Large State Space Issues in Dynamic Models

动态决策模型的估计由于需要计算与不同选择路径相关的未来收益而变得复杂。这些在未来表现最佳的预期未来收益被称为价值函数。计算一个复杂的动态博弈的值函数是非常昂贵的，因为有大量可能的选择路径。该奖项资助研究开发一种新的逼近价值函数的方法。该近似是基于筛法的，随着筛复杂度的增加，它具有良好的渐近性。这些方法不仅适用于个体决策模型，也适用于动态游戏（游戏邦注：即多个个体在一段时间内做出决策）。筛法可用于求解有限水平纳什均衡；它还可以用于测试在特定应用程序中个人是否正在发挥这种平衡。研究小组将把这种方法应用于分析六年级学生的样本数据；这里的动态游戏是建立友谊，以及学生如何随着时间的推移形成强大的同伴网络。这种新方法将潜在地推动应用微观经济学许多领域的实证工作。由于该方法的计算成本较低，因此它可能非常适合希望以合理成本估计动态博弈模型的研究人员使用。

The estimation of models of dynamic decision making is complicated by needing to calculate the future payoffs associated with different choice paths. These expected future payoffs from behaving optimally in the future are called the value function. Calculating a value function for a complicated dynamic game is computationally expensive because of the large number of possible choice paths. This award funds research to develop a new method for approximating value functions. The approximation is based on sieve methods, and it has good asymptotic properties as the complexity of the sieve increases.These methods will be useful for models of individual decision making and also useful for dynamic games, where several individuals make decisions over time. The sieve method can be used to solve for the finite horizon Nash equilibrium; it can also be used to test whether this equilibrium is being played by individuals in a particular application. The research team will apply this method to analyzing data from a sample of sixth grade students; the dynamic game here is the establishment of friendships and how students over time form strong peer networks.The new method will potentially advance empirical work in many areas of applied microeconomics. Because the method is computationally less expensive, it may be well suited for use by researchers who wish to estimate dynamic game models at a reasonable cost.