Chapter 12 - Limited dependent variable models. In this chapter, you will learn how to: Compare between different types of limited dependent variables and select the appropriate model, interpret and evaluate logit and probit models, distinguish between the binomial and multinomial cases, deal appropriately with censored and truncated dependent variables, estimate limited dependent variable models using maximum likelihood in EViews. | ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Chapter 12 Limited Dependent Variable Models ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Some Examples of when Limited Dependent Variables may be used There are numerous examples of instances where this may arise, for example where we want to model: Why firms choose to list their shares on the NASDAQ rather than the NYSE Why some stocks pay dividends while others do not What factors affect whether countries default on their sovereign debt Why some firms choose to issue new stock to finance an expansion while others issue bonds Why some firms choose to engage in stock splits while others do not. It is fairly easy to see in all these cases that the appropriate form for the dependent variable would be a 0-1 dummy variable since there are only two possible outcomes. There are, of course, also situations where it would be more useful to allow the dependent variable to take on other values, but these . | ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Chapter 12 Limited Dependent Variable Models ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Some Examples of when Limited Dependent Variables may be used There are numerous examples of instances where this may arise, for example where we want to model: Why firms choose to list their shares on the NASDAQ rather than the NYSE Why some stocks pay dividends while others do not What factors affect whether countries default on their sovereign debt Why some firms choose to issue new stock to finance an expansion while others issue bonds Why some firms choose to engage in stock splits while others do not. It is fairly easy to see in all these cases that the appropriate form for the dependent variable would be a 0-1 dummy variable since there are only two possible outcomes. There are, of course, also situations where it would be more useful to allow the dependent variable to take on other values, but these will be considered later. ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 The Linear Probability Model We will first examine a simple and obvious, but unfortunately flawed, method for dealing with binary dependent variables, known as the linear probability model. it is based on an assumption that the probability of an event occurring, Pi, is linearly related to a set of explanatory variables The actual probabilities cannot be observed, so we would estimate a model where the outcomes, yi (the series of zeros and ones), would be the dependent variable. This is then a linear regression model and would be estimated by OLS. The set of explanatory variables could include either quantitative variables or dummies or both. The fitted values from this regression are the estimated probabilities for yi =1 for each observation i. ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 The Linear Probability Model The slope estimates for the linear probability model can
