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

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Presentation transcript:

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