We report on an experiment in which buyers and sellers engage in semi-structured bargaining in two dimensions: how much of a good the seller will produce and how much money the buyer will offer the seller in exchange. Our aim is to evaluate the empirical relevance of two axiomatic bargaining solutions, the generalized Nash bargaining solution and Kalai's proportional bargaining solution. These bargaining solutions predict different outcomes when buyers are constrained in their money holdings. We first use the case when the buyer is not liquidity constrained to estimate the bargaining parameter, which we find is equal to 1/2. Further, we find strong evidence in support of the Kalai proportional solution and against the generalized Nash solution when buyers face liquidity constraints. Our findings have policy implications, e.g., for the welfare cost of inflation in search-theoretic models of money.
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