In this model, the time-1 fiscal stimulus S generates a contemporaneous increase in GDP by Sμ, where μ is the fiscal multipliers. Furthermore, the stimulus permanently increases potential GDP from time 2 onwards by Sμh, with the parameter h capturing the strength of the hysteresis effect.
Regarding the implications for the stock of debt and fiscal balances, the stimulus increases public debt by S(1 − τμ), where τ is the elasticity of the fiscal balance to GDP. Instead of requiring a subsequent phase of consolidation to bring the debt-to-GDP ratio back to the level it would have been at without the stimulus, DeLong and Summers only require the government to pay the growth-adjusted interest rates on the new debt. Therefore, from time 2 onwards the government has to collect additional taxes by S(1 − τμ)(r – g), where r and g are respectively the real interest rate on government debt and the GDP real growth rate.
By increasing potential GDP, the fiscal stimulus increases future fiscal revenues by τSμh, so that the government has to increase taxes only to cover the difference. This generates a contractionary effect on GDP equal to ξS((1 − τμ)(r – g) – τμh), where ξ is the distortionary impact of taxation, which we set to 0.5, as in DeLong and Summers.
The partial derivative of the PV of GDP with respect to the fiscal stimulus is thus given by:
Setting this derivative to zero, we can solve for the interest rate threshold shown in Figure 3:
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This paper builds on work initially presented in Fletcher and Sandri (2012). The authors thank Suman Basu, Olivier Blanchard, Ajai Chopra, Prakash Kannan, Christina Kolerus, Daniel Leigh, Marta Ruiz-Arranz, Krishna Srinivasan, Hajime Takizawa, and Jules Tapsoba for useful comments. All remaining errors are those solely of the authors.
Hysteresis occurs when the temporary underutilization of productive resources leads to a permanent reduction in potential output. This may occur, for example, as a result of the scrappage of idle capital or a deterioration in labor skills or labor force participation due to extended periods of unemployment.
Other recent studies finding some evidence of time-varying multipliers include IMF (2012), Batini et al. (2012), Baum et al. (2012), and Giavazzi and McMahon (2012). The latter find, using household-level data, that fiscal multipliers are larger when the unemployment rate is higher.
Note that, while we target the same final debt-to-GDP ratio as in the baseline scenario, the final stock of debt can be higher as long as it is matched by a proportionally higher GDP level.
This condition is also equivalent to equalizing debt at the end of time 4 as a ratio to time-4 GDP.
Closing the output gap at time 4 is also required to ensure equality in the debt-to-GDP ratio between the baseline and delayed consolidation model from time 4 onwards. We will avoid imposing the full closing of the output gap in the simulations presented in Section IV.
The gains in the left-hand chart are computed fixing the hysteresis parameter to 10 percent, while those in the right-hand chart are based on a fiscal multiplier equal to 0.8.
The simulations in this section build on those initially presented in Fletcher and Sandri (2012) and share some similarities with those in Abbas and others (2013) and Bi, Qu, and Roaf (2013). A key difference with the latter is that we constrain our simulations to focus on comparing alternative fiscal routes to the same terminal debt-to-GDP and CAPB ratios. In contrast, Bi, Qu, and Roaf (2013) show results for alternative fiscal paths that differ in the terminal values of one or both of these ratios.
We use the October 2012 projections because this is a point in time that is both relatively recent and a point at which advanced economies still planned significant fiscal consolidation going forward. Although the numbers do not represent actual outcomes for 2012 onward, this is immaterial, as the objective of the simulations is simply to investigate how the PV of GDP varies under alternative realistic fiscal paths and parameter assumptions.
This implies that, for example, if potential growth is 2 percent and the output gap is -2 percent (a sizeable gap by historical standards), then actual growth will be 2.8 percent in the absence of exogenous shocks. To check the plausibility of this pace of natural closing, we model the OECD output gap estimates for the US and UK for 1980-2011 as an AR(1) and ARMA(1,1) process, with the coefficient on the AR term interpreted as the “natural closing” and the MA term interpreted as capturing persistent exogenous shocks to the output gap. We find AR coefficients in the range of 0.3 to 0.7. Given that the output gap may close more slowly than normal under the present constrained conditions for monetary policy, we use a rate of output gap persistence (0.6) at the higher end of these estimates. The sensitivity of the results to this assumption is presented later in the paper.
Time-variations in fiscal multipliers raises interesting issues about how to design an optimal path of fiscal consolidation. We leave this topic for future research, but our analysis suggests that a continuous, but gradual, path of consolidation may have advantages if “second-derivative effects” are particularly strong.
Note that this argument that does not necessarily rely on the country having fiscal room to postpone consolidation only once. The simple presence of a constraint on the debt-to-GDP ratio, no matter how loose, implies that the country moves closer to the constraint each time it delays consolidation and thus has less fiscal space to further ease fiscal policies to offset possible negative shocks.