Abstract
An adequate stochastic model for shares as dependent variables is provided by the Dirichlet distribution. The paper considers two different parameterizations which lead to linear and nonlinear Dirichlet share equations. Using an inequality for the trigamma function the global concavity of the likelihood function for the nonlinear case is shown. The same inequality is employed in proving positive definiteness of the information matrix for the linear case. Suitability of the Dirichlet specification in econometric demand systems (such as AIDS and Translog) is discussed.
Research has been financially supported by DFG
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Ronning, G. (2002). Linear and Nonlinear Dirichlet Share Equations Models. In: Klein, I., Mittnik, S. (eds) Contributions to Modern Econometrics. Dynamic Modeling and Econometrics in Economics and Finance, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3602-1_13
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DOI: https://doi.org/10.1007/978-1-4757-3602-1_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5331-5
Online ISBN: 978-1-4757-3602-1
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