Before revision:  In addition, heterogeneity and margin constraints are shown to produce both pro- and counter-cyclical leverage cycles as seen in the data. Finally , more preference types causes a reduction in the severity of crisis and a lower relative deviation from complete markets in  all variables.
After revision:  In addition, heterogeneity and margin constraints are shown to produce both pro- and counter-cyclical leverage cycles . Beyond two types , more preference types causes a reduction in the severity of crisis and a lower relative deviation from complete markets in all variables.