The proposed specification falls between that of

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The proposed specification falls between that of Hamilton ( 1989 ), in which the common- factor means associated to normal and abnormal episodes are two constant values, and that of Eo and Kim ( 2016 ), in which the two means are separate random-walk processes, which gradually evolve over time, allowing for different observed growth rates in times of both normal and abnormal episodes. We justify our modelling choice as the minimal specification that is necessary to account for the obvious fact that recessionary episodes come with very different growth rates of the GDP, and other real activity indicators. On the one hand, the Global Financial Crisis of 2007–2008 was unusually severe for many economies that, compared to it, subsequent recessions look barely distinguishable from normal times. For example, based on the data for many European countries, one would almost certainly fail to detect any other recession but the one observed upon the Global Financial Crisis when using a Markov-switching model with the common factor of the Hamilton type. On the other hand, for many countries, there are so few recessionary episodes observed in the available data that a rich model that allows for independent recession- and expansion-specific common factor means of the Eo-Kim type would often be challenging to estimate without large model uncertainty. The model that we propose has a minimalistic structure due to potential lack of available data for the economies of interest, ECB Working Paper Series No 2381 / March 2020 7
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yet it is rich enough to account for the fact that every recession comes with a unique magnitude. Regarding the extraction of the factor from a set of observed information, each real ac- tivity indicator is assumed to be contemporaneously influenced by a common component and an idiosyncratic component. However, the treatment that each indicator receives depends on its corresponding frequency. In particular, indicators at the monthly frequency, y m i,t , can be expressed as: y m i,t = γ i f t + u i,t , (4) where γ i denotes the associated factor loading and u i,t represents the idiosyncratic component. Instead, when dealing with indicators at the quarterly frequency, y q j,t , we follow Mariano and Murasawa ( 2003 ) and express quarter-on-quarter growth rates into month-on-month unobserved growth rates: y q j,t = 1 3 y j,t + 2 3 y j,t - 1 + y j,t - 2 + 2 3 y j,t - 3 + 1 3 y j,t - 4 . (5) Then, a quarterly growth rate can be expressed in terms of its idiosyncratic component and the common factor, as follows: y q j,t = γ j 1 3 f t + 2 3 f t - 1 + f t - 2 + 2 3 f t - 3 + 1 3 f t - 4 + + 1 3 u j,t + 2 3 u j,t - 1 + u j,t - 2 + 2 3 u j,t - 3 + 1 3 u j,t - 4 . (6) Lastly, the idiosyncratic components, u i,t , contain information that is exclusively associated to a particular indicator, after accounting for its degree of commonality with the rest of variables.
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  • Fall '19
  • Economics, Recession, Late-2000s recession, GWI

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