Pairwise-difference estimation of incomplete information games
不完全信息博弈的成对差分估计AI 解读 ↓
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不完全信息博弈的成对差分估计
- 研究问题
- 在不完全信息且具有 Nash 均衡行为的博弈中，如何不指定收益冲击的参数分布、也不计算均衡，就估计收益参数？
- 方法与思路
- 作者提出两步成对差分程序，依赖冲击分布可逆性及退化的均衡选择机制；若收益对参数线性，估计量具有闭式表达。
- 材料陈述的贡献
- 摘要称，论文处理匹配变量和指数回归量均含非参数函数的情形，建立插入估计的渐近理论，并提出半参数残差设定检验。
- 阅读关注点
- 应核对可逆性与退化均衡选择的含义、第一步误差条件及闭式解范围，并确认摘要中一致性速率的原始公式记号。
- 阅读边界
- 仅据所给出版社摘要，不能将不计算均衡理解为无需均衡选择限制；速率记号、理论条件及模拟数值均需全文核对。
原文摘要
This paper contributes to the literature on econometric estimation of incomplete information games with Nash equilibrium behavior by introducing a two-step estimation procedure that makes no parametric assumptions about the distribution of unobservable payoffs shocks. Instead, its asymptotic properties rely on assuming only that these distributions satisfy an invertibility condition, and that the underlying equilibrium selection mechanism is degenerate. Our methodology relies on a pairwise-differencing procedure which, unlike Aradillas-Lopez (2010), does not require computing the equilibria of the game. Furthermore, if normal-form payoffs are linear in the parameters of interest, our procedure results in an estimator with a closed-form expression. We contribute to the pairwise-differencing econometric literature by introducing the first model, where both the control variables being matched and the regressors in the index function parameterized by θ contain nonparametric functions. In particular, the asymptotic theory developed in Aradillas-Lopez et al. (2007) does not cover this setting. We describe conditions under which nonparametrically estimated plug-ins yield a N-consistent and asymptotically normal estimator for the parameter of interest. A consistent specification test based on semiparametric residuals is also developed. It appears to be the first test of this type for a model involving nonparametric or “generated” regressors. Several extensions of our method are also discussed. A series of Monte Carlo experiments are used to investigate the properties of our estimator and our specification test.