We present estimators for nonparametric functions that are nonadditive in unobservable random terms. The distributions of the unobservable random terms are assumed to be unknown. We show that when a nonadditive, nonparametric function is strictly monotone in an unobservable random term, and it satisfies some other properties that may be implied by economic theory, such as homogeneity of degree one or separability, the function and the distribution of the unobservable random term are identified. We also present convenient normalizations, to use when the properties of the function, other than strict monotonicity in the unobservable random term, are unknown. The estimators for the nonparametric function and for the distribution of the unobservable random term are shown to be consistent and asymptotically normal. We extend the results to functions that depend on a multivariate random term. The results of a limited simulation study are presented.

The block bootstrap is the best known bootstrap method for time-series data when the analyst does not have a parametric model that reduces the data generation process to simple random sampling. However, the errors made by the block bootstrap converge to zero only slightly faster than those made by first-order asymptotic approximations. This paper describes a bootstrap procedure for data that are generated by a Markov process or a process that can be approximated by a Markov process with sufficient accuracy. The procedure is based on estimating the Markov transition density nonparametrically. Bootstrap samples are obtained by sampling the process implied by the estimated transition density. Conditions are given under which the errors made by the Markov bootstrap converge to zero more rapidly than those made by the block bootstrap.

I characterize the implications of the common prior assumption for finite orders of beliefs about beliefs at a state and show that in finite models, the only such implications are those stemming from the weaker assumption of a common support. More precisely, given any finite N and any finite partitions model where priors have the same support, there is another finite partitions model with common priors that has the same nth order beliefs and knowledge for all n≤N.

In econometrics there are many occasions where knowledge of the structural relationship among dependent variables is required to answer questions of interest. This paper gives identification and estimation results for nonparametric conditional moment restrictions. We characterize identification of structural functions as completeness of certain conditional distributions, and give sufficient identification conditions for exponential families and discrete variables. We also give a consistent, nonparametric estimator of the structural function. The estimator is nonparametric two-stage least squares based on series approximation, which overcomes an ill-posed inverse problem by placing bounds on integrals of higher-order derivatives.

We present a general method for computing the set of supergame equilibria in infinitely repeated games with perfect monitoring and public randomization. We present a three-stage algorithm that constructs a convex set containing the set of equilibrium values, constructs another convex set contained in the set of equilibrium values, and produces strategies that support them. We explore the properties of this algorithm by applying it to familiar games.