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Share equations in econometrics: A story of repression, frustation and dead ends

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  • Ronning, Gerd

Abstract

Share equations play an important role in applied economic research, notably in marketing and demand analysis. Both market shares and budget shares have been used as dependent variables in econometric models which were partly motivated by microeconomic theory. However attempts of econometricians (and other statisticians) to treat share equations adequately led mostly to unsatis-factory approaches: Some researchers although admitting that shares satisfy a sum constraint simply repressed the fact that shares cannot be norgially dls-tributed. Some researchers looked in vain for a stochastic specification which at the same time is consistent and allows a flexible covariance structure. Last not least almost nobody has properly taken care of additional problems arising from dynamic share models. The paper discusses these three issues and pro-poses a possible way out of this dilemma which was first suggested by Aitchison (1982) and has been applied to econometric demand analysis by Considine and Mount (1984). Demand-theoretic implications as well as methods of estimation are discussed. An example using German import data illustrates some of the results.

Suggested Citation

  • 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".
    • Handle: RePEc:zbw:kondp2:118
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    References listed on IDEAS

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    1. Anderson, G J & Blundell, R W, 1982. "Estimation and Hypothesis Testing in Dynamic Singular Equation Systems," Econometrica, Econometric Society, vol. 50(6), pages 1559-1571, November.
    2. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, October.
    3. 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".
    4. Blanciforti, Laura & Green, Richard, 1983. "An Almost Ideal Demand System Incorporating Habits: An Analysis of Expenditures on Food and Aggregate Commodity Groups," The Review of Economics and Statistics, MIT Press, vol. 65(3), pages 511-515, August.
    5. Berndt, Ernst R & Savin, N Eugene, 1975. "Estimation and Hypothesis Testing in Singular Equation Systems with Autoregressive Disturbances," Econometrica, Econometric Society, vol. 43(5-6), pages 937-957, Sept.-Nov.
    6. Klevmarken, N. Anders, 1979. "A comparative study of complete systems of demand functions," Journal of Econometrics, Elsevier, vol. 10(2), pages 165-191, June.
    7. Ed McKenzie, 1985. "An Autoregressive Process for Beta Random Variables," Management Science, INFORMS, vol. 31(8), pages 988-997, August.
    8. Chavas, Jean-Paul & Segerson, Kathleen, 1987. "Stochastic specification and estimation of share equation systems," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 337-358, July.
    9. 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.
    10. 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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    1. Lehmann, Harald, 2004. "Auswirkungen demografischer Veränderungen auf Niveau und Struktur des Privaten Verbrauchs – eine Prognose für Deutschland bis 2050 –," IWH Discussion Papers 195/2004, Halle Institute for Economic Research (IWH).

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