Comparative Static and Computational Methods for an Empirical One-to-one Transferable Utility Matching Model

I show that the equilibrium distribution of matches associated with the empirical transferable utility one-to-one matching (TUM) model introduced by Choo and Siow (2006a , 2006b) corresponds to the fixed point of system of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" altimg="si1.gif"> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> <mml:mi>L</mml:mi> </mml:math>nonlinear equations; with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" altimg="si2.gif"> <mml:mi>K</mml:mi> </mml:math>and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" altimg="si3.gif"> <mml:mi>L</mml:mi> </mml:math>respectively equal to the number of discrete types of women and men. I use this representation to derive new comparative static results, showing how the match distribution varies with match surplus and the marginal distributions of agent types.