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现代因果推断与数据整合中的局部过度识别及效率增益AI 解读

This paper studies nonparametric local (over-)identification and the semiparametric efficiency in modern causal frameworks. We develop a unified approach that begins by translating structural models with latent variables into their induced statistical models of observables and then analyzes local overidentification through conditional moment restrictions. We apply this approach to three popular classes of causal models: (1) the general treatment model under unconfoundedness;…

基于 ReLU 与深度神经网络的广义最大得分估计量AI 解读

We propose a new formulation of the maximum score estimator that uses compositions of rectified linear unit (ReLU) functions, instead of indicator functions as in Manski (1975,1985), to encode the sign alignment restrictions. Since the ReLU function is Lipschitz, our new ReLU-based maximum score criterion function is substantially easier to optimize using standard gradient-based optimization pacakges. We also show that our ReLU-based maximum score (RMS) estimator can be…

最优处理分配下福利与价值泛函的推断AI 解读

We provide theoretical results for the estimation and inference of a class of welfare and value functionals of the nonparametric conditional average treatment effect (CATE) function under optimal treatment assignment, i.e., treatment is assigned to an observed type if and only if its CATE is nonnegative. For the optimal welfare functional defined as the average value of CATE on the subpopulation with nonnegative CATE, we establish the $\sqrt{n}$ asymptotic normality of the…

高效的双重差分与事件研究估计量AI 解读

This paper investigates efficient Difference-in-Differences (DiD) and Event Study (ES) estimation using short panel data sets within the heterogeneous treatment effect framework, free from parametric functional form assumptions and allowing for variation in treatment timing. We provide an equivalent characterization of the DiD potential outcome model using sequential conditional moment restrictions on observables, which shows that the DiD identification assumptions typically…

未观测混杂下的分位数最优政策学习AI 解读

We study quantile-optimal policy learning where the goal is to find a policy whose reward distribution has the largest $α$-quantile for some $α\in (0, 1)$. We focus on the offline setting whose generating process involves unobserved confounders. Such a problem suffers from three main challenges: (i) nonlinearity of the quantile objective as a functional of the reward distribution, (ii) unobserved confounding issue, and (iii) insufficient coverage of the offline dataset. To…

非参数工具变量模型中的自适应最优速率假设检验AI 解读

We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modified leave-one-out sample analog of a quadratic distance between the restricted and unrestricted sieve two-stage least squares estimators. We provide computationally simple, data-driven choices of sieve tuning…

基于广义 Bierens 最大统计量的条件矩限制参数推断AI 解读

Many economic panel and dynamic models, such as rational behavior and Euler equations, imply that the parameters of interest are identified by conditional moment restrictions. We introduce a novel inference method without any prior information about which conditioning instruments are weak or irrelevant. Building on Bierens (1990), we propose penalized maximum statistics and combine bootstrap inference with model selection. Our method optimizes asymptotic power by solving a…

非参数结构函数与弹性的自适应估计及一致置信带AI 解读

We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least squares estimators. When implemented with this choice, estimators of both the structural function $h_0$ and its derivatives (such as elasticities) converge at the fastest possible (i.e., minimax) rates in sup-norm. The second is for constructing…

混杂变量维度增长时利用神经网络推断一般处理效应AI 解读

Semiparametric efficient estimation of various multi-valued causal effects, including quantile treatment effects, is important in economic, biomedical, and other social sciences. Under the unconfoundedness condition, adjustment for confounders requires estimating the nuisance functions relating outcome or treatment to confounders nonparametrically. This paper considers a generalized optimization framework for efficient estimation of general treatment effects using artificial…

非参数工具变量模型的有效估计：多种神经网络估计量比较AI 解读

Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional variables more effectively than linear sieves. We investigate the performance of various ANNs in nonparametric instrumental variables (NPIV) models of moderately high dimensional covariates that are relevant to empirical economics. We present two efficient procedures for estimation and inference on a weighted average derivative (WAD): an…

非参数分位数工具变量回归加权平均导数的惩罚筛广义经验似然AI 解读

This paper considers estimation and inference for a weighted average derivative (WAD) of a nonparametric quantile instrumental variables regression (NPQIV). NPQIV is a non-separable and nonlinear ill-posed inverse problem, which might be why there is no published work on the asymptotic properties of any estimator of its WAD. We first characterize the semiparametric efficiency bound for a WAD of a NPQIV, which, unfortunately, depends on an unknown conditional derivative…

识别集的蒙特卡洛置信集AI 解读

In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full parameters and of subvectors in models defined through a likelihood or a vector of moment equalities or inequalities. These CSs are based on level sets of optimal sample criterion functions (such as likelihood or optimally-weighted or…

非参数工具变量回归非线性泛函的最优上确界范数速率与一致推断AI 解读

This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function $h_0$ and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of $h_0$ and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating $h_0$ and its derivatives, and show that the…

半参数与非参数条件矩模型的筛 Wald 和 QLR 推断AI 解读

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill-posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root-$n$ estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid…

筛法非参数工具变量回归的最优一致收敛速度AI 解读

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound on the sup-norm (uniform) convergence rate of a sieve estimator, allowing for endogenous regressors and weakly dependent data. This result leads to the optimal sup-norm convergence…

非参数与半参数模型的局部识别AI 解读

In parametric, nonlinear structural models a classical sufficient condition for local identification, like Fisher (1966) and Rothenberg (1971), is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We derive an analogous result for the nonparametric, nonlinear structural models, establishing conditions under which an infinite-dimensional analog of the full rank condition is sufficient for local identification.…

计量经济学不适定逆问题的收敛速度最优性AI 解读

In this paper, we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error loss for the NPIR and the NPIV models under two basic regularity conditions that allow for both mildly ill-posed and severely ill-posed cases. We show that both a simple projection…