## Econometrics of Qualitative Dependent VariablesThis textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The final two chapters describe models which explain variables assumed by discrete or continuous positive variables. |

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### Contents

Introduction | 1 |

Modelling | 38 |

1 Existence of a Utility Function | 65 |

Estimation Methods and Tests | 72 |

The LogLinear Model and its Applications | 107 |

Qualitative Panel Data | 145 |

The Tobit Model | 170 |

1 Moments of the Truncated Norman Distribution | 203 |

Truncated Latent Variables Defined by a System | 224 |

1 A Model with Price Floors The Recursive Case | 249 |

Duration Models | 284 |

1 Asymptotic Properties of ML under Neglected | 360 |

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9 log algorithm applied assumption behaviour calculate chapter choice coefficients conditional distribution Consider consistent estimator constraints converges correlation corresponding covariance matrix defined demand denote density function derive dichotomous variables distribution of heterogeneity disturbance term duration Econometrics endogenous variable equilibrium equivalent error term estimation methods examine example exogenous explanatory variables exponential distribution expression first-order formulation gamma distribution given hazard function increasing independent individual latent variables likelihood equations likelihood function likelihood-ratio test linear model log F log-likelihood log-linear model Markov chain maximize maximum maximum-likelihood estimators maximum-likelihood method normal distribution null hypothesis observed variables obtain otherwise parameters Poisson polychotomous logit model Pr(y probit procedure Proposition qualitative variables quantity exchanged random regression represent residuals salary sample score solution specification statistic supply survival function truncated unemployment values assumed variance vector Weibull yields