INSEAD Library

Includes bibliographical references and index

Digitized

Measurement Error and Latent Variables in Econometrics Contents 1. Introduction 1.1 Measurement error and latent variables 1.2 About this book 1.3 Bibliographical notes 2. Regression and measurement error 2.1 The model 2.2 Asymptotic properties of the OLS estimators 2.3 Attenuation 2.4 Errors in a single regressor 2.5 Various additional results 2.6 Bibliographical notes 3. Bounds on the parameters 3.1 Reverse regression 3.2 Reverse regression and the analysis of discrimination 3.3 Bounds with multiple regression 3.4 Bounds on the measurement error 3.5 Uncorrelated measurement error 3.6 Bibliographical notes 4. Identification 4.1 Structural versus functional models 4.2 Maximum likelihood estimation in the structural model 4.3 Maximum likelihood estimation in the functional model 4.4 General identification theory 4.5 Identification of the measurement error model under normality 4.6 A general identification condition in the structural model 4.7 Bibliographical notes 1 1 4 7 9 10 12 17 22 25 30 33 34 36 43 46 52 56 59 60 65 70 74 78 82 87 X 5. Consistent adjusted least squares 5.1 The CALS estimator 5.2 Measurement error variance known 5.3 Weighted regression 5.4 Orthogonal regression 5.5 Bibliographical notes 6. Instrumental variables 6.1 Assumptions and estimation 6.2 Application to the measurement error model 6.3 Heteroskedasticity 6.4 Combining data from various sources 6.5 Limited information maximum likelihood 6.6 LIML and weak instruments 6.7 Grouping 6.8 Instrumental variables and nonnormality 6.9 Measurement error in panel data 6.10 Bibliographical notes 7. Factor analysis and related methods 7.1 Towards factor analysis 7.2 Estimation in the one-factor FA model 7.3 Multiple factor analysis 7.4 An example of factor analysis 7.5 Principal relations and principal factors 7.6 A taxonomy of eigenvalue-based methods 7.7 Bibliographical notes 8. Structural equation models 8.1 Confirmatory factor analysis 8.2 Multiple causes and the MIMIC model 8.3 The LISREL model 8.4 Other important general parameterizations 8.5 Scaling of the variables 8.6 Extensions of the model 8.7 Equivalent models 8.8 Bibliographical notes 89 90 94 101 104 107 109 110 114 118 120 123 128 131 135 138 143 147 148 151 159 171 175 178 182 185 186 191 194 202 207 214 218 222 xi 9. Generalized method of moments 9.1 The method of moments 9.2 Definition and notation 9.3 Basic properties of GMM estimators 9.4 Estimation of the covariance matrix of the sample moments 9.5 Covariance structures 9.6 Asymptotic efficiency and additional information 9.7 Conditional moments 9.8 Simulated GMM 9.9 The efficiency of GMM and ML 9.10 Bibliographical notes 10. Model evaluation 10.1 Specification tests 10.2 Comparison of the three tests 10.3 Test of overidentifying restrictions 10.4 Robustness 10.5 Model fit and model selection 10.6 Bibliographical notes 11. Nonlinear latent variable models 11.1 A simple nonlinear model 11.2 Polynomial models 11.3 Models for qualitative and limited-dependent variables 11.4 The LISCOMP model 11.5 General parametric nonlinear regression 11.6 Bibliographical notes Appendix A. Matrices, statistics, and calculus A.1 Some results from matrix algebra A.2 Some specific results A.3 Definite matrices A.4 0-1 matrices A.5 On the normal distribution A.6 Slutsky's theorem A.7 The implicit function theorem A.8 Bibliographical notes 227 228 232 236 243 252 257 261 262 266 273 279 280 290 296 301 303 311 317 318 319 325 331 339 342 349 349 353 356 361 364 369 371 373 xii Appendix B. The chi-square distribution B.1 Mean and variance B.2 The distribution of quadratic forms in general B.3 The idempotent case B.4 Robustness characterizations B.5 Bibliographical notes References Author Index Subject Index 375 375 376 378 380 385 387 421 429