# The fiscal cost of debt-financed government spending

The persistently low interest rates on government debt over past decades has prompted some leading economists to question the wisdom of fiscal policies that restrict the use of deficits to finance government spending. (Blanchard, 2019; Eichengreen et al., 2021; Furman and Summers, 2020). This position is based on a simple model of public debt dynamics which implies that when the real interest rate on public debt, r, is less than the growth rate of the economy, g, the ratio of the government debt to GDP, can be stabilized even if the government has a primary deficit, i.e. with current revenues less than current program expenditures. Mian, Straub, and Sufi (2022) argue that when r is less than g “the fiscal cost of increased debt may be zero or even negative” (p.2) and that higher deficits are a “free lunch” in the sense that “permanent increases in deficits do not require tax increases going forward, even if they lead to permanently greater (non-explosive) debt levels.” (p.13)

In our recent paper, we show that fiscal policies based on the current favourable differential between the interest rate on government debt and the growth rate of the economy can mislead policy makers into believing that debt-financed spending has a low or no fiscal cost. We review the econometric studies which indicate that higher public sector debt levels generally lead to higher real interest rates and lower economic growth rates. In particular, Turner and Spinelli (2012) and recent IMF working papers by Lian, Presbitero, and Wiriadinata (2020) and the European Central Bank by Checherita-Westphal and Domingues Semeano (2020) have focused on the impact of higher government debt ratios on the r – g differential. The latter study found that a 10-percentage point increase in the debt ratio increased the differential by 0.4-0.6 percentage points based on a sample of 12 euro area countries from 1985 to 2017. They also found that a one percentage point increase in the US r – g differential increased the euro area countries’ differential by 0.3 percentage points.

An increase in the r – g differential as a government’s debt ratio increases has important implications for the fiscal cost of debt government spending. We will define the average fiscal cost (AFC) of program spending is the ratio of the taxes to program spending. AFC = 1 + (r – g)(b/γ) where b is the debt ratio and γ is the ratio of program spending to GDP. When r – g is negative, the debt ratio can be stabilized with a primary deficit and the AFC is less than one. However, the marginal fiscal cost (MFC) of a debt-financed increase in government spending can be greater than one if r – g increases with the debt ratio. That is, the increase in taxes needed to stabilize the debt ratio can exceed the increase in program spending if the r – g differential increases with the debt ratio. It can be shown that MFC = 1 + (r – g)(1 + ε) where ε is the elasticity of (r – g) with respect to the debt ratio. If (r – g) is negative, MFC is greater than one if ε is less than -1.

We estimated a simple regression model of the two key determinants of the r – g gap in Canada—the debt ratio for the federal and provincial governments and the US (r – g) gap. The coefficient estimates for both the debt ratio and the US (r – g) gap are statistically significant at the 5 per cent level. In particular, a one-percentage point increase in the debt ratio increases the r – g differential by 6.74 basis points, which is within the range of estimated values in the Checherita-Westphal and Domingues Semeano (2020) study for the eurozone countries. Based on recent values for r – g and b in Canada (-0.0144 and 0.70 respectively), ε = -3.276. Therefore the condition for MFC to be greater than one is satisfied.

### Average and marginal fiscal cost of a debt-financed one percentage point increase in the program spending ratio

Increase in the Debt Ratio (Percentage Points) | Primary Deficit (Percentage of GDP) | r - g (Percentage Points) | Average Fiscal Cost | Marginal Fiscal Cost |
---|---|---|---|---|

1.00 | 0.976 | -1.375 | 0.974 | 1.032 |

2.00 | 0.944 | -1.311 | 0.974 | 1.067 |

3.00 | 0.910 | -1.246 | 0.975 | 1.104 |

4.00 | 0.874 | -1.181 | 0.976 | 1.144 |

5.00 | 0.837 | -1.117 | 0.977 | 1.187 |

*Notes: In the initial situation, the real interest rate is 0.36 per cent, the growth rate is 1.80 per cent, the debt ratio is 70 per cent, and the primary deficit is 1.018 per cent of GDP. Program spending is 37 per cent of GDP.*

In the above table we use this estimate of the elasticity of the r – g differential to simulate the average and marginal fiscal cost of a permanent debt-financed one percentage point increase in the program expenditure ratio by Canadian governments.

The first row in the table shows that if a one percentage point increase in program spending results in a one percentage point increase in the debt ratio, a smaller primary deficit (0.976 per cent versus 1.008 per cent of GDP) is required to stabilize the debt ratio, given the 6.74 basis point increase in the r - g differential.

As a result, the average fiscal cost increases from 0.973 to 0.974. The marginal fiscal cost is 1.032. In other words, a tax increase that is 3.2 per cent higher than the increase in program spending is required to stabilize the debt ratio when the debt ratio increases by one percentage point. The other rows in the table show the AFC and MFC of a one percentage point increase in program spending if the fiscal adjustment is delayed and the debt ratio increases by more than one percentage point. In particular, if the spending increase results in a five-percentage point increase in the debt ratio, an additional $1.00 of program spending means that taxes have to increase by $1.187 to stabilize the debt ratio. Therefore, contrary to the widely-held view, there is no fiscal free lunch from debt-financed increases in program spending even though the real interest rate on government debt is less than the economy’s growth rate.

It's also important to reiterate that the economic cost of debt-financed government spending is the loss of private-sector incomes when government borrowing crowds out private investment and lowers the economy’s productive potential.

An additional reason for exercising fiscal prudence in the current low real interest rate environment is that international conditions may quickly change and the gap between the interest rate and the growth rates could be reversed. Such a reversal would require a large fiscal adjustment to stabilize the public debt ratio at its current level.