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Undersized Samples And Maximum Likelihood Estimation Of Sum-Constrained Linear Models

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  • de Boer, P. M. C.
  • Harkema, R.

Abstract

Maximum likelihood procedures for estimating sum-constrained models like demand systems, brand choice models and so on, break down or produce very unstable estimates when the number of categories is large as compared with the number of observations available. In empirical studies this difficulty is mostly resolved by postulating the contemporaneous covariance matrix of the -1 dependent variables at time t to equal a 2 (I n n 1 1). In this paper we n n develop a maximum likelihood procedure based on a contemporaneous covariance matrix which allows that the variances per category may be different, while the number of observations required is substantially less than the number that would be required in the case of a completely unrestricted contemporaneous covariance matrix.

Suggested Citation

  • de Boer, P. M. C. & Harkema, R., 1983. "Undersized Samples And Maximum Likelihood Estimation Of Sum-Constrained Linear Models," Econometric Institute Archives 272283, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272283
    DOI: 10.22004/ag.econ.272283
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    References listed on IDEAS

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    1. Laitinen, Kenneth, 1978. "Why is demand homogeneity so often rejected?," Economics Letters, Elsevier, vol. 1(3), pages 187-191.
    2. Oberhofer, W & Kmenta, J, 1974. "A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models," Econometrica, Econometric Society, vol. 42(3), pages 579-590, May.
    3. BARTEN, Anton P., 1969. "Maximum likelihood estimation of a complete system of demand equations," LIDAM Reprints CORE 34, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Barten, A. P., 1969. "Maximum likelihood estimation of a complete system of demand equations," European Economic Review, Elsevier, vol. 1(1), pages 7-73.
    5. Theil, Henri, 1971. "An Economic Theory of the Second Moments of Disturbances of Behavioral Equations," American Economic Review, American Economic Association, vol. 61(1), pages 190-194, March.
    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. Harkema, R., 1985. "Minimum Sample Size Requirements For Maximum Likelihood Estimation Of Some Demand Models," Econometric Institute Archives 272292, Erasmus University Rotterdam.
    2. van Heeswijk, B J & de Boer, P M C & Harkema, R, 1993. "A Dynamic Specification of an AIDS Import Allocation Model," Empirical Economics, Springer, vol. 18(1), pages 57-73.
    3. Keller, W.J. & Van Driel, J., 1985. "Differential consumer demand systems," European Economic Review, Elsevier, vol. 27(3), pages 375-390.

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