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The author develops a bilateral Nash bargaining model under value uncertainty and private/asymmetric information, combining ideas from axiomatic and strategic bargaining theory. The solution to the model leads organically to a two-tier stochastic frontier (2TSF) setup with intra-error dependence. The author presents two different statistical specifications to estimate the model, one that accounts for regressor endogeneity using copulas, the other able to identify separately the bargaining power from the private information effects at the individual level. An empirical application using a matched employer–employee data set (MEEDS) from Zambia and a second using another one from Ghana showcase the applied potential of the approach.