Analysis of Microdata

by Winkelmann, Rainer; Boes, Stefan

• ISBN13: 9783540296058
• ISBN10: 3540296050
• Format: Hardcover
• Copyright: 2005-12-30
• Publisher: Springer Verlag

Summary

The book provides a simple, intuitive introduction to regression models for qualitative and discrete dependent variables, to sample selection models, and to event history models, all in the context of maximum likelihood estimation. It presents a wide range of commonly used models. The book thereby enables the reader to become a critical consumer of current empirical social science research and to conduct own empirical analyses. The book includes numerous examples, illustrations, and exercises. It can be used as a textbook for an advanced undergraduate, a Master's or a first-year Ph.D. course in microdata analysis, and as a reference for practitioners and researchers.

Table of Contents

1 Introduction	1	(20)
1.1 What Are Microdata?	1	(3)
1.2 Types of Microdata	4	(4)
1.2.1 Qualitative Data	4	(2)
1.2.2 Quantitative Data	6	(2)
1.3 Why Not Linear Regression?	8	(2)
1.4 Common Elements of Microdata Models	10	(1)
1.5 Examples	11	(8)
1.5.1 Determinants of Fertility	11	(5)
1.5.2 Secondary School Choice	16	(1)
1.5.3 Female Hours of Work and Wages	17	(2)
1.6 Overview of the Book	19	(2)
2 From Regression to Probability Models	21	(24)
2.1 Introduction	21	(2)
2.2 Conditional Probability Functions	23	(6)
2.2.1 Definition	23	(1)
2.2.2 Estimation	24	(1)
2.2.3 Interpretation	25	(4)
2.3 Probability and Probability Distributions	29	(10)
2.3.1 Axioms of Probability	29	(1)
2.3.2 Univariate Random Variables	30	(1)
2.3.3 Multivariate Random Variables	31	(3)
2.3.4 Conditional Probability Models	34	(5)
2.4 Further Exercises	39	(6)
3 Maximum Likelihood Estimation	45	(50)
3.1 Introduction	45	(1)
3.2 Likelihood Function	46	(7)
3.2.1 Score Function and Hessian Matrix	48	(2)
3.2.2 Conditional Models	50	(1)
3.2.3 Maximization	50	(3)
3.3 Properties of the Maximum Likelihood Estimator	53	(10)
3.3.1 Expected Score	54	(1)
3.3.2 Consistency	55	(1)
3.3.3 Information Matrix Equality	56	(3)
3.3.4 Asymptotic Distribution	59	(1)
3.3.5 Covariance Matrix	60	(3)
3.4 Normal Linear Model	63	(4)
3.5 Further Aspects of Maximum Likelihood Estimation	67	(9)
3.5.1 Invariance and Delta Method	67	(2)
3.5.2 Numerical Optimization	69	(5)
3.5.3 Identification	74	(2)
3.5.4 Quasi Maximum Likelihood	76	(1)
3.6 Testing	76	(13)
3.6.1 Introduction	76	(3)
3.6.2 Restricted Maximum Likelihood	79	(2)
3.6.3 Wald Test	81	(2)
3.6.4 Likelihood Ratio Test	83	(3)
3.6.5 Score Test	86	(2)
3.6.6 Model Selection	88	(1)
3.6.7 Goodness-of-Fit	89	(1)
3.7 Pros and Cons of Maximum Likelihood	89	(1)
3.8 Further Exercises	90	(5)
4 Binary Response Models	95	(42)
4.1 Introduction	95	(2)
4.2 Models for Binary Response Variables	97	(10)
4.2.1 General Framework	97	(1)
4.2.2 Linear Probability Model	98	(2)
4.2.3 Probit Model	100	(2)
4.2.4 Logit Model	102	(2)
4.2.5 Interpretation of Parameters	104	(3)
4.3 Discrete Choice Models	107	(3)
4.4 Estimation	110	(12)
4.4.1 Maximum Likelihood	110	(3)
4.4.2 Perfect Prediction	113	(1)
4.4.3 Properties of the Estimator	114	(2)
4.4.4 Endogenous Regressors in Binary Response Models	116	(2)
4.4.5 Estimation of Marginal Effects	118	(4)
4.5 Goodness-of-Fit	122	(5)
4.6 Non-Standard Sampling Schemes	127	(3)
4.6.1 Stratified Sampling	127	(1)
4.6.2 Exogenous Stratification	127	(1)
4.6.3 Endogenous Stratification	128	(2)
4.7 Further Exercises	130	(7)
5 Multinomial Response Models	137	(34)
5.1 Introduction	137	(2)
5.2 Multinomial Logit Model	139	(11)
5.2.1 Basic Model	139	(1)
5.2.2 Estimation	140	(4)
5.2.3 Interpretation of Parameters	144	(6)
5.3 Conditional Logit Model	150	(10)
5.3.1 Introduction	150	(1)
5.3.2 General Model of Choice	151	(1)
5.3.3 Modeling Conditional Logits	152	(3)
5.3.4 Interpretation of Parameters	155	(4)
5.3.5 Independence of Irrelevant Alternatives	159	(1)
5.4 Generalized Multinomial Response Models	160	(6)
5.4.1 Multinomial Probit Model	161	(2)
5.4.2 Mixed Logit Models	163	(1)
5.4.3 Nested Logit Models	164	(2)
5.5 Further Exercises	166	(5)
6 Ordered Response Models	171	(36)
6.1 Introduction	171	(3)
6.2 Standard Ordered Response Models	174	(14)
6.2.1 General Framework	174	(2)
6.2.2 Ordered Probit Model	176	(1)
6.2.3 Ordered Logit Model	177	(2)
6.2.4 Estimation	179	(1)
6.2.5 Interpretation of Parameters	179	(7)
6.2.6 Single Indices and Parallel Regression	186	(2)
6.3 Generalized Threshold Models	188	(6)
6.3.1 Generalized Ordered Logit and Probit Models	188	(1)
6.3.2 Interpretation of Parameters	189	(5)
6.4 Sequential Models	194	(6)
6.4.1 Modeling Conditional Transitions	194	(3)
6.4.2 Generalized Conditional Transition Probabilities	197	(1)
6.4.3 Marginal Effects	197	(1)
6.4.4 Estimation	198	(2)
6.5 Interval Data	200	(2)
6.6 Further Exercises	202	(5)
7 Limited Dependent Variables	207	(44)
7.1 Introduction	207	(4)
7.1.1 Corner Solution Outcomes	208	(1)
7.1.2 Sample Selection Models	209	(1)
7.1.3 Treatment Effect Models	210	(1)
7.2 Tobin's Corner Solution Model	211	(13)
7.2.1 Introduction	211	(1)
7.2.2 Tobit Model	212	(2)
7.2.3 Truncated Normal Distribution	214	(1)
7.2.4 Inverse Mills Ratio and its Properties	215	(3)
7.2.5 Interpretation of the Tobit Model	218	(3)
7.2.6 Comparing Tobit and OLS	221	(2)
7.2.7 Further Specification Issues	223	(1)
7.3 Sample Selection Models	224	(15)
7.3.1 Introduction	224	(2)
7.3.2 Censored Regression Model	226	(2)
7.3.3 Estimation of the Censored Regression Model	228	(2)
7.3.4 Truncated Regression Model	230	(1)
7.3.5 Incidental Censoring	231	(6)
7.3.6 Example: Estimating a Labor Supply Model	237	(2)
7.4 Treatment Effect Models	239	(7)
7.4.1 Introduction	239	(3)
7.4.2 Endogenous Binary Variable	242	(1)
7.4.3 Switching Regression Model	243	(3)
7.5 Appendix: Bivariate Normal Distribution	246	(1)
7.6 Further Exercises	247	(4)
8 Event History Models	251	(46)
8.1 Introduction	251	(3)
8.2 Duration Models	254	(25)
8.2.1 Introduction	254	(1)
8.2.2 Basic Concepts	254	(5)
8.2.3 Discrete Time Duration Models	259	(3)
8.2.4 Continuous Time Duration Models	262	(3)
8.2.5 Key Element: Hazard Function	265	(2)
8.2.6 Duration Dependence	267	(4)
8.2.7 Unobserved Heterogeneity	271	(8)
8.3 Count Data Models	279	(15)
8.3.1 The Poisson Regression Model	279	(5)
8.3.2 Unobserved Heterogeneity	284	(5)
8.3.3 Efficient versus Robust Estimation	289	(1)
8.3.4 Censoring and Truncation	289	(2)
8.3.5 Hurdle and Zero-Inflated Count Data Models	291	(3)
8.4 Further Exercises	294	(3)
List of Figures	297	(2)
List of Tables	299	(2)
References	301	(8)
Index	309