## Econometric Applications of Maximum Likelihood MethodsThe advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric research papers, or with the literature on the mathematical basis of Maximum Likelihood theory. They can also try their hand at some advanced econometric research of their own. |

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### Contents

The technology of estimation | 1 |

Likelihood | 11 |

Tests of simplifying assumptions | 30 |

The use of likelihood in econometrics | 45 |

Techniques of maximization | 56 |

Generalized classical regression | 79 |

Systems of linear regression equations | 100 |

The transformation of Box and Cox | 129 |

Time series data and dynamic models | 136 |

Discrete choice models | 150 |

Hybrid and mixed dependent variables | 172 |

Simple random process models | 184 |

194 | |

203 | |

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### Common terms and phrases

algorithm analysis applied argument assumption asymptotic distribution autoregressive behavior Box-Cox transformation Chapter chi-square coefficients computing concentrated loglikelihood conditional density consider constant constrained estimation convergence course covariance matrix denote density function dependent variable derivatives determined diagonal econometric elements ellipsoid exogenous variables expression GCR model given hence Hessian identical information matrix iterative Lagrange Multiplier Least Squares likelihood function likelihood theory linear regression linear regression model log L(0 log Lc logit model loglikelihood function maximizing log Maximum Likelihood method ML estimation nonlinear nonlinear regression Normal distribution notation obtain parameter space parameter vector positive definite probit model properties Questions and exercises random variable regression equation regressor variables residuals respect restrictions result sample sample statistics scalar score vector simplifying single Slutsky's theorem specification standard starting values stochastic independence substitution SURE model term test statistic theorem tion transformation truncated variance variates vector function yields zero