*This blog post accompanies the SDPR Morning Macro*

*segment that airs on Monday, Dece*

*mber*

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Interest rates attract enormous attention in the financial press, and no wonder: credit—and, so, the cost of financing credit—supports many of the economic activities in which households, firms, and governments around the world engage. In this regard, the U.S. is no exception. For example, as of the second quarter of 2019, aggregate household debt averaged roughly 84 percent of disposable income; meanwhile, household debt-service payments averaged roughly 10 percent of disposable income—the subject of the next * Morning Macro*. Conditional on the level of debt outstanding, the principal determinant of the amount of debt-service payments is the nominal interest rate or, more simply, the interest rate: the explicit, monetary cost of servicing debt.

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**Nevertheless, the nominal rate is not the whole story, or so says Irving Fisher; more on him in a moment**The nominal interest rate is the stated yield to maturity of a debt instrument, such as a government bond, a car loan, a credit-card debt, or a home mortgage. As such, the nominal interest rate measures the return to lenders—and, thus, the financing cost to borrowers—in terms of dollars. In Figure 1, I illustrate nominal interest rates on U.S. Treasury bonds—think, IOUs sold by the U.S. government and bought by savers, including U.S. households—that, in the case of Figure 1, mature in either five or ten years; most other interest rates, including those charged on car, consumer, and home loans, are based on the interest rates associated with these U.S. Treasury bonds, which present little if any default risk. (For more on U.S. Treasury debt, see the Morning Macro segment, “Fiscal Therapy.”)

During the time period illustrated in Figure 1, U.S. Treasury yields range from roughly 1 to 5 annual percentage points. So, for example, in October 2019, the interest rate on the ten-year U.S. Treasury bond (indicated by the red line) was 1.71 percent; thus, for every $100 the U.S. Treasury borrowed in October 2019, it must pay $1.71 of interest one year later. Because 1.71 percent is a nominal interest rate, it does not convey the purchasing power of $1.71 in terms of the value of money at the time the U.S. Treasury borrowed the $100. For example, will $101.71—the $100 the U.S. Treasury borrowed plus the $1.71 of accrued interest—purchase 1.71 percent more goods and services than $100 purchased in October 2019? If not, the nominal interest rate differs from the real interest rate, which measures the return to lenders—and the financing cost to borrowers—in terms of (real) purchasing power.

The difference between nominal and real interest rates is the expected inflation rate. Economists typically define inflation as a persistent, annual rise in the overall price level; or, put another way, inflation describes a persistent, annual fall in the purchasing power of money—the very same money that lenders surrender, for a time, to borrowers. (For more on inflation, see the Morning Macro segment, “Follow the Yellow Brick Road.”) All else equal, inflation reduces—think, erodes—the real return to lenders. In doing so, unexpected inflation rates—for which neither lenders nor borrowers bargained—redistribute income from lenders to borrowers; more on this redistribution effect later in this segment.

This relationship between nominal interest rates, real interest rates, and expected inflation rates occurs because of fierce competition among borrowers and lenders who effectively “price” into nominal interest rates—and, thus, the terms of a loan contract—expected inflation rates; borrowers and lenders do this in an attempt to secure some desired real interest rate. **This process of pricing expected inflation into nominal interest rates is called the Fisher effect, named for Irving Fisher, a leading early twentieth-century American economist.**

The Fisher effect is specified as the following.

i = r + π^{e}

In this expression, the term i is the nominal interest rate, r is the real interest rate, and π^{e} is the expected inflation rate—the inflation rate that borrowers and lenders expect to occur during the term of the loan (for which i is the nominal interest rate). In Figure 2, I illustrate the bond market’s expected inflation rates over five-year (blue line) and ten-year (red line) forecast horizons.

During the time period illustrated in Figure 2, expected inflation rates range from roughly 3 to negative 1.5 annual percentage points. Positive expected inflation rates reveal that the bond market expects a persistent, annual fall in the purchasing power of money; meanwhile, negative expected inflation rates, such as those during the Great Recession, reveal that the bond market expects a persistent, annual rise in the purchasing power of money—that is, a deflation. Negative expected inflation rates, which typically coincide with extremely weak economic activity, are thankfully rare. As of October 2019, expected inflation rates over the ten-year forecast horizon (red line) averaged an annual rate of roughly 1.56 percent, below the Federal Reserve’s 2-percent inflation target.

According to the Fisher effect, subtracting the expected inflation rate—say, the red line in Figure 2—from the nominal interest rate—say, the red line in Figure 1—yields the (expected or so-called ex-ante) real interest rate. In Figure 3, I illustrate nominal and real interest rates based on the ten-year forecast horizon; thus, the solid line in Figure 3, the nominal interest rate on U.S. Treasury bonds that mature in ten years, is precisely the red line in Figure 1.

In Figure 3, the vertical distance between the solid and dashed lines is the expected inflation rate (the red line in Figure 2), which, for the period illustrated, registered an annual rate of around 2.1 percent. The co-movement between the two series in Figure 3 illustrates the Fisher equation: the nominal interest rate and the expected inflation rate determine the real interest rate (the dashed line in Figure 3) that borrowers and lenders secure. * As of October 2019, the real interest rate over the ten-year forecast horizon was roughly 0 percent, revealing a relatively accommodative interest rate environment, to say the least*. In Figure 4, I illustrate the nominal and real interest rates based on the five-year forecast horizon; thus, the solid line in Figure 4, the nominal interest rate on U.S. Treasury bonds that mature in five years, is precisely the blue line in Figure 1.

Consider, in Figure 3 or 4, real interest rates (the dotted line) during the Great Recession, when, for a time, the nominal interest rate fell far less than one-for-one with the large fall of the expected inflation rate, causing the real interest rate to rise dramatically. In this case, the nominal interest rate did not keep pace with the very sudden turn in market sentiment toward expectations of deflation—a negative expected inflation rate. As Figures 3 and 4 illustrate, such outcomes are exceptions to the Fisher effect rule. Finally, consider (again in either Figure 3 or 4) the path of the real interest rate during much of 2012, when the nominal interest rate fell while the expected inflation rate did not; in this case, the real interest rate turned negative: in terms of purchasing power, lenders paid borrowers—a redistribution of income that lenders surely did not intend or wish to repeat.

* So what does the Fisher effect tell us about the current stance of monetary policy and, so, the current returns to saving and costs to borrowing imposed on households?* In Figure 5, I illustrate the nominal federal funds rate, the (interbank) interest rate that banks charge each other for bank reserves, along with the (ex-post) real federal funds rate (the dashed line); to calculate the latter, I subtract actual inflation from the nominal federal funds rate. (For more on targeting the federal funds rate as a tactic of monetary policy, see the Morning Macro segment, “Mind the Gaps.”)

Since the Great Recession, the Federal Reserve has kept monetary policy relatively accommodative. To be sure, for much of the last ten years, the federal funds rate has remained at or very near zero—at the so-called zero lower bound. And most interestingly, * although the Federal Reserve’s response to the Great Recession never included a policy of negative (nominal) interbank interest rates, the real federal funds rate has lingered below zero for much of the decade since the financial crisis*; and even now the real federal funds rate hovers between zero and 1 percent. Generally speaking, negative short-term real interest rates—including short-term interbank rates—are not unprecedented; though a decade-long episode is. For example, in Figure 6, I illustrate the nominal and real federal funds rates back to 1960; since then, the real federal funds rate has lingered below zero only once: between 1974 and 1977, during the Great Inflation.

As we covered in an earlier Morning Macro segment (“Mind the Gaps“), the U.S. economy has now very nearly achieved full employment (because the output gap is slightly positive) and price stability (because the inflation gap is slightly negative); thus, according to the Taylor rule, the current real federal funds rate should roughly equal r*, the long-run, natural real rate of interest. So, either the long-run, natural real rate of interest is between zero and 1 percent or current Federal Reserve monetary policy is exceptionally accommodative—that is, r < r*. Given our (human?) tendency to prefer consumption now to consumption later—and, thus, given our tendency to demand a positive real interest rate as our reward for saving (and forgoing current consumption)—it is difficult to imagine that the long-run, natural real rate of interest is equal to the current real federal funds rate.

In any case, households are not immune to the Federal Reserve’s relatively accommodative monetary policy stance since the Great Recession; this is to say, the effect of this stance is evident in the behavior of all real interest rates, not just those attached to U.S. Treasury bonds, say. For example, in Figure 7, I illustrate nominal and real interest rates on conventional 30-year residential mortgage loans; the vast majority of aggregate U.S. household debt consists of mortgage debt.

Since the Great Recession, the real interest rate on a conventional mortgage loan has mostly hovered around 2 percent; as of October 2019, the rate averaged 2.05 percent. Thus, like the U.S. Treasury since the Great Recession (see Figures 3 and 4), U.S. households have been able to borrow at relatively low real interest rates.

Finally, although the Fisher effect implies that, in market equilibrium, the expected inflation rate is the difference between the nominal interest rate and the real interest rate, households (or debtors more generally) already bound by the fixed terms of a loan contract cannot adjust to unexpected inflation, which capriciously redistributes income between borrowers and lenders. For example, a household servicing a mortgage with fixed nominal interest-rate terms will gain [lose] if the inflation rate rises [falls] unexpectedly. **Most debtors and creditors are acutely aware of changes in the nominal interest rate; they should be even more aware of changes in the real interest rate and, by Fisherian association, changes in the inflation rate.**