Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?

Morley, James; Nelson, Charles R.; Zivot, Eric

doi:10.1162/003465303765299765

Cited by 453 publications

(489 citation statements)

References 23 publications

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“…The results we find here, to some extent, highlights the similarities in the output gap process in the two countries. A highly persistent output cycles are likely explained by the assumption of no correlation between the trend and the cyclical component of the model ( Morley, Nelson, and Zivot 2003). We also test the implications of this assumption in the next section.…”

Section: Model 2 Results: Output Gap Is Unobservedmentioning

confidence: 92%

“…Note that the coefficient of trade-off is smaller in magnitude, but they are still not zero in a statistical sense. This implies that like the assumption of zero correlation between the trend and cyclical Morley, Nelson, and Zivot (2003), the assumption of observed/unobserved output gap is likely to have implications on the slope of the Phillips curve. The result of a flat slope of the Phillips curve is not entirely unexpected.…”

Section: Model 2 Results: Output Gap Is Unobservedmentioning

confidence: 99%

“…Consequently, an AR(2) dynamics for the unobserved measurement error term is an appropriate strategy based on the unobserved component modeling literature. Further, Morley, Nelson, and Zivot (2003) notes that in order to achieve a meaningful decomposition it is necessary to specify sufficient dynamics in the unobserved components of the model. 16 The rationale for this specification can also be found in the behavior of the inflation-indexed bonds market.…”

Section: The Unobserved Component Modelmentioning

confidence: 99%

“…Using this approach, the observed break-even inflation rate is decomposed into two unobserved components, namely the inflation expectations and the measurement error. Building on the economic intuition of Morley, Nelson, and Zivot (2003) and Lee and Nelson (2007), we model inflation expectations as a random walk process and the measurement error as an autoregressive process. One of the benefits of such specification is that it opens the possibility to estimate the correlation between shocks to expected inflation and shocks to measurement error ( Morley, Nelson, and Zivot 2003).…”

Section: Introductionmentioning

confidence: 99%

“…Building on the economic intuition of Morley, Nelson, and Zivot (2003) and Lee and Nelson (2007), we model inflation expectations as a random walk process and the measurement error as an autoregressive process. One of the benefits of such specification is that it opens the possibility to estimate the correlation between shocks to expected inflation and shocks to measurement error ( Morley, Nelson, and Zivot 2003). We also consider other correlation structures of the model to explore interconnection between different components of the model which would also provide robustness check.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Estimating the New Keynesian Phillips Curve for the UK: evidence from the inflation-indexed bonds market

Marfatia

2017

The B.E. Journal of Macroeconomics

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Abstract:This paper utilizes the information in the inflation-indexed bonds market to estimate the New Keynesian Phillips Curve for the UK using an unobserved component approach. The main advantage of this approach comes from using the Kalman filter to explicitly estimate the unobserved expected inflation from the observed break-even inflation rates -the yield difference between the inflation-indexed bonds and the nominal bonds. Our results show that the expected inflation estimated from the unobserved component model plays a significant role in explaining the inflation dynamics in the UK. The evidence also suggests that the estimated inflation expectations are better able to capture the evolution of actual inflation process as compared to the break-even inflation rate as a proxy for expected inflation.

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Section: Model 2 Results: Output Gap Is Unobservedmentioning

confidence: 92%

Section: Model 2 Results: Output Gap Is Unobservedmentioning

confidence: 99%

Section: The Unobserved Component Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimating the New Keynesian Phillips Curve for the UK: evidence from the inflation-indexed bonds market

Marfatia

2017

The B.E. Journal of Macroeconomics

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Kalman filtering and smoothing for model‐based signal extraction that depend on time‐varying spectra

Koopman

Wong

2010

Journal of Forecasting

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We develop a fl exible semi-parametric method for the introduction of timevarying parameters in a model-based signal extraction procedure. Dynamic model specifi cations for the parameters in the model are not required. We show that signal extraction based on Kalman fi ltering and smoothing can be made dependent on time-varying sample spectra. Our new procedure starts with specifying the time-varying spectrum as a semi-parametric fl exible spline function that can be formulated in state space form and can be treated by multivariate Kalman fi lter and smoothing methods. Next we show how a time series decomposition model can be made dependent on a time-varying sample spectrum in a frequency domain analysis. The key insight is that the spectral likelihood function depends on the sample spectrum. The estimates of the model parameters are obtained by maximizing the spectral likelihood function. A time-varying sample spectrum leads to a time-varying spectral likelihood and hence we obtain time-varying parameter estimates. The time series decomposition model with the resulting time-varying parameters refl ect the time-varying spectrum accurately. This approach to model-based signal extraction includes a bootstrap procedure to compute confi dence intervals for the time-varying parameter estimates. We illustrate the methodology by presenting a business cycle analysis for three quarterly US macroeconomic time series between 1947 and 2010. The empirical study provides strong evidence that the cyclical properties of macroeconomic time series have been changing over time.fl uctuations should typically last between 1.5 and 8 years. The business cycle is an important indicator of the state of the economy. Since it is unobserved, we require methods to extract the business cycle indicator from macroeconomic time series. For the purpose of cycle extraction, we can apply nonparametric fi lters or we may adopt parametric methods. Examples of nonparametric fi lters are those proposed by Hodrick and Prescott (1997), Baxter and King (1999) and Christiano and Fitzgerald (2003). As an alternative to nonparametric fi lters, model-based approaches can be considered to extract cyclical components from time series. An example is given by the Beveridge-Nelson decomposition, which is based on the modeling of the time series by an autoregressive integrated moving average model (see Beveridge and Nelson, 1981). Clark (1987), Harvey and Jaeger (1993) and Morley et al. (2003) discuss unobserved-components time series model formulations with trend and cycle factors that can be extracted from the observed time series using state space methods.In recent years there has been a growing need for, and interest in, extracting business cycle models with time-varying parameters, as it is unlikely that model parameters are constant over a period of a large number of years. provide evidence that the volatility in the business cycle has declined since the mid 1980s. We will focus on the time variation of both the volatility and the dynamic characteristics of th...

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Parameter Space Restrictions in State Space Models

Jun

Kim

Park

et al. 2011

Journal of Forecasting

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The state space model is widely used to handle time series data driven by related latent processes in many fi elds. In this article, we suggest a framework to examine the relationship between state space models and autoregressive integrated moving average (ARIMA) models by examining the existence and positive-defi niteness conditions implied by auto-covariance structures. This study covers broad types of state space models frequently used in previous studies. We also suggest a simple statistical test to check whether a certain state space model is appropriate for the specifi c data. For illustration, we apply the suggested procedure in the analysis of the United States real gross domestic product data. showed that the IND assumption restricts the parameter space of the equivalent autoregressive integrated moving average (ARIMA)(1, 1, 1) model and results in the spuriously decomposed trend and cycle. Lippi and Reichlin (1992) analytically proved that state space trend-cycle decomposition under the IND assumption (hereafter, we refer to this as the UC decomposition) 1 does not exist if the persistence measure calculated from ARIMA(p, 1, q) parameters is higher than unity. Morley et al. (2003) analytically and empirically showed that the IND assumption causes the empirical difference between the Beveridge-Nelson decomposition (Beveridge and Nelson, 1981; hereafter, the BN decomposition) and UC decomposition for the ARIMA(2, 1, 2) model. They also proved that relaxing the IND assumption leads to a result identical to that of the BN decomposition. ) models, respectively.All these studies emphasize that the IND assumption restricts the parameter space of the corresponding ARIMA model. In this study, we generalize this point by showing that the latent structure, including the IND assumption, of any state space model restricts the parameter space of the corresponding ARIMA model. We provide a general framework to study the relationship between state space models and ARIMA models. We derive the restricted parameter spaces for frequently used state space models as special cases of our general framework. We also suggest an easy statistical test to determine whether data can be modeled as a state space model or not. For illustration, we use the proposed framework and test procedure in the analysis of the US real gross domestic product (GDP) data. THE EXISTENCE AND POSITIVE-DEFINITENESS CONDITIONSConsider the following state space model: y t t t t t t n Parameter Space Restrictions in State Space Models 111 φ θ ε B y B t t (7) 112 D. B. Jun et al.where each noise e i,t is distributed by N(0, λ i σ 2 ε ) and ϕ p is not zero. The fi rst element of x t is the I(1) trend and the second element is the AR(p) cycle. Eliminating x t , we have Parameter Space Restrictions in State Space Models 117 between parameters of the state space model and those of the corresponding ARIMA model 4 can be derived as follows: DOI: 10.1002/for Figure 1. The relationship between ρ and λ given the ARIMA parameters: (a) θ > ϕ (ϕ = −0.3, θ = 0.0383); (b)...

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Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?

Cited by 453 publications

References 23 publications

Estimating the New Keynesian Phillips Curve for the UK: evidence from the inflation-indexed bonds market

Estimating the New Keynesian Phillips Curve for the UK: evidence from the inflation-indexed bonds market

Kalman filtering and smoothing for model‐based signal extraction that depend on time‐varying spectra

Parameter Space Restrictions in State Space Models

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