Disclosure of information in matching markets with non-transferable utility

•We analyze matching with non-transferable utility and costly disclosure of information.•Increasing differences are important for equilibrium characteristics.•Equilibria are characterized in terms of cutoff revelation and positive assortative matching.•Multiple equilibria can exist due to the endogenous value of the outside option.•Comparative statics analysis shows non-trivial externalities.

We present a model of two-sided matching where utility is non-transferable and information about individualsʼ skills is private, utilities are strictly increasing in the partnerʼs skill and satisfy increasing differences. Skills can be either revealed or kept hidden, but while agents on one side have verifiable skills, agents on the other side have skills that are unverifiable unless certified, and certification is costly. Agents who have revealed their skill enter a standard matching market, while others are matched randomly. We find that in equilibrium only agents with skills above a cutoff reveal, and then they match assortatively. We show that an equilibrium always exists, and we discuss multiplicity. Increasing differences play an important role to shape equilibria, and we remark that this is unusual in matching models with non-transferable utility. We close the paper with some comparative statics exercises where we show the existence of non-trivial externalities and welfare implications.