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

如果相对于当前期间的价格或利率存在风险厌恶，则所有统计指数的跟踪特性都是未知的，包括Divisia指数和最高指数。在之前的NSF拨款下，研究人员证明，离散时间Divisia指数的跟踪能力没有受到风险厌恶的严重影响。然而，这项研究使用了经济产生的数据。对经济数据的使用留下了许多问题没有得到解答。例如，规格误差可能很大，并且可能巧合地抵消了Divisia指数中的跟踪误差。如果这是真的，那么Divisia指数对避险情绪很强的结论可能是错误的。这个项目使用蒙特卡罗方法来生成模拟数据，其中只有一个可能的跟踪误差来源：风险厌恶程度。这个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。这项研究在方法论上也具有重要意义，因为它需要对最先进的非线性理性预期模型进行计算要求的复制。

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.