Nonrandom Sampling and Tobit Models

ECON 721

Different Types of Sampling

• Random sampling• Censored sampling• Truncated sampling• Nonrandom

– Exogenous stratified– Endogenous stratified

• Choice-based

Tobit Models

• Main reference: Amemiya, Chapter 10

Type I Tobit Model• Tobin’s (1958) example – expenditure on a durable good only

observed if expenditure exceeds the minimum price available.

Truncated Type I Tobit

• Only observe data for people who purchased the good (e.g. gather data at appliance store)

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

Heckman’s Two-Step Procedure

• NLLS

Tobit Type III Model

likelihood

Estimation by MLE

Example: Gronau’s female labor supply model

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

Type III Tobit Model (observe both wages and hours)

Estimation

• MLE• Two-step method

Type V Tobit Model