Long-Run Identification in a Fractionally Integrated System

We propose an extension of structural fractionally integrated vector autoregressive models that avoids certain undesirable effects on the impulse responses that occur if long-run identification restrictions are imposed. We derive the model’s Granger representation and investigate the effects of long-run restrictions. Simulations illustrate that enforcing integer integration orders can have severe consequences for impulse responses. In a system of U.S. real output and aggregate prices, the effects of structural shocks strongly depend on the specification of the integration orders. In the statistically preferred fractional model, shocks that are typically interpreted as demand disturbances have a very brief influence on GDP. Supplementary materials for this article are available online.     

Estimation of structural impulse responses: short-run versus long-run identifying restrictions

There is evidence that estimates of long-run impulse responses of structural vector autoregressive (VAR) models based on long-run identifying restrictions may not be very accurate. This finding suggests that using short-run identifying restrictions may be preferable. We compare structural VAR impulse response estimates based on long-run and short-run identifying restrictions and find that long-run identifying restrictions can result in much more precise estimates for the structural impulse responses than restrictions on the impact effects of the shocks.     

Some Observations,a Suggestion,and Some Comments on the Conway-Roberts Article

This article provides new tools for the evaluation of dynamic stochastic general equilibrium (DSGE) models and applies them to a large-scale new Keynesian model. We approximate the DSGE model by a vector autoregression, and then systematically relax the implied cross-equation restrictions and document how the model fit changes. We also compare the DSGE model's impulse responses to structural shocks with those obtained after relaxing its restrictions. We find that the degree of misspecification in this large-scale DSGE model is no longer so large as to prevent its use in day-to-day policy analysis, yet is not small enough to be ignored.     

Structural vector autoregressive analysis for cointegrated variables

Summary Vector autoregressive (VAR) models are capable of capturing the dynamic structure of many time series variables. Impulse response functions are typically used to investigate the relationships between the variables included in such models. In this context the relevant impulses or innovations or shocks to be traced out in an impulse response analysis have to be specified by imposing appropriate identifying restrictions. Taking into account the cointegration structure of the variables offers interesting possibilities for imposing identifying restrictions. Therefore VAR models which explicitly take into account the cointegration structure of the variables, so-called vector error correction models, are considered. Specification, estimation and validation of reduced form vector error correction models is briefly outlined and imposing structural short- and long-run restrictions within these models is discussed. I thank an anonymous reader for comments on an earlier draft of this paper that helped me to improve the exposition.     

Reducing confidence bands for simulated impulse responses

It is emphasized that the shocks in structural vector autoregressions are only identified up to sign and it is pointed out that this feature can result in very misleading confidence intervals for impulse responses if simulation methods such as Bayesian or bootstrap methods are used. The confidence intervals heavily depend on which variable is used for fixing the signs of the responses. In particular, when the shocks are identified via long-run restrictions the problem can be severe. It is pointed out that a suitable choice of variable for fixing the signs of the responses and, hence, of the shocks, can result in substantial reductions in the confidence bands for impulse responses.     

Macroeconomic Factors Strike Back: A Bayesian Change-Point Model of Time-Varying Risk Exposures and Premia in the U.S. Cross-Section

This article proposes a Bayesian estimation framework for a typical multi-factor model with time-varying risk exposures to macroeconomic risk factors and corresponding premia to price U.S. publicly traded assets. The model assumes that risk exposures and idiosyncratic volatility follow a break-point latent process, allowing for changes at any point on time but not restricting them to change at all points. The empirical application to 40 years of U.S. data and 23 portfolios shows that the approach yields sensible results compared to previous two-step methods based on naive recursive estimation schemes, as well as a set of alternative model restrictions. A variance decomposition test shows that although most of the predictable variation comes from the market risk premium, a number of additional macroeconomic risks, including real output and inflation shocks, are significantly priced in the cross-section. A Bayes factor analysis massively favors the proposed change-point model. Supplementary materials for this article are available online.     

外部冲击、需求管理与经济增长——基于中国数据的实证研究

通过建立外部冲击指数,研究外部冲击对中国宏观经济的影响。结果发现,外部冲击比国内政策能更好地解释中国宏观经济波动,且具有较强持续性;外部冲击对中国经济增长的影响主要表现在滞后1期和2期。当中国经济受到外部冲击时,采取货币政策和财政政策刺激需求,对于稳定宏观经济可以起到显著效果。     

Consumer Search Behavior in the Changing Credit Card Market

Many recent articles have identified behavioral disturbances in vector autoregressions by imposing restrictions on the long-run effects of shocks. This article demonstrates that this approach will be unreliable unless the underlying economy satisfies three types of strong restrictions. Although many aspects of these issues have been raised before, this article draws out and illustrates the implications for inferences under the long-run scheme. Furthermore, it provides strategies for dealing with the problems.     

货币国际化对国内宏观经济的影响

 本文利用新开放经济宏观经济学方法,构建了货币国际化对宏观经济影响的理论模型,从理论上分析了货币国际化对宏观经济短期和长期的影响。理论研究表明,货币国际化具有以下影响：（1）无论在短期还是长期,都将促使本国货币升值,但汇率未出现超调现象;（2）短期内刺激本国消费,长期内抑制本国消费;（3）短期内产出减少,长期内产出增加;（4）短期内改善贸易条件,长期内使贸易条件恶化;（5）无论短期还是长期,都将改善本国居民福利水平。在此基础上,基于结构VAR模型,利用美元经验数据实证分析了美元国际化对美国宏观经济的影响,实证结果表明：经验分析与理论研究结果高度一致。上述研究结论为人民币国际化提供了若干启示。     

Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes

This paper develops test procedures for testing the validity of general linear identifying restrictions imposed on cointegrating vectors in the context of a vector autoregressive model. In addition to overidentifying restrictions the considered restrictions may also involve normalizing restrictions. Tests for both types of restrictions are developed and their asymptotic properties are obtained. Under the null hypothesis tests for normalizing restrictions have an asymptotic "multivariate unit root distribution", similar to that obtained for the likelihood ratio test for cointegration, while tests for overidentifying restrictions have a standard chi-square limiting distribution. Since these two types of tests are asymptotically independent they are easy to cotnbine to an overall test for the spccifed identifying restrictions. An overall test of this kind can consistently reveal the failure of the identifying restrictions in a wider class of cases than previous tests which only test for overidentifying restrictions.     

Inference on Filtered and Smoothed Probabilities in Markov-Switching Autoregressive Models

ABSTRACT

We derive a statistical theory that provides useful asymptotic approximations to the distributions of the single inferences of filtered and smoothed probabilities, derived from time series characterized by Markov-switching dynamics. We show that the uncertainty in these probabilities diminishes when the states are separated, the variance of the shocks is low, and the time series or the regimes are persistent. As empirical illustrations of our approach, we analyze the U.S. GDP growth rates and the U.S. real interest rates. For both models, we illustrate the usefulness of the confidence intervals when identifying the business cycle phases and the interest rate regimes.     

State space modeling of multiple time series

Time series methods offer the possibility of making accurate forecasts even when the underlying structural model is unknown, by replacing the structural restrictions needed to reduce sampling error and improve forecasts with restrictions determined from the data. While there has been considerable success with relatively simple univariate time series modeling procedures, the complex interrela- tionships possible with multiple series requite more powerful techniques.Based on the insights of linear systems theory, a multivariate state space methos for both stationary and nonstationary problems is described and related to ARMA models. The states or dynamic factors of the procedure are chosen to be robust in the presence of model misspecification, in constrast to ARMA models which lack this property. In addition, by treating th emidel choice as a formal approximation problem certain new optimal properties of the procedure with respect to specification are established; in particular, it is shown that no other model of equal or smaller order fits the observed autocovariance sequence any better in the sense of a Hankel norm. Finally, in the treatment of nonstationary series, a natural decomposition into long run and short run dynamics results in easily implemented two step procedures that use characteristics of the data to identify and model trend and cycle components that correspond to cointegration and error correction models. Applications include annualo U.S. GNP and money stock growth rates, monthly California beef prices and inventories, and monthly stock prices for large retailers.     

国际油价冲击对中国宏观经济的影响

 长期以来,伴随油价冲击的往往是国际经济和社会的剧烈动荡,这使得油价冲击对宏观经济的影响成为日益重要的研究课题。本文首次运用结构向量自回归（SVAR）模型,研究了国际油价波动对我国宏观经济所产生的动态冲击效应。实证研究发现：国际油价上涨确实对产出有逆向影响,但冲击后的产出变化在回归到零值后会越过零值继续上升;国际油价上涨对CPI有正向影响,但影响不显著,且CPI并不会在当期就对油价冲击做出响应,而是有一个相当的滞后期,然后在达到一个高点之后慢慢下降,逐渐回归到0值,但在达到0值后还会继续向下;国际油价上涨对一年期存款利率基本没有影响。针对造成这种实证结果的原因,本文最后给出了相应的解释和政策建议。     

Adaptive Shrinkage in Bayesian Vector Autoregressive Models

Vector autoregressive (VAR) models are frequently used for forecasting and impulse response analysis. For both applications, shrinkage priors can help improving inference. In this article, we apply the Normal-Gamma shrinkage prior to the VAR with stochastic volatility case and derive its relevant conditional posterior distributions. This framework imposes a set of normally distributed priors on the autoregressive coefficients and the covariance parameters of the VAR along with Gamma priors on a set of local and global prior scaling parameters. In a second step, we modify this prior setup by introducing another layer of shrinkage with scaling parameters that push certain regions of the parameter space to zero. Two simulation exercises show that the proposed framework yields more precise estimates of model parameters and impulse response functions. In addition, a forecasting exercise applied to U.S. data shows that this prior performs well relative to other commonly used specifications in terms of point and density predictions. Finally, performing structural inference suggests that responses to monetary policy shocks appear to be reasonable.     

The Neutrality Properties of Competing Relative Price Models: Tests Using Linear Feedback

This article uses a variant of Geweke's (1982) linear feedback measure to test common characterizations of monetary neutrality implicit in classes of relative price models. The neutrality properties are defined in terms of relative price changes' response to monetary policy shocks in a system including average price changes, an interest rate, and industrial production growth. The magnitude and patterns of monetary feedback found in U.S. relative price data provide no support for any of the structurally neutral models.     

The Changing Transmission of Uncertainty Shocks in the U.S.

This article investigates if the impact of uncertainty shocks on the U.S. economy has changed over time. To this end, we develop an extended factor augmented vector autoregression (VAR) model that simultaneously allows the estimation of a measure of uncertainty and its time-varying impact on a range of variables. We find that the impact of uncertainty shocks on real activity and financial variables has declined systematically over time. In contrast, the response of inflation and the short-term interest rate to this shock has remained fairly stable. Simulations from a nonlinear dynamic stochastic general equilibrium (DSGE) model suggest that these empirical results are consistent with an increase in the monetary authorities’ antiinflation stance and a “flattening” of the Phillips curve. Supplementary materials for this article are available online.     

Dynamic Asymmetries in U.S. Unemployment

We examine dynamic asymmetries in U.S. unemployment using nonlinear time series models and Bayesian methods. We find strong statistical evidence in favor of a two-regime threshold auto-regressive model. Empirical results indicate that, once we take into account both parameter and model uncertainty, there are economically interesting asymmetries in the unemployment rate. One finding of particular interest is that shocks that lower the unemployment rate tend to have a smaller effect than shocks that raise the unemployment rate. This finding is consistent with unemployment rises being sudden and falls gradual.     

SVARMA模型的设定、方差分解分析和应用

本文首先研究了传统凯恩斯主义IS-LM-PC模型的SVARMA模型表示,为宏观经济计量分析建立SVARMA模型提供了模型设定依据;其次,建立了VARMA/SVARMA模型方差分解分析方法;另外,基于SVARMA模型对中国宏观经济政策的动态效应进行了实证分析,实证分析发现（1）SVARMA模型与SVAR模型的分析结果存在重要的区别;（2）在政策实施6-7期前后,财政政策和货币政策对抑制通货膨胀的效果发生逆转;（3）宏观经济的价格水平存在粘性;（4）货币供给冲击对通货膨胀率的变化具有滞后的正向影响,对实际产出的影响不明显等。     

Stochastic Model Specification Search for Time-Varying Parameter VARs

This article develops a new econometric methodology for performing stochastic model specification search (SMSS) in the vast model space of time-varying parameter vector autoregressions (VARs) with stochastic volatility and correlated state transitions. This is motivated by the concern of overfitting and the typically imprecise inference in these highly parameterized models. For each VAR coefficient, this new method automatically decides whether it is constant or time-varying. Moreover, it can be used to shrink an otherwise unrestricted time-varying parameter VAR to a stationary VAR, thus providing an easy way to (probabilistically) impose stationarity in time-varying parameter models. We demonstrate the effectiveness of the approach with a topical application, where we investigate the dynamic effects of structural shocks in government spending on U.S. taxes and gross domestic product (GDP) during a period of very low interest rates.     

Forecasting With Nonspurious Factors in U.S. Macroeconomic Time Series

This study examines the practical implications of the fact that structural changes in factor loadings can produce spurious factors (or irrelevant factors) in forecasting exercises. These spurious factors can induce an overfitting problem in factor-augmented forecasting models. To address this concern, we propose a method to estimate nonspurious factors by identifying the set of response variables that have no structural changes in their factor loadings. Our theoretical results show that the obtained set may include a fraction of unstable response variables. However, the fraction is so small that the original factors are able to be identified and estimated consistently. Moreover, using this approach, we find that a significant portion of 132 U.S. macroeconomic time series have structural changes in their factor loadings. Although traditional principal components provide eight or more factors, there are significantly fewer nonspurious factors. The forecasts using the nonspurious factors can significantly improve out-of-sample performance.