Long-term interest rates are not determined by term premiums alone: Reading the future of 5% through Fiscal Theory of the Price Level
In the previous article, I wrote that the reason the US 10-year Treasury yield rose to around 5% was split between “strong economic conditions” and “shaking credibility,” and that in John Cochrane’s model, the order of rate hikes itself is reversed. This article is a continuation of that. Standing on the Fiscal Theory of the Price Level (FTPL), what is the price of long-term interest rates? Can we read future interest rates by looking only at the interest rates themselves and the term premium?
Let me state the conclusion first. In FTPL, long-term interest rates are not a stack of blocks consisting of monetary policy expectations plus a premium. They are an equilibrium price determined by whether nominal government debt can be repaid with future real surpluses. Taking the fiscal situation into account means looking at the path of that repayment possibility. Yields and premiums are part of the result, not the entirety of the cause.
The value equation comes first
The core of the Fiscal Theory of the Price Level is the value equation for nominal government bonds. Roughly speaking, the real value of nominal debt divided by current prices is equal to the discounted present value of future primary surpluses.
The price on the left side moves to satisfy the equation. If the prospect of a surplus narrows, current prices rise. Existing debt decreases in real terms. This is what “fiscal policy determines prices” means. Inflation does not come solely from the gap between supply and demand. It is also the result of repayment plans being written into prices.
This is where monetary policy enters. When the Fed sets a path for short-term nominal interest rates, the combination of expected inflation and real interest rates is constrained through the Fisher relationship. Nominal interest rates are generally the sum of real interest rates, expected inflation, and risk premiums.
Long-term interest rates are usually described as the expectation of future short-term nominal interest rates plus the compensation for risk until maturity. This decomposition can also be used in FTPL. However, neither “future short-term interest rates” nor “inflation at that time” must contradict the value equation. If interest rates are raised and interest payments increase, and the surplus plan does not change, then future inflation, real interest rates, or risk premiums must be adjusted to satisfy the equation. Long-term interest rates are the price that preempts that adjustment.
What is determined simultaneously is generally the following set: the current price level; the path of inflation; real interest rates and the stochastic discount factor; the short-term interest rate set by policy and the long-term bond price it implies; and the prospect of future surpluses and their uncertainty.
The term premium is a residual that emerges from this set. It is not an independent “credibility meter.” The fact that Kim-Wright and Adrian-Crump-Moench pointed in opposite directions this year is also due to the fact that the decomposition of the residual depends on the model. Judging credibility by looking at whether the premium has risen or fallen is similar to the task of trying to integrate which thermometer is real in a room where there are two thermometers pointing in opposite directions.
When “taking fiscal policy into account” becomes operational
The usual reading is as follows: the 10-year yield is the average of expected policy rates plus the term premium. One counts the priced-in number of rate hikes and estimates the premium separately.
In FTPL, the average of expected policy rates already includes an inflation path consistent with fiscal policy. “How many times will they raise rates” without taking fiscal policy into account is looking at only one side of the value equation.
The fork in the road is concrete.
If the market believes that future surpluses will increase—through tax hikes, spending cuts, or growth—at the same time as a rate hike, the value equation does not demand high inflation immediately. The rise in real interest rates is the main factor, and long-term inflation expectations remain nearly unchanged. The observation from the previous article that “breakevens were small, and what rose was real rates” is compatible with this way of closing the equation.
If only interest rates are raised and surpluses do not increase, the increase in interest payments will swell the debt, and the value equation will eventually close with higher prices. Long-term inflation compensation or compensation for fiscal risk will remain. This is Cochrane’s unpleasant interest rate arithmetic. Even with the same “10-year at 5%,” the meaning of future interest rates differs depending on which way the market believes the equation is closing. If it is the latter, current rate hikes will not suppress long-term interest rates. What will suppress them is when the path of surpluses is rewritten.
War, tariffs, and tax cuts directly affect this right-hand side. If the Strait of Hormuz narrows, crude oil prices will rise. That is a relative price. At the same time, if the combination of military spending, tax cuts, and tariffs reduces the present value of future surpluses, the value equation will assign the work to prices. Rate hikes do not eliminate relative prices, and if the right-hand side narrows, raising nominal interest rates itself will further narrow the right-hand side via interest payments.
Therefore, “taking fiscal policy into account” is not just a matter of mindset. It is about asking whether the current curve is pricing in a closure where surpluses increase, or a closure where inflation rises. TIPS, the fiscal deficit-to-GDP ratio, auction absorption, holdings by overseas investors, and political budget proposals are materials for that question. The yield level and premium estimates alone cannot identify how it is closing.
Cochrane’s prescription is the manipulation of simultaneous determination
The order I wrote about in the previous article—replacing long-term bonds with short-term ones, and then fixing interest rates low for a long time—is not just about moving interest rates. When you change the maturity structure, the magnitude by which interest rate changes affect the market value of debt changes. When there are many long-term bonds, lowering interest rates increases the price of existing bonds, and the timing of the government’s real burden shifts. If it is only short-term, interest rate changes are almost directly linked to interest payments, and adjustments to the value equation are more likely to be reflected in the inflation path (or the way it is reflected changes).
In the model, if you shorten the maturity and then lower rates sustainably, inflation will fall in both the short and long term, and interest payments will also decrease. That is the strongest form of the “reason for rate cuts.” What he himself is hesitant about is the certainty of the path where short-term inflation also disappears due to maturity shortening. He places more weight on the long-term Fisher effect—that if you keep interest rates low for a long time and do not increase borrowing, inflation will eventually fall.
What we are observing now is the opposite combination. Long-term bonds remain. The deficit is thick at around 6% of GDP. Policy rates have risen. The Treasury’s buyback is a small-scale demand creation to suppress long-term yields, not an operation to replace maturities with short-term ones. The Trump administration’s demand for rate cuts is close to Cochrane only in direction, but it breaks the ‘ceteris paribus’ condition through spending and tax cuts. Policies with different conditions cannot be justified by the same theory.
It is understandable that central banks raise rates according to short-term textbooks. They respond to a strong economy and high oil prices with high real interest rates. What FTPL adds is how to close the loop after that response. If the surplus does not increase, high nominal interest rates leave behind high interest payments, and the valuation equation may demand inflation in the future. At that time, long-term interest rates are not ‘pricing in that rate hikes worked,’ but rather ‘pricing in a future where they did not.’
What can be observed and what cannot be read
What can be observed: Current short-term interest rates. The yield curve. TIPS break-evens. Term premiums by model. Daily correlation between stocks and bonds. Auctions and foreign flows.
That alone is not enough to read the future. The political path of future primary surpluses. Whether the market truly believes that rate hikes increase surpluses. How wars, tariffs, and tax cuts rewrite the right side of the valuation equation. How long the Fed will keep rates fixed. If it is a temporary hike, Fisher does not work. If they fix rates for a long time and the government does not increase borrowing, interest rates and inflation will move in the same direction in the long run.
Therefore, the following types of statements are weak under FTPL.
‘Credibility is fine because the term premium has fallen.’
‘Sell US assets because the premium has risen.’
‘Since the 10-year is at 5%, we know how many more rate hikes are coming.’
‘The bond market is saying the economy is strong because real interest rates have risen.’
All of these are interpretations made after deciding on one way to close the loop. When there are two ways to close the loop, the same numbers support both stories. The fact that KW and ACM in the previous article pointed in opposite directions is less of a technical accident and more of a surface manifestation of that structure.
The daily inverse correlation with stocks also falls into the same place. In a world with inflation concerns, a rise in yields is a rise in the discount rate, and stocks will fall unless accompanied by an increase in earnings. The reason stocks have risen throughout the year may be that another way of closing the loop—AI profits, real growth, or the hope that ‘surpluses will eventually increase’—is coexisting with daily inflation fears. That, too, is a bet on the right side of the valuation equation.
What I wanted to say in the two articles
Bonds do not speak with one voice. A ‘good 5%’ and a ‘bad 5%’ are simultaneously present on the same price. Cochrane’s model shifts the focus of that rift not to ‘whether to raise or lower interest rates,’ but to ‘how to handle maturities, how to promise surpluses, and how long to fix interest rates.’
If you stand on FTPL, long-term interest rates do not end with a discussion of term premiums. The real repayability of nominal debt is written into both prices and the curve simultaneously. Basing your view on fiscal policy means looking at the path of that repayment. Looking only at interest rates and premiums will not tell you future interest rates. All you can know is how much the current market is paying for which way of closing the loop. If the way of closing the loop changes, long-term interest rates will move even if the premium remains unchanged. Conversely, even if premium estimates fluctuate, if the right side remains the same, the story of future short-term rates will not be updated.
Practically speaking, setting it up this way changes the work. Before counting the number of rate hikes, write down whether those hikes will erode the right side through interest payments or thicken it through growth, tax increases, and spending cuts. Before trusting a premium estimate, write down which term of the valuation equation—inflation risk, variance of surplus, or foreign demand—that estimate is picking up. Before viewing buybacks as ‘yield suppression,’ write down whether maturities have shortened or if it is simply temporary demand.
If you rely solely on the expectations hypothesis, long-term interest rates are the average of future short-term interest rates. FTPL does not deny this. What it denies is the treatment that this average exists independently of fiscal policy. The content of the average already includes repayability. Therefore, if you want to know future interest rates, you must not only forecast future short-term rates but also forecast future surpluses. As long as the forecast of surpluses is political, the forecast of the curve also includes politics. This is not a resignation that ‘bonds are unknowable,’ but an organization of moving the unknown from interest rates to the budget.
The US today is simultaneously facing high deficits, remaining long-term debt, resumed rate hikes, supply-side wars, and long-term buybacks that have failed to be suppressed. Short-term textbooks react to the ‘rate hikes’ among these. The valuation equation looks at everything else. Whether 5% is the ceiling or the entrance depends not on the yield number, but on whether the path of the surplus is rewritten.