A Parsimonious Autocorrelation Correction for Singular Demand Systems.

The adding up condition of budget share equations is known to imply restrictions for the autoregresive structure of errors. The implications of these restrictions when estimation is in terms of additive normal errors of additive logistic normal errors is clarified, and a byproduct is a specification of the autocorrelation matrix with a structure consistent with the model, but with number of parameters equal to the number of goods. This is more appealing than the scalar diagonal matrix form, but more parsimonious than having number of parameters proportional to the square of the number of goods.