Using Adaptive Sparse Grids to Solve High‐Dimensional Dynamic Models

We present a flexible and scalable method for computing global solutions of high‐dimensional stochastic dynamic models. Within a time iteration or value function iteration setup, we interpolate functions using an adaptive sparse grid algorithm. With increasing dimensions, sparse grids grow much more slowly than standard tensor product grids. Moreover, adaptivity adds a second layer of sparsity, as grid points are added only where they are most needed, for instance, in regions with steep gradients or at nondifferentiabilities. To further speed up the solution process, our implementation is fully hybrid parallel, combining distributed and shared memory parallelization paradigms, and thus permits an efficient use of high‐performance computing architectures. To demonstrate the broad applicability of our method, we solve two very different types of dynamic models: first, high‐dimensional international real business cycle models with capital adjustment costs and irreversible investment; second, multiproduct menu‐cost models with temporary sales and economies of scope in price setting.     

Bayesian Estimation of Dynamic Discrete Choice Models

We propose a new methodology for structural estimation of infinite horizon dynamic discrete choice models. We combine the dynamic programming (DP) solution algorithm with the Bayesian Markov chain Monte Carlo algorithm into a single algorithm that solves the DP problem and estimates the parameters simultaneously. As a result, the computational burden of estimating a dynamic model becomes comparable to that of a static model. Another feature of our algorithm is that even though the number of grid points on the state variable is small per solution‐estimation iteration, the number of effective grid points increases with the number of estimation iterations. This is how we help ease the “curse of dimensionality.” We simulate and estimate several versions of a simple model of entry and exit to illustrate our methodology. We also prove that under standard conditions, the parameters converge in probability to the true posterior distribution, regardless of the starting values.     

Constrained Optimization Approaches to Estimation of Structural Models

Estimating structural models is often viewed as computationally difficult, an impression partly due to a focus on the nested fixed‐point (NFXP) approach. We propose a new constrained optimization approach for structural estimation. We show that our approach and the NFXP algorithm solve the same estimation problem, and yield the same estimates. Computationally, our approach can have speed advantages because we do not repeatedly solve the structural equation at each guess of structural parameters. Monte Carlo experiments on the canonical Zurcher bus‐repair model demonstrate that the constrained optimization approach can be significantly faster.     

Sequential Estimation of Structural Models With a Fixed Point Constraint

This paper considers the estimation problem of structural models for which empirical restrictions are characterized by a fixed point constraint, such as structural dynamic discrete choice models or models of dynamic games. We analyze a local condition under which the nested pseudo likelihood (NPL) algorithm converges to a consistent estimator, and derive its convergence rate. We find that the NPL algorithm may not necessarily converge to a consistent estimator when the fixed point mapping does not have a local contraction property. To address the issue of divergence, we propose alternative sequential estimation procedures that can converge to a consistent estimator even when the NPL algorithm does not.     

Local Identification of Nonparametric and Semiparametric Models

In parametric, nonlinear structural models, a classical sufficient condition for local identification, like Fisher (1966) and Rothenberg (1971), is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We derive an analogous result for the nonparametric, nonlinear structural models, establishing conditions under which an infinite dimensional analog of the full rank condition is sufficient for local identification. Importantly, we show that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. We give restrictions on a neighborhood of the true value that are sufficient for local identification. We apply these results to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models and semiparametric consumption‐based asset pricing models.     

Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models

This paper proposes a new nested algorithm (NPL) for the estimation of a class of discrete Markov decision models and studies its statistical and computational properties. Our method is based on a representation of the solution of the dynamic programming problem in the space of conditional choice probabilities. When the NPL algorithm is initialized with consistent nonparametric estimates of conditional choice probabilities, successive iterations return a sequence of estimators of the structural parameters which we call K–stage policy iteration estimators. We show that the sequence includes as extreme cases a Hotz–Miller estimator (for K=1) and Rust's nested fixed point estimator (in the limit when K→∞). Furthermore, the asymptotic distribution of all the estimators in the sequence is the same and equal to that of the maximum likelihood estimator. We illustrate the performance of our method with several examples based on Rust's bus replacement model. Monte Carlo experiments reveal a trade–off between finite sample precision and computational cost in the sequence of policy iteration estimators.     

Identifying Latent Structures in Panel Data

This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized techniques. We consider both linear and nonlinear models where the regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown. Two approaches are considered—penalized profile likelihood (PPL) estimation for the general nonlinear models without endogenous regressors, and penalized GMM (PGMM) estimation for linear models with endogeneity. In both cases, we develop a new variant of Lasso called classifier‐Lasso (C‐Lasso) that serves to shrink individual coefficients to the unknown group‐specific coefficients. C‐Lasso achieves simultaneous classification and consistent estimation in a single step and the classification exhibits the desirable property of uniform consistency. For PPL estimation, C‐Lasso also achieves the oracle property so that group‐specific parameter estimators are asymptotically equivalent to infeasible estimators that use individual group identity information. For PGMM estimation, the oracle property of C‐Lasso is preserved in some special cases. Simulations demonstrate good finite‐sample performance of the approach in both classification and estimation. Empirical applications to both linear and nonlinear models are presented.     

基于前向神经网络的非线性时变系统辨识

提出基于前向神经网络的非线性时变系统辨识方法 ,并用局部化推广卡尔曼滤波算法训练网络 .该算法与全局推广卡尔曼滤波算法相比 ,不需要矩阵求逆运算 ,具有更高的收敛速度和更小存储容量要求 .仿真结果表明本文提出的方法在对非线性时变系统辨识方面取得较好效果     

Positioning Inventory in Clinical Trial Supply Chains

As a result of slow patient recruitment and high patient costs in the United States, clinical trials are increasingly going global. While recruitment efforts benefit from a larger global footprint, the supply chain has to work harder at getting the right drug supply to the right place at the right time. Certain clinical trial supply chains, especially those supplying biologics, have a combination of unique attributes that have yet to be addressed by existing supply chain models. These attributes include a fixed patient horizon, an inflexible supply process, a unique set of service‐level requirements, and an inability to transfer drug supplies among testing sites. We provide a new class of multi‐echelon inventory models to address these unique aspects. The resulting mathematical program is a nonlinear integer programming problem with chance constraints. Despite this complexity, we develop a solution method that transforms the original formulation into a linear integer equivalent. By analyzing special cases and through numerical study of both real‐life and simulated examples, we demonstrate the effectiveness of the solution and develop insights into inventory positioning and the cost drivers in clinical trial supply chains.     

Estimating and Testing Structural Changes in Multivariate Regressions

This paper considers issues related to estimation, inference, and computation with multiple structural changes that occur at unknown dates in a system of equations. Changes can occur in the regression coefficients and/or the covariance matrix of the errors. We also allow arbitrary restrictions on these parameters, which permits the analysis of partial structural change models, common breaks that occur in all equations, breaks that occur in a subset of equations, and so forth. The method of estimation is quasi‐maximum likelihood based on Normal errors. The limiting distributions are obtained under more general assumptions than previous studies. For testing, we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes. Structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present. For computation, an algorithm for an efficient procedure is proposed to construct the estimates and test statistics. We also introduce a novel locally ordered breaks model, which allows the breaks in different equations to be related yet not occurring at the same dates.     

Inter-city bus scheduling under variable market share and uncertain market demands

Bus scheduling is essential to a carrier's profitability, its level of service and its competitiveness in the market. In past research most inter-city bus scheduling models have used only the projected (or average) market share and market demand, meaning that the variations in daily passenger demand that occur in actual operations are neglected. In this research, however, we do not utilize a fixed market share and market demand. Instead, passenger choice behaviors and uncertain market demands are considered. Stochastic and robust optimizations and a passenger choice model are used to develop the models. These models are formulated as a nonlinear integer program that is characterized as NP-hard. We also develop a solution algorithm to efficiently solve the models. They are tested using data from a major Taiwan inter-city bus operation. The results show the good performance of the models and the solution algorithm.     

时变参数模型的最优滚动窗宽选择标准及应用

宏观经济领域中存在严重的结构突变性,模型估计量的优劣对估计样本规模是敏感的。本文针对时变参数模型,建立了滚动窗宽选择标准,通过最小化估计量的近似二次损失函数及最大化各子样本估计量间的曼哈顿距离选择窗宽大小,权衡了模型估计量的准确性和时变性两个相悖目标。蒙特卡罗模拟实验表明,本文所提出的方法在各种结构突变情形下均适用,能够应用于线性关系和非线性关系的时变参数模型中,且均具有稳健性。将该方法应用于我国金融网络的结构突变识别过程,显著改善了传统窗宽选择方法的结果。     

金融市场高维波动率的扩展广义正交GARCH模型与参数估计方法研究

本文对Van der Weide(2002)的广义正交GARCH模型进行扩展,提出反映金融资产收益波动性特征,具有"杠杆效应"的广义正交GARCH模型。由于这种扩展的广义正交GARCH模型在高维数据中面临参数估计困难,本文从交互信息理论视角研究模型的参数估计问题,在理论上证明基于交互信息最小化的多元GARCH模型参数估计与基于极大似然函数参数估计的联系和区别,并在提出的扩展广义正交GARCH模型框架下,采用不同的统计技术实现基于交互信息最小化的参数估计方法,避免了传统极大似然函数估计需要事先正确指定标准化残差概率密度函数和高维运算困难,计算效率较高,使多元GARCH模型在高维数据中可以应用。最后,根据全球主要金融市场的15种股票指数数据,通过实证研究对建立的扩展广义正交GARCH模型及其参数估计方法有效性进行评价与检验。实证研究表明了本文提出的扩展广义正交GARCH模型与参数估计方法的优势。     

Estimation of Nonlinear Models with Measurement Error

This paper presents a solution to an important econometric problem, namely the root n consistent estimation of nonlinear models with measurement errors in the explanatory variables, when one repeated observation of each mismeasured regressor is available. While a root n consistent estimator has been derived for polynomial specifications (see Hausman, Ichimura, Newey, and Powell (1991)), such an estimator for general nonlinear specifications has so far not been available. Using the additional information provided by the repeated observation, the suggested estimator separates the measurement error from the “true” value of the regressors thanks to a useful property of the Fourier transform: The Fourier transform converts the integral equations that relate the distribution of the unobserved “true” variables to the observed variables measured with error into algebraic equations. The solution to these equations yields enough information to identify arbitrary moments of the “true,” unobserved variables. The value of these moments can then be used to construct any estimator that can be written in terms of moments, including traditional linear and nonlinear least squares estimators, or general extremum estimators. The proposed estimator is shown to admit a representation in terms of an influence function, thus establishing its root n consistency and asymptotic normality. Monte Carlo evidence and an application to Engel curve estimation illustrate the usefulness of this new approach.     

基于MDE资源分时段与活动平移并行的均衡优化

本文以资源均方差作为衡量工程网络计划资源均衡性的评价函数,基于非关键活动资源可以分段使用的状态,提出了对非关键活动机动时间及其各个时段的资源强度同时动态并行调整的优化策略,以弥补非关键活动平移幅度因受时差的限制而对均衡效果产生的影响,并以此构建了网络计划资源均衡优化模型;并针对网络计划均衡优化模型是一多峰值的非线性优化函数的特点,对基于种群的全局搜索策略的差分进化算法进行了改进和进行全局最优解的寻优,以优化各个非关键活动起止时间,求出各个非关键活动最优的安排;最后,通过实例分析,并与其它算法进行了对比分析,验证明了所提出的均衡优化方法的优越性和实用性.     

Nonparametric Instrumental Variable Estimation of Structural Quantile Effects

We study the asymptotic distribution of Tikhonov regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a minimum distance principle. We show that the minimum distance problem without regularization is locally ill‐posed, and we consider penalization by the norms of the parameter and its derivatives. We derive pointwise asymptotic normality and develop a consistent estimator of the asymptotic variance. We study the small sample properties via simulation results and provide an empirical illustration of estimation of nonlinear pricing curves for telecommunications services in the United States.     

Inference in Dynamic Discrete Choice Models With Serially orrelated Unobserved State Variables

This paper develops a method for inference in dynamic discrete choice models with serially correlated unobserved state variables. Estimation of these models involves computing high‐dimensional integrals that are present in the solution to the dynamic program and in the likelihood function. First, the paper proposes a Bayesian Markov chain Monte Carlo estimation procedure that can handle the problem of multidimensional integration in the likelihood function. Second, the paper presents an efficient algorithm for solving the dynamic program suitable for use in conjunction with the proposed estimation procedure.     

A Polynomial Optimization Approach to Principal–Agent Problems

This paper presents a new method for the analysis of moral hazard principal–agent problems. The new approach avoids the stringent assumptions on the distribution of outcomes made by the classical first‐order approach and instead only requires the agent's expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent's utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn transforms the principal's utility maximization problem into a nonlinear program. Under the additional assumptions that the principal's expected utility is a polynomial and the agent's expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows how to first approximate expected utility functions that are not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal–agent models with multidimensional action sets.     

An Expected Consequence Approach to Route Choice in the Maritime Transportation of Crude Oil

Maritime transportation is the major conduit of international trade, and the primary link for global crude oil movement. Given the volume of oil transported on international maritime links, it is not surprising that oil spills of both minor and major types result, although most of the risk‐related work has been confined to the local settings. We propose an expected consequence approach for assessing oil‐spill risk from intercontinental transportation of crude oil that not only adheres to the safety guidelines specified by the International Maritime Organization but also outlines a novel technique that makes use of coarse global data to estimate accident probabilities. The proposed estimation technique, together with four of the most popular cost‐of‐spill models from the literature, were applied to study and analyze a realistic size problem instance. Numerical analyses showed that: a shorter route may not necessarily be less risky; an understanding of the inherent oil‐spill risk of different routes could potentially facilitate tanker routing decisions; and the associated negotiations over insurance premium between the transport company and the not‐for‐profit prevention and indemnity clubs. Finally, we note that only the linear model should be used with one of the three nonlinear cost‐of‐spill models for evaluating tanker routes.