On the (im-)possibility of representing probability distributions as a difference of i.i.d. noise terms

Christian Ewerhart and Marco Serena

No 428, ECON - Working Papers from Department of Economics - University of 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. Specifcally, 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 dfference of noise terms rather than on its components.

Keywords: Differences of random variables; density functions; characteristic function; uniform distribution (search for similar items in EconPapers)
JEL-codes: C46 C6 (search for similar items in EconPapers)
Date: 2023-02, Revised 2023-10
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.zora.uzh.ch/id/eprint/231569/7/econwp428.pdf (application/pdf)

Related works:
Working Paper: On the (Im-)Possibility of Representing Probability Distributions as a Difference of I.I.D. Noise Terms (2023)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zur:econwp:428

Access Statistics for this paper

More papers in ECON - Working Papers from Department of Economics - University of Zurich Contact information at EDIRC.
Bibliographic data for series maintained by Severin Oswald ().