Exam 12: Limited Dependent Variables

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a)The model I would estimate is $Swi\widehat {tch ~J}obs _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Salary } _ { i } + \beta _ { 2 } \text { Experience } _ { i } + \beta _ { 3 } \text { Rent } _ { i } + \beta _ { 4 } \text { Children } _ { i }$
where the dependent variable is a binary dummy variable that takes on the value 1 if the individual switched jobs and 0 if the individual did not switch jobs.
b)Yes,I could estimate the above model by OLS.Doing so would be referred to as estimating a linear probability model.The potential shortcoming of such a model is that it predicts values for the dependent variable that are less than 0 and greater than 1 when it is impossible for such values to exist.The primary challenge of using OLS to estimate models with a binary dependent variable is that OLS constrains the marginal effects between the independent variables and the dependent variable to be constant when the true effect is likely non-linear.
c)Yes.An alternative estimator that would be preferred to a linear probability model would be one that would constrain all estimates to fall between 0 and 1,and a model that would allow a nonlinear relationship between then independent and dependent variable,which we know is actually the case for binary dependent variables.

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Coefficient estimates from the probit model indicate the general degree to which given independent variables are associated with the dependent variable.They do not represent true marginal effects.To generate true estimated marginal effects,you need to take the derivative of the probit function with respect to the independent variable and plug in the values of all independent variables to obtain the marginal effect at specific points in the distribution.This is typically done in an advanced statistical package.

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A categorical dependent variable is a dependent variable that only takes on specific integer values rather than continuous values.For instance,ratings of job performance from 0 to 4.
Categorical dependent variables present a challenge to OLS because OLS assumes the dependent variable ranges from negative infinity to positive infinity instead of taking on just a few integer values.