Should the US Federal Reserve raise the inflation target from its current level of 2 per cent? And will it? One benefit would be to make hitting the zero lower bound less likely, which would lead to less severe recessions, as Olivier Blanchard, Giovanni Dell’Ariccia, Paolo Mauro, Daniel Leigh and Laurence Ball have argued on this website. Other benefits of higher inflation that Kenneth Rogoff has been emphasising for a while might include accelerating the fall in real wages during the recession, and deflating away debt overhang.

One of the most indebted economic agents is the US government. The federal debt limit has had to be raised repeatedly in the past few years, and at the end of the 2013 fiscal year the gross federal debt outstanding was 101 per cent of US GDP -- the highest ratio since 1948. It is therefore natural to imagine -- like Joshua Aizenman and Nancy Marion -- that inflating away the public debt is possible, perhaps effective, and maybe even desirable. Using a simple rule of thumb to estimate the effect of higher inflation on the real value of debt, they venture that US inflation of 6 per cent for four years could reduce the debt-GDP ratio by roughly 20 per cent.

However, in our recent work we show that the probability that US inflation lowers the real value of the debt by even as little as 4.2 per cent of GDP is less than 1 per cent. Why is this estimate so small? We show that there are two reasons: first, the private sector holds shorter-maturity debt; second, high levels of inflation in the next few years are extremely unlikely.

__The peril of rules of thumb__

To quantify the reduction in debt value, one might use a simple rule of thumb: multiply the outstanding debt (101 per cent of GDP) by its weighted-average maturity (5.4 years at the end of 2012, according to the US Treasury) and by the extra inflation (4 per cent) to get an estimate of a 22 per cent fall in the real value of debt. Yet, each part of this calculation is inaccurate, making it a rather poor approximation.

First, the federal government would only see its burden reduced on the debt that is held by private agents. Any fall in the debt held by Social Security or by the Fed would just lead to lower fiscal surpluses or lower seignorage payments in the future, respectively. Privately held debt at the end of 2012 was just 51 per cent of GDP.

Second, weighted average maturity is a poor measure of the sensitivity of the value of debt to changes in inflation. A more accurate measure is the Fisher-Weil duration of the debt portfolio held by the private sector, and that was 3.7 in 2012.

Third, a permanent increase of 4 per cent is viewed by market participants as close to impossible -- after all, if such a large increase was likely, no one would hold the debt at the current high market prices. Given the difficulties that the Fed has had in even keeping inflation as high as 2 per cent, it is indeed hard to imagine 6 per cent inflation suddenly and unexpectedly materialising. Also, the local approximation holds only for small, sudden, and permanent increases in inflation, and cannot be used for gradual and sizeable increases.

All combined, the effect of 0.1 per cent higher inflation forever is only 0.18 per cent. But to get a better estimate, one needs to go beyond rules of thumb.

__A forward-looking formula__

We show that the way in which the real debt burden of the government depends on inflation can be written in a simple transparent formula. The formula discounts the nominal payments (coupons and principal payments) that the government owes today weighted by the expected (risk neutral) cumulative inflation year by year. Knowing the risk-adjusted probability function for inflation, and the maturity of payments, we can therefore easily calculate the debt burden and then see how higher inflation, through either higher realisations of future inflation or shifts in the distribution for inflation, affect this burden.

__Debt maturity and expected inflation in the US__

Figure 1 shows the government payments due to the private sector by maturity. Remarkably, they are extremely concentrated on the short end. In fact, three quarters of the payments are due in less than 4.5 years. This has an immediate consequence for the debt burden that the formula above makes clear: only inflation over the next few years can have any meaningful effect on the real value of the debt burden.

** Figure 1**:

*US government payments due to the private sector by maturity (Bt), December 2012*

Figure 2 shows the risk-adjusted expected average annual inflation for the next five years. We estimated these distributions using novel data on inflation options contracts. Notably, inflation expectations are quite anchored, and investors are putting only a very low weight on the probability that inflation is even above 4 per cent in the short run.

*Figure 2**: Risk-adjusted distributions for average inflation over different maturities, December 2012*

__Inflating away the debt?__

Figure 3 shows the probability that the real value of the debt will fall because of inflation. All the numbers are very small. For example, the risk-adjusted probability of a reduction of the debt burden by more than 4.2 per cent of GDP is less than 1 per cent.

*Figure 3**: Probability that the fall in the real value of the debt exceeds a threshold*

Looking at a series of counterfactuals, we show how different ways to raise inflation affect the estimates of debt debasement: whether the increase in inflation is permanent or transitory, gradual or sudden, raises or lowers uncertainty, is unexpected or partially anticipated. While these differences are important -- estimates can easily double or halve across different scenarios -- the conclusion remains: even for extreme counterfactuals, plausibly higher inflation has only a small impact on the real value of the debt.

Simply put, in the near term, there is much debt but little extra inflation, and for longer horizons, there can be significant inflation but there is little debt. The total resulting effect is always small.

__Financial repression__

Looking backwards instead of forwards in time, there is a common perception that the US paid its post-war debt via inflation. What is so different now? An important part of the answer is that the maturity of the debt was much longer back then. The Treasury cannot simply start today issuing longer-maturity debt. Investors would realise that, with such a large stock of debt outstanding, higher maturities would raise the temptation to inflate and would demand compensation for the possibility of higher inflation in the form of significantly higher interest rates. The current twin facts that we highlighted -- lower maturities and moderate inflation expectations -- are mutually consistent.

One way to increase maturity, albeit ex-post, is to engage in financial repression -- a situation where the private sector is essentially forced to hold long-term debt at below-market interest rates. In fact, Carmen Reinhart and Belen Sbrancia suggest that this was the determining factor in inflating away the post-war debt in the US. We show that if holders of the debt are forced to receive, as payment, required reserves that must be held at the central bank for N years, then this is equivalent to an ex-post maturity extension. If N is as large as 10 years, then 2.5 per cent more inflation on average over the next 30 years -- which previously lowered the real value of debt by 3.7 per cent -- now lowers it by 23 per cent of GDP, almost half of the value of privately-held debt. Of course, the side effects of such extreme repression on financial development might well be large.

One way or another, budget constraints will always hold. This is true as much for a household or a firm as it is for the central bank or the government as a whole. If the US government is to pay its debt, then it must either raise fiscal surpluses or hope for higher economic growth; the former is painful and the latter is hard to depend on. It is therefore tempting to yield to the mystique of central banking and believe in a seemingly feasible and reliable alternative: expansionary monetary policy and higher inflation. Crunching through the numbers, we find that this alternative is not really there.

*Ricardo Reis is Professor of Economics at Columbia University and a research affiliate at the Centre for Economic Policy Research.*