Large State Space Issues in Dynamic Models

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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.