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We propose SLIM (Stochastic Learning and Inference in overidentified Models), a scalable stochastic approximation framework for nonlinear GMM. Independent mini-batches of moments and derivatives yield unbiased update directions with martingale difference noise. Under suitable regularity conditions, SLIM yields consistent and asymptotically normal estimators without a consistent initial estimator or a globally convex GMM criterion. Our theory covers fixed-sample and…

大规模BLP估计的随机嵌套不动点算法AI 解读

We develop a stochastic nested fixed point (SNFP) estimator for random coefficients logit demand models that updates model parameters using stochastic gradients and performs demand inversion one market at a time. Relative to the conventional nested fixed point (NFP) estimator, SNFP substantially reduces memory requirements and computational cost, making estimation feasible in very large datasets. We establish the large-$T$ (number of markets) asymptotic properties of the…

SAUSS：有限因变量模型的无偏模拟得分随机逼近AI 解读

Multinomial choice models allow flexible substitution patterns but become computationally demanding with many alternatives or observations. With a fixed per-observation simulation budget, simulated maximum likelihood introduces simulation bias, while each optimization step requires a full-sample likelihood evaluation. We propose Stochastic Approximation with Unbiased Simulated Scores (SAUSS), an averaged stochastic approximation based on conditionally unbiased mini-batch…

工具变量究竟识别哪一种脉冲响应？AI 解读

The local projection-instrumental variable (LP-IV) literature has been largely silent on cases in which impulse responses are set-identified, arising when the shock of interest is composite and instruments are correlated with multiple components. We demonstrate that LP-IV estimands constructed using one instrument at a time identify affine combinations of impulse responses to structural shock components with instrument-specific and potentially negative weights, challenging…

动态面板门槛模型的自助推断AI 解读

This paper develops valid bootstrap inference methods for the dynamic short panel threshold regression. We show that the standard nonparametric bootstrap is inconsistent for the first-differenced generalized method of moments (GMM) estimator. The inconsistency arises from an $n^{1/4}$-consistent non-normal asymptotic distribution of the threshold estimator when the true parameter lies in the continuity region of the parameter space, which stems from the rank deficiency of…

大型线性时间序列模型中的最优结构突变检验AI 解读

We develop a class of optimal tests for a structural break occurring at an unknown date in infinite and growing-order time series regression models, such as AR($\infty$), linear regression with increasingly many covariates, and nonparametric regression. Under an auxiliary i.i.d. Gaussian error assumption, we derive an average power optimal test, establishing a growing-dimensional analog of the exponential tests of Andrews and Ploberger (1994) to handle identification failure…

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…

具有潜在大量协变量的断点回归设计AI 解读

This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform stably regardless of the number of covariates. The proposed methods combine the local approach using kernel weights with $\ell_{1}$-penalization to handle high-dimensional covariates. We provide theoretical and numerical results which…

面向数千万观测的分位数回归快速推断AI 解读

Big data analytics has opened new avenues in economic research, but the challenge of analyzing datasets with tens of millions of observations is substantial. Conventional econometric methods based on extreme estimators require large amounts of computing resources and memory, which are often not readily available. In this paper, we focus on linear quantile regression applied to "ultra-large" datasets, such as U.S. decennial censuses. A fast inference framework is presented,…

SGMM：广义矩估计的随机逼近AI 解读

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient…

折点阈值估计与连续性检验的极小极大风险AI 解读

We derive a risk lower bound in estimating the threshold parameter without knowing whether the threshold regression model is continuous or not. The bound goes to zero as the sample size $ n $ grows only at the cube root rate. Motivated by this finding, we develop a continuity test for the threshold regression model and a bootstrap to compute its \textit{p}-values. The validity of the bootstrap is established, and its finite sample property is explored through Monte Carlo…

通过随机缩放实现随机梯度下降的快速稳健在线推断AI 解读

We develop a new method of online inference for a vector of parameters estimated by the Polyak-Ruppert averaging procedure of stochastic gradient descent (SGD) algorithms. We leverage insights from time series regression in econometrics and construct asymptotically pivotal statistics via random scaling. Our approach is fully operational with online data and is rigorously underpinned by a functional central limit theorem. Our proposed inference method has a couple of key…

因子驱动的双区制回归AI 解读

We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold…

稀疏 HP 滤波：识别 COVID-19 接触率的折点AI 解读

In this paper, we estimate the time-varying COVID-19 contact rate of a Susceptible-Infected-Recovered (SIR) model. Our measurement of the contact rate is constructed using data on actively infected, recovered and deceased cases. We propose a new trend filtering method that is a variant of the Hodrick-Prescott (HP) filter, constrained by the number of possible kinks. We term it the $\textit{sparse HP filter}$ and apply it to daily data from five countries: Canada, China,…

高维分位数回归中变点的预言式估计AI 解读

In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold parameter. Our penalized estimators not only select covariates but also discriminate between a model with homogeneous sparsity and a model with a change point. As a result, it is not necessary to know or pretest whether the change point is…

稀疏结构的结构变化AI 解读

In the high-dimensional sparse modeling literature, it has been crucially assumed that the sparsity structure of the model is homogeneous over the entire population. That is, the identities of important regressors are invariant across the population and across the individuals in the collected sample. In practice, however, the sparsity structure may not always be invariant in the population, due to heterogeneity across different sub-populations. We consider a general,…

可能存在变点的高维回归中的 LassoAI 解读

We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the $\ell_1$ estimation loss for regression…