www.GetPedia.com *More than 150,000 articles in the search database *Learn how almost everything works Chapter 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 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 = β1 + β2 Xt + ut (1.01) 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 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 (1.01) links the observations on the dependent and the explanatory variables for each observation in terms of two unknown parameters, β1 and β2 , and an unobserved error term, ut Thus, of the five quantities that appear in (1.01), two, yt and Xt , are observed, and three, β1 , β2 , 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 (1.01) 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 measured in year t, and Xt could be measured disposable income of households in the same year In that case, (1.01) would represent what in elementary macroeconomics is called a consumption function Copyright c 1999, Russell Davidson and James G MacKinnon ... β1 and β2 , and an unobserved error term, ut Thus, of the five quantities that appear in (1.01), two, yt and Xt , are observed, and three, β1 , β2 , and ut , are not Three of them, yt , Xt , and. .. what in elementary macroeconomics is called a consumption function Copyright c 1999, Russell Davidson and James G MacKinnon ... 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