After the 2008 Global Crisis, the interest rate-growth differential (r-g) has turned negative in several economies and interest rates have remained low ever since (Teulings and Baldwin 2014). These two conditions offer strong arguments to pursue fiscal expansions to spur growth, as a negative long-run r-g implies a more sustainable public debt, and countercyclical fiscal policy is arguably more effective in a low rate environment (Blanchard 2019, Eggertsson and Summers 2016, Ubide 2016). However, even before the Covid-19 pandemic, public debt levels were already at historically high levels and growth rates had stagnated in many countries (Figure 1). In this context, a further fiscal expansion could entail significant risks, because of the potential feedback loop between high public debt and the risk premium (Alcidi and Gros 2019).

**Figure 1** Interest rate, growth, and public debt

*Notes*: This figure plots the time series of the world's interest rate r, growth rate g, interest-growth differential r-g, and public debt-to-GDP ratio based on 17 advanced economies over the period 1950-2019. The world's values are GDP-weighted averages. All variables are five-year moving averages.

In a recent paper (Lian et al. 2020), we find that high public debts are associated with a higher likelihood of r-g rising and turning positive, potentially amplifying the effect of adverse shocks in driving up r-g. A surge in r-g is a concern as it can generate large economic costs, put public debt on an unsustainable path, and lead to sovereign debt distress (Mauro and Zhou 2019).

## Negative r-g is not always the norm and the current episode may not last long

If history is any guide, there is no guarantee that r-g will remain negative (Rogoff 2020). While there may be reasons to argue ‘this time is different’, history often offers important lessons. The r-g evolution over the last 70 years warns that the current negative r-g episode may not last long and that public debt matters. First, the duration of negative r-g episodes is shorter, the higher the initial level of public debt (Figure 2, panel A). Second, high debt countries are more likely to experience a shift from a negative to a positive r-g regime. For example, defining a negative (positive) r-g episode as a period of at least two consecutive years of negative (positive) r-g, the probability of a reversal increases from about 25% to more than 75% as we compare countries of debt-to-GDP ratios below the median with those in the top quartile of the sample distribution (Figure 2, panel B).

**Figure 2** Negative r-g spells, reversals, and public debt

**a)** Negative r-g spells

**b)** r-g reversals

*Notes*: Panel A shows the lengths (in years) of negative r-g episodes as a function of the initial public debt-to-GDP ratios, Debt, defined in the year before the episodes. A negative r-g episode is defined as consecutive periods (three years or longer) of negative r-g. All data are annual. The sample consists of 17 AEs over the period is 1950-2019, during which there are 72 episodes starting from 1951 onward, with an average length of 7.7 years (minimum length of three years, and maximum length of 28 years). A linear regression of the length of the negative r-g spells against the public debt-to-GDP ratio, controlling for country and year fixed effects, gives a coefficient of -0.043 (s.e. = 0.020). Using the same sample, Panel B plots the estimated probabilities (and the associated 90% confidence intervals) that the average r-g over the next five years is positive, given at least two consecutive years of negative r-g, as a function of the current public debt-to-GDP ratio. The probabilities are estimated using a logit model and regressing an indicator of positive future r-g on an indicator of negative current r-g, indicators of debt groups based on the quartiles of the public debt-to-GDP distribution, and their interaction terms. See Lian et al. (2020) for details.

## High public debts raise r-g downside risks

Quintile regressions estimate the distribution of future r-g as a function of current public debt and show that, as current public debt increases, the r-g distribution becomes more right-skewed and entails a higher downside risk (a higher likelihood that r-g becomes exceptionally high in the future). For example, as the current debt-to-GDP ratio increases from 40% to 120%, the 90th percentile of the average r-g over the following five years increases from around 0% to 2%. At the same time, the median r-g only increases by around 0.8 percentage points. The increase in the downside risk is not compensated by higher upside risk; if anything, higher public debt today is also associated with a smaller decline in r-g in the very good state (e.g. the 10th percentile)—see Figure 3, panel A. In other words, countries with high public debt today both suffer more if the bad state materialises and gain less if the good state materialises.

Panel B of Figure 3 plots the point estimates and confidence intervals of the debt-to-GDP ratio coefficients in the quantile regressions from the 5th to the 95th quantiles, and shows that the debt coefficients at the upper quantiles are considerably higher than those at the median—meaning that the sensitivity of r-g to debt is stronger in bad states. This result holds true for different definitions of downside risk (i.e. not just the 90th percentile) and over different horizons.

**Figure 3** Public debt and r-g at risk

**a) **Estimated r-g distribution

**b) **Estimated coefficients of public debt

*Notes*: Panel A shows the estimated future r-g distribution as a function of current public debt based on the quantile regressions, for the 10th, 50th and 90th quantiles. Panel B plots the estimated coefficients of public debt (y axis) obtained in the quantile regressions, for different quantile values (x axis). Standard errors are obtained from bootstrapping techniques with 1,000 replications. The dotted lines represent the 90% confidence intervals. The sample includes 31 AEs and 25 EMs over the period 2000-2019. See Lian et al. (2020) for details.

## High public debts amplify the transmission of shocks to borrowing costs

To better understand the mechanisms driving the r-g dynamics, we look at the role of public debt in explaining the exposures of interest rates to negative shocks.

We start with estimating the response of long-term interest rates to a negative domestic growth shock, measured by the growth forecast error. We find that countries with high public debts, especially when denominated in a foreign currency, experience a large increase in interest rates following a lower-than-expected domestic growth shock. For instance, a negative growth shock—a realisation of GDP growth that is at least 1% lower than expected—is associated with an increase in interest rates by 155 basis points (bps) in countries with high public debt and high share of foreign currency debt. This result is consistent with the idea that, as risk premia increase in bad times, high-debt countries tend to experience a large increase in their borrowing costs, which limits their capacity to support growth and contributes to explain the worse dynamics of r-g.

Using daily data, we find that countries with higher public debt experience a larger (and persistent) increase in interest rates in response to adverse global volatility shocks, measured by the two-day change in the US VIX. In addition, for a given level of debt, the interest rate response is larger when the share of foreign currency-denominated public debt is higher. For instance, for the average country in the sample, a 5% increase in the US VIX is associated with a 33 basis points increase in long-term interest rates over the next ten days, but this effect increases to 130 basis points for countries with high debt and a high share of foreign currency denominated debt (Figure 4).

**Figure 4** Public debt and the interest rate exposure to global shocks

*Notes*: The chart plots the impulse response function of regressing daily changes in long-term nominal interest rates computed over a 20-day period against the previous two-day change in the US VIX. The impulse response functions are plotted separately for the entire sample (solid line, average effect) and only for countries that have high public debt and a high share of foreign currency denominated debt (dashed line). The groups are constructed based on the debt-to-GDP ratios and shares of foreign currency denominated debt in the year before the events. In each year, the high and low classifications are based on the respective cross-country median values in that year. The shaded areas show the 90% confidence intervals. The interest rates are the ten-year local currency government bond yield, from Bloomberg. The sample includes 50 countries over the period January 2000-December 2018. See Lian et al. (2020) for details.

By contrast, the response of long-term interest rates to changes in the US VIX shows no correlation with public debt levels for countries that are typically considered as safe havens (the US, the UK, Japan, Switzerland, and Germany), consistent with investors rebalancing their portfolios towards safe and liquid assets during periods of high global uncertainty.

## Policy discussion

Our results suggest that fiscal expansion still entails significant risks, even in a low r-g environment, and, importantly, these risks are increasing with the level of public debt, especially because the interest rate-growth differential is endogenous to the size and dynamics of public debt (Wyplosz 2019). Specifically, we find that, as public debts are higher today, a regime shift is more likely, tail risks are increasing, and countries are more vulnerable to adverse shocks. These concerns become more pressing with the unfolding of the Covid-19 pandemic, which warns that, when disasters do strike, interest rates can rise, increasing the risk of a bad equilibrium and heightening the tension between fiscal stimulus and future debt sustainability (Rogoff 2020).

To support these claims, we highlight three empirical patterns:

1. Negative r-g episodes are not the norm and they may not last long. Moreover, reversals from negative to positive values of the differential are more common when public debt is higher.

2. A higher (and increasing) public debt is associated with higher average r-g, and, more importantly, leads to a higher probability of extremely high r-g in the future, increasing downside risks.

3. A higher public debt amplifies the vulnerability of the dynamics of r-g to domestic and global shocks, especially when the share of public debt denominated in foreign currency is large.

There is a widespread consensus that countercyclical fiscal policy is less costly and more effective at the zero lower bound. Our findings do not question this argument, but they show the potential risks of loose fiscal policy amid the low interest rates environment. As the current pandemic crisis shows, disasters do strike, and a sound fiscal stance can help to weather the crisis. In particular, while safe haven countries may face very limited risks of surges in r-g and have more to gain from expansionary fiscal policy, the balance of risks is tilted to the downside for high-debt countries, especially when debt is mostly denominated in foreign currency.

*Authors’ note: The views expressed here are those of the authors and do not necessarily represent those of the institution with which they are affiliated.*

## References

Adrian, T, N Boyarchenko and D Giannone (2019), “Vulnerable Growth”, *American Economic Review* 109(4): 1263–1289.

Alcidi, C and D Gros (2029), “Public debt and the risk premium: A dangerous doom loop”, VoxEU.org, 23 May.

Blanchard, O J (2019), “Public Debt and Low Interest Rates”, *American Economic Review* 109(4): 1197–1229.

Eggertsson, G and L H Summers (2016), “Secular stagnation in the open economies: How it spreads, how it can be cured”, VoxEU.org, 22 July.

Lian, W, A F Presbitero and U Wiriadinata (2020), “Public Debt and r-g at Risk”, IMF Working Paper 20/137.

Mauro, P and J Zhou (2020), “r - g < 0: Can We Sleep More Soundly?”, IMF Working Paper 20/52, International Monetary Fund, Washington, DC.

Rogoff, K S (2020), “Falling real interest rates, rising debt: A free lunch?”, *Journal of Policy Modeling* 42(4): 778-790.

Teulings, C and R Baldwin (2014), *Secular Stagnation: Facts, Causes, and Cures*, a VoxEU.org eBook, CEPR Press.

Ubide, A (2016), “The case for an active fiscal policy”, VoxEU.org, 11 October.

Wyplosz, C (2019), “Olivier in Wonderland”, VoxEU.org, 17 June.