This study empirically quantifies the efficiency of a real-world bargaining game with two-sided incomplete information. Myerson and Satterthwaite (1983) and Williams (1987) derived the theoretical ex-ante efficient frontier for bilateral trade under two-sided uncertainty and demonstrated that it falls short of ex-post efficiency, but little is known about how well bargaining performs in practice. Using about 265,000 sequences of a game of alternating-offer bargaining following an ascending auction in the wholesale used-car industry, this study estimates (or bounds) distributions of buyer and seller values and evaluates where realized bargaining outcomes lie relative to efficient outcomes. Results demonstrate that the ex-ante and ex-post efficient outcomes are close to one another, but that the real bargaining falls short of both, suggesting that the bargaining is indeed inefficient but that this inefficiency is not solely due to the information constraints highlighted in Myerson and Satterthwaite (1983). Quantitatively, findings indicate that over one-half of failed negotiations are cases where gains from trade exist, leading an efficiency loss of 12–23% of the available gains from trade.

This study provides a structural analysis of detailed, alternating‐offer bargaining data from eBay, deriving bounds on buyers and sellers private value distributions and the gains from trade using a range of assumptions on behavior and the informational environment. These assumptions range from weak (assuming only that acceptance and rejection decisions are rational) to less weak (e.g., assuming that bargaining offers are weakly increasing in players' private values). We estimate the bounds and show what they imply for consumer negotiation behavior and inefficient breakdown. For the median product, bargaining ends in impasse in 37% of negotiations even when the buyer values the good more than the seller.

We present a methodology for estimating the distributional effects of an endogenous treatment that varies at the group level when there are group-level unobservables, a quantile extension of Hausman and Taylor, 1981. Because of the presence of group-level unobservables, standard quantile regression techniques are inconsistent in our setting even if the treatment is independent of unobservables. In contrast, our estimation technique is consistent as well as computationally simple, consisting of group-by-group quantile regression followed by two-stage least squares. Using the Bahadur representation of quantile estimators, we derive weak conditions on the growth of the number of observations per group that are sufficient for consistency and asymptotic zero-mean normality of our estimator. As in Hausman and Taylor, 1981, micro-level covariates can be used as internal instruments for the endogenous group-level treatment if they satisfy relevance and exogeneity conditions. Our approach applies to a broad range of settings including labor, public finance, industrial organization, urban economics, and development; we illustrate its usefulness with several such examples. Finally, an empirical application of our estimator finds that low-wage earners in the United States from 1990 to 2007 were significantly more affected by increased Chinese import competition than high-wage earners.

We present a new equilibrium search model where consumers initially search among discount opportunities, but are willing to pay more as a deadline approaches, eventually turning to full-price sellers. The model predicts equilibrium price dispersion and rationalizes discount and full-price sellers coexisting without relying on ex ante heterogeneity. We apply the model to online retail sales via auctions and posted prices, where failed attempts to purchase reveal consumers' reservation prices. We find robust evidence supporting the theory. We quantify dynamic search frictions arising from deadlines and show how, with deadline-constrained buyers, seemingly neutral platform fee increases can cause large market shifts.