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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,
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: C65 C32 C63 (search for similar items in EconPapers)
Date: 2020-06
New Economics Papers: this item is included in nep-ecm and nep-ore
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Working Paper: The Jacobian of the exponential function (2020) Downloads
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