Econometrics-Advanced

Question 1

What are two types of dichotomous choice models?

Answer 1

1. Probit –> Standard normal distribution functions (cdf, pdf)
2. Logit –> Logistic distribution functions (cdf, pdf)
   
   1. Uses random utility (doesn’t have error term)

Question 2

What are the problems associated with using a linear regression model where the dependent variable is discrete?

Answer 2

1. Can’t assume that residuals are normally distributed; since y is discrete, the errors will be discrete as well.
2. Heteroskedasticity: Non-constant variance for all individuals. Least squares estimation is no longer best linear unbiased.
3. Nothing to bound predicted range in the 0 - 1 interval.

Question 3

How does the logit differ from the probit model?

Answer 3

Differs only in the CDF that is used to define choice probabilities. CDF is not in integral form (like the probit) which makes the model easier to work with. The probit used the standard normal CDF while the logit uses the logistic CDF.

Question 4

What are the two types of muliple choice models?

Answer 4

1. Unordered multiple choice
2. Ordered multiple choice

Question 5

What are two types of unordered multiple choice models?

Answer 5

1. Multinomial logit
   
   1. Individual characteristics (w_i)
      
      1. w_i = characteristics of individual i; vary over individuals
2. Conditional logit
   
   1. Alternative-specific characteristics (z_ij)
      
      1. z_ij = attributes of choices j
      2. Vary over individuals and alternatives