xbeta
Censored regression model

In the censored regression model, we observe an outcome $y_{i}$ and covariates $x_{i}$ according to the model

(1)

\begin{aligned} y_{i}^{*} & = x_{i}^{⊤} β + ε_{i}, \\ y_{i} & = {\begin{array}{ll} y_{i}^{*}, & if y_{i}^{*} > 0 \\ 0, & if y_{i}^{*} \leq 0 \end{array}, \end{aligned}

where $ε_{i} \sim N (0, σ^{2})$ . $y_{i}^{*}$ is a latent variable which is only observed when it is above a certain threshold (normalized to zero here).

The expected value of $y_{i}$ and the likelihood function can be derived using the properties of the truncated normal distribution.

category: Econometrics

Created on March 22, 2007 22:26:39 by Jason Blevins (71.111.205.136)

xbeta Censored regression model

xbeta
Censored regression model