计量经济学理论与方法Econometric Theory and Methods.pdf

Chapter 1 Regression Models 1.1 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 estima- tion 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: = + + (101) 1 2 The subscript is used to index the observations of a sample. The total num- ber of observations, also called the sample size, will be denoted by . Thus, for a sample of size , the subscript runs from 1 to . Each observation comprises an observation on a dependent variable, written as for observa- tion , and an observation on a single explanatory variable, or independent variable, written as . The relation (1.01) links the observations on the dependent and the explana- tory variables for each observation in terms of two unknown parameters, 1 and , and an unobserved error term, . Thus, of the five quantities that 2 appear in (1.01), two, and , are observed, and three, , , and , are 1 2 not. Three of them, , , and , are specific to observation