The aim of the course is to acquaint the student with the general concepts of statistical estimation and inference, and with some econometric models used in decision making.
As concerns statistical estimation, we will introduce point estimation and its properties, namely unbiasedness, consistency, asymptotic normality and efficiency. As concerns statistical inference, we will introduce significance and hypothesis testing, i.e. respectively the Fisher and the Neyman-Pearson testing frameworks, and interval estimation. These general concepts will be illustrated in the context of the Maximum Likelihood (ML) method of estimation and inference. In particular, we will present the ML estimator along with the trinity of tests, a set of three general-purpose tests that can be used to draw inference on almost any economic hypothesis.
This method will be then applied to the estimation of some statistical and econometric models widely used in decision making.
First, we will deal with ML estimation in the linear regression model. Passing by, this will serve the purpose of illustrating the general philosophy of model building. In particular, we will briefly illustrate the distinction between specific-to-general (STG) and general-to-specific (GTS) approaches, the general concept of pretesting (variable selection and model validation), and the difference between exploratory, significance and diagnostic tests.
Second, we will introduce models dealing with choices between discrete alternatives. In doing so, we will discuss the relevance of reduced-form and structural models for the interpretation of economic hypotheses. In particular, using the latent regression approach, we will hint at several limited dependent variable models dealing with cases in which the dependent variable is affected by some form of unobservability (censoring, truncation, sample selection, etc.).
All the topics will be illustrated using Monte Carlo simulations or applications to real datasets.
- General concepts
- Point estimation
- Properties of point estimators (unbiasedness, consistency, asymptotic normality and efficiency)
- Fisher or significance testing theory
- Neyman-Pearson or hypothesis testing theory
- Interval estimation
- Maximum Likelihood method
- Properties of ML estimators
- Test trinity (Likelihood Ratio, Lagrange Multipliers, Wald tests)
- Linear regression models
- Assumptions of linear regression models
- Properties of the estimators
- General philosophies of model building
- Discrete choice models
- Regression models for dichotomic variables
- Stuctural and reduced-form interpretations
- Limited Dependent Variable models