## Econometric Analysis of Count DataThe book provides graduate students and researchers with an up-to-date survey of statistical and econometric techniques for the analysis of count data, with a focus on conditional distribution models. Proper count data probability models allow for rich inferences, both with respect to the stochastic count process that generated the data, and with respect to predicting the distribution of outcomes. The book starts with a presentation of the benchmark Poisson regression model. Alternative models address unobserved heterogeneity, state dependence, selectivity, endogeneity, underreporting, and clustered sampling. Testing and estimation is discussed from frequentist and Bayesian perspectives. Finally, applications are reviewed in fields such as economics, marketing, sociology, demography, and health sciences. The fourth edition contains several new sections, for example on nonnested hurdle models, quantile regression and on software. Many other sections have been entirely rewritten and extended. |

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### Contents

Introduction | 1 |

11 Poisson Regression Model | 2 |

12 Some Thoughts on Methodology | 3 |

13 Examples | 4 |

14 Organization of the Book | 6 |

Probability Models for Count Data | 7 |

22 Poisson Distribution | 8 |

222 Genesis of the Poisson Distribution | 12 |

452 Incidental Censoring | 136 |

453 Incidental Truncation | 137 |

46 Hurdle Count Data Models | 138 |

461 Hurdle Poisson Model | 141 |

462 Marginal Effects | 142 |

463 Hurdle Negative Binomial Model | 143 |

464 Nonnested Hurdle Models | 144 |

465 Unobserved Heterogeneity in Hurdle Models | 145 |

224 Generalizations of the Poisson Process | 15 |

225 Poisson Distribution as a Binomial Limit | 16 |

226 Exponential Interarrival Times | 18 |

227 NonPoissonness | 19 |

23 Further Distributions for Count Data | 22 |

232 Binomial Distribution | 27 |

233 Logarithmic Distribution | 29 |

234 Summary | 30 |

24 Modified Count Data Distributions | 33 |

242 Censoring and Grouping | 34 |

25 Generalizations | 35 |

251 Mixture Distributions | 36 |

252 Compound Distributions | 39 |

253 Birth Process Generalizations | 41 |

254 Katz Family of Distributions | 42 |

255 Linear Exponential Families | 44 |

256 Additive LogDifferenced Probability Models | 47 |

257 Summary | 48 |

261 Distributions for Interarrival Times | 49 |

262 Renewal Processes | 52 |

264 Gamma Count Distribution | 53 |

265 Duration Mixture Models | 56 |

Econometric Modeling Basic Issues | 61 |

312 Ordinary Least Squares and Other Alternatives | 63 |

313 Generalized Linear Model | 67 |

314 Interpretation of the Parameters | 68 |

315 Period at Risk | 71 |

32 Estimation | 74 |

322 PseudoMaximum Likelihood | 81 |

323 Generalized Method of Moments | 83 |

324 Bias Reduction Techniques | 85 |

33 Sources of Misspecification | 88 |

331 Mean Function | 89 |

333 Measurement Error | 92 |

334 Dependent Process | 94 |

336 Simultaneity and Endogeneity | 95 |

337 Underreporting | 96 |

339 Variance Function | 97 |

34 Testing for Misspecification | 99 |

341 Classical Speciftcation Tests | 100 |

342 Regression Based Tests | 105 |

343 GoodnessofFit Tests | 106 |

344 Tests for NonNested Models | 107 |

Econometric Modeling Extensions | 113 |

42 Unobserved Heterogeneity | 115 |

421 Parametric Mixture Models | 116 |

422 Negative Binomial Models | 119 |

423 Semiparametric Mixture Models | 124 |

424 Finite Mixture Models | 125 |

43 Dependent Count Process | 127 |

44 Censoring and Truncation | 128 |

441 Truncated Count Data Models | 129 |

443 Censored Count Data Models | 131 |

444 Grouped Poisson Regression Model | 132 |

451 Bivariate Normal Distribution | 133 |

466 Finite Mixture Versus Hurdle Models | 146 |

467 Correlated Hurdle Models | 147 |

47 ZeroInflated Count Data Models | 148 |

48 Underreporting | 151 |

482 Count Amount Model | 153 |

483 Endogenous Underreporting | 154 |

49 Endogenous Regressors | 156 |

491 Instrumental Variable Estimation | 157 |

492 Simultaneous Equations | 159 |

493 Binary Endogenous Variables | 161 |

494 Mixed DiscreteContinuous Models | 165 |

410 Generalized Variance Models | 166 |

4102 Generalized Poisson Regression | 168 |

4103 Robust Poisson Regression | 170 |

4104 NonParametric Variance Estimation | 175 |

411 Quantile Regression for Count Data | 177 |

Correlated Count Data | 181 |

511 Multivariate Poisson Distribution | 183 |

512 Multivariate Negative Binomial Model | 188 |

513 Multivariate PoissonGamma Mixture Model | 190 |

514 Multivariate PoissonLogNormal Model | 191 |

515 Latent PoissonNormal Model | 194 |

516 MomentBased Methods | 195 |

52 Panel Data Models | 197 |

521 Fixed Effects Poisson Model | 198 |

522 Fixed Effects Negative Binomial Model | 203 |

523 Random Effects Count Data Models | 204 |

524 MomentBased Methods | 205 |

53 TimeSeries Count Data Models | 208 |

Bayesian Analysis of Count Variables | 217 |

61 Bayesian Analysis of the Poisson Model | 218 |

62 A Poisson Model with Underreporting | 221 |

63 Estimation of the Multivariate PoissonLogNormal Model by MCMC | 223 |

64 Estimation of a Random Coefficients Model by MCMC | 224 |

Applications | 227 |

72 Crime | 228 |

74 Health Economics | 230 |

75 Demography | 233 |

76 Marketing and Management | 236 |

77 Labor Mobility | 237 |

771 Economics Models of Labor Mobility | 238 |

772 Previous Literature | 239 |

773 Data and Descriptive Statistics | 241 |

774 Regression Results | 245 |

775 Model Performance | 248 |

776 Marginal Probability Effects | 250 |

777 Structural Inferences | 254 |

Probability Generating Functions | 257 |

GaussHermite Quadrature | 261 |

Software | 265 |

Tables | 267 |

275 | |

295 | |

299 | |

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### Common terms and phrases

alternative applications assume assumption asymptotic bivariate censoring Chap coefficients conditional distribution conditional expectation correlation count data distribution count data models covariance matrix denote dependent variable derived distribution function duration dependence econometrics endogenous example expected value explanatory variables exponential family fixed effects gamma distribution given hurdle model independent instance integral job changes joint distribution labor mobility likelihood function linear exponential family linear model log-likelihood function logarithmic logit marginal distribution marginal probability marginal probability effects maximum likelihood estimator mean function methods misspecification mixture model multivariate negative binomial distribution negative binomial model Negbin II model non-negative normal distribution number of events Number of Job observed obtained outcomes overdispersion panel data Poisson distribution Poisson process Poisson regression model Poisson-log-normal model probability function probability generating function quantile random variable regressors restrictions robust sample Santos Silva simulation standard errors truncated underdispersion unobserved heterogeneity variance function vector Winkehuann zero zero-inflated

### Popular passages

Page 293 - Zimmermann (1995), Recent Developments in Count Data Modeling: Theory and Applications, Journal of Economic Surveys 9,1- 24.

Page 278 - Markov Chain Monte Carlo Analysis of Correlated Count Data," Journal of Business and Economic Statistics, 19. 428^35. Cincera, M. (1997), "Patents. R&D. and Technological Spillovers at the Firm Level: Some Evidence from Econometric Count Models for Panel Data.

### References to this book

Univariate Discrete Distributions Norman L. Johnson,Adrienne W. Kemp,Samuel Kotz Limited preview - 2005 |

Multivariate Statistical Modelling Based on Generalized Linear Models Ludwig Fahrmeir,Gerhard Tutz No preview available - 2001 |