Föreläsning 3 - Inference in Logit and Probit models

Question 1

What is two main problems regarding inference using Probit and Logit? How can we fix it?

Answer 1

1. The variance is not defined
   Solution: Calculate ratios of the coefficients then the variance cancels out.
2. Marginal effect is dependent on the value of X
   Solution: Calculate marginal effect at the mean

Question 2

Show how to calculate marginal effect with LPM, Probit and logit

Answer 2

Se FL3 koncept.

Question 3

What is the average marginal effect and the marginal effect at the mean?

Answer 3

Marginal effect at the mean: Räkna marginaleffekten vid medelvärdet på X. Denna som Palme rekommenderar

Average marginal effect: Räkna marginaleffekten för varje individ sedan tar man medel värdet på den.

Question 4

Vilka är de tre alternativa sätten till marginaleffekter vid Probit och Logit?

Answer 4

1. Ta ratio mellan olika coeffecienter.
2. Approximate transformation… hur mycket probit är av logit osv.
3. Predictions. Fattar ej, fråga Palme.

Question 5

When are LPM, Logit and Probit equivalent?

Answer 5

When we have a model with only binary indipendent variables, Thus, this is the case with saturated models. Then it only is more complicated to use logit & probit. LPM is easiest in this case, considering the nice interpretation of coefficients etc.

Question 6

What is a saturated model?

Answer 6

This is a fully parameterized model. We have dummys for all possible values and interactions in the model. This is not possible in the case with continuous variables. See FL3 för ett exempel.

Question 7

Use the latent variable approach with dummy to show that LPM is as good as probit when looking at the case with one binary dependent- and independent variable.

Answer 7

See FL3 concepts

Question 8

What are the common goodness of fit measures of Logit & Probit?

Answer 8

1. Pseudo R^2
   LRI = 1 - LnL/LnL0
   där L0 är en modell med bara ett intercept.
2. En RSS version. av den Pseudo R^2
3. The table….
   Se Koncept FL3.

Question 9

What is the model with as few parameters as possible called?

Answer 9

Parsimonius model: Detta är en modell med så få parametar som möjligt men utan att ha OVB.

Question 10

What is the alternative definitions of saturated models given by Simonoff?

Answer 10

Casewise

Contingency table approach

Collapsing approach.

FÖRSTÅ OCH LÄGG IN DE HÄR RÄTTA DEFENITIONERNA:

Question 11

Given (Ci, Gi, Li, Ti, S) s.t Yi = Gi + Gi och T = ti + Li

Derive a expression for the marginal valuation of consumption of good Gi in terms of Ti.

Answer 11

Se koncept 3.