Nonrandom Sampling and Tobit Models ECON 721. Different Types of Sampling Random sampling Censored sampling Truncated sampling Nonrandom –Exogenous stratified.

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