On the identification of multivariate correlated unobserved components models

Trenkler, Carsten; Weber, Enzo

doi:10.1016/j.econlet.2015.11.009

Cited by 14 publications

(7 citation statements)

References 13 publications

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“…All other parameters are merged into the MA part (Granger's Lemma.) To identify them, the system of non‐zero autocovariances of the MA part must contain enough independent equations which in turn depends on the lag length of the unobserved cycles p (compare Trenkler and Weber, for identification of multivariate correlated UC models).…”

Section: The Modelmentioning

confidence: 99%

Decomposing Beveridge Curve Dynamics By Correlated Unobserved Components

Klinger

Weber

2016

Oxf Bull Econ Stat

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Between 1979 and 2009, the German labour market moved along a Beveridge curve with changing slope that used to shift outwards but shifted inwards after severe labour market reforms had come into force. We analyse these dynamics and focus on the macroeconomic outcome of the reforms. For that purpose, we construct a new empirical model that links equilibrium unemployment theory to a flexible unobserved components model: we disentangle permanent and transitory components of matching efficiency and separation rate as well as unemployment and vacancies. Cointegration and identification are addressed. We find that matching efficiency and separation rate each account for about half of the inward shift. Thereby, the increase in trend matching efficiency is extraordinary and testifies to a permanent improvement on the labour market. Its visibility, however, was retarded by an overlay with a structural increase in tightness.

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Section: The Modelmentioning

confidence: 99%

Decomposing Beveridge Curve Dynamics By Correlated Unobserved Components

Klinger

Weber

2016

Oxf Bull Econ Stat

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“…In that case, imposing the restriction σ ηε = 0 yields a decomposition that is different to the one of Beveridge and Nelson (1981). The same is shown by Weber (2011) for the simultaneous unobserved components model identified by heteroscedasticity and by Trenkler and Weber (2016) for the multivariate UC model. In fact, d = 1 is the only case where the unobserved components model is not identified for p = 1.…”

Section: A Fractional Trend-cycle Decompositionmentioning

confidence: 77%

Fractional trends and cycles in macroeconomic time series

Hartl,

Tschernig,

Weber

2020

Preprint

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We develop a generalization of correlated trend-cycle decompositions that avoids prior assumptions about the long-run dynamic characteristics by modelling the permanent component as a fractionally integrated process and incorporating a fractional lag operator into the autoregressive polynomial of the cyclical component. The model allows for an endogenous estimation of the integration order jointly with the other model parameters and, therefore, no prior specification tests with respect to persistence are required. We relate the model to the Beveridge-Nelson decomposition and derive a modified Kalman filter estimator for the fractional components. Identification, consistency, and asymptotic normality of the maximum likelihood estimator are shown. For US macroeconomic data we demonstrate that, unlike I(1) correlated unobserved components models, the new model estimates a smooth trend together with a cycle hitting all NBER recessions. While I(1) unobserved components models yield an upward-biased signal-to-noise ratio whenever the integration order of the data-generating mechanism is greater than one, the fractionally integrated model attributes less variation to the long-run shocks due to the fractional trend specification and a higher variation to the cycle shocks due to the fractional lag operator, leading to more persistent cycles and smooth trend estimates that reflect macroeconomic common sense.

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“….−Φ p L P (I k being a k × k identity matrix) having all roots strictly outside the unit circle and, with ε t defined in the obvious way, E[ε t ε t ] = Σ εε . As usual in economic applications of multivariate UC models, such as Morley (2007), Sinclair (2009) or Ma and Wohar (2013), Φ(L) is assumed diagonal with the cycle in each variable having the same univariate order p. Empirical analyses typically employ p = 2, since this can both adequately capture short-term nonseasonal movements in economic data while also allowing the parameters of the correlated UC trend-cycle model to be identified; see MNZ for the univariate case and Trenkler and Weber (2016), hereafter TW, for a multivariate analysis 1 .…”

Section: Seasonal Uc Modelmentioning

confidence: 99%