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The Jacobian of the exponential function

Jan Magnus (), Henk G.J. Pijls and Enrique Sentana ()
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Henk G.J. Pijls: University of Amsterdam

No 20-035/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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: 2020-06-20
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Working Paper: The Jacobian of the Exponential Function (2020) Downloads
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