A seller and a buyer bargain over the terms of trade for an object. The seller receives a perfect signal that determines the value of the object to both players, whereas the buyer remains uninformed. We analyze the infinite-horizon bargaining game in which the buyer makes all the offers. When the static incentive constraints permit first-best efficiency, then under some regularity conditions the outcome of the sequential bargaining game becomes arbitrarily efficient as bargaining frictions vanish. When the static incentive constraints preclude first-best efficiency, the limiting bargaining outcome is not second-best efficient and may even perform worse than the outcome from the one-period bargaining game. With frequent buyer offers, the outcome is then characterized by recurring bursts of high probability of agreement, followed by long periods of delay in which the probability of agreement is negligible.

We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct the posterior distribution of the resulting ATE. Both adjustments make use of pilot estimators motivated by the semiparametric influence function for ATE estimation. We prove asymptotic equivalence of our Bayesian procedure and efficient frequentist ATE estimators by establishing a new semiparametric Bernstein–von Mises theorem under double robustness; that is, the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, our method provides precise point estimates of the ATE through the posterior mean and delivers credible intervals that closely align with the nominal coverage probability. Furthermore, our approach achieves a shorter interval length in comparison to existing methods. We illustrate our method in an application to the National Supported Work Demonstration following LaLonde (1986) and Dehejia and Wahba (1999).

We study the behavior of the U.S. labor share over the past 90 years. We find that the observed decline of the labor share is entirely explained by the capitalization of intellectual property products in the national income and product accounts.

One dominant approach to evaluate the causal effect of a treatment is through panel data analysis, whereby the behaviors of multiple units are observed over time. The information across time and units motivates two general approaches: (i) horizontal regression (i.e., unconfoundedness), which exploits time series patterns, and (ii) vertical regression (e.g., synthetic controls), which exploits cross‐sectional patterns. Conventional wisdom often considers the two approaches to be different. We establish this position to be partly false for estimation but generally true for inference. In the absence of any assumptions, we show that both approaches yield algebraically equivalent point estimates for several standard estimators. However, the source of randomness assumed by each approach leads to a distinct estimand and quantification of uncertainty even for the same point estimate. This emphasizes that researchers should carefully consider where the randomness stems from in their data, as it has direct implications for the accuracy of inference.

We present a new method for solving asset pricing models, which yields an analytic price-dividend function of one state variable. To illustrate our method we give a detailed analysis of Abel's asset pricing model. A function is analytic in an open interval if it can be represented as a convergent power series near every point of that interval. In addition to allowing us to solve for the exact equilibrium price-dividend function, the analyticity property also lets us assess the accuracy of any numerical solution procedure used in the asset pricing literature. Copyright The Econometric Society 2005.