price effects we construct a real commodity export price index as in Keyfitz (2004) that is weighted by trade shares using the World Bank WITS data set and deflating it by the GDP deflator for each country. We take a simple HP-filter on this series to get the commodity price cycle (CMD� � �CMD� �CMD���) (see Alberola et al. (2016) for an alternative measure).

� where the weights w� are calculated using the share of each commodity (Pcomm�) in total country exports in the base period (the average observed between 2009-2011) deflated using GDP deflator (P��).

The output gap minus the fitted line on the real commodity price gap yields an estimate of the noncommodity output gap :

# **_Cyclicality of Fiscal Policy: The Role of Cyclical Lengths_**

To investigate the possibility that policy makers incorrectly identified long-term growth, and adjusted their fiscal policy accordingly, we follow Strawczynski and Zeira (2013). They show that the extent to which expenditures respond to output depends on the length of the cycle. This is related to the simple illustration in the theory section above. Fiscal policy is prone to become procyclical in cases where shocks lengthen the duration of the cycle. We follow Strawczynski and Zeira (2013) and Aguiar and Gopinath (2007) to create a variable that measures how the cycle becomes the trend: Where y� is the log of per-capita real GDP and K is the number of lagged differences. We normalize � � the above to one using σ∆��� �σ∆� and express the time sequence as: This ratio provides a measure of long-run variability to short-run variability, or the degree to which the cycle is the trend. If the standard deviation of per capita real GDP for any period lagged is the same as the difference of one period lagged, then there is no cyclical trend. However, we interpret a persistent cycle as one where the lagged variance to that of one period ago is larger than one. Note that equation (10) essentially boils down to a variance ratio test (see Cochrane, 1988). In essence, it is testing for a random walk in GDP vs. temporal shifts in GDP. If GDP is trend stationary, then GDP will fluctuate around that trend over time – implying that shocks to GDP are only temporary. If GDP is a random walk with drift, then shocks may push GDP on different paths (i.e. there is no reason to assume trend correction). One way to interpret (10) is that a value of C� �1 implies a random walk, C� �1, implies mean reversion and C� �1 implies some very persistent movements in output. Table A1 in the annex summarizes the statistical significance for each country for various horizons.

In our sample, South Africa has the largest persistence (Figure 4): the long-run variability of output to short-run variability is more pronounced compared to its peers, reaching a maximum of about 12 years (this compares well with the average duration of business cycles as estimated by the South African Reserve Bank (according to the 2018 Quarterly Bulletin). The _trend is the cycle_ indicator is above 1 for most countries, indicating that cycles are persistent. The persistent cycle could create the illusion that GDP is on a long-term higher trajectory and could lead to fiscal policy becoming procyclical.

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