Tobit Models

Question 1

Type of outcome/DV

Answer 1

Both discrete and continous

Question 2

In which cases a Tobit Model?

Answer 2

1) Censored data -> e.g. points collected in a loyalty program with a max of 1000, although amount may be larger
2) Corner solutions -> Donated amount to charity, amount is either 0 or a positive number (continuous)

Question 3

Tobit Type 1, which data/cases are common?

Answer 3

Most common for censoring from below or at 0 or corner solutions.

Question 4

Formulas in a Type 1 model….

Answer 4

A probit for Y = 0 or Y > 0, and a linear regression for Y > 0 with the same IV’s in both parts.

Question 5

When do you use a Tobit Type 1 model?

Answer 5

1) DV subject to true censoring
2) More interested in the latent variable then the observed one
3) .. and thus are most interested in the marginal effects on the latent variable.

Question 6

When not to use a Tobit Type 1 model?

Answer 6

1) Assumption that the discrete and continuous part by a single variable is not realistic
2) When you have observations equal to zero, but hardly any observations close to zero.

Question 7

Hurdle model

Answer 7

Deals with the problems of a Tobit Type 1 model. Splits also the problem into two parts:
1) Probability of a value > 0
2) The outcome, given that Y > 0
Parts are estimated separately.
1) Logit/Probit & 2)Truncated log linear or normal.

Question 8

Tobit Type 2 model… similar as and different then…

Answer 8

Similar as Hurdle model in that it captures two parts of a proces. However different:

• Appropriate if the two parts describe a different decision (both captured in DV)
• But two decisions are not independent from each other
• Allows also for negative outcomes

Question 9

How do we know that in a type 2 Tobit model the 2 equations relate to each other?

Answer 9

We will know when the rho significant is, then the error terms of both equations are related.

Question 10

Heckit approach (or 2-step approach)

Answer 10

Alternative to the tobit type 2, consisting of 2 steps:

1) Estimate the paramaters of the selection part only (probit) and calculate the inverse mill’s ratio
2) Include the inverse mills ratio as an IV in the equation for the continuous part

Question 11

Inverse Mill’s Ratio

Answer 11

A transformation of the fitted values based on the estimates obtained in step 1. It is relating step 1 to step 2.

Question 12

2 step (heckit) approach or tobit type 2?

Answer 12

If the results differ, use the tobit type 2 model since that uses the maximum likelihood value.