Comparison of solutions to the incomplete markets model with aggregate uncertainty

This paper compares numerical solutions to the model of Krusell and Smith [1998. Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy 106, 867–896] generated by different algorithms. The algorithms have very similar implications for the correlations between different variables. Larger differences are observed for (i) the unconditional means and standard deviations of individual variables, (ii) the behavior of individual agents during particularly bad times, (iii) the volatility of the per capita capital stock, and (iv) the behavior of the higher-order moments of the cross-sectional distribution. For example, the two algorithms that differ the most from each other generate individual consumption series that have an average (maximum) difference of 1.63% (11.4%).     

Assessing the accuracy of the aggregate law of motion in models with heterogeneous agents

This paper shows that the R² and the standard error have fatal flaws and are inadequate accuracy tests. Using data from a Krusell–Smith economy, I show that approximations for the law of motion of aggregate capital, for which the true standard deviation of aggregate capital is up to 14% (119%) higher than the implied value and which are thus clearly inaccurate, can have an R² as high as 0.9999 (0.99). Key in generating a more powerful test is that predictions of the aggregate law of motion are not updated with the aggregated simulated individual data.     

Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty

This paper describes the first model considered in the computational suite project that compares different numerical algorithms. It is an incomplete markets economy with a continuum of agents and an inequality (borrowing) constraint.     

Computational suite of models with heterogeneous agents II: Multi-country real business cycle models

This paper describes the second model considered in the computational suite project that compares the performance of different numerical algorithms. It is a multi-country model in which countries face different productivity shocks. Solving such models is a challenging numerical problem unless the number of countries is small. The solutions are functions of a large set of arguments and the functional forms are unknown. Moreover, the solution procedures have to deal with high-dimensional integration problems.     

Solving the multi-country Real Business Cycle model using a perturbation method

This paper solves the multi-country RBC model described in den Haan et al. (this issue) and Juillard and Villemot (this issue), using a perturbation method. We explain how to apply first- and second-order versions of the gensys2.m algorithm to this model. The perturbation method is computationally cheap and can easily be applied to large models with possibly hundreds of state variables.     

Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method

I propose a Galerkin projection method for solving dynamic economic models with many state variables. This method employs non-product monomial integration formulas for the computation of weighted residuals, and its computational cost therefore increases only polynomially in the model's dimensionality. I illustrate the practical implementation of the proposed algorithm by solving several specifications of the multi-country Real Business Cycle model described in Den Haan et al. [2010. Computational suite of models with heterogeneous agents: multi-country Real Business Cycle models. Journal of Economic Dynamics and Control, this issue], and briefly discuss two possible routes for further improving its numerical accuracy.     

Solving the incomplete markets model with aggregate uncertainty using parameterized cross-sectional distributions

This note describes how the incomplete markets model with aggregate uncertainty in Den Haan et al. [Comparison of solutions to the incomplete markets model with aggregate uncertainty. Journal of Economic Dynamics and Control, this issue] is solved using standard quadrature and projection methods. This is made possible by linking the aggregate state variables to a parameterized density that describes the cross-sectional distribution. A simulation procedure is used to find the best shape of the density within the class of approximating densities considered. This note compares several simulation procedures in which there is—as in the model—no cross-sectional sampling variation.     

真实经济周期理论与凯恩斯主义经济周期理论的比较分析

20世纪80年代以后，基德兰德和普雷斯科特所开创的真实经济周期理论在宏观经济学中引起了人们极大的关注。这一理论丰富和发展了经济周期理论，并对凯恩斯主义经济周期理论产生了很大的冲击。主要在经济周期的性质、经济周期的原因及如何减少经济周期稳定经济这些问题上存在着很大的分歧。此外对经济学的未来，真实经济周期理论的发展方向具有重要的指导意义。     

Solving the incomplete markets model with aggregate uncertainty using the Krusell–Smith algorithm

This paper studies the properties of the solution to the heterogeneous agents model in Den Haan et al. [2009. Computational suite of models with heterogeneous agents: incomplete markets and aggregate uncertainty. Journal of Economic Dynamics and Control, this issue]. To solve for the individual policy rules, we use an Euler-equation method iterating on a grid of pre-specified points. To compute the aggregate law of motion, we use the stochastic-simulation approach of Krusell and Smith [1998. Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy 106, 868–896]. We also compare the stochastic- and non-stochastic-simulation versions of the Krusell–Smith algorithm, and we find that the two versions are similar in terms of their speed and accuracy.     

Approximate dynamic programming with post-decision states as a solution method for dynamic economic models

I introduce and evaluate a new stochastic simulation method for dynamic economic models. It is based on recent work in the operations research and engineering literatures (Van Roy et al., 1997, Powell, 2007, Bertsekas, 2011), but also had an early application in economics (Wright and Williams, 1982, Wright and Williams, 1984). The baseline method involves rewriting the household׳s dynamic program in terms of post-decision states. This makes it possible to choose controls optimally without computing an expectation. I add a subroutine to the original algorithm that updates the values of states not visited frequently on the simulation path; and adopt a stochastic stepsize that efficiently weights information. Finally, I modify the algorithm to exploit GPU computing.     

Solving the multi-country real business cycle model using ergodic set methods

We use the stochastic simulation algorithm, described in Judd et al. (2009), and the cluster-grid algorithm, developed in Judd et al. (2010a), to solve a collection of multi-country real business cycle models. The following ingredients help us reduce the cost in high-dimensional problems: an endogenous grid enclosing the ergodic set, linear approximation methods, fixed-point iteration and efficient integration methods, such as non-product monomial rules and Monte Carlo integration combined with regression. We show that high accuracy in intratemporal choice is crucial for the overall accuracy of solutions and offer two approaches, precomputation and iteration-on-allocation, that can solve for intratemporal choice both accurately and quickly. We also implement a hybrid solution algorithm that combines the perturbation and accurate intratemporal-choice methods.     

中国经济周期特征与太阳黑子均衡

本文在Benhabib、Farmer（1994）、Farmar、Guo（1994,1995）的不确定性均衡模型框架上,构建了一个考虑了信念偏差所代表的不确定因素和政府支出冲击的太阳黑子RBC模型来解释宏观经济的周期波动;并利用中国改革开放以来的经济数据,对该模型进行了实证检验。我们发现,该模型能够解释80%以上的中国经济波动特征;可以合理预测各宏观经济变量与产出之间的协动关系,合理预测各变量与劳动生产率之间的相关关系;对中国经济的解释力远远高于标准RBC模型,说明这一模型比较适合解释中国经济波动。另外,还发现信念冲击与政府支出冲击均是中国宏观经济波动的重要冲击来源,分别可以解释约30%、60%的经济波动,表明二者均是中国经济波动不可忽略的重要影响因素。我们的发现从不确定均衡和财政政策变动角度对宏观经济波动(比如,消费、就业、投资)的一些现象提供了合理解释。     

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.     

An Integrated Approach to the Business Cycle

Die Konjunkturschwankungen : Theoretische Gunglagen der Wirtschafts-politik, Bd. II.
The Japanese Village in Transition. By A. F. Raper, T. Tsuchiyama, H. Passin and D. L. Sills.
Public Finance and Fiscal Policy. By Richard W. Lindholm.
Business and Government. By C. C. Rohlfing, E. W. Carter, B. W. West and J. G. Hervey.
The Economy of Latin America. By Wendell C. Gordon.
Price Theory. By Sidney Weintraub.
Pricing in Planned Economy. By B. V. Krishnamurti.
Pressure of Population and Economic Efficiency in India. By D. Ghosh.
Studies in Genius. By Walter G.     

基于扩散指数模型的房地产市场景气循环研究——以北京市为例

基于扩散指数模型构建房地产市场景气循环指标体系,采用北京市住宅市场与经济基本面的历史数据,计算不同时期北京市房地产市场的扩散指数,绘制北京市房地产市场的景气循环曲线,并根据景气循环曲线与历史数据对北京市未来房地产市场的景气情况进行预测。最后,提出在上述市场预测情况下的市场调控策略。     

销售循环中会计业务流程再造模型之比较

文章基于案例分析建立了2个销售循环中应收账款管理与账龄分析模型.通过对模型17个不同观察点的对比分析,提炼出模型4个类别的基本适应性特征和6个类别的BPR适应性特征,并对模型的应用进行了分析.     

Assessing the Empirical Relevance of Labour Frictions to Business Cycle Fluctuations

This paper describes a dynamic stochastic general equilibrium model augmented with labour frictions, namely: indivisible labour, predetermined employment and adjustment costs. This improves the fit to the data as shown by a higher log marginal likelihood and closer match to key business cycle statistics. The labour frictions introduced are relevant for model dynamics and economic policy: the effect of total factor productivity shocks on most macroeconomic variables is substantially mitigated; fiscal policy leads to a greater crowding out of private sector activity and monetary policy has a lower impact on output. Labour frictions also provide a better match to impulse response functions from vector autoregressive models.     

The Austrian Theory of the Business Cycle

The Austrian school theory of the business cycle is based on the proposition that an artificial expansion of the money supply reduces the transaction rate of interest below its natural rate, which stimulates excessive investment in capital goods of long duration, and then when the rate of interest rises back up, these investments stop, and the economy falls into recession.     

BN周期成分的符号与我国GDP的真实周期

本文从理论上证明了以下的定理：当度量序列持久性的方差比大于1时,BN周期成分的符号应予反号,否则,不予反号。为验证定理,我们设计Monter-Carlo仿真实验,其结果也证实了理论定理。本文的理论结论和仿真结果,第一次从持久性的角度解释了文献中的“周期之谜”。在此基础上,我们应用BN周期分解方法和本文的理论结果,分解我国GDP的BN周期。结果显示,由于我国GDP的方差比为1.97,所以周期成分的符号应反号,由此形成我国GDP的真实周期。样本期内（2000Q2-2011Q4）我国共经历了六轮周期,这六轮周期不仅与我国实际经济增长的波动基本一致,而且与我国所遭遇的主要冲击相吻合;我国经济增长的周期具有波动幅度较大、持续时间又存在明显差异的特征。基于这些特征,本文认为,减弱我国经济增长的周期性波动,应成为宏观调控的重要内容。     

Solving the multi-country real business cycle model using a Smolyak-collocation method

We describe a sparse-grid collocation method to compute recursive solutions of dynamic economies with a sizable number of state variables. We show how powerful this method can be in applications by computing the non-linear recursive solution of an international real business cycle model with a substantial number of countries, complete insurance markets and frictions that impede frictionless international capital flows. In this economy, the aggregate state vector includes the distribution of world capital across different countries as well as the exogenous country-specific technology shocks. We use the algorithm to efficiently solve models with up to 10 countries (i.e., up to 20 continuous-valued state variables).