Theoretical and Empirical Research of Investment under Uncertainty

本研究对不确定性投资理论的贡献主要体现在以下几个方面：1.为了研究不确定性规避的作用，将不确定性引入到随机投资模型中。结果表明，随着不确定性的增加，投资必然减少，而均值保持价差对投资的影响主要取决于不确定性的水平。2.回复Saltari和Ticchi（2005）对我以前研究的评论（中村，1999），我明确指出了将跨期可替代性与风险厌恶分离的重要性。3.呼吁非预期效用模型的连续时间版本，这使得我们能够研究跨期替代性的独立变化对风险规避的影响，我表明，人们可以很容易地解释投资函数的一些无法解释的性质，使用基本的经济推理。4.使用解析方法和Mathematica的数值模拟，我研究了不确定性下的投资，当资本的寿命是有限的。很明显，如果投资的边际调整成本很大，投资会随着不确定性而增加，而如果投资的边际调整成本很小，投资会随着不确定性而减少。如果边际调整成本介于两者之间，则投资与不确定性的关系可能呈倒U型。在实证研究中，考虑到新产品和新技术扩散的不确定性，笔者证明了日本国内企业固定投资将在一段时间内保持目前的高水平。虽然使用日本的制造业数据，基于考虑了需求和价格的不确定性的M-GARCH模型，对投资函数进行了实证估计，但至今还没有得到明确的结果。这是该项目的剩余研究。

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.