Analysis of Microdata

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1 Rainer Winkelmann Stefan Boes Analysis of Microdata With 38 Figures and 41 Tables 4y Springer

2 Contents 1 Introduction What Are Microdata? Types of Microdata Qualitative Data Quantitative Data Why Not Linear Regression? Common Elements of Microdata Models Examples Determinants of Fertility Secondary School Choice Female Hours of Work and Wages Overview of the Book 19 2 From Regression to Probability Models Introduction Conditional Probability Functions Definition Estimation Interpretation Probability and Probability Distributions Axioms of Probability Univariate Random Variables Multivariate Random Variables Conditional Probability Models Further Exercises 39 3 Maximum Likelihood Estimation Introduction Likelihood Function Score Function and Hessian Matrix Conditional Models 50

3 VIII Contents Maximization Properties of the Maximum Likelihood Estimator Expected Score Consistency Information Matrix Equality Asymptotic Distribution Covariance Matrix Normal Linear Model Further Aspects of Maximum Likelihood Estimation Invariance and Delta Method Numerical Optimization Identification Quasi Maximum Likelihood Testing Introduction Restricted Maximum Likelihood Wald Test Likelihood Ratio Test Score Test Model Selection Goodness-of-Fit Pros and Cons of Maximum Likelihood Further Exercises 90 4 Binary Response Models Introduction Models for Binary Response Variables General Framework Linear Probability Model Probit Model Logit Model Interpretation of Parameters Discrete Choice Models Estimation Maximum Likelihood Perfect Prediction Properties of the Estimator Endogenous Regressors in Binary Response Models Estimation of Marginal Effects Goodness-of-Fit Non-Standard Sampling Schemes Stratified Sampling Exogenous Stratification Endogenous Stratification Further Exercises 130

4 Contents Multinomial Response Models Introduction Multinomial Logit Model Basic Model Estimation Interpretation of Parameters Conditional Logit Model Introduction General Model of Choice Modeling Conditional Logits Interpretation of Parameters Independence of Irrelevant Alternatives Generalized Multinomial Response Models Multinomial Probit Model Mixed Logit Models Nested Logit Models Further Exercises 166 Ordered Response Models Introduction Standard Ordered Response Models General Framework Ordered Probit Model Ordered Logit Model Estimation Interpretation of Parameters Single Indices and Parallel Regression Generalized Threshold Models Generalized Ordered Logit and Probit Models Interpretation of Parameters Sequential Models Modeling Conditional Transitions Generalized Conditional Transition Probabilities Marginal Effects Estimation Interval Data Further Exercises 202 Limited Dependent Variables Introduction Corner Solution Outcomes Sample Selection Models Treatment Effect Models Tobin's Corner Solution Model Introduction 211 IX

5 X Contents Tobit Model Truncated Normal Distribution Inverse Mills Ratio and its Properties Interpretation of the Tobit Model Comparing Tobit and OLS Further Specification Issues Sample Selection Models Introduction Censored Regression Model Estimation of the Censored Regression Model Truncated Regression Model Incidental Censoring Example: Estimating a Labor Supply Model Treatment Effect Models Introduction Endogenous Binary Variable Switching Regression Model Appendix: Bivariate Normal Distribution Further Exercises Event History Models Introduction Duration Models Introduction Basic Concepts Discrete Time Duration Models Continuous Time Duration Models Key Element: Hazard Function Duration Dependence Unobserved Heterogeneity Count Data Models The Poisson Regression Model Unobserved Heterogeneity Efficient versus Robust Estimation Censoring and Truncation Hurdle and Zero-Inflated Count Data Models Further Exercises 294 List of Figures 297 List of Tables 299 References 301 Index 309

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