Qualitative and Limited Dependent Variable Models Chapter 18

Binary dependent variables • Many economic choices are either or; • Farmers either use a computer or they don’t; • People either buy organic food or they don’t; • What are the factors that influence such decisions?

The Linear Probability Model

Problems with the LPM • Heteroscedasticity • Implausible predicted values – a consequence of the linear relationship.

The Probit Model

Maximum Likelihood Estimation What is the probability of observing three observations: yi xi 1 15 1 20 0 5

Interpretation of the Probit Model Normal pdf

Example

Logit model PDF: CDF

Other Models • Multinomial – Influence of individual’s 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.

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.