I will discuss and compare a number of estimation strategies for censored data with endogenous regressors, for which common methods are insufficient. Censored data are common in nature, but when seeking to make causal claims about these phenomena, the standard econometric approaches often fall short. One common approach is to use Tobit IV, but this makes strict assumptions that the probability of censoring and behavior of uncensored observations are governed by the same parameters. Another approach is to separately estimate probability of censoring, which can lead to incorrect estimates.
In this paper we compare common methodology to three alternatives. The first is a Full-Information Maximum Likelihood approach. The second attempts to find posterior distributions for the parameters. The third is a semi-parametric causal method for Instrumental Variables.
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