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I am trying to estimate the following censored model: $y_{it}=\beta X_{it} + \epsilon_{it}$.

I only observe $y_{it}$ if $y_{it}\leq z_{it}$, otherwise $y_{it}=z_{it}$. The trick is that $z_{it}$ itself is random, and comes from some distribution $f\left(\cdot\right)$.

I think standard Tobit models do not apply since the threshold is random. Does this correspond to any standard model/application/package in R? Any non-parametric ideas are also welcome. Thanks!

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  • $\begingroup$ I'm not aware of any R implementations, but the model you're looking for is Nelson (1977). $\endgroup$
    – Durden
    Commented Apr 16, 2023 at 19:31

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