Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/270435 
Year of Publication: 
2023
Series/Report no.: 
Working Paper No. 428
Publisher: 
University of Zurich, Department of Economics, Zurich
Abstract: 
A random variable is difference-form decomposable (DFD) if it may be written as the difference of two i.i.d. random terms. We show that densities of such variables exhibit a remarkable degree of structure. Specifically, a DFD density can be neither approximately uniform, nor quasiconvex, nor strictly concave. On the other hand, a DFD density need, in general, be neither unimodal nor logconcave. Regarding smoothness, we show that a compactly supported DFD density cannot be analytic and will often exhibit a kink even if its components are smooth. The analysis highlights the risks for model consistency resulting from the strategy widely adopted in the economics literature of imposing assumptions directly on a difference of noise terms rather than on its components.
Subjects: 
Differences of random variables
density functions
characteristic function
uniform distribution
JEL: 
C46
C6
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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