Winkelmann Econometric Analysis of Count Data

5. Auflage 2008
ISBN: 978-3-540-78389-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 320 Seiten

The “count data” ?eld has further ?ourished since the previous edition of this book was published in 2003. The development of new methods has not slowed down by any means, and the application of existing ones in applied work has expanded in many areas of social science research. This, in itself, would be reason enough for updating the material in this book, to ensure that it continues to provide a fair representation of the current state of research. In addition, however, I have seized the opportunity to undertake some major changes to the organization of the book itself. The core material on cross-section models for count data is now presented in four chapters, rather than in two as previously. The ?rst of these four chapters introduces the Poissonregressionmodel,anditsestimationbymaximumlikelihoodorpseudo maximum likelihood. The second focuses on unobserved heterogeneity, the third on endogeneity and non-random sample selection. The fourth chapter provides an extended and uni?ed discussion of zeros in count data models. This topic deserves, in my view, special emphasis, as it relates to aspects of modeling and estimation that are speci?c to counts, as opposed to general exponential regression models for non-negative dependent variables. Count distributions put positive probability mass on single o- comes, and thus o?er a richer set of interesting inferences.

Autoren/Hrsg.

Winkelmann, Rainer

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;List of Figures;13
4;List of Tables;15
5;1 Introduction;16
5.1;1.1 Poisson Regression Model;16
5.2;1.2 Examples;17
5.3;1.3 Organization of the Book;19
6;2 Probability Models for Count Data;22
6.1;2.1 Introduction;22
6.2;2.2 Poisson Distribution;22
6.2.1;2.2.1 De.nitions and Properties;22
6.2.2;2.2.2 Genesis of the Poisson Distribution;25
6.2.3;2.2.3 Poisson Process;26
6.2.4;2.2.4 Generalizations of the Poisson Process;29
6.2.5;2.2.5 Poisson Distribution as a Binomial Limit;30
6.2.6;2.2.6 Exponential Interarrival Times;31
6.2.7;2.2.7 Non-Poissonness;32
6.3;2.3 Further Distributions for Count Data;35
6.3.1;2.3.1 Negative Binomial Distribution;35
6.3.2;2.3.2 Binomial Distribution;40
6.3.3;2.3.3 Logarithmic Distribution;42
6.3.4;2.3.4 Summary;43
6.4;2.4 Modified Count Data Distributions;45
6.4.1;2.4.1 Truncation;45
6.4.2;2.4.2 Censoring and Grouping;46
6.4.3;2.4.3 Altered Distributions;47
6.5;2.5 Generalizations;48
6.5.1;2.5.1 Mixture Distributions;48
6.5.2;2.5.2 Compound Distributions;51
6.5.3;2.5.3 Birth Process Generalizations;54
6.5.4;2.5.4 Katz Family of Distributions;55
6.5.5;2.5.5 Additive Log-Di.erenced Probability Models;56
6.5.6;2.5.6 Linear Exponential Families;57
6.5.7;2.5.7 Summary;59
6.6;2.6 Distributions for Over- and Underdispersion;60
6.6.1;2.6.1 Generalized Event Count Model;60
6.6.2;2.6.2 Generalized Poisson Distribution;61
6.6.3;2.6.3 Poisson Polynomial Distribution;62
6.6.4;2.6.4 Double Poisson Distribution;64
6.6.5;2.6.5 Summary;64
6.7;2.7 Duration Analysis and Count Data;65
6.7.1;2.7.1 Distributions for Interarrival Times;67
6.7.2;2.7.2 Renewal Processes;69
6.7.3;2.7.3 Gamma Count Distribution;71
6.7.4;2.7.4 Duration Mixture Models;74
7;3 Poisson Regression;78
7.1;3.1 Specification;78
7.1.1;3.1.1 Introduction;78
7.1.2;3.1.2 Assumptions of the Poisson Regression Model;78
7.1.3;3.1.3 Ordinary Least Squares and Other Alternatives;80
7.1.4;3.1.4 Interpretation of Parameters;85
7.1.5;3.1.5 Period at Risk;89
7.2;3.2 Maximum Likelihood Estimation;92
7.2.1;3.2.1 Introduction;92
7.2.2;3.2.2 Likelihood Function and Maximization;92
7.2.3;3.2.3 Newton-Raphson Algorithm;93
7.2.4;3.2.4 Properties of the Maximum Likelihood Estimator;95
7.2.5;3.2.5 Estimation of the Variance Matrix;97
7.2.6;3.2.6 Approximate Distribution of the Poisson Regression Coefficients;98
7.2.7;3.2.7 Bias Reduction Techniques;99
7.3;3.3 Pseudo-Maximum Likelihood;102
7.3.1;3.3.1 Linear Exponential Families;104
7.3.2;3.3.2 Biased Poisson Maximum Likelihood Inference;105
7.3.3;3.3.3 Robust Poisson Regression;106
7.3.4;3.3.4 Non-Parametric Variance Estimation;110
7.3.5;3.3.5 Poisson Regression and Log-Linear Models;112
7.3.6;3.3.6 Generalized Method of Moments;113
7.3.7;Application to the Poisson Model;116
7.4;3.4 Sources of Misspecification;117
7.4.1;3.4.1 Mean Function;117
7.4.2;3.4.2 Unobserved Heterogeneity;118
7.4.3;3.4.3 Measurement Error;120
7.4.4;3.4.4 Dependent Process;122
7.4.5;3.4.5 Selectivity;122
7.4.6;3.4.6 Simultaneity and Endogeneity;123
7.4.7;3.4.7 Underreporting;124
7.4.8;3.4.8 Excess Zeros;124
7.4.9;3.4.9 Variance Function;125
7.5;3.5 Testing for Misspecification;127
7.5.1;3.5.1 Classical Speci.cation Tests;127
7.5.2;3.5.2 Regression Based Tests;133
7.5.3;3.5.3 Goodness-of-Fit Tests;133
7.5.4;3.5.4 Tests for Non-Nested Models;135
7.6;3.6 Outlook;140
8;4 Unobserved Heterogeneity;142
8.1;4.1 Introduction;142
8.1.1;4.1.1 Conditional Mean Function;142
8.1.2;4.1.2 Partial E.ects with Unobserved Heterogeneity;143
8.1.3;4.1.3 Unobserved Heterogeneity in the Poisson Model;144
8.1.4;4.1.4 Parametric and Semi-Parametric Models;145
8.2;4.2 Parametric Mixture Models;145
8.2.1;4.2.1 Gamma Mixture;146
8.2.2;4.2.2 Inverse Gaussian Mixture;146
8.2.3;4.2.3 Log-Normal Mixture;147
8.3;4.3 Negative Binomial Models;149
8.3.1;4.3.1 Negbin II Model;150
8.3.2;4.3.2 Negbin I Model;151
8.3.3;4.3.3 Negbink Model;151
8.3.4;4.3.4 NegbinX Model;152
8.4;4.4 Semiparametric Mixture Models;153
8.4.1;4.4.1 Series Expansions;153
8.4.2;4.4.2 Finite Mixture Models;154
9;5 Sample Selection and Endogeneity;158
9.1;5.1 Censoring and Truncation;158
9.1.1;5.1.1 Truncated Count Data Models;159
9.1.2;5.1.2 Endogenous Sampling;159
9.1.3;5.1.3 Censored Count Data Models;161
9.1.4;5.1.4 Grouped Poisson Regression Model;162
9.2;5.2 Incidental Censoring and Truncation;163
9.2.1;5.2.1 Outcome and Selection Model;163
9.2.2;5.2.2 Models of Non-Random Selection;164
9.2.3;5.2.3 Bivariate Normal Error Distribution;165
9.2.4;5.2.4 Outcome Distribution;167
9.2.5;5.2.5 Incidental Censoring;168
9.2.6;5.2.6 Incidental Truncation;169
9.3;5.3 Endogeneity in Count Data Models;171
9.3.1;5.3.1 Introduction and Examples;171
9.3.2;5.3.2 Parameter Ancillarity;172
9.3.3;5.3.3 Endogeneity and Mean Function;174
9.3.4;5.3.4 A Two-Equation Framework;176
9.3.5;5.3.5 Instrumental Variable Estimation;177
9.3.6;5.3.6 Estimation in Stages;180
9.4;5.4 Switching Regression;182
9.4.1;5.4.1 Full Information Maximum Likelihood Estimation;183
9.4.2;5.4.2 Moment-Based Estimation;185
9.4.3;5.4.3 Non-Normality;186
9.5;5.5 Mixed Discrete-Continuous Models;186
10;6 Zeros in Count Data Models;188
10.1;6.1 Introduction;188
10.2;6.2 Zeros in the Poisson Model;189
10.2.1;6.2.1 Excess Zeros and Overdispersion;189
10.2.2;6.2.2 Two-Crossings Theorem;190
10.2.3;6.2.3 Effects at the Extensive Margin;191
10.2.4;6.2.4 Multi-Index Models;192
10.2.5;6.2.5 A General Decomposition Result;192
10.3;6.3 Hurdle Count Data Models;193
10.3.1;6.3.1 Hurdle Poisson Model;196
10.3.2;6.3.2 Marginal E.ects;197
10.3.3;6.3.3 Hurdle Negative Binomial Model;198
10.3.4;6.3.4 Non-nested Hurdle Models;198
10.3.5;6.3.5 Unobserved Heterogeneity in Hurdle Models;200
10.3.6;6.3.6 Finite Mixture Versus Hurdle Models;201
10.3.7;6.3.7 Correlated Hurdle Models;202
10.4;6.4 Zero-Inflated Count Data Models;203
10.4.1;6.4.1 Introduction;203
10.4.2;6.4.2 Zero-Inflated Poisson Model;204
10.4.3;6.4.3 Zero-Inflated Negative Binomial Model;206
10.4.4;6.4.4 Marginal Effets;206
10.5;6.5 Compound Count Data Models;207
10.5.1;6.5.1 Multi-Episode Models;208
10.5.2;6.5.2 Underreporting;208
10.5.3;6.5.3 Count Amount Model;211
10.5.4;6.5.4 Endogenous Underreporting;212
10.6;6.6 Quantile Regression for Count Data;214
11;7 Correlated Count Data;218
11.1;7.1 Multivariate Count Data;218
11.1.1;7.1.1 Multivariate Poisson Distribution;220
11.1.2;7.1.2 Multivariate Negative Binomial Model;225
11.1.3;7.1.3 Multivariate Poisson-Gamma Mixture Model;227
11.1.4;7.1.4 Multivariate Poisson-Log-Normal Model;228
11.1.5;7.1.5 Latent Poisson-Normal Model;231
11.1.6;7.1.6 Moment-Based Methods;232
11.1.7;7.1.7 Copula Functions;234
11.2;7.2 Panel Data Models;235
11.2.1;7.2.1 Fixed Effects Poisson Model;237
11.2.2;7.2.2 Moment-based Estimation of the Fixed Effects Model;240
11.2.3;7.2.3 Fixed Effects Negative Binomial Model;242
11.2.4;7.2.4 Random Effects Count Data Models;243
11.2.5;7.2.5 Dynamic Panel Count Data Models;245
11.3;7.3 Time-Series Count Data Models;247
12;8 Bayesian Analysis of Count Data;256
12.1;8.1 Bayesian Analysis of the Poisson Model;257
12.2;8.2 A Poisson Model with Underreporting;260
12.3;8.3 Estimation of the Multivariate Poisson-Log-Normal Model by MCMC;262
12.4;8.4 Estimation of a Random Coefficients Model by MCMC;263
13;9 Applications;266
13.1;9.1 Accidents;266
13.2;9.2 Crime;267
13.3;9.3 Trip Frequency;267
13.4;9.4 Health Economics;269
13.5;9.5 Demography;272
13.6;9.6 Marketing and Management;275
13.7;9.7 Labor Mobility;276
13.7.1;9.7.1 Economics Models of Labor Mobility;277
13.7.2;9.7.2 Previous Literature;278
13.7.3;9.7.3 Data and Descriptive Statistics;280
13.7.4;direct;280
13.7.5;job changes;280
13.7.6;unemployment spells;280
13.7.7;direct job change;280
13.7.8;unemployment spell;280
13.7.9;unemployment spells;280
13.7.10;direct job changes.;281
13.7.11;direct job changes;281
13.7.12;unemployment;281
13.7.13;spells;281
13.7.14;direct job changes;281
13.7.15;unemployment spells,;281
13.7.16;direct job changes;281
13.7.17;unemployment;281
13.7.18;spells;281
13.7.19;Education;281
13.7.20;experience.;281
13.7.21;Quali.ed White Collar;281
13.7.22;Ordinary White Collar;281
13.7.23;Quali.ed Blue Collar;281
13.7.24;Ordinary Blue Collar;281
13.7.25;German;281
13.7.26;Single;281
13.7.27;Union;281
13.7.28;direct job changes;281
13.7.29;unemployment;281
13.7.30;spells);281
13.7.31;experience.;281
13.7.32;direct;282
13.7.33;job changes,;282
13.7.34;unemployment spells;282
13.7.35;education;283
13.7.36;direct job;283
13.7.37;changes.;283
13.7.38;unemployment spells,;283
13.7.39;direct job changes;283
13.7.40;unemployment spells;283
13.7.41;9.7.4 Regression Results;284
13.7.42;number of job changes.;284
13.7.43;education, experience, squared experience, union,;284
13.7.44;single, German, quali.ed white collar, ordinary white collar,;284
13.7.45;quali.ed blue collar;284
13.7.46;number of job changes;284
13.7.47;education;285
13.7.48;direct job changes,;285
13.7.49;9.7.5 Model Performance;287
13.7.50;9.7.6 Marginal Probability E.ects;289
13.7.51;9.7.7 Structural Inferences;293
14;A Probability Generating Functions;296
15;B Gauss-Hermite Quadrature;300
16;C Software;304
17;D Tables;306
18;References;314
19;Author’s Index;336
20;Subject Index;342