A new approach to maximum likelihood estimation of sum-constrained linear models in case of undersized samples

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 ( n ) is large as compared with the number of observations ( T ). In applied research, this problem is usually resolved by postulating the contemporaneous covariance matrix of the dependent variables to be known apart from a constant of proportionality. In this paper we develop a maximum likelihood procedure for sum-constrained models with large numbers of categories, which does not require too many observations, but nevertheless allows for n covariance parameters to be estimated freely.