The economic case for growth-indexed bonds is clear. By indexing interest payments to growth, they limit the increase in the debt ratio in bad times, thus decreasing the probability that the debt becomes unsustainable. As a result, they reduce the default risk premium, further improving the distribution of the debt ratio. However, as interest payments become more volatile, growth-indexed bonds might have to pay a premium in order to compensate investors for the GDP growth risk. If the premium is too high, the benefits of a smaller upper tail may be more than offset by faster increases in the debt ratio under the baseline.

In this column, we explore these issues quantitatively. To anticipate our conclusions, we believe that, today, there is a case for a large issuance of growth-indexed bonds in advanced economies in general, and in the Eurozone members in particular.

## Issuing growth-indexed bonds: Why advanced economies? Why now?

The economic rationale for issuing growth-indexed bonds has a long intellectual history (see Barr *et al.* 2014 for a recent contribution and Borensztein and Mauro 2004 for a review). The case for linking debt repayments to measures of economic activity gained prominence in the aftermath of the debt crisis of the 1980s. Further interest originated from Robert Shiller’s (1993) proposal to create ‘macro markets’ for perpetual claims on a fraction of a country’s GDP. Interest in the topic typically re-emerges in the aftermath of debt crises followed by difficult restructurings, when economists revisit the question of how to avoid debt defaults and their associated output costs. Indeed, in practice, securities with a return linked to economic growth have been issued only in the context of debt restructurings (including Bulgaria in 1994, Argentina 2005, Greece 2012, and Ukraine 2015). To date, no advanced economy has issued growth-indexed bonds in normal times. We believe this is the right time to do so.

Growth-indexed bonds are potentially most useful when the debt ratio is high, but not catastrophically high. The decrease in the upper tail of the distribution from the introduction of growth-indexed bonds is unimportant when the level of debt is low to start with, and irrelevant when the level of debt is already too high. Most advanced economies with debt ratios often close to 100% find themselves in between and, as shown in the simulations below, the reduction of the upper tail can make a substantial difference in that case.

Playing in the opposite direction is the premium that may be required by investors to hold these bonds, which may depend on four factors:

- Default risk

To the extent that growth-indexed bonds are issued in sufficient quantity to reduce default risk, this actually reinforces the case for growth-indexed bonds. Lower default risk means a lower premium on public debt in general, for both growth-indexed bonds and nominal (i.e. unindexed) bonds.

- Novelty risk

Like inflation-indexed bonds in the past, growth-indexed bonds will have to pay a novelty premium for some time. This premium may be lower for advanced economies than for emerging markets that issued GDP-linked warrants in the past. With relatively strong institutions and an independent statistical agency, advanced economies are in a better position to give confidence to investors that data on economic growth will remain untampered and reliable.

- Liquidity risk

A frequent problem with new financial instruments is lack of liquidity in the secondary market. This suggests that successful introduction may require large scale right from the start, to reassure investors that the market will be liquid in the event they decide to unwind positions. Standardisation of instruments (with similar contracts in the countries involved) can facilitate scale and portfolio diversification. At a recent workshop, the Bank of England put forward a common term sheet template.^{1} The evolution of the novelty and liquidity premia is difficult to predict, but the available evidence, in particular from the inflation-indexed bonds in the UK, suggests that they can gradually decrease and become small.

- Growth risk

Growth-indexed bonds are higher beta instruments than ordinary bonds, because their return is more volatile and procyclical. From that perspective, other things equal, growth bonds would require a premium relative to nominal or inflation-indexed bonds. Because growth rates are imperfectly correlated across countries, the country-specific growth risk is lower when the bonds are held by foreign investors. This is another argument for the simultaneous introduction of growth-indexed bonds in a number of advanced economies. In the context of the Eurozone, such cross-border holdings of growth bonds can indeed be seen as a (partial) market solution to a fiscal transfer union, which is likely to occur slowly, if at all, as evidenced by the cautious tone of the Five Presidents’ report on completing Europe’s economic and monetary union.

## Simulations to gauge the benefits of growth indexation

Our starting point is the well-known equation for the dynamics of debt as a share of GDP.^{2} Our objective is to compare the debt dynamics under the two scenarios in which the government finances itself through ordinary nominal bonds or growth-indexed bonds.

We present results for Spain, whose gross general government debt-to-GDP ratio at end-2015 is estimated at about 100%, close to the average for the advanced economies. In a longer note (Blanchard *et al.* 2016), we report results for other countries as well.

Throughout, we take the expected values of the nominal interest rate, the nominal growth rate, and the ratio of the primary surplus to GDP to be equal to the IMF’s October 2015 *World Economic Outlook* (WEO) forecasts up to 2020 and extrapolate at the same values from then on. We proceed in two steps.

In the first step, we focus only on the uncertainty associated with* the interest rate* and *growth rate *through the term (interest rate – GDP growth rate)*(lagged debt/GDP). To do so, we assume the ratio of the primary surplus to GDP is known with certainty. The key assumptions in this step are straightforward.

In the simulation showing debt dynamics when nominal bonds are used, we assume the distribution of shocks for the interest rate and the GDP growth rate are normal, and independently and identically distributed, with the covariance matrix estimated over 1999–2014.

- In the simulation showing debt dynamics when growth-indexed bonds are used, we assume the bonds pay an interest rate equal to the growth rate plus a constant.

By virtue of growth indexation, the gap between the interest paid and the growth rate is constant; i.e. it does not vary even when there are shocks to the market interest rate and the growth rate.

- We choose the constant so that the expected return on growth-indexed bonds is the same as the expected return on nominal bonds in the simulation above.

In other words, for the moment the risk premium on growth-indexed bonds is zero.

- Using these assumptions, debt dynamics up to 2035 are generated through random draws on the interest and growth rates.

Figure 1a shows the fan chart for the debt-to-GDP ratio when nominal bonds are used.

- By 2035, the 98% interval for the debt ratio (i.e., leaving out the top and bottom 1% of the distribution) ranges from 44% to 117%.

Figure 1b shows the evolution of the debt-to-GDP ratio under growth-indexed bonds.

- With full growth indexation and a non-stochastic primary surplus, the debt ratio is non-stochastic, and declines to 72% at the end of the projection period.

This first set of simulations is simplistic, but it conveys the key message. Growth-indexed bonds can decrease the worrisome upper tail of the distribution of the debt ratio.

**Figure 1**. Debt-to-GDP ratio 2010-35 with non-indexed vs. indexed debt, non-stochastic primary surplus, Spain

*Sources and notes*: Authors’ calculations. The fan charts report the debt-to-GDP paths corresponding to the 1st, 5th, 35th, 50th (solid line), 65th, 95th and 99th percentiles of the distribution.

## Allow for uncertainty in the primary surplus

In the second step, we allow for uncertainty in the primary surplus.

- For the case of normal bonds (with nominal interest rates), we use the covariance matrix of market interest rate, the GDP growth rate and the primary surplus as a share of GDP.
- For growth-indexed bonds, we use the covariance matrix for the GDP growth rate and the primary surplus as a share of GDP.
- As before, we start by assuming that growth-indexed bonds pay the growth rate plus a constant, and the value of the constant is set to equalise expected returns on nominal bonds and growth-indexed bonds.
- To allow the default premium to depend on the debt ratio, we assume that the interest rate increases (decreases) by 2 basis points for every percentage point deviation of the debt-to-GDP ratio from the baseline and by 3 basis points per percentage point when the debt ratio exceeds 140%.

The results are reported in Figures 2a and 2b. These reinforce our earlier conclusions. The probability that the debt ratio exceeds 140% is now about 10% for nominal bonds but it remains essentially zero for growth-indexed bonds.

**Figure 2**. Debt-to-GDP ratio with non-indexed vs indexed debt, stochastic primary surplus, 2010-35, Spain

*Sources and notes*: Authors’ calculations. The fan charts report the debt-to-GDP paths corresponding to the 1st, 5th, 35th, 50th (solid line), 65th, 95th and 99th percentiles of the distribution.

This simulation, however, still ignores the possibility of a positive premium stemming from liquidity, novelty, and growth risks. We believe, based on the existing evidence about inflation-indexed bonds and discussions with potential investors, that it is reasonable to expect, once the novelty and liquidity premia stabilise, a premium substantially below 100 basis points.

If we redo the simulations in Figure 2, but now allowing for a premium of 100 basis points, the probability that under growth-indexed bonds, the debt ratio exceeds 140% increases from zero to 7%. The gain is smaller but remains relevant. The effect of the premium is, however, non-linear. If we allow for a constant premium of 200 basis points, then the probability that the debt ratio exceeds 140% increases to 34%. Under those assumptions, nominal bonds dominate. The size of the premium is crucial to the case.

## Conclusions

Introducing growth-indexed bonds on a large scale in the advanced economies could substantially reduce ‘tail risks’ associated with explosive debt paths starting from today’s high ratios. Governments would also be able to pursue more countercyclical policies, and, by doing so, further stabilise growth and debt.

The exercises also show that a crucial issue is the size of the premium that such bonds would require. The absence of the market suggests that today the implicit premium required by potential investors to buy the new instruments is too high for governments to find them desirable to issue. The question is whether there is another equilibrium with a sufficiently low premium that such bonds are attractive to both governments and investors.

We believe that there may well be, and this is the time to explore it. The novelty premium can be reduced by discussions between potential investors and governments, and by the type of constructive ground work spurred by the Bank of England. The liquidity premium can be lessened by the introduction of these bonds on a sufficiently large scale, and by the identification of potential investors willing to hold them to maturity. The growth risk premium may be limited if the bonds are largely held by foreign investors as part of a diversified international portfolio. If this ground work is brought to fruition, the introduction of growth-indexed bonds will benefit highly indebted advanced economies and, in the Eurozone, might provide a partial market-based solution to attain valuable insurance benefits well ahead of a formal fiscal union.

## References

Barr, D, O Bush and A Pienkowski (2014), “GDP-linked bonds and sovereign default”, Working Paper No. 484. London: Bank of England.

Blanchard, O, P Mauro and J Acalin (2016), “The Case for Growth-Indexed Bonds in the Advanced Economies Today”, Policy Brief No, Peterson Institute for International Economics.

Borensztein, E, and P Mauro (2004), “The Case for GDP-Indexed Bonds”, *Economic Policy*, 38, April, 165–216.

Shiller, R J (1993), *Macro Markets: Creating Institutions for Managing Society’s Largest Economic Risks*. Clarendon Press, Oxford.

## Footnotes

2 Namely, the change in debt/GDP equals (interest rate – GDP growth rate)*(lagged debt/GDP) minus the primary surplus as a share of GDP. In symbols, , where *d* is the debt-to-GDP ratio, *r* and *g* are the interest and growth rates, and *s* is the primary fiscal balance (surplus) as a share of GDP.