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

包含不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函数（因此是可处理的）。如果个人拥有不对称的信息，并通过观察内生变量——价格、总产出或类似的东西——来获取信息，那么在技术上就很难解决这些内生总量的模型。标准的待定系数法仅限于特殊情况。研究者开发了两种有前途的新解决方法，在这个项目中，他将它们扩展到更普遍的环境中。他将表明，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殊情况，其中经济、信息和统计结构通过指定解析函数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来严格建模和经验估计。求解这个模型需要对矩阵进行因式分解。第一种方法设计模型，使矩阵仅由外生元素组成——这些元素很容易被分解——然后扰动模型以实现经济上有趣的模型的解。第二种方法使用收缩映射不动点法。该模型将信息外部性微观文献与理性预期文献进行整合。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其他政策制度的福利特征。研究者已经展示了信息外部性如何导致在随机驱动过程的特殊情况下模拟商业周期的总体波动。本项目研究了当驱动过程更为普遍时，经济总量的持续性、幅度和协同运动如何受到此类外部性的影响。

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.