The typical size of estimated demand systems is largely a function of time : thus in early days most studies were of single equation systems e,g. Engel curve analysis while in recent times many demand systems have been estimated with up to fifteen commodities and there is the occasional study which involves more commodities than this. The larger the system to be estimated the greater the requirements of the data and of the computing facilities necessary. In one obvious sense the data must be richer the larger the system there must at least be available data on the individual quantities and prices. However, since the number of parameters to be estimated is frequently a function of only the number of commodities, then individual explanatory series (generally prices and incomes) must on average be less correlated in a large system than in a small system if the parameters are to be estimated with a similar degree of precision. Thus, if with, say 50 commodities, the first say five principal components explain as much of the variance in the independent variables as in a 5 commodity system then one would only expect to be able to determine a similar number of parameters in both systems with a given degree of precision. One question which arises then concerns the multi collinearity of aggregate and disaggregated price data.
Simmons, P. (1977). Specification and Estimation of Large Demand Systems (Working Papers Institut des sciences économiques 7705). https://hdl.handle.net/2078.5/278363