Efficient Resampling and Simulation Methods for Nonlinear Econometric Models

非线性计量经济模型的高效重采样和模拟方法

• 批准号: 1325805
• 负责人: Han Hong
• 金额: $ 17.67万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-15 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1325805&HistoricalAwards=false
• 关键词: Efficient; Resampling; Simulation; Methods; Nonlinear

Many procedures of statistical estimation and inference in economics and in other disciplines rely on intensive computation, which include the use of computer simulations and resampling methods that reuse a random set of the data that is being used for economic analysis. This proposal consists mainly of two projects that study the statistical properties of simulation and resampling based estimators, which are applicable to highly nonlinear and computationally intensive models. This is important because ignoring the statistical uncertainty introduced by simulation and resampling methods can lead to erroneous conclusion in the statistical and economic analysis. Generating the random numbers is easy but computing the moment condition or the likelihood function is typically difficult. Whether using overlapping simulations for all observations presents an improvement in computational efficiency depends on the specific model.The goal of the first project is to study the large sample distribution of a particular type of simulation based estimator procedures where the same set of simulation draws are used for all observations.Two important cases are considered. These include estimators that solve a system of simulated moments (MSM) and estimators that maximize a simulated likelihood (MSL). The theory being developed in this project applies to many simulation estimators used in empirical work which involve both overlapping simulation draws and non-differentiable moment functions. It is proven that both MSM and MSL are consistent when both the sample size and the number of simulations increase without bound. Under suitable regularity conditions, both MSM and MSL converge at the rate of the square root of the minimum of the number of observations and the number of simulation draws, to a limiting normal distribution.The conditions differ between MSM and MSL. For MSL, on the one hand, the condition that the number of simulations has to increase faster than the square root of the sample size is needed for asymptotic normality with independent random draws. On the other hand, with overlapping draws, asymptotic normality holds as long as both the number of simulations and the number of observations increase to infinity. It is also found that the total number of simulations has to increase without bound but can be much smaller than the total number of observations. In this case, the error in the parameter estimates is dominated by the simulation errors. This is a necessary cost of inference when the simulation model is very intensive to compute.The second project proposes a fast resample method that can be used to provide valid inference in nonlinear parametric and semiparametric models. This method does not require recomputation of the second stage estimator during each resample iteration but still provides valid inference under very weak assumptions for a large class of nonlinear models. These models can be highly nonlinear in the parameters that need to be estimated and can also be semiparametric through dependence on a first stage nonparametric functional estimation procedure. The fast resample method directly exploits the score function representations computed on each bootstrap sample, thereby reducing computational time considerably. The method presented here can also be extended to models in which the first stage computation is more intensive than the second stage, by making use of a linear representation for the first stage when resampling the second stage estimation procedure. The desirable performance and vast improvement in the numerical speed of the fast bootstrap method are demonstrated in the Monte Carlo experiments that have thus far been conducted.Developing sampling theorems with overlapping draws and nonsmooth functions in the first project provides an important complement to the existing results in the literature on the asymptotics of simulation estimators. The fast resampling method in the second project is used to approximate the limit distribution of parametric and semiparametric estimators, possibly simulation based, that admit an asymptotic linear representation. It can also be used for bias reduction and variance estimation, which are important components for the econometric inference of empirical models. The results obtained from the project can provide very useful guidance to empirical researchers who make extensive use of computational intensive nonlinear models for which obtaining the estimator and conducting inference on the parameter of interest can both be numerically challenging. Beyond applications in economics, nonlinear models are also widely used in statistics and various disciplines in social sciences and natural sciences, where researchers often resort to simulation and resampling based methods for estimation and inference. This analysis can provide guidance to empirical researchers making use of these models by shedding light on understanding and accounting for the statistical uncertainty introduced by the simulation and resampling procedures.

经济学和其他学科中的许多统计估计和推断程序都依赖于密集计算，其中包括使用计算机模拟和重复使用随机数据集进行经济分析的方法。该提案主要包括两个项目，研究基于模拟和恢复的估计，这是适用于高度非线性和计算密集型模型的统计特性。这一点很重要，因为忽略模拟和回归方法引入的统计不确定性可能导致统计和经济分析中的错误结论。生成随机数很容易，但计算矩条件或似然函数通常很困难。是否使用重叠模拟的所有观测提出了一个提高计算效率取决于特定的model.The第一个项目的目标是研究大样本分布的一种特定类型的模拟为基础的估计程序，其中相同的模拟绘制用于所有observation.Two重要的情况下被认为是。这些方法包括求解模拟矩系统（MSM）的估计器和最大化模拟似然（MSL）的估计器。在这个项目中开发的理论适用于许多模拟估计经验工作中使用的，其中涉及重叠模拟绘制和不可微的矩函数。证明了当样本容量和模拟次数无限制增加时，MSM和MSL是一致的。在适当的正则性条件下，MSM和MSL都以观测数和模拟图数的最小值的平方根的速率收敛于极限正态分布，但MSM和MSL的收敛条件不同。对于MSL，一方面，对于独立随机抽取的渐近正态性，需要模拟次数增加得比样本量的平方根快的条件。另一方面，在重叠绘制的情况下，只要模拟次数和观测次数都增加到无穷大，渐近正态性就成立。它还发现，模拟的总数增加没有限制，但可以远远小于观察的总数。在这种情况下，参数估计中的误差主要由模拟误差决定。这是一个必要的成本推理时，仿真模型是非常密集的computation.Second项目提出了一种快速重采样方法，可用于提供有效的推理在非线性参数和半参数模型。该方法不需要在每次重采样迭代期间重新计算第二阶段估计量，但对于大类非线性模型，在非常弱的假设下仍然提供有效的推断。这些模型在需要估计的参数中可以是高度非线性的，并且也可以通过依赖于第一阶段非参数函数估计过程而成为半参数的。快速重采样方法直接利用在每个自举样本上计算的分数函数表示，从而大大减少了计算时间。这里提出的方法也可以扩展到模型中的第一阶段的计算是更密集的比第二阶段，通过使用线性表示的第一阶段时，重新排序的第二阶段的估计过程。所需的性能和巨大的改善，在数值速度的快速引导方法证明在Monte Carlo实验中，迄今为止已经进行了，开发的抽样定理与重叠的绘制和非光滑函数在第一个项目提供了一个重要的补充，现有的结果在文献中的渐近模拟估计。在第二个项目中的快速restaurant方法是用来近似极限分布的参数和半参数估计，可能模拟为基础，承认一个渐近线性表示。它还可以用于偏差减少和方差估计，这是经验模型的计量经济学推断的重要组成部分。从该项目中获得的结果可以提供非常有用的指导经验研究人员，他们广泛使用计算密集型非线性模型，获得估计量和对感兴趣的参数进行推断都具有数值挑战性。除了在经济学中的应用外，非线性模型还广泛应用于统计学以及社会科学和自然科学的各个学科，研究人员经常采用基于模拟和回归的方法进行估计和推理。这一分析可以提供指导，实证研究人员利用这些模型的理解和会计模拟和重新验证程序引入的统计不确定性。