Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2020-06-20
Number: 20-035/III
Author-Name: Jan R. Magnus
Author-Workplace-Name: Vrije Universiteit Amsterdam
Author-Name: Henk G.J. Pijls
Author-Workplace-Name: University of Amsterdam
Author-Name: Enrique Sentana
Author-Workplace-Name: CEMFI
Title: The Jacobian of the exponential function
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.
Classification-JEL: C65, C32, C63
Keywords: Matrix differential calculus, Orthogonal matrix, Continuous-time Markov chain, Ornstein-Uhlenbeck process
File-URL: https://papers.tinbergen.nl/20035.pdf
File-Format: application/pdf
File-Size: 288839 bytes
Handle: RePEc:tin:wpaper:20200035