基于交叉验证的广义矩估计模型选择
Cross Validation Based Model Selection via Generalized Method of Moments
摘要：
结构估计是经验经济学中的一种重要方法，广义矩估计（GMM）是对大量结构模型进行估计的方法。传统上，结构模型的选择是基于估计的模型拟合来进行的，这需要整个观察样本。在本文中，我们提出了一个基于交叉验证（CV）的模型选择过程，它利用样本分裂技术，以避免过度拟合等问题。虽然CV在机器学习社区中被广泛使用，但我们是第一个在GMM框架中证明其模型选择一致性的人。通过对IV回归和寡头垄断市场模型的模拟，将其经验性质与现有方法进行了比较。此外，我们提出了如何将我们的方法应用到平衡约束数学规划（MPEC）方法。最后，我们将我们的方法应用于在线零售数据，比较动态市场模型和静态模型。
英文摘要：
Structural estimation is an important methodology in empirical economics, and a large class of structural models are estimated through the generalized method of moments (GMM). Traditionally, selection of structural models has been performed based on model fit upon estimation, which take the entire observed samples. In this paper, we propose a model selection procedure based on cross-validation (CV), which utilizes sample-splitting technique to avoid issues such as over-fitting. While CV is widely used in machine learning communities, we are the first to prove its consistency in model selection in GMM framework. Its empirical property is compared to existing methods by simulations of IV regressions and oligopoly market model. In addition, we propose the way to apply our method to Mathematical Programming of Equilibrium Constraint (MPEC) approach. Finally, we perform our method to online-retail sales data to compare dynamic market model to static model.
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