The Jacobian of the Exponential Function

Jan R. Magnus (), Henk G. J. Pijls () and Enrique Sentana
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Jan R. Magnus: Vrije Universiteit Amsterdam and Tinbergen Institu, https://www.vu.nl/en/
Henk G. J. Pijls: University of Amsterdam

Working Papers from CEMFI

Abstract: We derive closed-form expressions for the Jacobian of the matrix exponential function for both diagonalizable and defective matrices. The results are applied to two cases of interest in macroeconometrics: a continuous-time macro model and the parametrization of rotation matrices governing impulse response functions in structural vector autoregressions.

Keywords: Matrix differential calculus; orthogonal matrix; continuous-time Markov chain; Ornstein-Uhlenbeck process. (search for similar items in EconPapers)
JEL-codes: C32 C63 C65 (search for similar items in EconPapers)
Date: 2020-06
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: The Jacobian of the exponential function (2021)
Working Paper: The Jacobian of the exponential function (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:cmf:wpaper:wp2020_2005

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