We estimate in a bayesian fashion a constant mean

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We estimate, in a Bayesian fashion, a constant mean factor model by extending the approach in Chauvet and Piger ( 2008 ) to allow for mixed frequency data, and include quarterly real GDP growth to the set of monthly real activity indicators. This extension constitutes our constant mean factor model. Our data starts in 1947 and ends in 2020, as shown in Table 1 . This sample period allows us to evaluate the performance of the model over the last eleven NBER recessionary episodes. 5 The estimated probability of low real activity regime, P r ( s t = 1), is shown in Chart A of Figure 1 , along with the data on GDP growth, for comparison purposes. Although the estimated probability reaches values close to one during eight of the eleven recessionary episodes, the model does not provide a high recession probability for the three remaining recessions; 1969:12–1970:11, 1990:07–1991:03, and 2001:03–2001:11. This is because these three recessions seem to be either less severe, less persistent, or both, than the rest. Therefore, since the model assumes that the mean growth across all recessionary episodes is the same based on the entire sample, the estimated mean of the factor during recessions is dominated by the eleven stronger and more persistent recessions, and consequently, the model fails to produce a high probability attained to the three remaining recessionary episodes. In order to account for the fact that some U.S. recessions could be substantially more severe than others, we estimate the time-varying mean factor model proposed in this paper, and plot its associated probability of low growth regime in Chart B of Figure 1 . The figure shows that the estimated probability reaches values close to one during all the NBER recessions, with no 5 In particular, the last eleven U.S. recession, as defined by the NBER, are dated as follows: 1948:11– 1949:10, 1953:07–1954:05, 1957:08–1958:04, 1960:04–1961:02, 1969:12–1970:11, 1973:11–1975:03, 1980:01–1980:07, 1981:07–1982:11, 1990:07–1991:03, 2001:03–2001:11, 2007:12–2009:06. ECB Working Paper Series No 2381 / March 2020 11
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exceptions, outperforming the constant mean factor model. The reason for the success of the proposed framework relies on the premise that the growth rate during each recession is unique, in line with Eo and Kim ( 2016 ). However, unlike these authors, our approach is more parsimo- nious and simply assumes that recession means have two components. The first component is deterministic and given by the estimated parameter μ 1 , which provides an assessment about the average growth across all recessionary episodes in the sample. Instead, the second component is random, given by the normally distributed variable x t , which provides the uniqueness associated to each recessionary episodes. The random term x t can be interpreted as deviations from the deterministic component μ 1 . Hence, negative (positive) values of x t indicate weaker (stronger) growth than the average across all recessionary episodes, μ 1 . Chart A of Figure 21 , in the Ap- pendix, plots the empirical mean and median of the random variable x t over time for the case of U.S., illustrating the need for an adjustment factor, especially, during the 1973:11–1975:03 and 2007:12–2009:06 recessions.
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  • Fall '19
  • Economics, Recession, Late-2000s recession, GWI

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