Censored Regression, Sample Selection, Endogenous Switching, and Treatment-Effect Regression Models
نویسنده
چکیده
Truncated and censored regression models are useful when the dependent variable is observed in some ranges but not in others. A classical example is Tobin’s (1958) study of household expenditures, in which expenditures on durable goods were seen to generally increase with income, but a non-trivial number of households had no expenditures on durable goods. The problem, in this case, is how to model the response.1 It is clearly inappropriate for a classical linear model due to the presence of many observations with values of 0. However, a model can be constructed using a latent variable approach. Suppose that we consider a latent continuous variable Y ∗ that is normally distributed with mean μ and variance σ2. The standard Tobit model is given by Y ∗ = Xβ + ε Y = Y ∗ if Y ∗ > 0 = 0 if Y ∗ ≤ 0.
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