英文文献：Priors and Posterior Computation in Linear Endogenous Variable Models with Imperfect Instruments-工具不完善的线性内生变量模型的前验计算
英文文献作者：Joshua C.C. Chan,Justin L. Tobias
英文文献摘要：
Estimation in models with endogeneity concerns typically begins by searching for instruments. This search is inherently subjective and identification is generally achieved upon imposing the researcher's strong prior belief that such variables have no conditional impacts on the outcome. Results obtained from such analyses are necessarily conditioned upon the untestable opinions of the researcher, and such beliefs may not be widely shared. In this paper we, like several studies in the recent literature, employ a Bayesian approach to estimation and inference in models with endogeneity concerns by imposing weaker prior assumptions than complete excludability. When allowing for instrument imperfection of this type, the model is only partially identified, and as a consequence, standard estimates obtained from the Gibbs simulations can be unacceptably imprecise. We thus describe a substantially improved \semi-analytic" method for calculating parameter marginal posteriors of interest that only requires use of the well-mixing simulations associated with the identifiable model parameters and the form of the conditional prior. Our methods are also applied in an illustrative application involving the impact of Body Mass Index (BMI) on earnings.

在考虑内生性的模型中，估计通常从寻找工具开始。这种搜索本质上是主观的，识别通常是通过强加研究人员强烈的先验信念来实现的，即这些变量对结果没有条件影响。从这些分析中获得的结果必然是建立在研究者无法验证的观点之上的，而这些观点可能不会得到广泛的认同。在这篇论文中，我们像最近文献中的一些研究一样，通过强加较弱的先验假设而非完全排他性，在考虑内生性的模型中使用贝叶斯方法来估计和推断。当考虑到这种类型的仪器缺陷时，模型只能部分确定，因此，从吉布斯模拟中获得的标准估计值可能不精确得令人无法接受。因此，我们描述了一种实质上改进的\半解析的"方法，用于计算感兴趣的参数边缘后验，它只需要使用与可识别模型参数和条件先验形式相关联的良好混合模拟。我们的方法还被用于一个说明性应用，涉及身体质量指数(BMI)对收入的影响。