The price variables are expressed relative to the price of coal as a restriction to ensure homogeneity in the system ie a rise in the price of oil has the same effect on shares as an equivalent fall in the prices of coal and gas, apart from the effect on the aggregate fuel consumption. The Equations (4) are estimated separately using ordinary least squares (OLS). Each equation is estimated using the same set of variables. This is required as the sum of the shares....,and so there is adding up across the share equations ie: