Nonrandom Sampling and Tobit Models ECON 721. Different Types of Sampling Random sampling Censored...
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Transcript of Nonrandom Sampling and Tobit Models ECON 721. Different Types of Sampling Random sampling Censored...
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Nonrandom Sampling and Tobit Models
ECON 721
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Different Types of Sampling
• Random sampling• Censored sampling• Truncated sampling• Nonrandom
– Exogenous stratified– Endogenous stratified
• Choice-based
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Tobit Models
• Main reference: Amemiya, Chapter 10
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Type I Tobit Model• Tobin’s (1958) example – expenditure on a durable good only
observed if expenditure exceeds the minimum price available.
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Truncated Type I Tobit
• Only observe data for people who purchased the good (e.g. gather data at appliance store)
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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
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Heckman’s Two-Step Procedure
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• NLLS
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Tobit Type III Model
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likelihood
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Estimation by MLE
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Example: Gronau’s female labor supply model
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Heckman’s female labor supply model (explains choice of H as well)
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Type III Tobit Model (observe both wages and hours)
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Estimation
• MLE• Two-step method
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Type V Tobit Model
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