Monte Carlo Investigation of Three Issues: Exact Monetary Aggregation under Risk, Tests for Nonlinearity and Chaos, and the AIM Model's Regularity Properties

如果存在相对于当期价格或利率的风险规避，则所有统计指数（包括division指数和最高级指数）的跟踪属性都是未知的。在先前的NSF资助下，研究者证明了离散时间分裂指数的跟踪能力不会受到风险规避的严重损害。然而，该研究使用的是经济产生的数据。经济数据的使用留下了许多未解之谜。例如，规范错误可能很大，并且可能恰好抵消了Divisia索引中的跟踪错误。如果这是真的，那么关于Divisia指数对风险厌恶反应强劲的结论可能是错误的。本项目使用蒙特卡罗方法生成模拟数据，其中只有一个可能的跟踪误差来源：风险规避程度。该项目的结果对货币政策很重要，因为货币当局使用货币总量来跟踪经济表现。这项研究在方法上也很重要，因为它需要对最先进的非线性理性期望模型进行计算上的严格复制。

If there is risk aversion relative to current period prices or interest rates, the tracking properties of all statistical index numbers, including the Divisia and superlative index numbers, are unknown. Under the previous NSF grant, the investigator demonstrated that the tracking ability of the discrete time Divisia index is not seriously compromised by risk aversion. However, that study used data produced by the economy. The use of data from the economy leaves many problems unanswered. For example, it is possible that specification errors might be large and might coincidentally offset the tracking error in the Divisia index. If that were true, the conclusion that the Divisia index is robust to risk aversion might be wrong. This project uses a Monte Carlo approach to generate simulated data in which only one possible source of tracking error remains: the degree of risk aversion. The results of this project are important for monetary policy because monetary aggregates are used by monetary authorities to track the performance of the economy. The research is also methodologically significant because it requires computationally demanding replications of state of the art nonlinear rational expectations models.