Kullback-Leibler-based characterizations of score-driven updates

Ramon Punder, Timo Dimitriadis and Rutger-Jan Lange
Additional contact information
Timo Dimitriadis: Heidelberg University and Heidelberg Institute for Theoretical Studies

No 24-051/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: Score-driven models have been applied in some 400 published articles over the last decade. Much of this literature cites the optimality result in Blasques et al. (2015), which, roughly, states that sufficiently small score-driven updates are unique in locally reducing the Kullback-Leibler divergence relative to the true density for every observation. This is at odds with other well-known optimality results; the Kalman filter, for example, is optimal in a mean-squared-error sense, but occasionally moves away from the true state. We show that score-driven updates are, similarly, not guaranteed to improve the localized Kullback-Leibler divergence at every observation. The seemingly stronger result in Blasques et al. (2015) is due to their use of an improper (localized) scoring rule. Even as a guaranteed improvement for every observation is unattainable, we prove that sufficiently small score-driven updates are unique in reducing the Kullback-Leibler divergence relative to the true density in expectation. This positive, albeit weaker, result justifies the continued use of score-driven models and places their information-theoretic properties on solid footing. In our numerical study, when there is less uncertainty: the second-best and third-best tolls achieve welfares closer to that of the first-best toll, and the three schemes become identical without uncertainty. As the degree of uncertainty falls, the uniform and single-step tolls attain higher welfare gains. Also, when demand becomes more price-sensitive, the uniform and single-step tolls attain relatively higher welfare gains. Our step toll would lower the generalised price without uncertainty but raises it in our stochastic setting.

Keywords: generalized autoregressive score (GAS); dynamic conditional score (DCS); Kullback Leibler; censoring; scoring rule; divergence (search for similar items in EconPapers)
JEL-codes: C10 C22 C58 (search for similar items in EconPapers)
Date: 2024-08-06, Revised 2024-10-22
New Economics Papers: this item is included in nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://papers.tinbergen.nl/24051.pdf (application/pdf)

Related works:
Working Paper: Kullback-Leibler-based characterizations of score-driven updates (2024)
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:tin:wpaper:20240051

Access Statistics for this paper

More papers in Tinbergen Institute Discussion Papers from Tinbergen Institute Contact information at EDIRC.
Bibliographic data for series maintained by Tinbergen Office +31 (0)10-4088900 ().