Instrumental cardinal concerns for social status in two-sided matching with non-transferable utility

In this paper we apply the instrumental approach to social preferences in order to distinguish among various shapes of preferences for social status. In particular, we consider the shape of reduced preferences that emerge in the equilibrium of a two-sided matching model with non-transferable utility. Cole et al. (1992, 1995) show that, under full observability of potential mates' attributes, instrumental concerns for social status are ordinal, i.e., only one's own rank in the distribution of attributes matters. We show that when we depart from full observability, instrumental concerns for social status become cardinal, i.e., also other features of the distribution of attributes matter. We also show that the actual shape of cardinal concerns depends on how individuals can deal with the informational asymmetry, alternatively leading to upward concerns, i.e., making comparisons with higher rank people; downward concerns, i.e., making comparisons with lower rank people; or bidirectional concerns, i.e, being both upward and downward.