Generalized Forecast Error Variance Decomposition for Linear and Nonlinear Multivariate Models

We propose a new generalized forecast error variance decomposition with the attractive property that the proportions of the impact accounted for by innovations in each variable sum to unity. Our decomposition is based on the generalized impulse response function, and it can easily be obtained by simulation. The new decomposition is illustrated in an empirical application to US output growth and interest rate spread data.     

BAYESIAN MODEL SELECTION AND FORECASTING IN NONCAUSAL AUTOREGRESSIVE MODELS

In this paper, we propose a Bayesian estimation and forecasting procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, yielding predictive densities as a by‐product. We show that the posterior model probabilities provide a convenient model selection criterion in discriminating between alternative causal and noncausal specifications. As an empirical application, we consider US inflation. The posterior probability of noncausality is found to be high—over 98%. Furthermore, the purely noncausal specifications yield more accurate inflation forecasts than alternative causal and noncausal AR models. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling Conditional Skewness in Stock Returns

Abstract

In this paper, we propose a new GARCH-in-Mean (GARCH-M) model allowing for conditional skewness. The model is based on the so-called z distribution capable of modeling skewness and kurtosis of the size typically encountered in stock return series. The need to allow for skewness can also be readily tested. The model is consistent with the volatility feedback effect in that conditional skewness is dependent on conditional variance. Compared to previously presented GARCH models allowing for conditional skewness, the model is analytically tractable, parsimonious and facilitates straightforward interpretation.Our empirical results indicate the presence of conditional skewness in the monthly postwar US stock returns. Small positive news is also found to have a smaller impact on conditional variance than no news at all. Moreover, the symmetric GARCH-M model not allowing for conditional skewness is found to systematically overpredict conditional variance and average excess returns.     

Does Output Gap,Labour's Share or Unemployment Rate Drive Inflation?

We propose a new methodology for ranking in probability the commonly proposed drivers of inflation in the new Keynesian model. The approach is based on Bayesian model selection among restricted vector autoregressive (VAR) models, each of which embodies only one or none of the candidate variables as the driver. Simulation experiments suggest that our procedure is superior to the previously used conventional pairwise Granger causality tests in detecting the true driver. Empirical results lend little support to labour share, output gap or unemployment rate as the driver of US inflation.     

GMM Estimation with Non‐causal Instruments*

This note provides a warning against careless use of the generalized method of moments (GMM) with time series data. We show that if time series follow non‐causal autoregressive processes, their lags are not valid instruments, and the GMM estimator is inconsistent. Moreover, endogeneity of the instruments may not be revealed by the J‐test of overidentifying restrictions that may be inconsistent and has, in general, low finite‐sample power. Our explicit results pertain to a simple linear regression, but they can easily be generalized. Our empirical results indicate that non‐causality is quite common among economic variables, making these problems highly relevant.     

Noncausal Bayesian Vector Autoregression

We consider Bayesian analysis of the noncausal vector autoregressive model that is capable of capturing nonlinearities and effects of missing variables. Specifically, we devise a fast and reliable posterior simulator that yields the predictive distribution as a by‐product. We apply the methods to postwar US inflation and GDP growth. The noncausal model is found superior in terms of both in‐sample fit and out‐of‐sample forecasting performance over its conventional causal counterpart. Economic shocks based on the noncausal model turn out to be highly anticipated in advance. We also find the GDP growth to have predictive power for future inflation, but not vice versa. Copyright © 2016 John Wiley & Sons, Ltd.     

Near unit root and the relationship between inflation and interest rates: A reexamination of the Fisher effect

Tests of the Fisher effect are plagued by high persistence in interest rates. Instead of standard regression analysis and asymptotic results, methods relying on local-to-unity asymptotics are employed in testing for the Fisher effect with monthly U.S. data covering the period 1953:1–1990:12. These procedures are extensions of a recently presented method (Cavanagh, Elliott and Stock (1995)) based on simultaneous confidence intervals, and they have the advantage of being asymptotically valid whether interest rates are integrated of order one or zero, or near unit root processes. Taking appropriately account of the near unit root problem the findings in most of the previous literature are reconfirmed. There is support for the Fisher effect in the interest rate targeting period (1953:1–1979:10) of the Federal Reserve but not in the 1979:11–1990:12 period. First version received: July 1999/Final version received: April 2000     

Nonlinear dynamics of interest rate and inflation

According to several empirical studies US inflation and nominal interest rates as well as the real interest rate can be described as unit root processes. These results imply that nominal interest rates and expected inflation do not move one‐for‐one in the long run, which is incongruent with theoretical models. In this paper we introduce a new nonlinear bivariate mixture autoregressive model that seems to fit quarterly US data (1953 : II–2004 : IV) reasonably well. It is found that the three‐month Treasury bill rate and inflation share a common nonlinear component that explains a large part of their persistence. The real interest rate is devoid of this component, indicating one‐for‐one movement of the nominal interest rate and inflation in the long run and, hence, stationarity of the real interest rate. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling the U.S. Short-Term Interest Rate by Mixture Autoregressive Processes

A new kind of mixture autoregressive model with GARCH errorsis introduced and applied to the U.S. short-term interest rate.According to the diagnostic tests developed in the article andfurther informal checks, the model is capable of capturing bothof the typical characteristics of the short-term interest rate:volatility persistence and the dependence of volatility on thelevel of the interest rate. The model also allows for regimeswitches whose presence has been a third central result emergingfrom the recent empirical literature on the U.S. short-terminterest rate. Realizations generated from the estimated modelseem stable and their properties resemble those of the observedseries closely. The drift and diffusion functions implied bythe new model are in accordance with the results in much ofthe literature on continuous-time diffusion models for the short-terminterest rate, and the term structure implications agree withhistorically observed patterns.     

Data‐Driven Identification Constraints for DSGE Models

We propose imposing data‐driven identification constraints to alleviate the multimodality problem arising in the estimation of poorly identified dynamic stochastic general equilibrium models under non‐informative prior distributions. We also devise an iterative procedure based on the posterior density of the parameters for finding these constraints. An empirical application to the Smets and Wouters ( 2007 ) model demonstrates the properties of the estimation method, and shows how the problem of multimodal posterior distributions caused by parameter redundancy is eliminated by identification constraints. Out‐of‐sample forecast comparisons as well as Bayes factors lend support to the constrained model.