Integrative Noise and Fixed Point Methods as Solution Techniques for Generalized Linear-Quadratic Models of Endogenous Information

纳入非对称信息的宏观经济学理性预期模型通常使用线性-二次技术框架，因为个人的预测或决策是可观察变量的线性(因此也是容易处理的)函数。如果个人拥有不对称信息，并通过观察内生变量--价格、总产出或诸如此类--来获得信息，那么从技术上讲，很难为内生集合体求解这样的模型。标准法，待定系数法，仅限于特殊情况。这位研究人员开发了两种很有前途的新解决方法，在这个项目中，他将它们扩展到更一般的环境。他将证明，所有具有不对称信息的线性理性预期模型都可以表示为一般结构的特例，在这种结构中，经济、信息和统计结构通过指定分析函数的矩阵的维度和元素来捕获。任何经济结构都可以通过指定这些矩阵的细节进行严格的建模和经验估计。求解该模型需要对矩阵进行因式分解。第一种方法设计模型，使矩阵只由外生元素组成--这些元素很容易被分解--然后对模型进行扰动，以获得经济上感兴趣的模型的解。第二种方法使用压缩映射不动点方法。该模型将信息外部性微观文献与理性预期文献相结合。这为进一步分析铺平了道路，特别是利用我们从微观文献中了解到的信息，对替代政策体制的福利特征进行分析。这位研究人员已经展示了信息外部性如何导致模拟随机驾驶过程特殊情况下的商业周期的总波动。这个项目调查了当驱动过程更一般时，这种外部性是如何影响经济总量的持久性、幅度和协动性的。

Rational expectations models of macroeconomics that incorporate asymmetric information typically use a linear-quadratic technical framework because individuals' predictions or decisions are then linear (and hence tractable) functions of observable variables. If individuals have asymmetric information and obtain information by observing endogenous variables -- prices, aggregate output or the like -- then it becomes technically difficult to solve such models for the endogenous aggregates. The standard method, the method of undetermined coefficients, is limited to special cases. The investigator developed two promising new solution methods and in this project he expands them to a more general setting. He will show that all linear rational expectations models with asymmetric information are expressible as special cases of a general structure in which economic, informational, and statistical structure is captured by specifying the dimensions and elements of matrices of analytic functions. Any economic structure can be rigorously modelled and empirically estimated by specifying the details of these matrices. Solving this model requires factoring the matrix. The first approach designs the model so that the matrix is comprised solely of exogenous elements -- which are easily factored -- and then perturbing the model to achieve the solution of the economically interesting model. The second approach uses a contraction mapping fixed point method. The model will integrate the informational externality micro literature with the rational expectations literature. This paves the way for further analysis, particularly of the welfare characteristics of alternative policy regimes, using what we know from the micro literature. The investigator has already shown how informational externalities lead to aggregate fluctuations that mimic business cycles for special cases of stochastic driving processes. This project investigates how the persistence, amplitudes and co-movements of economic aggregates are affected by such externalities when the driving processes are more general.