This paper develops a penalized GMM (PGMM) framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators. We derive convergence rates for the PGMM estimator and provide conditions for root-n consistency and asymptotic normality of debiased functional estimates, covering both linear and nonlinear functionals. Monte Carlo experiments on average derivative show that the PGMM-based debiased estimator performs on par with the analytical debiased estimator that uses the known closed-form Riesz representer, achieving 90-96% coverage while the plug-in estimator falls below 5%. We apply our procedure to estimate mean own-price elasticities in a semiparametric demand model for differentiated products. Simulations confirm near-nominal coverage while the plug-in severely undercovers. Applied to IRI scanner data on carbonated beverages, debiased semiparametric estimates are approximately 20% more elastic compared to the logit benchmark, and debiasing corrections are heterogeneous across products, ranging from negligible to several times the standard error.

翻译：本文提出了一种惩罚性广义矩方法（PGMM）框架，用于对非参数工具变量估计量的泛函进行自动去偏推断。我们推导了PGMM估计量的收敛速度，并给出了去偏泛函估计达到根号n一致性和渐近正态性的条件，涵盖线性和非线性泛函。关于平均导数的蒙特卡洛实验表明，基于PGMM的去偏估计量性能与使用已知闭式Riesz表示子的解析去偏估计量相当，覆盖率可达90-96%，而插件估计量覆盖率低于5%。我们将该方法应用于差异化产品半参数需求模型中自身价格弹性的均值估计。仿真实验证实去偏估计量接近名义覆盖率，而插件估计量严重欠覆盖。将方法应用于碳酸饮料的IRI扫描数据集时，去偏半参数估计值相较于logit基准模型弹性高出约20%，且去偏修正量在产品间呈现异质性，取值范围可忽略不计至标准误差的数倍。