Monetary and fiscal policy, the Taylor rule and the yield curve

Level 1 Plain words

For every reader: the idea in plain words, no formulas.

What the central bank does

The Federal Reserve sets a target for the overnight rate at which banks lend to each other. When inflation runs too high, it raises that rate, which makes borrowing dearer across the economy and slows spending. When the economy weakens, it cuts the rate. It can also buy or sell government bonds in large amounts to push longer-term rates down or up.

What the government's budget does

Congress decides what the government spends and how much it taxes. Spending more or taxing less puts money in people's hands and can lift demand in a slump. It also adds to the national debt, which has to be serviced from future taxes. Some of this happens without a vote: in a recession tax receipts fall and unemployment benefits rise by themselves, which cushions the fall.

What the yield curve shows

Treasury bonds come in maturities from a few weeks to thirty years. Plotting their yields against maturity gives the yield curve. Usually it slopes up, since lenders want more to tie money up longer. When the curve flattens or inverts, so that short rates sit above long ones, markets are saying they expect the Federal Reserve to cut rates later, often because they expect a slowdown.

Level 2 How it works

For readers who want the mechanism, with the diagrams.

Beginner path stops here

The dual mandate

Congress gave the Federal Reserve two goals: maximum employment and stable prices, along with moderate long-term interest rates. Since January 2012 the Federal Open Market Committee has stated a formal goal of 2 % inflation, measured by the PCE price index. Employment has no fixed number, because the level of unemployment consistent with stable inflation shifts over time and cannot be measured directly.

The tools

The main tool is a target range for the federal funds rate, the overnight rate between banks, set in quarter-point steps at eight scheduled meetings a year. The Fed holds the market rate inside the range mainly through interest on reserve balances (IORB), the rate it pays banks on money they keep at the Fed, with an overnight reverse repurchase facility as a floor for other lenders. Open market operations, buying and selling Treasuries, adjust the supply of reserves. Quantitative easing (QE) means buying long-term Treasuries and mortgage securities in large amounts to push long rates down; quantitative tightening (QT) lets them run off. The discount window lends to banks against collateral, a backstop in a panic. And forward guidance, telling markets where rates are likely to go, moves long rates before any change in the short rate.

The transmission chain

A rate change reaches the economy through a chain of links, each with its own delay.

Higher short rates lift the rates on car loans, credit cards and business credit within days. Longer rates move by how far markets expect the policy rate to stay high. Higher rates lower the present value of future profits and rents, so stock and property prices tend to fall, and they draw money into the dollar, which makes imports cheaper. Households with less wealth and dearer credit spend less; firms with dearer funding invest and hire less. Only then does inflation slow. Milton Friedman called these lags "long and variable"; most estimates put the full effect on inflation at one to two years.

What QE does

Quantitative easing works mainly by taking long-duration bonds out of private hands. Investors who sold Treasuries and mortgage securities to the Fed hold cash instead, and many of them buy other long assets, such as corporate bonds or shares, pushing those prices up and their yields down. Economists call that the portfolio balance channel. QE also signals that the Fed plans to keep short rates low for a long time, which pulls down expected future short rates and so long yields. Quantitative tightening runs the same channels in reverse, though more slowly, since the Fed usually lets bonds mature instead of selling them.

Fiscal policy, multipliers and stabilisers

A dollar of government spending can raise GDP by more or less than a dollar. The fiscal multiplier measures how much. It is larger when the economy has idle workers and machines, when the central bank holds rates steady instead of offsetting the boost, and when the money goes to people likely to spend it. It is smaller when the economy is at full stretch, when higher spending pushes rates up and crowds out private investment, and when much of the extra spending leaks abroad through imports.

Automatic stabilisers work without new laws. Progressive income taxes take a smaller amount when incomes fall, and unemployment insurance pays more when jobs are lost. Both support spending in a recession and restrain it in a boom.

When the two arms act together

Monetary and fiscal policy can push in the same direction or against each other. In 2020 they pushed together: the Fed cut to zero and bought bonds on a large scale while Congress passed relief packages, and the economy rebounded within months. In the early 1980s they pulled apart, with tight money and large deficits, which pushed real interest rates and the dollar high. The mix matters for investors because it decides which assets carry the adjustment: tight money with loose budgets tends to mean high real yields and a strong currency, while loose money with tight budgets tends to mean low yields and a weaker currency.

Debt dynamics

What matters for a country's debt burden is debt relative to GDP. That ratio rises with the deficit before interest, the primary deficit, and with the gap between the interest rate the government pays, $r$, and the growth rate of the economy, $g$. When $r$ sits below $g$, the economy outgrows the debt, and the ratio can stay steady even with small primary deficits. When $r$ rises above $g$, the government needs a primary surplus to keep the ratio from climbing.

The yield curve's shapes

A normal or steep curve, with long yields well above short ones, often comes early in a recovery when the Fed holds short rates low and markets expect them to rise. A flat curve tends to appear late in an expansion. An inverted curve, short above long, usually appears when the Fed has raised short rates high and markets expect cuts.

Two forces shape the curve. Under the expectations view, a long yield equals the average of the short rates expected over its life, so a rising curve means rising expected rates. On top of that sits a term premium, the extra yield investors want for holding a long bond whose price can swing. The term premium has been positive on average and varies over time; Federal Reserve staff estimates put it near zero or below for parts of the 2010s.

The Taylor rule as a yardstick

John Taylor proposed in 1993 a simple rule that matched the Fed's choices from 1987 to 1992 well. It sets the policy rate from two inputs, inflation and the output gap. Policymakers do not follow it mechanically, and it comes in many variants, yet it gives a useful benchmark for asking whether policy looks tight or loose.

Level 3 The math

For Series 65 and CFA readers: formulas and worked examples.

Series 65 path stops here

The Taylor rule

With inflation $\pi$ over the past four quarters, the inflation target $\pi^{*}$, the neutral real rate $r^{*}$ and the output gap $y$ in percent, Taylor's 1993 rule reads as follows, with $r^{*} = 2$ and $\pi^{*} = 2$.

In words, the policy rate equals the neutral real rate plus inflation, plus half the gap between inflation and its target, plus half the output gap.

The rule raises the nominal rate by one and a half points for each point of extra inflation, so the real rate rises when inflation rises. Taylor called that the stabilising feature: a rule that lifted the nominal rate by less than one for one would let real rates fall as inflation climbed, feeding it further.

We add two cautions for both quarters. Many economists think the neutral real rate fell well below Taylor's 2 % after 2008, which would lower the rule's answer in 2019 by a point or more and make policy look less loose. And the output gap depends on the CBO's estimate of potential GDP, which gets revised; the numbers here use the estimates on FRED at our data date, not those available at the time. Even with a lower $r^{*}$, the 2022 gap stays large: the rule called for rates far above where the Fed had them as inflation took off.

How hard the rule leans on inflation

Differentiating the rule with respect to inflation gives its key property.

In words, each extra point of inflation raises the rule's policy rate by one and a half points.

Going from 2 % to 5 % inflation with no change in the output gap moves the rule from 4.00 % to 8.50 %, three points of inflation and four and a half points of rate. An output gap of −4 %, the size Okun's law gives for unemployment two points above normal, lowers the rule by two points. So a deep recession with low inflation can push the rule below zero: with inflation at 1 % and a gap of −6 %, it gives −0.50 %. A central bank cannot set a rate that low, which is why it turns to QE.

Basis points and the 2022 cycle

A basis point is one hundredth of a percentage point. The Fed raised the top of its target range from 0.25 % on 16 March 2022 to 4.50 % on 14 December 2022, an increase of +425 bp in nine months, the fastest pace since the early 1980s.

Expectations and the term premium

Suppose the one-year rate is 4 % today and markets expect 5 % for next year. Under pure expectations, a two-year bond must give the same result as rolling two one-year bonds.

In words, two years at the two-year yield must match a year at today's one-year rate followed by a year at next year's expected one-year rate, plus any term premium.

Without a term premium the two-year yield comes to 4.50 %. With a term premium of 0.3 points it comes to 4.80 %. Reading expected policy from the curve means first taking a view on the term premium, which is why two analysts can see the same curve and disagree about what the market expects.

The fiscal multiplier

In the simplest model each dollar of income is spent at a rate $c$, the marginal propensity to consume, with a tax rate $t$ and an import share $m$ of each dollar of income leaking out.

In words, the multiplier is one over one minus the share of each dollar that is spent again at home.

With $c = 0.8$ and no taxes or imports the multiplier is 5.00, a number nobody finds in data. Adding a 25 % tax rate and a 15 % import share brings it to 1.82. Empirical estimates sit lower still, mostly between about half and two, because rates and prices respond and some people save windfalls.

Debt dynamics: the r minus g equation

Let $d_t$ be debt over GDP, $r$ the interest rate on the debt, $g$ nominal GDP growth and $\text{pb}$ the primary balance as a share of GDP (negative for a deficit).

In words, next year's debt ratio is this year's grown by one plus the interest rate over one plus the growth rate, minus the primary surplus.

Level 4 History, analysed

For readers who want past episodes run through the Level 3 math.

1979 to 1982: Volcker breaks inflation

Consumer prices were 14.8 % higher in March 1980 than a year before. Subtracting the year's inflation from the June 1981 funds rate gives a real policy rate of about +9.5 %, the tightest in the postwar era. Run on core PCE inflation of 8.86 % and an output gap of −0.07 % in the first quarter of 1980, the Taylor rule gives 14.2 % against an actual average of 15.05 %: by that quarter, policy had caught up with the rule. Long rates followed short ones: the ten-year Treasury yield peaked at 15.84 % on 30 September 1981. Two recessions followed, and inflation came down for good; bondholders who bought near that peak earned high real returns for the next two decades as yields fell.

1994: the bond market's bad year

That move in the ten-year yield comes to +286 bp. A ten-year Treasury bought at par with a 5.19 % coupon had a modified duration of 7.73 years. Duration alone predicts a price change of −22.1 %; repricing the bond at 8.05 % gives −19.4 %, a smaller loss because of convexity, the curve in the price-yield line that softens losses as yields rise. Coupons received during the year offset part of that. Investors who had borrowed to hold long bonds, expecting rates to stay low, took the full loss with leverage; Orange County in California, whose investment pool had done that, filed for bankruptcy in December 1994. Inflation stayed low after 1994 and the economy did not fall into recession, which is why many economists count it as a successful pre-emptive tightening.

2008 to 2014: zero rates and quantitative easing

With the short rate at zero, the Fed worked on long rates instead. Its total assets went from $0.91 trillion on 3 September 2008 to $4.52 trillion on 14 January 2015, 5.0 times as large (Federal Reserve H.4.1 via FRED). In the Taylor rule's terms the rule called for a negative rate in 2009, which the Fed could not set, and QE was its substitute. Short rates stayed near zero for seven years: the effective rate averaged 0.24 % in December 2015, the month of the first rise. Low long rates lifted the present value of distant cash flows, the effect Chapter 4 shows for Japan.

2022: late, then fast

Level 3 showed the Taylor rule calling for 9.3 % in the second quarter of 2022 while the funds rate averaged 0.77 %. Catching up hit bonds hard. From 1.52 % at the end of 2021 the ten-year yield climbed to 3.88 % at the end of 2022. With a duration of about 6.6 years going in, the Bloomberg US Aggregate bond index should have lost about −15.6 % on duration alone. It returned about −13.0 % for the year (Bloomberg). Coupon income and convexity account for most of the difference, and the index's own yields rose by a different amount from the ten-year Treasury's. Stocks fell in the same year, so a mix of stocks and bonds lost on both sides at once, the pairing Chapter 2 traced in 1973 and 1974. Over the same period the Fed's balance sheet, which had reached $8.97 trillion in April 2022, 9.9 times its size in September 2008, began to shrink under QT.

What the four episodes share

In each case the gap between the policy rate and where a simple rule put it told investors something. The gap was large and positive in 2022, as it had been through much of the 1970s, and the correction came fast and hurt bond holders. In 1994 the Fed moved before inflation showed, and bonds took the loss up front with no recession. After 2008 the rule pointed below zero, and the Fed used its balance sheet to do what the rate could not. We do not use the Taylor rule to forecast the next meeting. We use it to ask how far rates could have to move if inflation does not behave, and to size the bond loss with duration if they do. A gap of four points between the rule and the funds rate, closed within a year, means roughly a four-point rise in the funds rate; how much of that reaches ten-year yields decides most of what a bond fund loses. In 2022 a little over half of it did.