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Invalid Proxies and Volatility Changes

无效代理变量与波动率变化

When in proxy-SVARs the covariance matrix of VAR disturbances is subject to exogenous, permanent breaks that cause IRFs to change across volatility regimes, even strong, exogenous external instruments yield inconsistent estimates of the dynamic causal effects. However, if these volatility shifts are properly incorporated into the analysis through (testable) "stability restrictions", we demonstrate that the target IRFs are point-identified and can be estimated consistently…

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ARMA-Design: Optimal Treatment Allocation Strategies for A/B Testing in Partially Observable Experiments

ARMA-Design:部分可观测实验中 A/B 测试的最优处理分配

Online experiments are frequently employed in technological companies to evaluate the performance of a newly developed policy, product, or treatment relative to a baseline control. In many applications, the experimental units receive a sequence of treatments over time. To handle these time-dependent settings, existing A/B testing solutions typically assume a fully observable experimental environment that satisfies the Markov condition. However, this assumption often does not…

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Noncausal AR processes driven by causal GARCH volatility

由因果 GARCH 波动驱动的非因果自回归过程

This paper studies the introduction of causal conditional heteroskedasticity in noncausal autoregressive (AR) models. We demonstrate that, in this framework, large shocks to the innovation process driving the GARCH error term of a noncausal AR model result in heightened volatility immediately before and after a bubble crash. The non-coincidence of the σ-fields generated by past observations and past values of the GARCH process makes statistical inference nonstandard. In…

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Time domain estimation of non-fundamental ARMA models in the presence of heteroskedasticity of unknown form

未知形式异方差下非基本 ARMA 模型的时域估计

This paper considers time domain estimation of possibly non-fundamental (that is, non-causal and/or non-invertible) non-Gaussian linear ARMA models with martingale difference innovations that may display conditional heteroskedasticity of unknown form. Instead of explicitly parametrizing the underlying volatility process (the higher order dependence) and employing maximum likelihood procedures, we propose a time domain minimum distance objective function based on innovations…

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TOWARD A UNIFORM ASYMPTOTIC THEORY FOR MILDLY EXPLOSIVE AUTOREGRESSION

迈向轻度爆炸自回归的统一渐近理论

Abstract This article provides a general asymptotic theory for mildly explosive autoregression. We confirm that Cauchy limit theory remains invariant across a broad range of error processes, including general linear processes with martingale difference innovations, stationary causal processes, and nonlinear autoregressive time series, such as threshold autoregressive and bilinear models. Our results unify the Cauchy limit theory for long memory, short memory, and…

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Dynamic Causal Effects in a Nonlinear World: the Good, the Bad, and the Ugly

非线性世界中的动态因果效应:良好、不佳与棘手的情形

Applied macroeconomists frequently use impulse response estimators motivated by linear models. We study whether the estimands of such procedures have a causal interpretation when the data generating process is in fact nonlinear. We show that vector autoregressions and linear local projections onto observed shocks or proxies identify weighted averages of causal effects regardless of the extent of nonlinearities. By contrast, identification approaches that exploit…

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Discussion of “Dynamic Causal Effects in a Nonlinear World: The Good, the Bad, and the Ugly”

《非线性世界中的动态因果效应》讨论

This comment discusses Kolesár and Plagbord-Møller finding that the standard linear local projection (LP) estimator recovers the average marginal effect (AME) even in nonlinear settings. We apply and discuss a subset their results using a simple nonlinear time series model, emphasizing the role of the weighting function and the impact of nonlinearities on small-sample properties.

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Nonlinearity in Dynamic Causal Effects: Making the Bad into the Good, and the Good into the Great?

动态因果效应中的非线性:能否改善不佳情形并强化良好情形?

This article was prepared as a comment on “Dynamic Causal Effects in a Nonlinear World: the Good, the Bad, and the Ugly” by Michal Kolesár and Mikkel Plagborg-Møller. We make three comments, including a novel contribution to the literature, showing how a reasonable economic interpretation can potentially be restored for average-effect estimators with negative weights.

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Comment: Dynamic Causal Effects in a Nonlinear World: The Good, the Bad, and the Ugly

评论:非线性世界中的动态因果效应

It is a pleasure to comment on the paper by Kolesár and Plagborg-Møller (KPM henceforth). Their research is of the highest technical rigor yet written accessibly for the applied practitioner, with ...

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Discussion of: “Dynamic Causal Effects in a Nonlinear World: the Good, the Bad, and the Ugly”

《非线性世界中的动态因果效应》讨论:效应大小与大冲击

The ease of estimating linear local projections has made them a popular tool for impulse response function analysis. Kolesár and Plagborg-Møller’s main goal is to inquire whether local projections (LP) estimands of impulse response functions have a causal interpretation when the data generating process (DGP) is nonlinear. This discussion focuses on two questions. First, how should we interpret the magnitude of the linear LP estimands in nonlinear environments? Second, is the…

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Quantile Granger causality in the presence of instability

不稳定环境下的分位数格兰杰因果关系

We propose a new framework for assessing Granger causality in quantiles in unstable environments, for a fixed quantile or over a continuum of quantile levels. Our proposed test statistics are consistent against fixed alternatives, they have nontrivial power against local alternatives, and they are pivotal in certain important special cases. In addition, we show the validity of a bootstrap procedure when asymptotic distributions depend on nuisance parameters. Monte Carlo…

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Inference on time series nonparametric conditional moment restrictions using nonlinear sieves

使用非线性筛方法推断时间序列非参数条件矩限制

This paper studies estimation of and inference on dynamic nonparametric conditional moment restrictions of high dimensional variables for weakly dependent data, where the unknown functions of endogenous variables can be approximated via nonlinear sieves such as neural networks and Gaussian radial bases. The true unknown functions and their sieve approximations are allowed to be in general weighted function spaces with unbounded supports, which is important for time series…

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Statistical Identification of Independent Shocks with Kernel-based Maximum Likelihood Estimation and an Application to the Global Crude Oil Market

独立冲击的核最大似然统计识别及全球原油市场应用

Independent component analysis has emerged as a promising approach for revealing structural relationships in multivariate dynamic systems, particularly in scenarios with limited knowledge of causal patterns. This article introduces a robust kernel-based maximum likelihood (KML) estimation method that accommodates the distributional characteristics of the structural sources of data variation. Our Monte Carlo study demonstrates the superior performance of the KML estimator…

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A new central limit theorem for the augmented IPW estimator: Variance inflation, cross-fit covariance and beyond

Estimation of the average treatment effect (ATE) is a central problem in causal inference. In recent times, inference for the ATE in the presence of high-dimensional covariates has been extensively studied. Among the diverse approaches that have been proposed, augmented inverse probability weighting (AIPW) with cross-fitting has emerged a popular choice in practice. In this work, we study this cross-fit AIPW estimator under well-specified outcome regression and propensity…

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Belief Shocks and Implications of Expectations About Growth‐at‐Risk

信念冲击与增长风险预期的影响

ABSTRACT This paper revisits the question of how shocks to expectations of market participants can cause business cycle fluctuations. We use a vector autoregression to estimate dynamic causal effects of belief shocks which are extracted from nowcast errors about output growth. In a first step, we replicate and corroborate the findings of Enders, Kleemann, and Müller (2021). The second step computes nowcast errors about growth‐at‐risk at various quantiles. This involves both…

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Quantile Policy Effects: An Application to U.S. Macroprudential Policy

分位数政策效应:美国宏观审慎政策应用

To assess the dynamic distributional impacts of macroeconomic policy, we propose quantile policy effects to quantify disparities between the quantiles of potential outcomes under different policies. We first identify quantile policy effects under the unconfoundedness assumption and propose an inverse probability weighting estimator. We then examine the asymptotic behavior of the proposed estimator in a time series framework and suggest a blockwise bootstrap method for…

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Consistent causal inference for high-dimensional time series

高维时间序列的一致因果推断

A methodology for high-dimensional causal inference in a time series context is introduced. Time series dynamics are captured by a Gaussian copula, and estimation of the marginal distribution of the data is not required. The procedure can consistently identify the parameters that describe the dynamics of the process and the conditional causal relations among the possibly high-dimensional variables, under sparsity conditions. Identification of the causal relations is in the…

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Counterfactual Imputation: Comments on “Imputation of Counterfactual Outcomes when the Errors are Predictable” by Silvia Gonçalves and Serena Ng

反事实插补:对可预测误差下反事实结果插补方法的评论

The measurement of treatment (intervention) effects on a single (or just a few) treated unit(s) based on counterfactuals constructed from artificial controls has become a popular practice in applied statistics and economics since the proposal of the synthetic control method. However, most of the literature has ignored the time-series properties of the data. The work of Gonçalves and Ng fills this gap by proposing a simple correction for existing estimators to take into…

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Estimation of continuous-time linear DSGE models from discrete-time measurements

利用离散时间观测估计连续时间线性 DSGE 模型

We provide a general state space framework for estimation of the parameters of continuous-time linear DSGE models from discrete-time data. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, hence avoiding discretization errors. We construct the exact likelihood for data sampled either as stocks or flows, based on the Kalman filter, and provide necessary and sufficient conditions for local identification of the frequency-invariant…

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Rajendra Bhansali’s contribution to the Discussion of ‘Parameterizing and simulating from causal models’ by Evans and Didelez

Rajendra Bhansali 对《因果模型的参数化与模拟》的讨论意见

Contribution: My own introduction to the subject area of this paper is through the notion of Granger causality, a topic which has attracted much attention in time series analysis and related disciplines, including signal processing. The authors have proposed a new approach to causal models. However, this involves working with full density functions. It seems to me that, from a data analysis point of view, the authors’ approach might be a bit too general, and it might be…

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FNETS: Factor-Adjusted Network Estimation and Forecasting for High-Dimensional Time Series

FNETS:高维时间序列的因子调整网络估计与预测

–We propose FNETS, a methodology for network estimation and forecasting of high-dimensional time series exhibiting strong serial- and cross-sectional correlations. We operate under a factor-adjusted vector autoregressive (VAR) model which, after accounting for pervasive co-movements of the variables by common factors, models the remaining idiosyncratic dynamic dependence between the variables as a sparse VAR process. Network estimation of FNETS consists of three steps: (i)…

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Estimation of prediction error in time series

时间序列预测误差的估计

Summary The accurate estimation of prediction errors in time series is an important problem, which has immediate implications for the accuracy of prediction intervals as well as the quality of a number of widely used time series model selection criteria such as the Akaike information criterion. Except for simple cases, however, it is difficult or even impossible to obtain exact analytical expressions for one-step and multi-step predictions. This may be one of the reasons…

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Characterization of causal ancestral graphs for time series with latent confounders

含潜在混杂的时间序列因果祖先图刻画

In this paper, we introduce a novel class of graphical models for representing time-lag specific causal relationships and independencies of multivariate time series with unobserved confounders. We completely characterize these graphs and show that they constitute proper subsets of the currently employed model classes. As we show, from the novel graphs one can thus draw stronger causal inferences—without additional assumptions. We further introduce a graphical representation…

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Generalized Covariance Estimator

广义协方差估计量

We consider a class of semi-parametric dynamic models with iid errors, including the nonlinear mixed causal-noncausal Vector Autoregressive (VAR), Double-Autoregressive (DAR) and stochastic volatility models. To estimate the parameters characterizing the (nonlinear) serial dependence, we introduce a generic Generalized Covariance (GCov) estimator, which minimizes a residual-based multivariate portmanteau statistic. In comparison to the standard methods of moments, the GCov…

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