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The Jacobian of the exponential function

Author

Listed:
  • Jan R. Magnus

    (Vrije Universiteit Amsterdam)

  • Henk G.J. Pijls

    (University of Amsterdam)

  • Enrique Sentana

    (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.

Suggested Citation

  • Jan R. Magnus & Henk G.J. Pijls & Enrique Sentana, 2020. "The Jacobian of the exponential function," Tinbergen Institute Discussion Papers 20-035/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20200035
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    References listed on IDEAS

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    Cited by:

    1. Lee, Adam & Mesters, Geert, 2024. "Locally robust inference for non-Gaussian linear simultaneous equations models," Journal of Econometrics, Elsevier, vol. 240(1).
    2. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "Moment tests of independent components," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(1), pages 429-474, May.
    3. Fiorentini, Gabriele & Sentana, Enrique, 2023. "Discrete mixtures of normals pseudo maximum likelihood estimators of structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 235(2), pages 643-665.

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    More about this item

    Keywords

    Matrix differential calculus; Orthogonal matrix; Continuous-time Markov chain; Ornstein-Uhlenbeck process;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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