The Jacobian of the exponential function

Jan R. Magnus, Henk G.J. Pijls and Enrique Sentana

Journal of Economic Dynamics and Control, 2021, vol. 127, issue C

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 parameterization of rotation matrices governing impulse response functions in structural vector autoregressions.

Keywords: Matrix differential calculus; Orthogonal matrix; Impulse response analysis; 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: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Working Paper: The Jacobian of the Exponential Function (2020)
Working Paper: The Jacobian of the exponential function (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:127:y:2021:i:c:s0165188921000579

DOI: 10.1016/j.jedc.2021.104122

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