46. The HP-filtered series
where Xt and
47. Implementing the HP filter requires an appropriate choice of the smoothing parameter, λ. If that is close to zero, the smoothed series converges to the actual one: changes in Xt are mostly attributed to the trend and the filter does not allow for much of a cycle. In contrast, λ → ∞ yields an almost linear trend because the filter heavily penalizes variations in the growth rate of
48. There is a vast literature on the appropriate value for λ (see Röger and Ongena, 1999, for a survey). While there is broad agreement that λ = 1600 is appropriate for quarterly data, the recommended values for annual data vary between the 3-5 range (Pedersen, 2001) and 100 (Hodrick and Prescott, 1997). In line with the suggestion of King and Baxter (1999), this paper retains the conventional λ = 1600 for quarterly data18 and uses l = 10 for annual data. This implies that cycles lasting up to 8 years will be fully attributed to the cyclical component of the filtered series and longer cycles will be deemed structural (i.e., capturing acceleration and deceleration in potential growth) and incorporated into the trend
49. Another important practical issue in implementing the HP filter is the end-point bias. HP filtering amounts to deriving the trend series
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Prepared by Xavier Debrun (FAD). This chapter benefited from insightful comments by IMF colleagues and staff of the South African National Treasury, and in particular Fabrizio Balassone, Mark Horton, Matthew Simmonds, Joan Stott, and Noekie Steyn.
Outturns for the consolidated general government are also presented.
Of course, policy actions as captured by the CAB may differ from policy intent, often for reasons that escape policymakers, such as natural disasters that require emergency relief, the cost of social unrest, etc. Other transitory components also affect CABs. Removing these items from CABs gives “structural” budget balances.
In Chile, however, CAB estimates account for the direct budgetary impact of copper price cycles.
Annual expenditures of the Unemployment Insurance Fund amount to about 0.2 percent of GDP (Table IV.2), while other social transfers to households (about 4.7 percent of GDP in 2005/06) do not primarily serve to insure against cyclical fluctuations (Horton, 2005). Hence, a correction for cyclical unemployment would not significantly affect CAB estimates for the general government in South Africa. This chapter’s focus on national government and the corresponding assumption of zero elasticity of public expenditure to the output gap thus seem reasonable. As a comparison, and despite broader social safety nets in the OECD, Girouard and André (2005) find expenditure elasticities of the general government between −0.02 (Luxembourg) and −0.23 (the Netherlands), with an average −0.1. Bouthevillain and others (2001) obtain similar numbers.
The method still leaves out the effect of changes in relative price deflators accompanying GDP cycle (see Langenus, 1999, for a more detailed discussion).
Gaps are calculated with series in real terms. For the last two series, nominal figures have been deflated by GDP prices.
The HP filter is applied to calendar-year data. FY gaps result from a mechanical correction of the original series and its HP trend.
While no sample adjustment seemed necessary for the equations linking revenue elasticities to the tax base (Table IV.3), statistically significant breaks were identified in the early 1980s for the relationships between the output gap and two proxy tax bases (i.e. the compensation of employees and the gross operating surplus).
An alternative to (7) is to perform a cointegration analysis to explicitly disentangle short-run and long-run elasticities (see Bouthevillain and others, 2001). Given the small size of the sample, a parsimonious specification seemed more appropriate here.
Looking at European Union member states, Bouthevillain and others (2001) find CIT elasticities to the gross operating surplus of between 0.7 (Belgium) and 1.5 (France); PIT elasticities to worker’s compensation between 1.2 (France) and 2.6 (the Netherlands); and elasticities of indirect taxes to private consumption between 0.7 (Luxembourg) and 1.2 (Sweden).
The model uses two exchange rate variables, one interacted with a dummy for years 2000-05, and the other interacted with a dummy for previous years.
Total expenditures of the national government represent close to 28 percent of GDP. The fact that tax policy has aimed at enlarging the tax base while lowering tax rates may also have dampened somewhat cyclical influences on the budget.