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.