Dependent Variable and Duration Models

The following 20 observations are drawn from a censored normal distribution  

The OLS estimator of u in the context of this tobit model is simply the sample mean. Compute the mean of all 20 observations. Would you expect this estimator to over- or underestimate p If we consider only the nonzero observations, the truncated regression model applies. The sample mean of the nonlimit observations is the least squares estimator in this context. Compute it, then comment on whether this should be an overestimate or an underestimate of the true mean. 

We now consider the tobit model that applies to the frill data set. 

The necessary conditions for maximizing this with respect to y and 0 are 

There are a few different ways one might solve these two equations. A grid search over the values of y and 0 is a possibility. A direct maximum likelihood estimator for the tobit model is the simpler choice if one is available. The model with only a constant term is otheiwise the same as the usual model. Using the data 

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