Ceilings and Floors

Abstract

There are situations where the data or the theory suggest or require, respectively, that one estimate the boundary lines that separate regions of observations from regions of no observations. Of particular interest are ceiling or floor lines. For example, many theories use terms such as veto player, constraint, only if, and so on, which suggest ceilings. Ceiling hypotheses have a nonstandard form claiming the probability of Y will be zero for all values of Y greater than the ceiling value of Yc for a given value of X. Conversely, ceiling hypotheses make no specific prediction about the value of Y for a given value of X except that it will be less than the ceiling value. Floors work by guaranteeing minimum levels. The article gives numerous examples of theories that imply ceiling or floor hypotheses and numerous examples of data that fit such hypotheses. The article proposes quantile regression as a means of estimating the boundaries of the no-data zone as well as criteria for evaluating the importance of the boundary variable. These techniques are illustrated for ceiling and floor hypotheses relating gross domestic product/capita and democracy.