tailieunhanh - Book Econometric Analysis of Cross Section and Panel Data By Wooldridge - Chapter 16

Corner Solution Outcomes and Censored Regression Models Introduction and Motivation In this chapter we cover a class of models traditionally called censored regression models. Censored regression models generally apply when the variable to be explained is partly continuous but has positive probability mass | Corner Solution Outcomes and Censored Regression Models Introduction and Motivation In this chapter we cover a class of models traditionally called censored regression models. Censored regression models generally apply when the variable to be explained is partly continuous but has positive probability mass at one or more points. In order to apply these methods effectively we must understand that the statistical model underlying censored regression analysis applies to problems that are conceptually very different. For the most part censored regression applications can be put into one of two categories. In the first case there is a variable with quantitative meaning call it y and we are interested in the population regression E y x . If y and x were observed for everyone in the population there would be nothing new we could use standard regression methods ordinary or nonlinear least squares . But a data problem arises because y is censored above or below some value that is it is not observable for part of the population. An example is top coding in survey data. For example assume that y is family wealth and for a randomly drawn family the actual value of wealth is recorded up to some threshold say 200 000 but above that level only the fact that wealth was more than 200 000 is recorded. Top coding is an example of data censoring and is analogous to the data-coding problem we discussed in Section in connection with interval regression. Example Top Coding of Wealth In the population of all families in the United States let wealth denote actual family wealth measured in thousands of dollars. Suppose that wealth follows the linear regression model E wealth x xfi where x is a 1 x K vector of conditioning variables. However we observe wealth only when wealth 200. When wealth is greater than 200 we know that it is but we do not know the actual value of wealth. Define observed wealth as wealth min wealth 200 The definition wealth 200 when wealth 200 is .