Some Simple Fiscal Arithmetic

There are nearly 30 trillion dollars’ worth of outstanding U.S. government debt. Who pays for it when it expires? Let us approach this problem from a practical perspective. The payment has to come from two sources. First, the government can raise tax revenue in excess of spending needs, and use the excess revenue to pay back the debt. Second, the government can issue new debt to investors, and use the proceeds to retire the expiring debt. In practice, governments use a mixture of both approaches. Sometimes, when the spending needs overwhelm the tax revenue the government is willing to or able to collect, the government needs to issue even more debt to both fund the spending and repay the expiring debt.

The first approach gives rise to simple fiscal arithmetic: once we know the government is able to gather enough tax revenue when the current debt expires, we know the debt is safe. No more questions asked. The second approach, on the other hand, requires a bit more thoughts. The debtholders need to look further into the future, and ask how the new debt that is issued to pay back the current debt is going to be paid back. If the government cannot honor the new debt in the more distant future, debt market investors will refuse to finance its issuance in the first place, which in turn questions the government’s ability to pay back the current debt outstanding. This inquiry into the ever more distant future only stops when we find a horizon by which the government is able to collect enough fiscal cash flows to honor the outstanding debt. In other words, to evaluate the government’s fiscal situation today, we need to examine the fiscal cash flows today, next year, and potentially all the way into the distant future. What this also means is that the value of government debt is ultimately backed by government tax revenue in excess of spending, although the government has limited ability to delay the timing at which these cash flows are collected.

How do we aggregate these fiscal cash flows across time? This is where a financial valuation method can be useful. In corporate finance, we face a very similar question: how to determine the valuation of a firm based on the aggregation of its current and future cash flows? While the specific methods differ based on the situation, the basic idea is always to (i) assess the amount of expected cash flows, and (ii) assign appropriate discount rates for these future cash flows based on their risk characteristics. We can apply a very similar valuation method to evaluating the government balance sheet.

The Public Debt Valuation Gap

To implement this valuation method, we need to know (i) the amount of future tax revenue and government spending we expect in the future and (ii) the levels of the appropriate discount rates that we assign to these fiscal cash flows. To figure out the expected cash flows, the data since WWII suggest that the U.S. on average has similar levels of tax revenue and government spending as fractions of the GDP. If we zoom into the past 15 years, government spending surpassed tax revenue by a large margin. Feeling optimistic, let us assume the U.S. fiscal cash flows will revert to the historical norm over time, exhibiting a similar magnitude in the average tax revenue and government spending.

To figure out the appropriate discount rates, we note that the standard interest rates are not the right ones to use. The financial valuation method holds that riskier cash flows need to be discounted at higher rates, and the riskiness is primarily determined by how the cash flows comove with the business cycles. Specifically, cash flows are risky if they tend to be higher during economic expansions and lower during economic recessions. The stock market is a good example. As corporate revenues decline dramatically during economic recessions and financial crises, investors regard stocks as risky assets and therefore require a high compensation to hold them. This is why stocks tend to have higher returns than risk-free bonds over a long enough time period, and why, for the purpose of valuation, corporate cash flows are discounted at much higher rates than the standard interest rates. The data since WWII suggest that the U.S. tax revenue also exhibits a cyclical behavior, which warrants high discount rates on the tax revenue. In comparison, the U.S. government spending exhibits the opposite cyclicality: it tends to increase during recessions, as unemployment benefits and other welfare payments tend to be higher in the downturns. The government may also decide to spend more on public projects to stimulate the economy. This means that the U.S. government spending is a stream of counter-cyclical cash flows, and therefore deserves lower discount rates.

To put everything together, we need to compute the difference between the expected tax revenue and government spending, discounted at their appropriate discount rates. As these cash flows have similar levels on average, while the tax revenue has higher discount rates than the government spending, then, the valuation of the tax cash flows should be lower than that of the spending cash flows. Noting that the fiscal resources that pay off the debt comprise tax revenue minus government spending, we therefore conclude that they have a negative valuation. In other words, if we regard the U.S. government as a firm, this firm is in a sticky situation in which the valuation of its cash flows is below the amount of its outstanding liability. We call this gap between the valuation of government cash flows and the market value of outstanding government debt as the U.S. public debt valuation gap.

This valuation gap is a robust feature of the U.S. fiscal situation, as my coauthors and I confirm using more advanced valuation methods. It signifies a clash of different perspectives when we apply financial valuation methods designed for individual stock and bond securities to evaluating the aggregate U.S. government balance sheet. That said, we emphasize that this valuation gap does not necessarily show up in all governments’ balance sheets. The valuation of fiscal cash flows can be consistent with the market value of government debt when the government either has higher average tax rate than spending rate, or different business cycle cyclicality and hence discount rates for the tax and spending processes.

What Does It Mean and Where Do We Go From Here?

Our analysis suggests this valuation gap of U.S. public debt has persisted for many decades, but will it continue to exist? To evaluate its sustainability, we need to move to the realm of economic intuitions from that of financial calculations. There are multiple views that are potentially useful for thinking about this valuation gap.

First, bubbles are always a candidate explanation when the fundamentals of an asset deviates from its valuation. In the context of government debt, this view has an additional appeal: cash is a bubble, since it’s essentially a zero-interest debt that the government owes but never needs to pay back. Is it possible that the government debt is similarly special? Indeed, some economists have argued that government debt shares money-like properties because it provides valuable insurance to the risks that investors face. That said, the amount of cash is small relative to that of outstanding government debt, and there is evidence that the bubble-based premium vanishes as more money-like assets are supplied. Therefore, bubbles are unlikely to provide unconditional support for a large amount of government debt.

Moreover, this bubble-like property may have roots in the special status of the U.S. government debt as the reserve asset in the international monetary system, which enables the valuation of the U.S. government debt to escape its economic fundamentals. Consistent with this hypothesis, foreign investors have been playing a major role in financing the U.S. government debt. In particular, they purchase U.S. government debt precisely when the economy is in recession and the debt is expensive, and as a result earn low financial returns from their debt holdings. This flight to U.S. government debt finances the government spending during recessions, which helps support the debt valuation. However, alarmingly, this pattern seems to have reversed in the past decade, as foreign investors became net sellers of the U.S. government debt. So, once again, we have to be very careful when we extrapolate the bubble-based view to analyze a future scenario with even more debt outstanding.

Second, a dramatic tax hike and/or spending cut that raises government cash flows and pays down the government debt remains a possibility. Right now the U.S. government debt-to-GDP ratio is about 100%, and the U.S. tax-to-GDP ratio is about 25%. If the U.S. government raises tax revenue by 10% of the GDP, then, the outstanding debt can be paid down in 10 years. So, it is possible that investors are willing to purchase government debt because they expect a decade of extreme fiscal austerity. In practice, however, a higher tax rate may hurt the economy and reduce the tax base, which requires a much more drastic increase in the tax rate to raise the required revenue. Moreover, paying off the debtholders at the expense of taxpayers is politically unpopular, making this a challenging option.

Third, it is possible investors have been consistently mispricing the government debt. This is a variant of the second explanation, because the investors in this case wrongly expect fiscal consolidation that is unlikely to happen. This may be a more likely case, as my coauthors and I find evidence that fiscal forecasts have been overly optimistic in the past decades. If so, caution is needed when extrapolating to the future, since investors may eventually wake up to the fiscal facts and realize the mispricing. Such an event can greatly destabilize the Treasury market and the overall financial system, and the day of reckoning may come precisely when fiscal stability is needed the most.

In summary, we have discussed a couple of ways to interpret the observed valuation gap in the government debt. Despite the obvious differences in these views, they all suggest certain degrees of fragility in the valuation of the government debt. These views do not support the claim that we can comfortably accumulate debt at the current pace, without facing repercussions from the financial markets.