SUMMARYThis paper is a study of the application of Bayesian exponentially tilted empirical likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys' method. For regression quantiles we derive the asymptotic form of the posterior density. We also examine Markov chain Monte Carlo simulations with a proposal density formed from an overdispersed version of the limiting normal density. We show that the algorithm works well even in models with an endogenous regressor when the instruments are not too weak.
Summary This paper contains an extension of the identification method proposed in Jun et al. (2011), hereafter JPX, which is based on a generated collection of sets, that is a ‘Dynkin system’. We demonstrate the usefulness of this extension in the context of the model proposed by Vytlacil and Yildiz (2007), hereafter VY. VY formulate a fully non‐parametric model featuring a nested weakly separable structure in which an endogenous regressor is binary‐valued. The extension of the JPX approach considered here allows for non‐binary‐valued discrete endogenous regressors and requires weaker support conditions than VY in the binary case, which substantially broadens the range of potential applications of the VY model. In this paper we focus on the binary case for which we provide several alternative simpler sufficient conditions and outline an estimation strategy.
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