The Jacobian of the exponential function - Jan R. Magnus; Henk G.J. Pijls; Enrique Sentana (Tinbergen Institute, 2020)
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: C65; C32; C63; 330; Matrix differential calculus; Orthogonal matrix; Continuous-time Markov chain; Ornstein-Uhlenbeck process