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Linear and nonlinear dirichlet share equations models

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  • Ronning, Gerd

Abstract

An adequate stochastic model for shares as dependent variables is provided by the Dirichlet distribution. The paper considers two different parametrizations 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.

Suggested Citation

  • Ronning, Gerd, 1989. "Linear and nonlinear dirichlet share equations models," Discussion Papers, Series II 80, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    • Handle: RePEc:zbw:kondp2:80
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    References listed on IDEAS

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    3. Lee, Lung-Fei & Pitt, Mark M, 1986. "Microeconometric Demand Systems with Binding Nonnegativity Constraints: The Dual Approach," Econometrica, Econometric Society, vol. 54(5), pages 1237-1242, September.
    4. Considine, Timothy J & Mount, Timothy D, 1984. "The Use of Linear Logit Models for Dynamic Input Demand Systems," The Review of Economics and Statistics, MIT Press, vol. 66(3), pages 434-443, August.
    5. Woodland, A. D., 1979. "Stochastic specification and the estimation of share equations," Journal of Econometrics, Elsevier, vol. 10(3), pages 361-383, August.
    6. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
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    Cited by:

    1. Ronning, Gerd, 1990. "Share equations in econometrics: A story of repression, frustation and dead ends," Discussion Papers, Series II 118, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".

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