Why is it customary to report price elasticity of demand in absolute value terms, while cross elasticities and income elasticities are reported with their sign attached?

Price elasticity of demand is always negative, since the law of demand says that an increase in price will reduce quantity demanded. It is simpler to use the absolute value, recognizing that the true sign is always negative. Cross elasticities and income elasticities can be positive or negative, with the signs giving information. A positive cross elasticity indicates that as the price of product Y increases, purchases of X increase, so the two goods are substitutes. Income elasticities are typically positive, as increased income leads to a greater quantity purchased, but the opposite does occasionally happen for inferior goods such as Spam.