  Many forecasting applications have a limited distributed target variable,
which is zero for most observations and positive for the remaining
observations. In the econometrics literature, there is much research about
statistical model building for limited distributed target variables.
Especially, there are two component model approaches, where one model is build
for the probability of the target to be positive and one model for the actual
value of the target, given that it is positive. However, the econometric
literature focuses on effect estimation and does not provide theory for
predictive modeling. Nevertheless, some concepts like the two component model
approach and Heckmann's sample selection correction also appear in the
predictive modeling literature, without a sound theoretical foundation. In this
paper, we theoretically analyze predictive modeling for limited dependent
variables and derive best practices. By analyzing various real-world data sets,
we also use the derived theoretical results to explain which predictive
modeling approach works best on which application.
