Extensions and Applications of Efficient Method of Moments

拟进行的研究将继续和扩展非线性计量经济学方法的长期研究计划。这种观点认为，计量经济学规范是对基本数据生成机制的近似。与此观点相一致，方法已经开发，顺序地改善近似信息变得可用，并允许可靠的推理模型演变的每个中间阶段。这些目标已经完成了一般性的水平，包括最非线性计量经济学推理程序。其基本思想是通过用截断级数展开替换结构模型，用截断展开替换误差密度，或两者兼而有之，赋予过程非参数特性。通过使截断点随样本大小自适应地增长，近似在每个中间阶段都足够精确，以允许可靠的推断，并确保最终收敛到底层数据生成机制。这个想法是要求结构模型所隐含的时刻与根据上述方法开发的模型的分数相匹配。该估计器具有某些优点。估计可以像采用最大似然法一样有效。与最大似然不同的是，如果状态向量被部分观测，计算负担不会增加，因为结构模型包含潜在变量或因为数据丢失。学生化分数用作诊断测试，并且由于分数对应于数据的可识别特征，因此未能通过诊断表明紧密参数化结构模型无法解释数据的哪些特征。这是一个宝贵的援助模型development.The具体的建议是建立上述声称的优势，从假设是更原始的比高层次的假设使用日期，以提高计算效率，并继续进行计划的实证工作，利用新的方法上面讨论。初步工作将侧重于结构宏观模型的估计，同时注意时间序列和面板数据的使用。简化形式的应用程序将集中在方法提取连续时间波动过程从离散采样的资产价格和有效地预测连续时间过程的泛函，如集成的远期波动。

The proposed research to be undertaken will continue and extend a long-standing program of research in nonlinear econometric methods. The view is that an econometric specification is an approximation to the underlying data generating mechanism. In keeping with this view, methodologies have been developed that sequentially improve the approximation as information becomes available, and permit reliable inference at each intermediate stage of model evolution. These objectives have been accomplished at a level of generality that encompasses most nonlinear econometric inference procedures. The basic idea is to endow a procedure with nonparametric properties by replacing the structural model with a truncated series expansion, the error density with a truncated expansion, or both. By letting the truncation point grow adaptively with sample size, the approximation is accurate enough at each intermediate stage to permit reliable inference and ultimate convergence to the underlying data generating mechanism is assured.Tightly parameterized structural modeling can be carried out within this paradigm. The idea is to require that moments implied by the structural model match the scores of a model developed according to the methodology described above. This estimator has certain advantages. Estimates can be made as efficient as if maximum likelihood had been employed. Unlike maximum likelihood, the computational burden does not increase if the state vector is partially observed either because the structural model contains latent variables or because data is missing. Studentized scores serve as diagnostic tests and, because the scores correspond to identifiable features of data, failure to pass a diagnostic indicates which features of data a tightly parameterized structural model cannot explain. This is an invaluable aid to model development.The specific proposal is to establish that the advantages claimed above follow from assumptions that are more primitive than the high level assumptions used to date, to improve computational efficiency, and to continue an ongoing program of empirical work that exploits the new methodologies discussed above. Initial work will focus on the estimation of structural macro models with attention to the simultaneous use of time series and panel data. Reduced form applications will focus on methods for extracting the continuous time volatility process from discretely sampled asset prices and efficiently predicting functionals of the continuous time process such as integrated forward volatility.