Weathering Uncertainty in the Long Run

物质或人力资本的投资决策迫使经济主体向前看并预测未来。它们还需要对复杂环境下不确定的增长前景进行评估。当经济主体使用概率模型时，他们面临的问题与统计决策理论和控制理论相似。是否有一个或多个选定的基准模型？这些模型是否依赖于未知参数或隐藏状态？模型是否被错误指定？如何使用数据来为决策提供信息？从长远来看，对这些隐藏状态的推断是不确定性的重要来源吗？本提案研究了三个主题，探讨了以增长不确定性为核心成分的动态模型的含义。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，该研究建立了分散经济的模型，其中决策者，私人代理人和决策者以稳健的方式面对隐藏的状态马尔可夫链。这些模型允许研究者探索资本积累的前瞻性方面，广泛的构想，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化或不频繁地变化。当决策者不能直接观察这种状态时，他们被迫使用信号的历史数据来推断这种状态及其变化的时间。这些隐藏的状态可能是不确定性的来源，并带来长期的后果。该建议将隐状态马尔可夫模型与鲁棒决策的递归公式相结合。对鲁棒性的关注既适用于潜在动力学的说明，也适用于隐藏增长状态的估计。其次，在未来很长一段时间内具有重要支付成分的资产的经济价值包含了风险或不确定性的长期概念。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潜在状态变量的转变动态中推断长期后果的方法。在建议的研究中，这些方法将适合于研究资产价值的长期组成部分。估值运营商将不同期限的收益价格联系起来。一个特定的估值操作者将未来的投资回报映射为当前价值。一类这样的操作符可以根据支付和当前值之间的时间来构造。当支付日期和估值日期之间的时间间隔很长时，这些估值操作符可以通过少量成分甚至单个成分很好地近似。例如，可能存在一个主导成分或特征函数，它决定了价值与长期收益之间的关系。这些算子方法应用于可能的非线性马尔可夫环境，产生了明确定义的主导定价因素的概念，以及明确定义的方法来表征这些组件何时是重要的。这些操作方法给出了动态经济模型所隐含的资产价值的长期组成部分的度量。虽然这些方法更普遍地适用，但在拟议的研究中，将特别关注以不确定性的长期成分为特征的一类经济模型。第三，决策者在采取行动时可能会由于成本或信息流动的限制而使信息平滑。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。对隐藏状态的平滑预测可能会降低处理成本。信息理论的结果表明，这一机制为信号在马尔可夫决策问题中的作用提供了一个有用的视角。信号处理可以作为信息约束下优化的结果出现。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.