conditional) Logit......Page 409 11.1.4 Random-Utility Interpretation......Page 412 11.1.6 Generalized Extreme-Value Distribution......Page 414 11.2 Multinomial Logit Models with Random Effects......Page 416 Relation with Nonlinear Random-Effects Poisson Model......Page 417 11.3 Transition (Markov) Models......Page 418 Unordered Categorical Response......Page 419 Higher Order Markov Models......Page 426 11.4 Survival Models......Page 429 Appendix 11A Conditional Likelihood Estimation for Multinomial Logit Models with Heterogeneity Terms......Page 433 A.1 Basic Terminology......Page 435 A.3 Additional Definitions......Page 436 A.4 Matrix Decompositions......Page 437 A.5 Partitioned Matrices......Page 438 A.6 Kronecker (Direct) Product......Page 439 B.2 Multivariate Normal Distribution......Page 440 B.4 Conditional Distributions......Page 441 C.1 Characteristics of Likelihood Functions......Page 442 C.2 Maximum Likelihood Estimators......Page 443 C.3 Iterated Reweighted Least Squares......Page 444 C.5 Quasi-Likelihood......Page 445 C.6 Estimating Equations......Page 446 C.7 Hypothesis Tests......Page 449 C.8 Goodness-of-Fit Statistics......Page 450 C.9 Information Criteria......Page 451 D.1 Basic State Space Model......Page 452 D.2 Kalman Filter Algorithm......Page 453 D.4 Extended State Space Model and Mixed Linear Models......Page 454 D.5 Likelihood Equations for Mixed Linear Models......Page 455 Appendix E Symbols and Notation......Page 457 Appendix F Selected Longitudinal and Panel Data Sets......Page 463 Biological Sciences Longitudinal Data References (B)......Page 469 Econometrics Panel Data References (E)......Page 470 Educational Science and Psychology References (EP)......Page 473 Other Social Science References (O)......Page 474 Statistical Longitudinal Data References (S)......Page 476 General Statistics References (G)......Page 478 Index......Page 481

Focusing on an analysis of models and data that arise from repeated observations of a cross-section of individuals, households or firms, this book also covers important applications within business, economics, education, political science and other social science disciplines. The author introduces the foundations of longitudinal and panel data analysis at a level suitable for quantitatively oriented social science graduate students as well as individual researchers. He emphasizes mathematical and statistical fundamentals but also demonstrates substantive applications from across the social sciences. These applications are enhanced by real-world data sets and software programs in SAS and Stata.