Impulse Response Confidence Intervals for Persistent Data: What Have We Learned?

This paper is a comprehensive comparison of existing methods for constructing confidence bands for univariate impulse response functions in the presence of high persistence. Monte Carlo results show that Kilian (1998a), Wright (2000), Gospodinov (2004) and Pesavento and Rossi (2005) have favorable coverage properties, although they differ in terms of robustness at various horizons, median unbiasedness, and reliability in the possible presence of a unit or mildly explosive root. On the other hand, methods like Runkleís (1987) bootstrap, Andrews and Chen (1994), and regressions in levels or first differences (even when based on pre-tests) may not have accurate coverage properties. The paper makes recommendations as to the appropriateness of each method in empirical work.Local to unity asymptotics, persistence, impulse response functions

Impulse Response Confidence Intervals for Persistent Data: What Have We Learned?

This paper is a comprehensive comparison of existing methods for constructing confidence bands for univariate impulse response functions in the presence of high persistence. Monte Carlo results show that Kilian (1998a), Wright (2000), Gospodinov (2004) and Pesavento and Rossi (2005) have favorable coverage properties, although they differ in terms of robustness at various horizons, median unbiasedness, and reliability in the possible presence of a unit or mildly explosive root. On the other hand, methods like Runkle’s (1987) bootstrap, Andrews and Chen (1994), and regressions in levels or first differences (even when based on pre-tests) may not have accurate coverage properties. The paper makes recommendations as to the appropriateness of each method in empirical work.Local to unity asymptotics, persistence, impulse response functions

Do Technology Shocks Drive Hours Up or Down? A Little Evidence From an Agnostic Procedure

This paper analyzes the robustness of the estimate of a positive productivity shock on hours to the presence of a possible unit root in hours. Estimations in levels or in first differences provide opposite conclusions. We rely on an agnostic procedure in which the researcher does not have to choose between a specification in levels or in first differences. We find that a positive productivity shock has a negative impact effect on hours, as in Francis and Ramey (2001), but the effect is much more short-lived, and disappears after two quarters. The effect becomes positive at business cycle frequencies, as in Christiano et al. (2003), although it is not significant.Technology shocks, persistence, impulse response functions, Real Business Cycle Theory

Do Technology Shocks Drive Hours Up or Down?

This paper analyzes the robustness of the estimate of a positive productivity shock on hours to the presence of a possible unit root in hours. Estimations in levels or in first differences provide opposite conclusions. We rely on an agnostic procedure in which the researcher does not have to choose between a specification in levels or in first differences. The method uses alternative approximations based on local-to-unity asymptotic theory and allows the lead-time of the impulse response function to be a fixed fraction of the sample size. These devices provide better approximations in small samples and give confidence bands that have better coverage properties at medium and long horizons than existing methods. We find that a positive productivity shock has a negative effect on hours, as in Francis and Ramey (2001), but the effect is much more short-lived, and disappears after two quarters. The effect becomes positive at business cycle frequencies, as in Christiano et al. (2003)Technology shocks, persistence, impulse response functions, Real Business Cycle.

Small Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons

Existing methods for constructing confidence bands for multivatiate impulse response functions depend on auxiliary assumptions on the order of integration of the variables. Thus, they may have poor coverage at long lead times when variables are highly persistent. Solutions that have been proposed in the literature may be computationally challenging. The goal of this paper is to propose a simple method for constructing confidence bands for impulse response functions that are robust to the presence of highly persistent processes. The method uses alternative approximations based on local-to-unity asymptotic theory and allows the lead time of the impulse response function to be a fixed fraction of the sample size. Monte Carlo simulations show that our method has better coverage properties than existing methods. We also investigate the properties of the various methods in terms of the length of their confidence bands. Finally, we show, with empirical applications, that our method may provide different economic interpretations of the data. Applications to real GDP and to nominal versus real sources of fluctuations in exchange rates are discussed.

Impulse Response Confidence Intervals for Persistent Data: What Have We Learned?

Abstract. This paper is a comprehensive comparison of existing methods for constructing confidence bands for univariate impulse response functions in the presence of high persistence. Monte Carlo results show that Kilian (1998a), Wright (2000), Gospodinov (2004) and Pesavento and Rossi (2005) have favorable coverage properties, although they differ in terms of robustness at various horizons, median unbiasedness, and reliability in the possible presence of a unit or mildly explosive root. On the other hand, methods like Runkle’s (1987) bootstrap, Andrews and Chen (1994), and regressions in levels or first differences (even when based on pre-tests) may not have accurate coverage properties. The paper makes recommendations as to the appropriateness of each method in empirical work

Impulse Responses Confidence Intervals for Persistent Data: What Have We Learned?

This paper is a comprehensive comparison of existing methods for constructing confidence bands for univariate impulse response functions in the presence of high persistence. Monte Carlo results show that Kilian (1998a), Wright (2000), Gospodinov (2004), and Pesavento and Rossi (2005) have favorable coverage properties, although they differ in terms of robustness at various horizons, median unbiasedness, and reliability in the possible presence of a unit or mildly explosive root. On the other hand, methods like Runkle's (1987) bootstrap, Andrews and Chen (1994), and regressions in levels or first differences (even when based on pre-tests) may not have accurate coverage properties. The paper makes recommendations as to the appropriateness of each method in empirical work.

DO TECHNOLOGY SHOCKS DRIVE HOURS UP OR DOWN? A LITTLE EVIDENCE FROM AN AGNOSTIC PROCEDURE

This paper analyzes the robustness of the estimate of a positive productivity shock on hours to the presence of a possible unit root in hours. Estimations in levels or in first differences provide opposite conclusions. We rely on an agnostic procedure in which the researcher does not have to choose between a specification in levels or in first differences. We find that a positive productivity shock has a negative impact effect on hours, but the effect is much shorter lived, and disappears after two quarters. The effect becomes positive at business-cycle frequencies, although it is not significant.

Small Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons

Existing methods for constructing confidence bands for multivariate impulse response functions depend on auxiliary assumptions on the order of integration of the variables. Thus, they may have poor coverage at long lead times when variables are highly persistent. Solutions that have been proposed in the literature may be computationally challenging. The goal of this Paper is to propose a simple method for constructing confidence bands for impulse response functions that is not pointwise and that is robust to the presence of highly persistent processes. The method uses alternative approximations based on local-to-unity asymptotic theory and allows the lead time of the impulse response function to be a fixed fraction of the sample size. These devices provide better approximations in small samples. Monte Carlo simulations show that our method tends to have better coverage properties at long horizons than existing methods. We also investigate the properties of the various methods in terms of the length of their confidence bands. Finally, we show, with empirical applications, that our method may provide different economic interpretations of the data. Applications to real GDP and to nominal versus real sources of fluctuations in exchange rates are discussed.impulse response functions; local to unity asymptotics; persistence; VARs