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A method of moments approach to asymptotically unbiased Synthetic Controls

以矩方法构造渐近无偏的合成控制

A common approach to constructing a Synthetic Control unit is to fit on the outcome variable and covariates in pre-treatment time periods, but it has been shown by Ferman and Pinto (2021) that this approach does not provide asymptotic unbiasedness when the fit is imperfect and the number of controls is fixed. Many related panel methods have a similar limitation when the number of units is fixed. I introduce and evaluate a new method in which the Synthetic Control is…

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Testing for sparse idiosyncratic components in factor-augmented regression models

因子增广回归中稀疏特异成分的检验

We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative model augmented with sparse idiosyncratic components. The asymptotic properties of the test are established under time series dependence and polynomial tails. We outline a data-driven rule to select the tuning parameter and prove its theoretical validity. In simulation experiments, our procedure exhibits high power against sparse alternatives and low power…

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Threshold spatial autoregressive model

门槛空间自回归模型

In this paper, we consider the estimation and inferential issues of the threshold spatial autoregressive (TSAR) model, which is a hybrid of the threshold and spatial autoregressive models. We use the quasi maximum likelihood (QML) method to estimate the model. In addition, we prove the tightness and the Hájek–Rényi type inequality for a quadratic form and establish a full inferential theory of the QML estimator under the setup that threshold effect shrinks to zero as the…

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Fixed- b asymptotics for panel models with two-way clustering

双向聚类面板模型的固定 b 渐近理论

This paper studies a cluster robust variance estimator proposed by Chiang, Hansen and Sasaki (2024) for linear panels. First, we show algebraically that this variance estimator (CHS estimator, hereafter) is a linear combination of three common variance estimators: the one-way unit cluster estimator, the “HAC of averages” estimator, and the “average of HACs” estimator. Based on this finding, we obtain a fixed-b asymptotic result for the CHS estimator and corresponding test…

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An unbounded intensity model for point processes

点过程的局部无界强度模型

We develop a model for point processes on the real line, where the intensity can be locally unbounded without inducing an explosion. In contrast to an orderly point process, for which the probability of observing more than one event over a short time interval is negligible, the bursting intensity causes an extreme clustering of events around the singularity. We propose a nonparametric approach to detect such bursts in the intensity. It relies on a heavy traffic condition,…

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Tuning-parameter-free propensity score matching approach for causal inference under shape restriction

形状约束下无需调参的倾向得分匹配因果推断

Propensity score matching (PSM) is a pseudo-experimental method that uses statistical techniques to construct an artificial control group by matching each treated unit with one or more untreated units of similar characteristics. To date, the problem of determining the optimal number of matches per unit, which plays an important role in PSM, has not been adequately addressed. We propose a tuning-parameter-free PSM approach to causal inference based on the nonparametric…

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ON GMM INFERENCE: PARTIAL IDENTIFICATION, IDENTIFICATION STRENGTH, AND NONSTANDARD ASYMPTOTICS

GMM 推断:部分识别、识别强度与非标准渐近理论

This paper analyses aspects of generalized method of moments (GMM) inference in moment equality models in settings where standard regularity conditions may break down. Explicit analytic formulations for the asymptotic distributions of estimable functions of the GMM estimator and statistics based on the GMM criterion function are derived under relatively mild assumptions. The moment Jacobian is allowed to be rank deficient, so first order identification may fail, the values…

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TESTING A CLASS OF SEMI- OR NONPARAMETRIC CONDITIONAL MOMENT RESTRICTION MODELS USING SERIES METHODS

利用级数方法检验一类半参数或非参数条件矩限制模型

This paper proposes a new test for a class of conditional moment restrictions (CMRs) whose parameterization involves unknown, unrestricted conditional expectation functions. Motivating examples of such CMRs arise from models of discrete choice under uncertainty including certain static games of incomplete information. The proposed test may be viewed as a semi-/nonparametric extension of the Bierens (1982, Journal of Econometrics 20, 105–134) goodness-of-fit test of a…

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LARGE SAMPLE JUSTIFICATIONS FOR THE BAYESIAN EMPIRICAL LIKELIHOOD

贝叶斯经验似然的大样本依据

This study investigates the asymptotic properties of the Bayesian empirical likelihood (BEL), which uses the empirical likelihood as an alternative to a parametric likelihood for Bayesian inference. We establish two asymptotic equivalence results based on the Bernstein–von Mises (BvM) theorem by introducing a new formulation of the moment restriction model. First, the limiting posterior distribution of the BEL is the same as that of a parametric Bayesian method that uses the…

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WEAK CONVERGENCE TO DERIVATIVES OF FRACTIONAL BROWNIAN MOTION

向分数布朗运动导数的弱收敛

It is well known that, under suitable regularity conditions, the normalized fractional process with fractional parameter d converges weakly to fractional Brownian motion (fBm) for $d>\frac {1}{2}$ . We show that, for any nonnegative integer M , derivatives of order $m=0,1,\dots ,M$ of the normalized fractional process with respect to the fractional parameter d jointly converge weakly to the corresponding derivatives of fBm. As an illustration, we apply the results to the…

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INSTRUMENTAL VARIABLES INFERENCE IN A SMALL-DIMENSIONAL VAR MODEL WITH DYNAMIC LATENT FACTORS

含动态潜在因子的小维度 VAR 模型中的工具变量推断

We study semiparametric inference in a small-dimensional vector autoregressive (VAR) model of order p augmented by unobservable common factors with a dynamic described by a VAR process of order q . This state-space specification is useful to measure separately the direct causality effects and the responses to dynamic common factors. We show that the state-space parameters are identifiable from the autocovariance function of the observed process. We estimate the model by…

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HIGHER-ORDER APPROXIMATION OF IV ESTIMATORS WITH INVALID INSTRUMENTS

无效工具变量下 IV 估计量的高阶近似

This paper analyzes the higher-order approximation of instrumental variable (IV) estimators in a linear homoskedastic IV regression model when a large set of instruments with potential invalidity is present. We establish theoretical results on the higher-order mean-squared error (MSE) approximation of the two-stage least-squares (2SLS), the limited information maximum likelihood (LIML), the Fuller (FULL), the bias-adjusted 2SLS, and jackknife version of the LIML and FULL…

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EXPONENTIAL REALIZED GARCH-ITÔ VOLATILITY MODELS

指数已实现 GARCH–Itô 波动率模型

This paper introduces a novel Itô diffusion process to model high-frequency financial data that can accommodate low-frequency volatility dynamics by embedding the discrete-time nonlinear exponential generalized autoregressive conditional heteroskedasticity (GARCH) structure with log-integrated volatility in a continuous instantaneous volatility process. The key feature of the proposed model is that, unlike existing GARCH-Itô models, the instantaneous volatility process has a…

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Expecting the unexpected: Stressed scenarios for economic growth

应对意外:经济增长的压力情景

Summary We propose the construction of conditional growth densities under stressed factor scenarios to assess the level of exposure of an economy to small probability but potentially catastrophic economic and/or financial scenarios, which can be either domestic or international. The choice of severe yet plausible stress scenarios is based on the joint probability distribution of the underlying factors driving growth, which are extracted with a multilevel dynamic factor model…

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Terrorism and education: Evidence from instrumental variables estimators

恐怖主义与教育:工具变量估计的证据

Summary This paper estimates the effect of exposure to terrorist violence on education. Since terrorists may choose targets endogenously, we construct a set of novel instruments. To that end, we leverage exogenous variation from a local terrorist group's revenues and its affiliation with al‐Qaeda. Across several Kenyan datasets, we find that attacks suppress school enrolment more than predicted by difference‐in‐differences‐type estimators. This indicates that terrorists…

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Tests for equal forecast accuracy under heteroskedasticity

异方差下的预测准确性相等检验

Summary Heteroskedasticity is a common feature in empirical time series analysis, and in this paper, we consider the effects of heteroskedasticity on statistical tests for equal forecast accuracy. In such a context, we propose two new Diebold–Mariano‐type tests for equal accuracy that employ nonparametric estimation of the loss differential variance function. We demonstrate that these tests have the potential to achieve power improvements relative to the original…

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Scaling and measurement error sensitivity of scoring rules for distribution forecasts

分布预测评分规则对缩放和测量误差的敏感性

Summary This paper examines the impact of data rescaling and measurement error on scoring rules for distribution forecast. First, I show that all commonly used scoring rules for distribution forecasts are robust to rescaling the data. Second, the forecast ranking based on the continuous ranked probability score is less sensitive to gross measurement error than the ranking based on the log score. The theoretical results are complemented by a simulation study aligned with…

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Real‐time weakness of the global economy

全球经济疲弱程度的实时测度

Summary We propose an empirical framework to measure the real‐time weakness of the global economy. This framework relies on nonlinear factor models to identify recessionary and expansionary episodes, fitted to several macroeconomic variables, for the largest advanced and emerging economies. The country‐specific inferences are then combined to construct both a Global Weakness Index and a Global Intensity Index. As new economic data become available from different regions,…

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Constructing density forecasts from quantile regressions: Multimodality in macrofinancial dynamics

由分位数回归构造密度预测:宏观金融动态中的多峰性

Summary Quantile regression methods are increasingly used to forecast tail risks and uncertainties in macroeconomic outcomes. This paper reconsiders how to construct predictive densities from quantile regressions. We compare a popular two‐step approach that fits a specific parametric density to the quantile forecasts with a nonparametric alternative that lets the “data speak.” Simulation evidence and an application revisiting GDP growth uncertainties in the United States…

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Identification and forecasting of bull and bear markets using multivariate returns

利用多元收益识别和预测牛熊市场

Summary Bull and bear market identification generally focuses on a broad index of returns through a univariate analysis. This paper proposes a new approach to identify and forecast bull and bear markets through multivariate returns. The model assumes that all assets are directed by a common discrete state variable from a hierarchical Markov switching model. The hierarchical specification allows the cross‐section of state‐specific means and variances to differ over bull and…

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Bayesian model selection via mean-field variational approximation

通过平均场变分近似进行贝叶斯模型选择

Abstract This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference that allows latent variables and model misspecification. Concretely, we show a Bernstein–von Mises (BvM) theorem for the variational distribution from MF under possible model misspecification, which implies the distributional convergence of MF variational approximation to a normal distribution…

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

Heather Battey对《因果模型的参数化与模拟》的讨论评论

My brief comment relates to the inferential discussion of Section 5. The sample-space factorization of the joint probability from the marginal structural model induces a parameter-space factorization of the likelihood function, with the implication that θZX is orthogonal to (⁠θY|X*,ϕYZ|X*⁠) in the sense of, e.g. Cox and Reid (1987), and leading to the simplified asymptotic covariance matrix of Theorem 5.1. The parameter cut discussed at the beginning of Section 5 also…

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

Richard Guo 对《因果模型的参数化与模拟》的讨论:两种分解与密度比

I congratulate Evans and Didelez warmly on this innovative and inspiring paper. Here, I offer my interpretation of the approach in terms of two factorizations and a density ratio. Any distribution over Z,X,Y can be factorized in two ways: Factorization C−1 is the usual one; it is factorization A−1 that is the focus of the two authors. More concretely, suppose ϕZY∣X(z,y∣x) is a conditional copula density, i.e. for every value of x, (z,y)↦ϕZY∣X(z,y∣x) is a density function…

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