1. Nonrandom Sampling and Tobit Models ECON 721

2. Different Types of Sampling Random sampling Censored sampling Truncated sampling Nonrandom –Exogenous stratified –Endogenous stratified Choice-based

6. Tobit Models Main reference: Amemiya, Chapter 10

7. Type I Tobit Model Tobin’s (1958) example – expenditure on a durable good only observed if expenditure exceeds the minimum price available.

9. Truncated Type I Tobit Only observe data for people who purchased the good (e.g. gather data at appliance store)

10. Ways of Estimating Tobit Model MLE If censored, estimating probit and get coefficients up to scale By OLS using results for conditional means of truncated normal random variables

12. Heckman’s Two-Step Procedure

13. NLLS

14. Tobit Type III Model

16. likelihood

18. Estimation by MLE

20. Example: Gronau’s female labor supply model

23. Heckman’s female labor supply model (explains choice of H as well)

25. Type III Tobit Model (observe both wages and hours)

27. Estimation MLE Two-step method

28. Type V Tobit Model