Comparing solution methods for dynamic equilibrium economies

This paper compares solution methods for dynamic equilibrium economies. We compute and simulate the stochastic neoclassical growth model with leisure choice using first, second, and fifth order perturbations in levels and in logs, the finite elements method, Chebyshev polynomials, and value function iteration for several calibrations. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy, and we present some conclusions based on the reported evidence.     

Robust dynamic clustering

The dynamic clustering (DC) algorithm is a method for discovering clusters in a given population. Unfortunately the classical DC algorithms fail to perform well in the presence of outliers. A robust dynamic clustering (RDC) algorithm is introduced to overcome this problem. Robust estimates of the location vector and the covariance matrix are calculated in the affine invariant case. A simulation study is presented to demonstrate the basic difference between the DC and the RDC algorithms. Three kinds of optimization criteria are used in case of contaminated multivariate normal distributions.     

Joint Bayesian Analysis of Parameters and States in Nonlinear non‐Gaussian State Space Models

We propose a new methodology for designing flexible proposal densities for the joint posterior density of parameters and states in a nonlinear, non‐Gaussian state space model. We show that a highly efficient Bayesian procedure emerges when these proposal densities are used in an independent Metropolis–Hastings algorithm or in importance sampling. Our method provides a computationally more efficient alternative to several recently proposed algorithms. We present extensive simulation evidence for stochastic intensity and stochastic volatility models based on Ornstein–Uhlenbeck processes. For our empirical study, we analyse the performance of our methods for corporate default panel data and stock index returns. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical solution of dynamic equilibrium models under Poisson uncertainty

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.     

The structure of dynamic correlations in multivariate stochastic volatility models

This paper proposes two types of stochastic correlation structures for Multivariate Stochastic Volatility (MSV) models, namely the constant correlation (CC) MSV and dynamic correlation (DC) MSV models, from which the stochastic covariance structures can easily be obtained. Both structures can be used for purposes of determining optimal portfolio and risk management strategies through the use of correlation matrices, and for calculating Value-at-Risk (VaR) forecasts and optimal capital charges under the Basel Accord through the use of covariance matrices. A technique is developed to estimate the DC MSV model using the Markov Chain Monte Carlo (MCMC) procedure, and simulated data show that the estimation method works well. Various multivariate conditional volatility and MSV models are compared via simulation, including an evaluation of alternative VaR estimators. The DC MSV model is also estimated using three sets of empirical data, namely Nikkei 225 Index, Hang Seng Index and Straits Times Index returns, and significant dynamic correlations are found. The Dynamic Conditional Correlation (DCC) model is also estimated, and is found to be far less sensitive to the covariation in the shocks to the indexes. The correlation process for the DCC model also appears to have a unit root, and hence constant conditional correlations in the long run. In contrast, the estimates arising from the DC MSV model indicate that the dynamic correlation process is stationary.     

Econometric analysis of linearized singular dynamic stochastic general equilibrium models

In this paper I propose an alternative to calibration of linearized singular dynamic stochastic general equilibrium models. Given an a-theoretical econometric model as a representative of the data generating process, I will construct an information measure which compares the conditional distribution of the econometric model variables with the corresponding singular conditional distribution of the theoretical model variables. The singularity problem will be solved by using convolutions of both distributions with a non-singular distribution. This information measure will then be maximized to the deep parameters of the theoretical model, which links these parameters to the parameters of the econometric model and provides an alternative to calibration. This approach will be illustrated by an application to a linearized version of the stochastic growth model of King, Plosser and Rebelo.     

OSGi及其QoS获益驱动动态软件体系结构研究

随着软件领域中移动计算、分布计算和Web Service等技术的迅速发展,软件计算环境变得越来越开放、复杂、多元。如何应对不断变化的计算环境,构建一个自适应的动态软件架构,受到了越来越多的关注。文章首先介绍一个成功的软件系统结构框架实例——Open Service Gateway Initiative(OSGi)。然后,以请求质量QoS为核心,对面向服务的OSGi框架进行扩展,提出了一个动态自适应软件架构解决方案,它以用户QoS属性为目标驱动,通过动态调整软件自身结构,以进一步提高用户期望的服务质量。实验结果证明了该调度框架的有效性。     

Asymmetric outcome in a symmetric dynamic duopoly

In a dynamic duopoly, will an initial asymmetry between firms increase or decrease over time? We examine this issue within a stochastic dynamic alternate-move duopoly model that explicitly accounts for action and reaction between firms. We consider two firms that are symmetric with regard to all primitives such as demand, cost and production functions, and which are subject to the same stochastic environment. The only asymmetry is with regard to their initial capital stocks which in turn asymmetrically influences their current and future profit and investment possibilities. We offer a characterization of the stochastic steady state and its supporting ergodic set for each firm. We are then able to identify the precise restrictions on the initial conditions under which the two firms either converge or diverge in the long run.     

The method of endogenous gridpoints in theory and practice

The method of endogenous gridpoints (ENDG) significantly speeds up the solution to dynamic stochastic optimization problems with continuous state and control variables by avoiding repeated computations of expected outcomes while searching for optimal policy functions. I provide an interpolation technique for non-rectilinear grids that allow ENDG to be used in n-dimensional problems in an intuitive and computationally efficient way: the acceleration of ENDG with non-linear grid interpolation is nearly constant in the density of the grid. Further, ENDG has only been shown by example and has never been formally characterized. Using a theoretical framework for dynamic stochastic optimization problems, I formalize the method of endogenous gridpoints and present conditions for the class of models for which it can be used.     

Bayesian analysis of a dynamic stochastic model of labor supply and saving

This paper empirically implements a dynamic, stochastic model of life-cycle labor supply and human capital investment. The model allows agents to be forward looking. But, in contrast to prior literature in this area, it does not require that expectations be formed “rationally”. By avoiding strong assumptions about expectations, I avoid sources of bias stemming from misspecification of the expectation process. A Bayesian econometric method based on Geweke and Keane (in: R.S. Mariano, T. Schuermann, M. Weeks (Eds.), Simulation Based Inference and Econometrics: Methods and Applications, Cambridge University Press, Cambridge, 1999) is used to relax assumptions over expectations. The results of this study are consistent with findings from previous research in the labor supply literature that makes the rational expectations assumption.     

Estimation of a dynamic stochastic frontier model using likelihood-based approaches

This paper considers a panel stochastic production frontier model that allows the dynamic adjustment of technical inefficiency. In particular, we assume that inefficiency follows an AR(1) process. That is, the current year's inefficiency for a firm depends on its past inefficiency plus a transient inefficiency incurred in the current year. Interfirm variations in the transient inefficiency are explained by some firm-specific covariates. We consider four likelihood-based approaches to estimate the model: the full maximum likelihood, pairwise composite likelihood, marginal composite likelihood, and quasi-maximum likelihood approaches. Moreover, we provide Monte Carlo simulation results to examine and compare the finite-sample performances of the four above-mentioned likelihood-based estimators of the parameters. Finally, we provide an empirical application of a panel of 73 Finnish electricity distribution companies observed during 2008–2014 to illustrate the working of our proposed models.     

SEQUENTIAL MONTE CARLO SAMPLING FOR DSGE MODELS

We develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models; wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using two empirical illustrations consisting of the Smets and Wouters model and a larger news shock model we show that the SMC algorithm is better suited for multimodal and irregular posterior distributions than the widely used random walk Metropolis–Hastings algorithm. We find that a more diffuse prior for the Smets and Wouters model improves its marginal data density and that a slight modification of the prior for the news shock model leads to drastic changes in the posterior inference about the importance of news shocks for fluctuations in hours worked. Unlike standard Markov chain Monte Carlo (MCMC) techniques; the SMC algorithm is well suited for parallel computing. Copyright © 2014 John Wiley & Sons, Ltd.     

Using dynamic programming with adaptive grid scheme for optimal control problems in economics

The study of the solutions of dynamic models with optimizing agents has often been limited by a lack of available analytical techniques to explicitly find the global solution paths. On the other hand, the application of numerical techniques such as dynamic programming to find the solution in interesting regions of the state was restricted by the use of fixed grid size techniques. Following Grüne (Numer. Math. 75 (3) (1997) 319; University of Bayreuth, submitted, 2003), in this paper an adaptive grid scheme is used for finding the global solutions of discrete time Hamilton–Jacobi–Bellman equations. Local error estimates are established and an adapting iteration for the discretization of the state space is developed. The advantage of the use of adaptive grid scheme is demonstrated by computing the solutions of one- and two-dimensional economic models which exhibit steep curvature, complicated dynamics due to multiple equilibria, thresholds (Skiba sets) separating domains of attraction and periodic solutions. We consider deterministic and stochastic model variants. The studied examples are from economic growth, investment theory, environmental and resource economics.     

A new vaccine supply chain network under COVID-19 conditions considering system dynamic: Artificial intelligence algorithms

With the discovery of the COVID-19 vaccine, what has always been worrying the decision-makers is related to the distribution management, the vaccination centers' location, and the inventory control of all types of vaccines. As the COVID-19 vaccine is highly demanded, planning for its fair distribution is a must. University is one of the most densely populated areas in a city, so it is critical to vaccinate university students so that the spread of this virus is curbed. As a result, in the present study, a new stochastic multi-objective, multi-period, and multi-commodity simulation-optimization model has been developed for the COVID-19 vaccine's production, distribution, location, allocation, and inventory control decisions. In this study, the proposed supply chain network includes four echelons of manufacturers, hospitals, vaccination centers, and volunteer vaccine students. Vaccine manufacturers send the vaccines to the vaccination centers and hospitals after production. The students with a history of special diseases such as heart disease, corticosteroids, blood clots, etc. are vaccinated in hospitals because of accessing more medical care, and the rest of the students are vaccinated in the vaccination centers. Then, a system dynamic structure of the prevalence of COVID -19 in universities is developed and the vaccine demand is estimated using simulation, in which the demand enters the mathematical model as a given stochastic parameter. Thus, the model pursues some goals, namely, to minimize supply chain costs, maximize student desirability for vaccination, and maximize justice in vaccine distribution. To solve the proposed model, Variable Neighborhood Search (VNS) and Whale Optimization Algorithm (WOA) algorithms are used. In terms of novelties, the most important novelties in the simulation model are considering the virtual education and exerted quarantine effect on estimating the number of the vaccines. In terms of the mathematical model, one of the remarkable contributions is paying attention to social distancing while receiving the injection and the possibility of the injection during working and non-working hours, and regarding the novelties in the solution methodology, a new heuristic method based on a meta-heuristic algorithm called Modified WOA with VNS (MVWOA) is developed. In terms of the performance metrics and the CPU time, the MOWOA is discovered with a superior performance than other given algorithms. Moreover, regarding the data, a case study related to the COVID-19 pandemic period in Tehran/Iran is provided to validate the proposed algorithm. The outcomes indicate that with the demand increase, the costs increase sharply while the vaccination desirability for students decreases with a slight slope.     

并联混合动力汽车性能仿真分析

文章建立了并联混合动力汽车的动力性能数学模型,并在MATLAB平台下开发了并联混合动力汽车动力性能仿真软件系统。基于此软件,对某并联混合动力汽车的动力性能进行了仿真,并将其与试验结果进行了对比,证明了模型的有效性。最后,依据仿真结果,分析了影响并联混合动力汽车动力性能的各项参数,并据此提出了改进其性能参数以提高其动力性能的方法。     

Solving the incomplete markets model with aggregate uncertainty using explicit aggregation

We propose a method to solve models with heterogeneous agents and aggregate uncertainty. The law of motion describing aggregate behavior is obtained by explicitly aggregating the individual policy rule. The algorithm is simpler and faster than existing algorithms that rely on parameterization of the cross-sectional distribution and/or a computationally intensive simulation step. Explicit aggregation establishes a link between the individual policy rule and the set of necessary aggregate state variables, an insight that can be helpful in determining what state variables to include in other algorithms as well.     

Accelerated gaussian importance sampler with application to dynamic latent variable models

We propose a new generic and highly efficient Accelerated Gaussian Importance Sampler (AGIS) for the numerical evaluation of (very) high-dimensional density functions. A specific case of interest to us is the evaluation of likelihood functions for a broad class of dynamic latent variable models. The feasibility of our method is strikingly illustrated by means of an application to a first-order dynamic stochastic volatility model for daily stock returns, whose likelihood for an actual sample of size 2022 (!) is evaluated with high numerical accuracy by means of 10,000 Monte Carlo replications. The estimated model parsimoniously dominates ARCH and GARCH alternatives, one of which includes twelve lags.     

Low-frequency robust cointegration testing

Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1)$I\left(1\right)$ model for the common stochastic trends, which may not accurately describe the data’s persistence. This paper considers low-frequency tests about cointegrating vectors under a range of restrictions on the common stochastic trends. We quantify how much power can potentially be gained by exploiting correct restrictions, as well as the magnitude of size distortions if such restrictions are imposed erroneously. A simple test motivated by the analysis in Wright (2000) is developed and shown to be approximately optimal for inference about a single cointegrating vector in the unrestricted stochastic trend model.     

Modeling spot rate using a realized stochastic volatility model with level effect and dynamic drift☆

This paper proposes a class of realized stochastic volatility model based on both various realized volatility measures and spot rate. It applies the realized stochastic volatility model (Takahashi, Omori, & Watanabe, 2009, and Koopman & Scharth, 2013) to the spot rate model with dynamic drift and level effect setups (RSVL). A jointly approximated maximum likelihood procedure is used to estimate this model. The simulation results show that the RSVL model can be consistently estimated and noise-and-jump-robust realized volatility measures improve the accuracy of the estimation. This study empirically investigates the Chinese interbank repo market with RSVL model, which manifested the advantage of taking the level effect and nonlinear drift into consideration. The noise-and-jump-robust realized volatility measures (e.g. subsample realized volatility and threshold pre-average realized volatility) decrease the volatility fitting error. The nonparametric testing suggests that the RSVL model with noise-and-jump-robust realized volatility measures has more power on forecasting excess kurtosis and fat tails and predicting dynamics of higher order autocorrelations.     

Equilibrium pricing and advertising strategies for nondurable experience products in a dynamic duopoly

The quality of many consumer nondurable goods or services is sufficiently complex or obscure that consumers cannot completely verify the true quality in a single usage. For such ‘experience’ products or services, the accumulated consumer consumption experience of a brand is an important determinant of its sales or market share. The market share of a brand is in turn directly influenced by its own and the competitive price and advertising strategies, given the different levels of quality (among other factors). In this paper, we investigate the impact of the aggregate consumption experience on the firm's dynamic pricing and advertising strategies by developing a formal game-theoretic model of a dynamic duopoly. The model of competition does not yield explicit closed-form expressions for the dynamic price and advertising paths of the two firms. Hence, we simulate the equilibrium paths using a discrete-time algorithm. Our simulation results provide interesting insights into the dynamic equilibrium price and advertising paths, under a variety of realistic competitive scenarios.