Theoretical and Empirical Research of Investment under Uncertainty

本研究项目对不确定性下投资理论的贡献如下：1。为了研究不确定性厌恶的作用，我将奈特不确定性纳入到投资的随机模型中。结果表明，奈特不确定性的增加肯定会减少投资，而均值保持价差对投资的影响关键取决于奈特不确定性的水平。在回应Saltari和Ticchi（2005）对我之前的研究（Nakamura,1999）的评论时，我明确指出了将跨期可替代性与风险厌恶区分开来的重要性。利用非预期实用新型的连续时间版本，它使我们能够研究跨期可替代性的独立变化对风险厌恶的影响，我表明人们可以很容易地用基本的经济推理来解释投资函数的一些不可解释的特性。本文利用数学分析软件Mathematica的数值模拟和解析方法，研究了当资本的生命周期有限时，不确定条件下的投资问题。很明显，当投资边际调整成本较大时，投资随不确定性增加而增加；当投资边际调整成本较小时，投资随不确定性减少。如果边际调整成本介于两者之间，则投资不确定性关系可能是倒u型的。在实证调查中，考虑到新产品和新技术传播的不确定性，我证明了日本国内企业固定投资在一段时间内仍保持在目前的高水平。虽然我利用日本制造业的数据，基于M-GARCH模型对投资函数进行了实证估计，其中考虑了需求和价格的不确定性，但到目前为止还没有得到明确的结果。这是这个项目剩下的研究。

The contributions to the theory of investment under uncertainty made by this research project are as follows :1.In order to investigate the role of uncertainty-aversion, I incorporate the Knightian uncertainty into the stochastic model of investment. As a result, it is shown that an increase in the Knightian uncertainty surely decreases investment while the effect of a mean-preserving spread on investment depends crucially on the level of the Knightian uncertainty.2.In reply to the comment by Saltari and Ticchi (2005) to my previous research (Nakamura,1999), I clearly point out the importance of separating the intertemporal substitutability from the risk-aversion.3.Appealing to the continuous-time version of non-expected utility model, which allows us to investigate the effect of independent changes in intertemporal substitutability from those in risk-aversion, I show that one can easily explain some of unexplainable properties of the investment function using basic economic reasoning.4.Using the analytical method and the numerical simulations by Mathematica, I investigate investment under uncertainty when the lifetime of capital is finite. It becomes clear that investment increases with uncertainty if marginal adjustment costs of investment are large while it decreases with uncertainty if they are small. If the marginal adjustment costs are in between, the investment-uncertainty relationship may be reverse U-shaped.In the empirical investigation, considering the uncertainties over the spreads of new product and technology, I demonstrate that the domestic business fixed investment in Japan remains at its current high level for a while. Although, using the Japanese manufacturing industry data, I have conducted the empirical estimations of the investment functions based on M-GARCH models, in which the uncertainties over demands and prices are considered, no clear results have not yet been derived so far. This is the remaining research in this project.