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Asymptotic properties of the maximum likelihood estimator in regime-switching models with time-varying transition probabilities

时变转移概率状态转换模型中最大似然估计量的渐近性质

Summary Time-varying transition probability (TVTP) regime-switching models extend the constant regime transition probability in Markov-switching models to include information from observations. We show consistency and asymptotic normality of the maximum likelihood estimator (MLE) in general TVTP regime-switching models where the conditional distribution of $Y_t$ depends on lagged regimes. Consistency of the MLE is also shown under misspecification. The assumptions are…

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Bubble testing under polynomial trends

多项式趋势下的泡沫检验

Summary This paper develops the asymptotic theory of the least squares estimator of the autoregressive (AR) coefficient in an AR(1) regression with intercept when data is generated from a polynomial trend model in different forms. It is shown that the commonly used right-tailed unit root tests tend to favour the explosive alternative. A new procedure, which implements the right-tailed unit root tests in an AR(2) regression, is proposed. It is shown that, when the data…

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Doubly robust identification for causal panel data models

因果面板数据模型的双重稳健识别

Summary We study identification and estimation of causal effects in settings with panel data. Traditionally, researchers follow model-based identification strategies relying on assumptions governing the relation between the potential outcomes and the observed and unobserved confounders. We focus on a different, complementary approach to identification, where assumptions are made about the connection between the treatment assignment and the unobserved confounders. Such…

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Evaluating (weighted) dynamic treatment effects by double machine learning

利用双重机器学习评估加权动态处理效应

Summary We consider evaluating the causal effects of dynamic treatments, i.e., of mul-tiple treatment sequences in various periods, based on double machine learning to control for observed, time-varying covariates in a data-driven way under a selection-on-observables assumption. To this end, we make use of so-called Neyman-orthogonal score functions, which imply the robustness of treatment effect estimation to moderate (local) misspecifications of the dynamic outcome and…

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Double machine learning-based programme evaluation under unconfoundedness

无混杂条件下基于双重机器学习的项目评估

Summary This paper reviews, applies, and extends recently proposed methods based on double machine learning (DML) with a focus on programme evaluation under unconfoundedness. DML-based methods leverage flexible prediction models to adjust for confounding variables in the estimation of (a) standard average effects, (b) different forms of heterogeneous effects, and (c) optimal treatment assignment rules. An evaluation of multiple programmes of the Swiss Active Labour Market…

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Debiased machine learning of global and local parameters using regularized Riesz representers

利用正则化 Riesz 表示元对全局与局部参数进行去偏机器学习

Summary We provide adaptive inference methods, based on $\ell _1$ regularization, for regular (semiparametric) and nonregular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of nonregular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a…

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Estimation and inference on treatment effects under treatment-based sampling designs

基于处理状态抽样设计下的处理效应估计与推断

Summary Causal inference in a programme evaluation setting faces the problem of external validity when the treatment effect in the target population is different from the treatment effect identified from the population of which the sample is representative. This paper focuses on a situation where such discrepancy arises by a stratified sampling design based on the individual treatment status and other characteristics. In such settings, the design probability is known from…

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Relative contagiousness of emerging virus variants: An analysis of the Alpha, Delta, and Omicron SARS-CoV-2 variants

新出现病毒变异株的相对传染性:Alpha、Delta与Omicron分析

Summary We propose a simple dynamic model for estimating the relative contagiousness of two virus variants. Maximum likelihood estimation and inference is conveniently invariant to variation in the total number of cases over the sample period and can be expressed as a logistic regression. We apply the model to Danish SARS-CoV-2 variant data. We estimate the reproduction numbers of Alpha and Delta to be larger than that of the ancestral variant by a factor of 1.51 [CI 95%:…

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The triple difference estimator

三重差分估计量

Summary Triple difference has become a widely used estimator in empirical work. A close reading of articles in top economics journals reveals that the use of the estimator to a large extent rests on intuition. The identifying assumptions are neither formally derived nor generally agreed on. We give a complete presentation of the triple difference estimator, and show that even though the estimator can be computed as the difference between two difference-in-differences…

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Algorithms for inference in SVARs identified with sign and zero restrictions

Summary I develop algorithms to facilitate Bayesian inference in structural vector autoregressions that are set-identified with sign and zero restrictions by showing that the system of restrictions is equivalent to a system of sign restrictions in a lower-dimensional space. Consequently, algorithms applicable under sign restrictions can be extended to allow for zero restrictions. Specifically, I extend algorithms proposed in Amir-Ahmadi and Drautzburg (2021) to check whether…

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Distribution regression in duration analysis: an application to unemployment spells

持续时间分析中的分布回归:失业持续期应用

Summary This article proposes inference procedures for distribution regression models in duration analysis using randomly right-censored data. This generalizes classical duration models by allowing situations where explanatory variables’ marginal effects freely vary with duration time. The article discusses applications to testing uniform restrictions on the varying coefficients, inferences on average marginal effects, and others involving conditional distribution estimates.…

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Causal mediation analysis with double machine learning

双重机器学习下的因果中介分析

Summary This paper combines causal mediation analysis with double machine learning for a data-driven control of observed confounders in a high-dimensional setting. The average indirect effect of a binary treatment and the unmediated direct effect are estimated based on efficient score functions, which are robust with respect to misspecifications of the outcome, mediator, and treatment models. This property is key for selecting these models by double machine learning, which…

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Misclassification-robust semiparametric estimation of single-index binary-choice models

对误分类稳健的单指标二元选择模型半参数估计

Summary In this paper, a new class of semiparametric estimators for single-index binary-choice models is introduced. The proposed estimators are based on the semiparametric indirect inference that identifies and estimates the parameters of the model via possibly misspecified auxiliary criteria. A large class of considered auxiliary criteria includes the ordinary least squares, nonlinear least squares, and nonlinear least absolute deviations estimators. Besides deriving the…

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Single step estimation of ARMA roots for nonfundamental nonstationary fractional models

非基本非平稳分数阶模型中 ARMA 根的单步估计

Summary We propose a single step estimator for the autoregressive and moving average roots (without imposing causality or invertibility restrictions) of a nonstationary Fractional ARMA process. These estimators employ an efficient tapering procedure, which allows for a long memory component in the process, but avoids estimating the nonstationarity component, which can be stochastic and/or deterministic. After selecting automatically the order of the model, we robustly…

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Permanent-Transitory decomposition of cointegrated time series via dynamic factor models, with an application to commodity prices

基于动态因子模型的协整时间序列永久—暂时分解:商品价格应用

Summary We propose a cointegration-based Permanent-Transitory decomposition for nonstationary dynamic factor models (DFMs). Our methodology exploits the cointegration relations among the observable variables and assumes they are driven by a common and an idiosyncratic component. The common component is further split into a long-term nonstationary and a short-term stationary part. A Monte Carlo experiment shows that incorporating the cointegration structure into the DFM leads…

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Nonparametric bounds on treatment effects with imperfect instruments

工具变量不完美时处理效应的非参数界限

Summary This paper extends the identification results in Nevo and Rosen (2012) to nonparametric models. We derive nonparametric bounds on the average treatment effect when an imperfect instrument is available. As in Nevo and Rosen (2012), we assume that the correlation between the imperfect instrument and the unobserved latent variables has the same sign as the correlation between the endogenous variable and the latent variables. We show that the monotone treatment selection…

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Two-stage instrumental variable estimation of linear panel data models with interactive effects

含交互效应的线性面板模型两阶段工具变量估计

Summary This paper analyses the instrumental variables (IV) approach put forward by Norkute et al. (2021), in the context of static linear panel data models with interactive effects present in the error term and the regressors. Instruments are obtained from transformed regressors, thereby it is not necessary to search for external instruments. We consider a two-stage IV (2SIV) and a mean-group IV (MGIV) estimator for homogeneous and heterogeneous slope models, respectively.…

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Testing conditional moment restriction models using empirical likelihood

利用经验似然检验条件矩限制模型

Summary An empirical likelihood test is proposed for parameters of models defined by conditional moment restrictions, such as models with nonlinear endogenous covariates, with and without heteroscedastic errors and non-separable transformation models. The number of empirical likelihood constraints is given by the size of the parameter, unlike alternative semi-parametric approaches. We show that the empirical likelihood ratio test is asymptotically pivotal, without explicit…

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Distributional robustness of K-class estimators and the PULSE

K类估计量与PULSE的分布稳健性

Summary While causal models are robust in that they are prediction optimal under arbitrarily strong interventions, they may not be optimal when the interventions are bounded. We prove that the classical K-class estimator satisfies such optimality by establishing a connection between K-class estimators and anchor regression. This connection further motivates a novel estimator in instrumental variable settings that minimizes the mean squared prediction error subject to the…

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Optimal minimax rates against nonsmooth alternatives

非光滑备择下的最优极小极大速率

Summary This study investigates optimal minimax rates for specification testing when the alternative hypothesis is built on a set of nonsmooth functions. The set consists of bounded functions that are not necessarily differentiable with no smoothness constraints imposed on their derivatives. In the instrumental variable regression set up with an unknown error variance structure, we find that the optimal minimax rate is $n^{-1/4}$, where n is the sample size. The rate is…

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Detecting common breaks in the means of high dimensional cross-dependent panels

高维截面相关面板均值共同断点的检测

Summary The problem of detecting change points in the mean of high dimensional panel data with potentially strong cross-sectional dependence is considered. Under the assumption that the cross-sectional dependence is captured by an unknown number of common factors, a new CUSUM-type statistic is proposed. We derive its asymptotic properties under three scenarios depending on to what extent the common factors are asymptotically dominant. With panel data consisting of N cross…

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Designed quadrature to approximate integrals in maximum simulated likelihood estimation

用设计求积近似最大模拟似然估计中的积分

Summary Maximum simulated likelihood estimation of mixed multinomial logit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as Halton sequences and modified Latin hypercube sampling are workhorse methods for integral approximation. Earlier studies explored the potential of sparse grid quadrature (SGQ), but SGQ suffers from negative weights. As an alternative to QMC and SGQ, we looked into the recently developed designed…

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The sooner the better: lives saved by the lockdown during the COVID-19 outbreak. The case of Italy

越早越好:意大利新冠疫情封锁挽救的生命

Summary This paper estimates the effects of non-pharmaceutical interventions – mainly, the lockdown – on the COVID-19 mortality rate for the case of Italy, the first Western country to impose a national shelter-in-place order. We use a new estimator, the augmented synthetic control method (ASCM), that overcomes some limits of the standard synthetic control method (SCM). The results are twofold. From a methodological point of view, the ASCM outperforms the SCM in that the…

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R-estimators in GARCH models: asymptotics and applications

GARCH模型中的R估计量:渐近理论与应用

Summary The quasi-maximum likelihood estimation is a commonly-used method for estimating the generalized autoregressive conditional heteroscedastic parameters. However, such estimators are sensitive to outliers and their asymptotic normality is proved under the finite fourth moment assumption on the underlying error distribution. In this paper, we propose a novel class of estimators of the generalized autoregressive conditional heteroscedastic parameters based on ranks of…

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