Week 9: Chapter 17 Flashcards
What is a Limited Dependent Variable (LDV)
A variable with a restricted range of values,
- Strictly non-negative variables: wages, prices, interest rates
- Binary variables: values restricted to zero and one
Whats a limitation of the LPM model?
Can produce negative predicted values and the partial effects are constant
Binary Response model:
P(y = 1|x) = G(b0 + b1x1 + b2x2 + … + bk xk ) = G(b0 + xb)
Logit Model
G(z)= e^z/1+ez =ʌ(z)
Probit model
G(z) = … = see notes
3 similarities between logit and probit models:
- Similar slope
- Both ensure 0 < P(y=1|x) < 1
- Both increasing
Which model is preferred by economists?
Probit model due to its normal distribution
Whats the formula for elasticity?
notes
What are the two potential outcomes of a maximum likelihood estimation?
P(y = 1|x) = G(b0 +xb)
P(y=0|x)=1- G(b0+xb)
What are 3 properties of MLE under general conditions?
- Consistent
- Asymptotically efficient and normal
What are three tests for MLE?
- The Lagrange multiplier
- The Wald Test
- The likelihood ratio test (LR)
LR test formula
LR = 2(Lur - Lr )
What happens to L when we drop variables in the LR?
Because MLE maximises L, dropping variables cannot increase it - it reduces or leaves unchanged L
Because Lur > Lr, WHAT does this imply for LR?
LR is non-negative and usually strictly positive
pseudo R2 measures such as McFadden’s R-squared: (formula)
1 Lur/Lo
- where Lo is the log-likelihood function in a model with only an intercept, and Lur is the full unrestricted model
