tailieunhanh - Econometric theory and methods, Russell Davidson - Chapter 1

Chapter 1 Regression Models Introduction Regression models form the core of the discipline of econometrics. Although econometricians routinely estimate a wide variety of statistical models, using many different types of data, the vast majority of these are either regression models | More than 150 000 articles in the search database Learn how almost everything works Chapter 1 Regression Models Introduction Regression models form the core of the discipline of econometrics. Although econometricians routinely estimate a wide variety of statistical models using many different types of data the vast majority of these are either regression models or close relatives of them. In this chapter we introduce the concept of a regression model discuss several varieties of them and introduce the estimation method that is most commonly used with regression models namely least squares. This estimation method is derived by using the method of moments which is a very general principle of estimation that has many applications in econometrics. The most elementary type of regression model is the simple linear regression model which can be expressed by the following equation yt 31 32Xt Ut- The subscript t is used to index the observations of a sample. The total number of observations also called the sample size will be denoted by n. Thus for a sample of size n the subscript t runs from 1 to n. Each observation comprises an observation on a dependent variable written as yt for observation t and an observation on a single explanatory variable or independent variable written as Xt. The relation links the observations on the dependent and the explanatory variables for each observation in terms of two unknown parameters 31 and 32 and an unobserved error term ut. Thus of the five quantities that appear in two yt and Xt are observed and three 31 32 and ut are not. Three of them yt Xt and ut are specific to observation t while the other two the parameters are common to all n observations. Here is a simple example of how a regression model like could arise in economics. Suppose that the index t is a time index as the notation suggests. Each value of t could represent a year for instance. Then yt could be household consumption as .