# **Data**

19 advanced economies are included in the sample. Country coverage is defined by data availability, especially data on debt structure.<sup>5</sup> Macro variables over 2018-22, such as b�, s�, g�, and π� are drawn from the IMF WEO Projection (April 2018) to construct the baseline scenarios. π� is the GDP deflator so that the nominal GDP growth can be decomposed into g� and π�. Share of short-term and medium and long-term debt at the start of the simulation comes from SNA data on short/long debt ratio (assumed to be constant). The rollover ratio that controls the trajectory of the medium-to-long-term debt comes from the April 2018 Fiscal Monitor for 2018-20. For 202122, the rollover ratio is assumed to be identical to 2020.

We consider a temporary, 1 percentage point shock to inflation in 2018 only, to be comparable with the impulse response function estimated in section IV.<sup>6</sup>

# **B.   Responses to temporary inflation shock**

# **Benchmark case**

Results are shown in Figure 1. It shows the percentage deviations of the debt-to-GDP ratio from the baseline levels in response to a temporary 1 percentage point shock to inflation, or a one-time shift in price level. Deviation is the largest for Japan, about 2 percentage points, and the smallest for Czech Republic. On average, the deviation is about 0.7 percentage points. Reflecting the temporary nature of the shock, the debt reduction effect is concentrated in the first year.

# **Differences across countries**

The difference in the size of the initial debt reduction across countries is mostly explained by the initial debt level, as the debt reduction is measured in terms of percent of GDP (Figure 2). Most of the variation in the size of debt reduction disappears when the initial level of debt-to- GDP ratio is set at 84 percent, average for the sample (panel (a)). Since countries with high initial debt tend to also have high long-term debt that is affected by the inflation shock, a higher initial debt level is associated with the size of debt reduction (panel (b)). However, the rollover ratio also matters given the same level of initial public debt. Once we control the initial debt level, there is a clear relationship between the rollover ratio and the size of debt reduction, and in countries where the rollover ratio is higher such as the Czech Republic and Hungary, the effect is smaller (panel (c)). This is because the interest rates on a larger portion of the total public debt in these countries are adjusted upward in response to the inflation shock and therefore the corresponding proportion of the debt-to-GDP ratio is not affected by the inflation shock.

> 5Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Hungary, Ireland, Italy, Japan, Netherlands, Poland, Portugal, Spain, Sweden, United Kingdom, and United States. Some countries (Australia, Greece, and Norway) are excluded because we use government bond yields as the interest rates in our estimation approach and the share of their debt securities (against loans) in these three countries were low in certain periods.

> 6 We also consider a persistent shock that raises inflation to 6% over 2018-22, following Akitoby et al. (2014), and find that the results are broadly comparable with those in their paper. Summary results are in the appendix.

6