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The Conventional Impulse Response Prior in VAR Models With Sign Restrictions

符号约束 VAR 模型中的常规冲击响应先验

ABSTRACT Some studies have expressed concern that the Gaussian‐inverse Wishart–Haar prior typically employed in estimating sign‐identified VAR models may be unintentionally informative about the prior for the structural responses. We discuss what features to look for in this prior in the absence of specific prior information about the responses, building on the notion of weakly informative priors in Gelman et al. (2013), and in the presence of such information. Empirical…

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Inference for local projections

局部投影的统计推断

Summary Inference for impulse responses estimated with local projections presents interesting challenges and opportunities. Analysts typically want to assess the precision of individual estimates, explore the dynamic evolution of the response over particular regions, and generally determine whether the impulse generates a response that is any different from the null of no effect. Each of these goals requires a different approach to inference. In this article, we provide an…

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Local projections in unstable environments

不稳定环境中的局部投影

This paper develops a local projection estimator for estimating impulse responses in the presence of time variation. Importantly, we allow local instabilities in both slope coefficients and variances. Monte Carlo simulations illustrate that the method performs well in practice. Using our proposed estimator, we shed new light on the effects of fiscal policy shocks and the size of government spending multipliers. Our analysis uncovers the existence of instabilities that were…

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Joint Bayesian inference about impulse responses in VAR models

VAR 模型中脉冲响应的联合贝叶斯推断

We derive the Bayes estimator of vectors of structural VAR impulse responses under a range of alternative loss functions. We also discuss the construction of joint credible regions for vectors of impulse responses as the lowest posterior risk region under the same loss functions. We show that conventional impulse response estimators such as the posterior median response function or the posterior mean response function are not in general the Bayes estimator of the impulse…

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INSTRUMENTAL VARIABLE ESTIMATION OF STRUCTURAL VAR MODELS ROBUST TO POSSIBLE NONSTATIONARITY

对潜在非平稳性稳健的结构 VAR 工具变量估计

This paper considers the estimation of dynamic causal effects using a proxy structural vector-autoregressive model with possibly nonstationary regressors. We provide general conditions under which the asymptotic normal approximation remains valid. In this case, the asymptotic variance depends on the persistence property of each series. We further provide a consistent asymptotic covariance matrix estimator that requires neither knowledge of the presistence properties of the…

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Confidence Intervals for Bias and Size Distortion in IV and Local Projections-IV Models

工具变量与局部投影工具变量模型中偏误和检验尺寸扭曲的置信区间

In this article, we propose methods to construct confidence intervals for the bias of the two-stage least squares estimator, and the size distortion of the associated Wald test in instrumental variables models with heteroscedasticity and serial correlation. Importantly our framework covers the local projections—instrumental variable model as well. Unlike tests for weak instruments, whose distributions are nonstandard and depend on nuisance parameters that cannot be…

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A new approach to measuring economic policy shocks, with an application to conventional and unconventional monetary policy

经济政策冲击的新度量:常规与非常规货币政策应用

We propose a new approach to analyze economic shocks. Our new procedure identifies economic shocks as exogenous shifts in a function; hence, we call them “ functional shocks. ” We show how to identify such shocks and how to trace their effects in the economy via VARs using “ VARs with functional shocks ” and “ functional local projections. ” Using our new procedure, we address the crucial question of studying the effects of monetary policy by identifying monetary policy…

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The uniform validity of impulse response inference in autoregressions

自回归模型中脉冲响应推断的一致有效性

Existing proofs of the asymptotic validity of conventional methods of impulse response inference based on higher-order autoregressions are pointwise only. In this paper, we establish the uniform asymptotic validity of conventional asymptotic and bootstrap inference about individual impulse responses and vectors of impulse responses when the horizon is fixed with respect to the sample size. For inference about vectors of impulse responses based on Wald test statistics to be…

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Quasi-Bayesian model selection

准贝叶斯模型选择

In this paper, we establish the consistency of the model selection criterion based on the quasi‐marginal likelihood (QML) obtained from Laplace‐type estimators. We consider cases in which parameters are strongly identified, weakly identified and partially identified. Our Monte Carlo results confirm our consistency results. Our proposed procedure is applied to select among New Keynesian macroeconomic models using US data.

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Rolling window selection for out-of-sample forecasting with time-varying parameters

时变参数样本外预测的滚动窗口选择

There is strong evidence of structural changes in macroeconomic time series, and the forecasting performance is often sensitive to the choice of estimation window size. This paper develops a method for selecting the window size for forecasting. Our proposed method is to choose the optimal size that minimizes the forecaster’s quadratic loss function, and we prove the asymptotic validity of our approach. Our Monte Carlo experiments show that our method performs well under…

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Impulse response matching estimators for DSGE models

DSGE 模型的脉冲响应匹配估计

The existing asymptotic theory for VAR-based impulse response matching estimators of the structural parameters of DSGE models does not cover situations in which the number of impulse responses exceeds the number of VAR model parameters. We establish the consistency of the estimator in this situation, we derive its asymptotic distribution, and we show how this distribution can be approximated by bootstrap methods. We also demonstrate that under our assumptions special care is…

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Joint confidence sets for structural impulse responses

结构脉冲响应的联合置信集

Many questions of economic interest in structural VAR analysis involve estimates of multiple impulse response functions. Other questions relate to the shape of a given impulse response function. Answering these questions requires joint inference about sets of structural impulse responses, allowing for dependencies across time as well as across response functions. Such joint inference is complicated by the fact that the joint distribution of the structural impulse response…

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TESTS FOR PARAMETER INSTABILITY IN DYNAMIC FACTOR MODELS

动态因子模型中的参数不稳定性检验

In this paper, we develop tests for structural breaks of factor loadings in dynamic factor models. We focus on the joint null hypothesis that all factor loadings are constant over time. Because the number of factor loading parameters goes to infinity as the sample size grows, conventional tests cannot be used. Based on the fact that the presence of a structural change in factor loadings yields a structural change in second moments of factors obtained from the full sample…

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Inference on impulse response functions in structural VAR models

结构 VAR 模型中脉冲响应函数的推断

Skepticism toward traditional identifying assumptions based on exclusion restrictions has led to a surge in the use of structural VAR models in which structural shocks are identified by restricting the sign of the responses of selected macroeconomic aggregates to these shocks. Researchers commonly report the vector of pointwise posterior medians of the impulse responses as a measure of central tendency of the estimated response functions, along with pointwise 68% posterior…

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Frequentist inference in weakly identified dynamic stochastic general equilibrium models

弱识别动态随机一般均衡模型的频率学派推断

A common problem in estimating dynamic stochastic general equilibrium models is that the structural parameters of economic interest are only weakly identified. As a result, classical confidence sets and Bayesian credible sets will not coincide even asymptotically, and the mean, mode, or median of the posterior distribution of the structural parameters can no longer be viewed as a consistent estimator. We propose two methods of constructing confidence intervals for structural…

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Information criteria for impulse response function matching estimation of DSGE models

DSGE模型脉冲响应匹配估计的信息准则

We propose new information criteria for impulse response function matching estimators (IRFMEs). These estimators yield sampling distributions of the structural parameters of dynamic stochastic general equilibrium (DSGE) models by minimizing the distance between sample and theoretical impulse responses. First, we propose an information criterion to select only the responses that produce consistent estimates of the true but unknown structural parameters: the Valid Impulse…

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Out-of-Sample Forecast Tests Robust to the Choice of Window Size

对估计窗口大小选择稳健的样本外预测检验

This article proposes new methodologies for evaluating economic models’ out-of-sample forecasting performance that are robust to the choice of the estimation window size. The methodologies involve evaluating the predictive ability of forecasting models over a wide range of window sizes. The study shows that the tests proposed in the literature may lack the power to detect predictive ability and might be subject to data snooping across different window sizes if used…

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Testing for weak identification in possibly nonlinear models

可能非线性模型中的弱识别检验

In this paper we propose a chi-square test for identification. Our proposed test statistic is based on the distance between two shrinkage extremum estimators. The two estimators converge in probability to the same limit when identification is strong, and their asymptotic distributions are different when identification is weak. The proposed test is consistent not only for the alternative hypothesis of no identification but also for the alternative of weak identification,…

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Two-Sample Instrumental Variables Estimators

两样本工具变量估计量

Following an influential article by Angrist and Krueger (1992) on two-sample instrumental variables (TSIV) estimation, numerous empirical researchers have applied a computationally convenient two-sample two-stage least squares (TS2SLS) variant of Angrist and Krueger's estimator. In the two-sample context, unlike the single-sample situation, the IV and 2SLS estimators are numerically distinct. We derive and compare the asymptotic distributions of the two estimators and find…

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How Useful Is Bagging in Forecasting Economic Time Series? A Case Study of U.S. Consumer Price Inflation

装袋法对经济时间序列预测有多大帮助?美国消费价格通胀案例

This article focuses on the widely studied question of whether the inclusion of indicators of real economic activity lowers the prediction mean squared error of forecasting models of U.S. consumer price inflation. We propose three variants of the bagging algorithm specifically designed for this type of forecasting problem and evaluate their empirical performance. Although bagging predictors in our application are clearly more accurate than equally weighted forecasts, median…

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Information in generalized method of moments estimation and entropy-based moment selection

广义矩估计中的信息与基于熵的矩条件选择

In this paper, we make five contributions to the literature on information and entropy in generalized method of moments (GMM) estimation. First, we introduce the concept of the long run canonical correlations (LRCCs) between the true score vector and the moment function f (vt, θ0) and show that they provide a metric for the information contained in the population moment condition E [f (vt, θ0)] = 0. Second, we show that the entropy of the limiting distribution of the GMM…

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A PORTMANTEAU TEST FOR SERIALLY CORRELATED ERRORS IN FIXED EFFECTS MODELS

固定效应模型误差序列相关的 Portmanteau 检验

We propose a portmanteau test for serial correlation of the error term in a fixed effects model. The test is derived as a Lagrange multiplier test, but it also has a straightforward Wald test interpretation. In Monte Carlo experiments, the test displays good size and power properties.The authors thank the co-editor, the referee, David Drukker, Christian Hansen, and Jeffrey Wooldridge for their helpful comments.

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