5. Limited Dependent Variables Flashcards
What is a LDV?
A dependent variable is limited if the values it can take are restricted
What is the interpretation of Bj in the LPM?
Bj measures the change in probability of y taking the value 1 owing to a unit change in Xj
How should we interpret R^2?
We cant really
What can we use instead of R^2 in the LPM?
We can measure the % of within sample observations that our model gets correct
What are problems with LPM?
We can ontain predicted probabilities of less than zero or greater than 1.
The variance of thr error term depends on x so there is heteroscedasticity
How does heteroscedasticity effect the LPM?
The estimated coefficients are still unbiased and consistent but our inferences may be wrong owing to biases in estimated standard errors. These biases are rarely large and can be adjusted for in STATA
What is the equation for a logit or probit model?
P(y=1|x) = G(B0+B1X1+…+BkXk) =G(B0+Bx)
Logit model
The cumulative distribution function for a standard logistic random variable
Probit model
The standard normal distribution function
What assumptions do we make about e?
- e is independent of x
- E(e)=0
- e has either the standard logistic distribution or the standard normal distribution
- e is symmetrically distributed around 0
How do the marginal effects of a continuous variable in our three binary dependent variable models compare?
LPM- the marginal effect is constant Bj
Logit- the marginal effect depends on x
Probit- the marginal effect depends on x
What do we use instead of OLS for probit and logit?
Maximum likelihood estimation MLE
How does MLE work?
We find values of the Bj that maximises the likelihood of observed yi for our sample goven the xi for our sample
What qualities do logit and probit estimators have?
Usually consistent (unbaised when n is large) and asymptotically normal. They already account for heteroscedasticity
What do we use to test the joint significance of several xj in the probit and logit models?
We use a likelihood ratio which is twice the difference between the log likelihood of the unrestricted model and the restricted model
