关键词：
Economics
摘要：
Many econometric models restrict the set of parameters consistent with the underlying model theory or observable data. These restrictions may come from a priori beliefs about the model–such as monotonicity of demand curves–or from statistical or economic theory–such as non-crossing quantile functions or first-price auction models which restrict the set of observable bids. When these restrictions are binding or close to binding, standard asymptotic theory provides poor approximations to the finite-sample behavior of the restricted estimator. This dissertation concerns the construction of estimators and inference procedures for shape-restricted models. The first chapter proposes a uniformly valid inference method for a parameter vector satisfying certain shape-restrictions. The method applies generally to a range of finite dimensional and nonparametric problems, such as regressions or instrumental variable estimation, to both kernel or series estimators, and to many shape restrictions. The bands are asymptotically equivalent to standard, unrestricted confidence bands if the true parameter strictly satisfies all shape restrictions, but they can be much smaller if some of the shape restrictions are binding or close to binding. We illustrate these sizable width gains in Monte Carlo simulations and in an empirical application. The second chapter proposes a general method for constructing asymptotically normally distributed estimators from shape-restricted estimators which applies in both parametric and nonparametric settings. Due to the asymptotically normality, our estimator avoids the non-standard distribution of shape-restricted estimators. Consequently, our resulting confidence sets are easy to obtain and simple to report. As our main application of interest, we provide low-level assumptions under which our method applies to the estimation of first-price auctions with independent, private valuations. In this context, our method provides the first inference result in t
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