Weathering Uncertainty in the Long Run

对物质资本或人力资本的投资决定迫使经济主体向前看并预测未来。它们还需要对复杂环境中不确定的增长前景进行评估。当经济主体使用概率模型时，他们面临着统计决策理论和控制理论中常见的问题。是否有选定的基准模型或模型？这些模型依赖于未知参数或隐藏状态吗？模型是否可能被错误指定？如何使用数据为决策提供信息？从长远来看，关于这些隐藏状态的推论是不确定性的重要来源吗？本提案探讨了三个主题，探讨了增长不确定性是核心因素的动态模型的影响。 这项研究可能会对经济学的所有子领域产生更广泛的影响，特别是对金融市场、商业周期和经济增长的研究。首先，这项研究建立了分散经济的模型，其中决策者、私人代理人和政策制定者以稳健的方式面对隐状态马尔可夫链。这些模型使研究者能够探索资本积累的前瞻性方面，广泛的设想，及其相关的估值。 隐状态马尔可夫模型是包括经济学在内的各种科学学科的宝贵工具。马尔可夫链的隐藏状态可以缓慢地演变或不频繁地改变。当决策者没有直接观察到这种状态时，他们被迫使用信号的历史数据来推断这种状态以及它何时发生变化。这些隐藏的状态可能是不确定性的来源，具有长期的后果。该建议使用隐状态马尔可夫模型结合递归公式的强大的决策。 对鲁棒性的关注既适用于基本动态的规范，也适用于隐藏的增长状态的估计。第二，具有重要未来支出成分的资产的经济价值包含了长期风险或不确定性的概念。算子方法将应用于马尔可夫环境。这些方法提供了从经济中基本状态变量的转变动态推断长期后果的方法。在拟议的研究中，这些方法将适合于研究资产价值的长期组成部分。估值算子将不同期限的收益价格联系起来。一个特定的估值算子将未来的投资收益映射到当前的价值。可以根据回报和当前值之间的时间来构造此类运算符族。当支付日和估值日之间的时间很长时，这些估值算子可以很好地近似于少量的分量，甚至是单个分量。例如，可能存在一个主导成分或特征函数，它规定了价值如何与长期收益相关。这些运营商的方法应用到可能的非线性马尔可夫环境中产生了明确的概念，主导定价因素和明确的方式来表征这些组件是重要的。这些运营商的方法给出的措施，长期组成部分的资产价值所隐含的动态经济模型。虽然这些方法是更普遍适用的，在拟议的研究中，特别注意将给予一类的经济模型，功能的长期组成部分的不确定性。第三，决策者可能会平滑的信息时，采取行动，因为成本或限制的信息流。本研究探讨了这些信息流约束对具有增长不确定性的动态经济模型的影响。 隐藏状态的平滑预测处理起来可能成本更低。信息论的结果表明，这种机制提供了一个有用的角度信号的作用，在马尔可夫决策问题。信号处理可以作为受信息约束的优化的结果出现。经济学家发现，这是一个有趣的模型，可以解释为什么经济主体对信息反应迟钝。

Investment decisions in physical or human capital compel economic agents to look forward and predict the future. They also require an assessment of uncertain growth prospects in a complex environment. When economic agents use probability models, they face questions that are familiar from statistical decision theory and control theory. Is there a chosen benchmark model or models? Do these models depend on unknown parameters or hidden states? Could the models be misspecified? How might data be used to inform decisions? Are inferences about these hidden states important sources of uncertainty in the long run? This proposal investigates three topics that explore implications of dynamic models in which growth uncertainty is a central ingredient. This research could have broader impacts on all subfields of economics and especially the study of financial markets, business cycles and economic growth.First, the research builds models of decentralized economies in which decision makers, private agents and policy makers, confront hidden state Markov chains in a robust manner. These models allow the investigator to explore the forward-looking aspects of capital accumulation, broadly conceived, and its associated valuation. Hidden state Markov models are valuable tools for a variety of scientific disciplines, including economics. A hidden state of a Markov chain can evolve slowly or change infrequently. When decision makers do not directly observe this state, they are compelled to use historical data on signals to make inferences about this state and when it changes. These hidden states can be sources of uncertainty with prolonged consequences. This proposal uses hidden state Markov models in conjunction with recursive formulations of robust decision making. Concerns about robustness apply both to the specification of the underlying dynamics and to the estimation of the hidden growth states. Second, the economic values of assets that have important payout components far into the future incorporate long-run notions of risk or uncertainty. Operator methods will be applied to Markov environments. These methods give ways to infer long-run consequences from the transition dynamics of underlying state variables in an economy. In the proposed research, these methods will be tailored to the study of the long run components of asset values. Valuation operators link prices of payoffs with different maturities. A specific valuation operator maps investment payoffs in the future into current values. A family of such operators can be constructed depending on the time between the payoff and the current value. These valuation operators may be well approximated by a small number of components or even a single component when the elapsed time between the payoff date and the valuation date is large. For instance, a dominant component or eigen function may exist that dictates how values are related to payoffs in the long run. These operator methods applied to possibly nonlinear Markov environments give rise to well defined notions of dominant pricing factors and well defined ways to characterize when these components are important. These operator methods give measures of the long-run components of asset values implied by dynamic economic models. While these methods are applicable more generally, in the proposed research particular attention will be given to the class of economic models that feature long-run components of uncertainty.Third, decision-makers may smooth information when taking actions because of costs or constraints on the flow of information. This research explores what implications these information flow constraints have for dynamic economic models with growth uncertainty. Smooth predictions of hidden states may be less costly to process. Results from information theory suggest that this mechanism provides a useful perspective on the role of signals in Markov decision problems. Signal processing can emerge as the outcome of optimization subject to information constraints. Economists have found this to be an intriguing model of why economic agents respond sluggishly to information.