Qualitative and Limited Dependent Variable Models

1
Qualitative and Limited Dependent Variable Models

• Chapter 18

2
Binary dependent variables

• Many economic choices are either or
• Farmers either use a computer or they dont
• People either buy organic food or they dont
• What are the factors that influence such
  decisions?

3
The Linear Probability Model
4
Problems with the LPM

• Heteroscedasticity
• Implausible predicted values
• a consequence of the linear relationship.

5
The Probit Model
6
Maximum Likelihood Estimation
What is the probability of observing three
observations
yi xi
1 15
1 20
0 5
7
Interpretation of the Probit Model
Normal pdf
8
Example
9
Logit model
PDF
CDF
10
Other Models

• Multinomial
• Influence of individuals attribute on choice of
  shop.
• Influence of product attributes on choice of
  product (choice experiments, conjoint analysis)
• Multinomial logit, conditional logit, multinomial
  probit.
• Ordered choice
• Strongly disagree, disagree neutral etc.
• Ordered probit/logit.
• Count data
• Number of trips to the supermarket.
• Poisson regression.

11
Limited Dependent Variables

• Tobit
• Deals with the problem of censoring at zero.
• Subsistence farmers sales on the market.
• OLS is biassed
• Sample selection
• Average earnings of women.
• Heckman procedure
• equation 1 probit to explain participation.
• equation 2 least squares wage equation including
  the inverse mills ratio.