An algorithm for solving a constrained least squares problem for estimating the effects of an unknown monotonically intervening factor

Abstract

The conventional least squares method cannot estimate any hidden causal factor which is assumed to shift the regression hyperplane monotonically upwards (downwards). A constrained least squares problem has been formulated by S. Thore to model this phenomenon. A compact and efficient algorithm is developed and presented to solve this constrained problem. Computational results are presented which illustrate the effectiveness of this algorithm. The new method is then used to estimate the price elasticity of cigarettes and the monotonic shifts of the demand curve. A causal factor is found which may reflect the awareness among the general public of the harmful effects of smoking.