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Asymptotics of Cointegration Tests for High-Dimensional Var(k)

高维 VAR(k) 协整检验的渐近理论

Abstract The paper studies nonstationary high-dimensional vector autoregressions of order k, VAR(k). Additional deterministic terms such as trend or seasonality are allowed. The number of time periods, T, and the number of coordinates, N, are assumed to be large and of the same order. Under this regime the first-order asymptotics of the Johansen likelihood ratio (LR), Pillai-Bartlett, and Hotelling-Lawley tests for cointegration are derived: The test statistics converge to…

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Weak Identification in Low-Dimensional Factor Models with One or Two Factors

单因子或双因子低维因子模型中的弱识别

Abstract This paper describes how to reparametrize low-dimensional factor models with one or two factors to fit weak identification theory developed for generalized method of moments models. Some identification-robust tests, here called “plug-in” tests, require a reparametrization to distinguish weakly identified parameters from strongly identified parameters. The reparametrizations in this paper make plug-in tests available for subvector hypotheses in low-dimensional factor…

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Bayesian Local Projections

贝叶斯局部投影

Abstract We propose a Bayesian approach to Local Projections (LPs) that optimally addresses the empirical bias-variance trade-off intrinsic in the choice between direct and iterative methods. Bayesian Local Projections (BLPs) regularize LP regressions via informative priors and estimate impulse response functions that capture the properties of the data more accurately than iterative VARs. BLPs preserve the flexibility of LPs while retaining a degree of estimation uncertainty…

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Nonparametric Time Varying IV-SVARs: Estimation and Inference

非参数时变工具变量结构 VAR:估计与推断

Abstract This paper studies the estimation and inference of time-varying impulse response functions in structural vector autoregressions (SVARs) identified with external instruments. Building on kernel estimators that allow for nonparametric time variation, we derive the asymptotic distributions of the relevant quantities. Our estimators are simple and computationally trivial and allow for potentially weak instruments. Simulations suggest satisfactory empirical coverage even…

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ℓ 2 -Relaxation: With Applications to Forecast Combination and Portfolio Analysis

ℓ2 松弛:预测组合与投资组合分析的应用

Abstract We propose ℓ2-relaxation, which is a novel convex optimization problem, to tackle a forecast combination with many forecasts or a minimum variance portfolio with many assets. ℓ2-relaxation minimizes the squared Euclidean norm of the weight vector subject to a set of relaxed linear inequalities to balance the bias and variance. It delivers optimality with approximately equal within-group weights when latent block equicorrelation patterns dominate the high-dimensional…

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Random Subspace Local Projections

随机子空间局部投影

Abstract We show how random subspace methods can be adapted to estimating local projections with many controls. Random subspace methods have their roots in the machine learning literature and are implemented by averaging over regressions estimated over different combinations of subsets of these controls. We document three key results: (i) Our approach can successfully recover the impulse response functions across Monte Carlo experiments representative of different…

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Sparse Trend Estimation

稀疏趋势估计

Abstract The low-frequency movements of economic variables play a prominent role in policy analysis and decision-making. We develop a robust estimation approach for these slow-moving trend processes which is guided by a judicious choice of priors and is characterized by sparsity. We present novel stylized facts from longer-run survey expectations that inform the structure of the estimation procedure. The general version of the proposed Bayesian estimator with a…

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Measuring the Output Gap using Large Datasets

利用大型数据集测量产出缺口

Abstract We propose a new measure of the output gap based on a dynamic factor model that is estimated on a large number of U.S. macroeconomic indicators and which incorporates relevant stylized facts about macroeconomic data (comovements, nonstationarity, and the slow drift in long-run output growth over time). We find that (1) from the mid-1990s to 2008, the U.S. economy operated above its potential and (2) in 2018:Q4, the labor market was tighter than the market for goods…

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Employment Protection Deregulation and Labor Shares in Advanced Economies

发达经济体就业保护放松与劳动份额

Abstract This paper assesses the impact of job protection deregulation on the labor share in a sample of 26 advanced economies during the 1970–2013 period, using a newly constructed dataset of major reforms in this area. We employ a difference-in-differences identification strategy using two identifying assumptions grounded in theory—deregulation has larger effects in industries characterized by (i) a higher “natural” propensity to regularly adjust the workforce and (ii) a…

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Robust Inference in Models Identified via Heteroskedasticity

通过异方差识别的模型中的稳健推断

Abstract Identification via heteroskedasticity exploits variance changes between regimes to identify parameters in simultaneous equations. Weak identification occurs when shock variances change very little or multiple variances change close to proportionally, making standard inference unreliable. I propose an F-test for weak identification in a common simple version of the model. More generally, I establish conditions for validity of nonconservative robust inference on…

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The Time-Varying Effect of Monetary Policy on Asset Prices

货币政策对资产价格的时变影响

This paper studies how monetary policy jointly affects asset prices and the real economy in the United States. I develop an estimator that uses high-frequency surprises as a proxy for the structural monetary policy shocks. This is achieved by integrating the surprises into a vector autoregressive model as an exogenous variable. I use current short-term rate surprises because these are least affected by an information effect. When allowing for time-varying model parameters, I…

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Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors

多期限预测误差的时变不确定性建模

We estimate uncertainty measures for point forecasts obtained from survey data, pooling information embedded in observed forecast errors for different forecast horizons. To track time-varying uncertainty in the associated forecast errors, we derive a multiple-horizon specification of stochastic volatility. We apply our method to forecasts for various macroeconomic variables from the Survey of Professional Forecasters. Compared to simple variance approaches, our stochastic…

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Impulse Response Estimation by Smooth Local Projections

通过平滑局部投影估计脉冲响应

Local projections (LP) is a popular methodology for the estimation of impulse responses (IR). Compared to the traditional VAR approach, LP allow for more flexible IR estimation by imposing weaker assumptions on the dynamics of the data. The nonparametric nature of LP comes at an efficiency cost, and in practice, the LP estimator may suffer from excessive variability. In this work, we propose an IR estimation methodology based on B-spline smoothing called smooth local…

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Robots at Work

工作中的机器人

We analyze for the first time the economic contributions of modern industrial robots, which are flexible, versatile, and autonomous machines. We use novel panel data on robot adoption within industries in seventeen countries from 1993 to 2007 and new instrumental variables that rely on robots’ comparative advantage in specific tasks. Our findings suggest that increased robot use contributed approximately 0.36 percentage points to annual labor productivity growth, while at…

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Prediction Using Several Macroeconomic Models

利用多个宏观经济模型进行预测

We establish methods that improve the predictions of macroeconometric models—dynamic factor models, dynamic stochastic general equilibrium models, and vector autoregressions—using a quarterly U.S. data set. We measure prediction quality with one-step-ahead probability densities assigned in real time. Two steps lead to substantial improvements: (a) the use of full Bayesian predictive distributions rather than conditioning on the posterior mode for parameters and (b) the use…

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Empirical Bayes Methods for Dynamic Factor Models

动态因子模型的经验贝叶斯方法

We consider the dynamic factor model where the loading matrix, the dynamic factors, and the disturbances are treated as latent stochastic processes. We present empirical Bayes methods that enable the shrinkagebased estimation of the loadings and factors. We investigate the methods in a large Monte Carlo study where we evaluate the finite sample properties of the empirical Bayes methods for quadratic loss functions. Finally, we present and discuss the results of an empirical…

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Is There a Debt-Threshold Effect on Output Growth?

公共债务对产出增长存在门槛效应吗?

This paper studies the relationship between public debt expansion and economic growth and investigates whether the debt-growth relation varies with the level of indebtedness. We contribute theoretically by developing tests for threshold effects in the context of dynamic heterogeneous panel data models with cross-sectionally dependent errors. In the empirical application, using data on a sample of forty countries over the 1965–2010 period, we find no evidence for a…

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Maximum Likelihood Estimation and Inference for Approximate Factor Models of High Dimension

高维近似因子模型的最大似然估计与推断

An approximate factor model of high dimension has two key features. First, the idiosyncratic errors are correlated and heteroskedastic over both the cross-section and time dimensions; the correlations and heteroskedasticities are of unknown forms. Second, the number of variables is comparable or even greater than the sample size. Thus, a large number of parameters exist under a high-dimensional approximate factor model. Most widely used approaches to estimation are principal…

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Competition Policy and Productivity Growth: An Empirical Assessment

竞争政策与生产率增长:一项实证评估

Abstract This paper estimates the impact of competition policy on total factor productivity growth for 22 industries in twelve OECD countries over 1995 to 2005. We find a positive and significant effect of competition policy as measured by created indexes. We provide results based on instrumental variables estimators and heterogeneous effects to support the causal nature of the established link. The effect is particularly strong for specific aspects of competition policy…

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Determinants of Economic Growth: A Bayesian Panel Data Approach

经济增长的决定因素:贝叶斯面板数据方法

Model uncertainty hampers consensus on the key determinants of economic growth. Some recent cross-country cross-sectional analyses have employed Bayesian model averaging to tackle the issue of model uncertainty. This paper extends that approach to panel data models with country-specific fixed effects in order to simultaneously address model uncertainty and endogeneity issues. The empirical findings suggest that in a panel setting, the most robust growth determinants are the…

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Distributional Tests in Multivariate Dynamic Models with Normal and Student- t Innovations

具有正态与Student-t新息的多元动态模型分布检验

We derive Lagrange multiplier and likelihood ratio specification tests for the null hypotheses of multivariate normal and Student-t innovations using the generalized hyperbolic distribution as our alternative hypothesis. We decompose the corresponding Lagrange multiplier-type tests into skewness and kurtosis components. We also obtain more powerful one-sided Kuhn-Tucker versions that are equivalent to the likelihood ratio test, whose asymptotic distribution we provide.…

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How Reliable Are Local Projection Estimators of Impulse Responses?

局部投影脉冲响应估计量有多可靠?

We compare the finite-sample performance of impulse response confidence intervals based on local projections (LPs) and vector autoregressive (VAR) models in linear stationary settings. We find that in small samples, the asymptotic LP interval often is less accurate than the bias-adjusted bootstrap VAR interval, notwithstanding its excessive average length. Although the asymptotic LP interval has adequate coverage in sufficiently large samples, its average length still far…

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Causal Effects of Monetary Shocks: Semiparametric Conditional Independence Tests with a Multinomial Propensity Score

货币冲击的因果效应:基于多项倾向得分的半参数条件独立检验

We develop semiparametric tests for conditional independence in time series models of causal effects. Our approach is motivated by empirical studies of monetary policy effects and is semiparametric in the sense that we model the process determining the distribution of treatment—the policy propensity score—but leave the model for outcomes unspecified. A conceptual innovation is that we adapt the cross-sectional potential outcomes framework to a time series setting. We also…

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Determining the Number of Factors from Empirical Distribution of Eigenvalues

利用特征值经验分布确定因子数

We develop a new estimator of the number of factors in the approximate factor models. The estimator works well even when the idiosyncratic terms are substantially correlated. It is based on the fact, established in the paper, that any finite number of the largest "idiosyncratic" eigenvalues of the sample covariance matrix cluster around a single point. In contrast, all the "systematic" eigenvalues, the number of which equals the number of factors, diverge to infinity. The…

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