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

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 (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.

Trade liberalization and the allocation over domestic and foreign supplies: a case study for Spanish manufacturing

“…To that end we shall use a restricted speci® cation which has been introduced by de Boer and Harkema (1997). Letting diag fzg denote a diagonal matrix with the vector z on the main diagonal , the speci® cation reads as follows:…”

“…This property may successfully be used to devise an iterative procedure for the computation of the ML estimators. As regards the elements of the covariance matrix å n , de Boer and Harkema (1997) have shown that the ML estimatorsd i for the parameters d i …iˆ1;. .…”

“…Apart from one special case that occurs with probability zero, Equations 11 can be solved in a unique way by means of a one-dimensional search procedure that works very quickly. The algorithm is described in de Boer and Harkema (1997).…”