The matrix approach to evaluating demand equations

Abstract

As there is a plethora of demand models, which one should be used to estimate income and price elasticities? The paper sheds light on this important practical problem by developing a matrix approach to simulating (MAS) demand equations to analyse their performance under idealized circumstances. Artificial data on the dependent variable are generated by one model, and these are then used for the estimation of another model. As an illustrative application, using four popular models, a 4 × 4 matrix is generated which gives all pair-wise comparisons. The performance of the models is then evaluated on the basis of the quality of the income and own-price elasticity estimates.

Simulating Demand Systems

“…If i and j denote the true and estimated models and if k is the number of models, then the pairs of indices i, j = l, ... ,k identify the k 2 cells of a comparison matrix. Clements et al (1998) call this procedure the "matrix approach" to simulating (MAS) demand equations. In this section we illustrate MAS with the estimated coefficients (by contrast, Clements et al apply the methodology to the estimated elasticities).…”

“…) This chapter extends this work by applying a procedure to simulate demand systems in which the "true" model generating the data is unknown. The approach was introduced by Clements et al (1998), who refer to it as the "matrix approach to simulation", or MAS, as it involves all pairwise comparisons between a number of true and estimated models which are summarised in the form of a matrix. There is some earlier research related to MAS which includes Kiefer and MacKinnon (1976) and Chen (1995); see Clements et al (1998) for details.…”

Similarities in the Consumption Patterns of the Five Asian Tigers

“…In a recent paper, Barten (1993), using measures of information inaccuracy (Theil, 1967;Parkes, 1969) and nested and non-nested tests (Deaton, 1978), compared a number of differential demand systems. For a closely related recent work on this topic, see Clements et al (2001). All necessary computations for this paper were performed using the Demand Analysis Package 2000 (Yang et al, 2000) and DEMMOD-3 (Barten et al, 1989).…”

Regional Agricultural Production Systems: Estimates for Western Australia

“…A more sophisticated method such as the matrix approach to simulation(Clements et al, 1998) can be used to choose an optimal value for k.16 We have carried out the monotonicity test for our 5-column model. For the monotonicity condition to hold, as mentioned earlier, the estimated quantities of output supply and input demand must be positive at all data points.…”