Extensions and Applications of Efficient Method of Moments

拟进行的研究将继续并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底层数据生成机制的近似。为了与这种观点保持一致，随着信息的可用性，已经开发出了一些方法，这些方法依次改进了近似，并允许在模型演化的每个中间阶段进行可靠的推断。这些目标已经在包含大多数非线性计量经济学推理程序的一般水平上完成。其基本思想是通过将结构模型替换为截断的级数展开，或将误差密度替换为截断的展开，或两者兼而有之，从而赋予过程非参数性质。通过让截断点随样本量自适应增长，在每个中间阶段的近似足够精确，从而允许可靠的推断，并确保最终收敛到底层数据生成机制。紧参数化的结构建模可以在这个范例中进行。其思想是要求结构模型隐含的矩与根据上述方法开发的模型的分数相匹配。这个估计器有一定的优点。估计可以像使用最大似然法一样有效。与最大似然不同，如果状态向量被部分观察到，或者因为结构模型包含潜在变量，或者因为数据缺失，计算负担不会增加。学生化分数可以作为诊断测试，因为分数对应于数据的可识别特征，诊断失败表明严格参数化结构模型无法解释数据的哪些特征。这对模型开发是一个无价的帮助。具体的建议是确定上述优势来自于比迄今为止使用的高级假设更原始的假设，以提高计算效率，并继续正在进行的利用上述新方法的经验工作计划。最初的工作将集中在结构宏观模型的估计上，注意同时使用时间序列和面板数据。简化形式的应用将侧重于从离散采样的资产价格中提取连续时间波动过程的方法，以及有效预测连续时间过程的函数，如积分远期波动。

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.