动态离散选择模型的平滑和筛选方法
Solving Dynamic Discrete Choice Models Using Smoothing and Sieve Methods
摘要：
我们建议结合平滑，模拟和筛分近似解决集成或期望价值函数在一般类的动态离散选择（DDC）模型。我们使用重要性抽样来近似定义这两个函数的Bellman算子。随机Bellman算子以及相应的解通常是非光滑的，这是不期望的。为了避免这个问题，我们引入了一个平滑版本的随机贝尔曼算子和解决相应的平滑价值函数使用筛子的方法。我们表明，可以避免使用筛子的推广和适应的“自我逼近”方法的鲁斯特（1997年），我们的设置。我们提供了一个渐近理论的近似解决方案，并表明他们收敛的根N率，其中$N$是蒙特卡罗提请，朝高斯过程。我们通过一组数值实验研究了它们在实践中的表现，发现这两种方法都表现良好，其中筛法在计算速度和精度方面特别有吸引力。
英文摘要：
We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the Bellman operators defining the two functions. The random Bellman operators, and therefore also the corresponding solutions, are generally non-smooth which is undesirable. To circumvent this issue, we introduce a smoothed version of the random Bellman operator and solve for the corresponding smoothed value function using sieve methods. We show that one can avoid using sieves by generalizing and adapting the `self-approximating' method of Rust (1997) to our setting. We provide an asymptotic theory for the approximate solutions and show that they converge with root-N-rate, where $N$ is number of Monte Carlo draws, towards Gaussian processes. We examine their performance in practice through a set of numerical experiments and find that both methods perform well with the sieve method being particularly attractive in terms of computational speed and accuracy.
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