TAILIEUCHUNG - Econometric theory and methods, Russell Davidson - Chapter 11

Chapter 11 Discrete and Limited Dependent Variables Introduction Although regression models are useful for modeling many types of data, they are not suitable for modeling every type. In particular, they should not be used when the dependent variable is discrete | Chapter 11 Discrete and Limited Dependent Variables Introduction Although regression models are useful for modeling many types of data they are not suitable for modeling every type. In particular they should not be used when the dependent variable is discrete and can therefore take on only a countable number of values or when it is continuous but is limited in the range of values it can take on. Since variables of these two types arise quite often it is important to be able to deal with them and a large number of models has been proposed for doing so. In this chapter we discuss some of the simplest and most commonly used models for discrete and limited dependent variables. The most commonly encountered type of dependent variable that cannot be handled properly using a regression model is a binary dependent variable. Such a variable can take on only two values which for practical reasons are almost always coded as 0 and 1. For example a person may be in or out of the labor force a commuter may drive to work or take public transit a household may own or rent the home it resides in and so on. In each case the economic agent chooses between two alternatives one of which is coded as 0 and one of which is coded as 1. A binary response model then tries to explain the probability that the agent will choose alternative 1 as a function of some observed explanatory variables. We discuss binary response models at some length in Sections and A binary dependent variable is a special case of a discrete dependent variable. In Section we briefly discuss several models for dealing with discrete dependent variables that can take on a fixed number of values. We consider two different cases one in which the values have a natural ordering and one in which they do not. Then in Section we discuss models for count data in which the dependent variable can in principle take on any nonnegative integer value. Sometimes a dependent variable is continuous but can take on

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