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Local Projections vs. VARs: Lessons From Thousands of DGPs

局部投影与VAR:来自数千种数据生成过程的经验

We conduct a simulation study of Local Projection (LP) and Vector Autoregression (VAR) estimators of structural impulse responses across thousands of data generating processes, designed to mimic the properties of the universe of U.S. macroeconomic data. Our analysis considers various identification schemes and several variants of LP and VAR estimators, employing bias correction, shrinkage, or model averaging. A clear bias-variance trade-off emerges: LP estimators have lower…

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Volatility of Volatility and Leverage Effect from Options

利用期权估计波动率的波动率与杠杆效应

We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the conditional characteristic function of the price increment until the options' expiration and we use these estimates to recover spot volatility. Our volatility of volatility estimator is then formed from the sample variance and first-order…

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GLS under Monotone Heteroskedasticity

单调异方差下的广义最小二乘

The generalized least square (GLS) is one of the most basic tools in regression analyses. A major issue in implementing the GLS is estimation of the conditional variance function of the error term, which typically requires a restrictive functional form assumption for parametric estimation or smoothing parameters for nonparametric estimation. In this paper, we propose an alternative approach to estimate the conditional variance function under nonparametric monotonicity…

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Nonparametric Estimation of Mediation Effects with A General Treatment

一般处理类型下中介效应的非参数估计

To investigate causal mechanisms, causal mediation analysis decomposes the total treatment effect into the natural direct and indirect effects. This paper examines the estimation of the direct and indirect effects in a general treatment effect model, where the treatment can be binary, multi-valued, continuous, or a mixture. We propose generalized weighting estimators with weights estimated by solving an expanding set of equations. Under some sufficient conditions, we show…

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SubgroupTE: Advancing Treatment Effect Estimation with Subgroup Identification

SubgroupTE:结合子群识别的治疗效应估计

Precise estimation of treatment effects is crucial for evaluating intervention effectiveness. While deep learning models have exhibited promising performance in learning counterfactual representations for treatment effect estimation (TEE), a major limitation in most of these models is that they treat the entire population as a homogeneous group, overlooking the diversity of treatment effects across potential subgroups that have varying treatment effects. This limitation…

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A Bracketing Relationship for Long-Term Policy Evaluation with Combined Experimental and Observational Data

结合实验与观察数据进行长期政策评估的夹逼关系

Combining short-term experimental data with observational data enables credible long-term policy evaluation. The literature offers two key but non-nested assumptions, namely the latent unconfoundedness (LU; Athey et al., 2020) and equi-confounding bias (ECB; Ghassami et al., 2022) conditions, to correct observational selection. Committing to the wrong assumption leads to biased estimation. To mitigate such risks, we provide a novel bracketing relationship (cf. Angrist and…

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Extremal Random Forests

极值随机森林

Classical methods for quantile regression fail in cases where the quantile of interest is extreme and only few or no training data points exceed it. Asymptotic results from extreme value theory can be used to extrapolate beyond the range of the data, and several approaches exist that use linear regression, kernel methods or generalized additive models. Most of these methods break down if the predictor space has more than a few dimensions or if the regression function of…

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Generator Identification for Linear SDEs with Additive and Multiplicative Noise

带加性与乘性噪声的线性随机微分方程生成元识别

In this paper, we present conditions for identifying the generator of a linear stochastic differential equation (SDE) from the distribution of its solution process with a given fixed initial state. These identifiability conditions are crucial in causal inference using linear SDEs as they enable the identification of the post-intervention distributions from its observational distribution. Specifically, we derive a sufficient and necessary condition for identifying the…

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When exposure affects subgroup membership: Framing relevant causal questions in perinatal epidemiology and beyond

当暴露影响子群成员资格:围产期流行病学及其他情境中的因果问题

Perinatal epidemiology often aims to evaluate exposures on infant outcomes. When the exposure affects the composition of people who give birth to live infants (e.g., by affecting fertility, behavior, or birth outcomes), this "live birth process" mediates the exposure effect on infant outcomes. Causal estimands previously proposed for this setting include the total exposure effect on composite birth and infant outcomes, controlled direct effects (e.g., enforcing birth), and…

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The Exact Risks of Reference Panel-based Regularized Estimators

基于参考面板的正则化估计量的精确风险

Reference panel-based estimators have become widely used in genetic prediction of complex traits due to their ability to address data privacy concerns and reduce computational and communication costs. These estimators estimate the covariance matrix of predictors using an external reference panel, instead of relying solely on the original training data. In this paper, we investigate the performance of reference panel-based $L_1$ and $L_2$ regularized estimators within a…

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High-dimensional Inference and FDR Control for Simulated Markov Random Fields

模拟马尔可夫随机场的高维推断与FDR控制

Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a methodology based on Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization. Under mild conditions on the MCMC method, our penalized MCMC-MLE method achieves $\ell_{1}$-consistency. We propose a…

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Learning from Aggregate responses: Instance Level versus Bag Level Loss Functions

聚合响应学习:实例级与袋级损失函数

Due to the rise of privacy concerns, in many practical applications the training data is aggregated before being shared with the learner, in order to protect privacy of users' sensitive responses. In an aggregate learning framework, the dataset is grouped into bags of samples, where each bag is available only with an aggregate response, providing a summary of individuals' responses in that bag. In this paper, we study two natural loss functions for learning from aggregate…

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Financial-cycle ratios and medium-term predictions of GDP: Evidence from the United States

金融周期比率与美国GDP的中期预测

Using a large quarterly macroeconomic dataset for the period 1960-2017, we document the ability of specific financial ratios from the housing market and firms' aggregate balance sheets to predict GDP over medium-term horizons in the United States. A cyclically adjusted house price-to-rent ratio and the liabilities-to-income ratio of the non-financial non-corporate business sector provide the best in-sample and out-of-sample predictions of GDP growth over horizons of one to…

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Least squares approximations in linear statistical inverse learning problems

线性统计反问题学习中的最小二乘近似

Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend statistical inverse learning theory with the classical regularization strategy of applying finite-dimensional projections. Our key finding is that coupling the number of random point evaluations with the choice of projection dimension, one can…

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Causal Layering via Conditional Entropy

通过条件熵恢复因果分层

Causal discovery aims to recover information about an unobserved causal graph from the observable data it generates. Layerings are orderings of the variables which place causes before effects. In this paper, we provide ways to recover layerings of a graph by accessing the data via a conditional entropy oracle, when distributions are discrete. Our algorithms work by repeatedly removing sources or sinks from the graph. Under appropriate assumptions and conditioning, we can…

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Factorized Binary Search: change point detection in the network structure of multivariate high-dimensional time series

因子化二分搜索:高维多变量时间序列网络结构的变点检测

Functional magnetic resonance imaging (fMRI) time series data presents a unique opportunity to understand the behavior of temporal brain connectivity, and models that uncover the complex dynamic workings of this organ are of keen interest in neuroscience. We are motivated to develop accurate change point detection and network estimation techniques for high-dimensional whole-brain fMRI data. To this end, we introduce factorized binary search (FaBiSearch), a novel change point…

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Nowcasting economic activity in European regions using a mixed-frequency dynamic factor model

利用混频动态因子模型即时预测欧洲地区经济活动

Timely information about the state of regional economies can be essential for planning, implementing and evaluating locally targeted economic policies. However, European regional accounts for output are published at an annual frequency and with a two-year delay. To obtain robust and more timely measures in a computationally efficient manner, we propose a mixed-frequency dynamic factor model that accounts for national information to produce high-frequency estimates of the…

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Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters

少量聚类与弱识别下工具变量回归的野生自助法

We study the wild bootstrap inference for instrumental variable regressions in the framework of a small number of large clusters in which the number of clusters is viewed as fixed and the number of observations for each cluster diverges to infinity. We first show that the wild bootstrap Wald test, with or without using the cluster-robust covariance estimator, controls size asymptotically up to a small error as long as the parameters of endogenous variables are strongly…

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Use of Prior Knowledge to Discover Causal Additive Models with Unobserved Variables and its Application to Time Series Data

利用先验知识发现含未观测变量的因果加性模型及其时间序列应用

This paper proposes two methods for causal additive models with unobserved variables (CAM-UV). CAM-UV assumes that the causal functions take the form of generalized additive models and that latent confounders are present. First, we propose a method that leverages prior knowledge for efficient causal discovery. Then, we propose an extension of this method for inferring causality in time series data. The original CAM-UV algorithm differs from other existing causal function…

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Functional Linear Non-Gaussian Acyclic Model for Causal Discovery

用于因果发现的函数型线性非高斯无环模型

In causal discovery, non-Gaussianity has been used to characterize the complete configuration of a Linear Non-Gaussian Acyclic Model (LiNGAM), encompassing both the causal ordering of variables and their respective connection strengths. However, LiNGAM can only deal with the finite-dimensional case. To expand this concept, we extend the notion of variables to encompass vectors and even functions, leading to the Functional Linear Non-Gaussian Acyclic Model (Func-LiNGAM). Our…

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Frequency Domain Statistical Inference for High-Dimensional Time Series

高维时间序列的频域统计推断

Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence or the partial coherence, encode comprehensively the complex linear relations between the component processes of the multivariate system. In this paper, we develop inference procedures for such parameters in a high-dimensional, time…

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Testing Firm Conduct

企业竞争行为检验

Evaluating policy in imperfectly competitive markets requires understanding firm behavior. While researchers test conduct via model selection and assessment, we present advantages of Rivers and Vuong (2002) (RV) model selection under misspecification. However, degeneracy of RV invalidates inference. With a novel definition of weak instruments for testing, we connect degeneracy to instrument strength, derive weak instrument properties of RV, and provide a diagnostic for weak…

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Linear Regression with Weak Exogeneity

弱外生性下的线性回归

This paper studies linear time series regressions with many regressors. Weak exogeneity is the most used identifying assumption in time series. Weak exogeneity requires the structural error to have zero conditional expectation given the present and past regressor values, allowing errors to correlate with future regressor realizations. We show that weak exogeneity in time series regressions with many controls may produce substantial biases and even render the least squares…

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Revisiting Event Study Designs: Robust and Efficient Estimation

重新审视事件研究设计:稳健且有效的估计

We develop a framework for difference-in-differences designs with staggered treatment adoption and heterogeneous causal effects. We show that conventional regression-based estimators fail to provide unbiased estimates of relevant estimands absent strong restrictions on treatment-effect homogeneity. We then derive the efficient estimator addressing this challenge, which takes an intuitive "imputation" form when treatment-effect heterogeneity is unrestricted. We characterize…

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