Measurement Error and Latent Variables in Econometrics Book

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