TAILIEUCHUNG - Book Econometric Analysis of Cross Section and Panel Data By Wooldridge - Chapter 15

NONLINEAR MODELS AND RELATED TOPICS We now apply the general methods of Part III to study specific nonlinear models that often arise in applications. Many nonlinear econometric models are intended to explain limited dependent variables. Roughly, a limited dependent variable is a variable whose range is restricted | NONLINEAR MODELS AND RELATED TOPICS We now apply the general methods of Part III to study specific nonlinear models that often arise in applications. Many nonlinear econometric models are intended to explain limited dependent variables. Roughly a limited dependent variable is a variable whose range is restricted in some important way. Most variables encountered in economics are limited in range but not all require special treatment. For example many variables wage population and food consumption to name just a few can only take on positive values. If a strictly positive variable takes on numerous values special econometric methods are rarely called for. Often taking the log of the variable and then using a linear model suffices. When the variable to be explained y is discrete and takes on a finite number of values it makes little sense to treat it as an approximately continuous variable. Discreteness of y does not in itself mean that a linear model for E y x is inappropriate. However in Chapter 15 we will see that linear models have certain drawbacks for modeling binary responses and we will treat nonlinear models such as probit and logit. We also cover basic multinomial response models in Chapter 15 including the case when the response has a natural ordering. Other kinds of limited dependent variables arise in econometric analysis especially when modeling choices by individuals families or firms. Optimizing behavior often leads to corner solutions for some nontrivial fraction of the population. For example during any given time a fairly large fraction of the working age population does not work outside the home. Annual hours worked has a population distribution spread out over a range of values but with a pileup at the value zero. While it could be that a linear model is appropriate for modeling expected hours worked a linear model will likely lead to negative predicted hours worked for some people. Taking the natural log is not possible because of the corner .

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