Why should inventories rise when demand falls in housing and other markets?

"Inventories and price changes are correlated. The inverse relation is most obvious in housing where inventories build in low demand markets and shrink in high demand markets. This is a puzzle. If sellers and buyers had symmetric views of the world, one would think that sellers would lower their reservation value at the same rate that buyers lower their offer price. Because there is heterogeneity among buyers in the valuation of a given house and because houses are not homogeneous, sellers set prices strategically. When demand falls, it is optimal for sellers to lower their prices but not by enough to keep the probability of sale constant. As a result, inventories grow. This is consistent with the most basic theory of monopoly pricing and requires no irrationality on the part of sellers or buyers. Furthermore, a distinguishing feature of this theory is that it implies that the negative correlation between inventories and price changes should not be observed in perfectly competitive markets where goods are homogeneous, e.g., stock or commodity markets"--National Bureau of Economic Research web site.