In most macroeconomic models, time is infinite. Agents are endowed with rational expectations including the cognitive ability to solve complex infinite-horizon planning problems. This is a heroic assumption; but when does it matter? In “Monetary Policy Analysis When Planning Horizons Are Finite,” Michael Woodford reconsiders this unrealistic feature, introduces a novel bounded-rationality framework to address it, and explores under what circumstances this affects the policy conclusions of the standard New Keynesian paradigm. Woodford develops a new cognitive framework in which agents transform their infinite-horizon problem into a sequence of simpler, finite-horizon ones. The solution method used by the agent is to backward induct over a finite set of periods given some perceived value function he has assigned to his perceived terminal nodes. This solution method seems quite natural; in fact, Woodford is motivated by a beautiful analogy to how state-of-the-art artificial intelligence (AI) programs play the games of chess or go. Take chess—a gamewith a finite strategy space and thereby in theory solvable via backward induction. In practice, however, the space of strategies is so large that solving the game in this fashion would require unfathomableprocessing power. Consider then themost effectiveAI programs. A typical decision-making process may be described as follows: at each turn, the machine looks forward at all possible moves for both itself and its opponent a finite number of turns, thereby creating a decision tree with finite nodes. It assigns a value to each of the different possible terminal nodes; these values may be based on past experience or data. Finally, given these terminal node values, the machine backward

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在大多数宏观经济模型中，时间是无限的。代理被赋予了理性预期，包括解决复杂的无限范围规划问题的认知能力。这是一个英勇的假设；但什么时候重要？在“规划视野有限时的货币政策分析”中，迈克尔伍德福德重新考虑了这一不切实际的特征，引入了一个新的有限理性框架来解决它，并探讨在什么情况下这会影响标准新凯恩斯主义范式的政策结论。伍德福德开发了一个新的认知框架，在这个框架中，代理将他们的无限范围问题转化为一系列更简单的、有限范围的问题。代理使用的解决方法是在给定他分配给他的感知终端节点的感知价值函数的有限周期内反向归纳。这种解决方法看起来很自然；事实上，伍德福德的灵感来自于最先进的人工智能 (AI) 程序如何下国际象棋或围棋的美丽类比。以国际象棋为例——一种具有有限策略空间的游戏，因此理论上可以通过反向归纳来解决。然而，在实践中，策略的空间如此之大，以这种方式解决游戏将需要深不可测的处理能力。然后考虑最有效的人工智能程序。一个典型的决策过程可以描述如下：在每一回合，机器在有限的回合数内为自己和对手寻找所有可能的动作，从而创建一个具有有限节点的决策树。它为每个不同的可能终端节点分配一个值；这些值可能基于过去的经验或数据。最后，