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How Interest Rates Are Set: The Fed's New Tools Explained

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Read these articles in order.

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Must Read!!!

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Why did the Fed start paying Interest on Excess Reserves?

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Four decades ago, Milton Friedman recommended that central banks like the Federal Reserve pay interest to depository institutions on the reserves they are required to hold against their deposit liabilities. This proposal was intended to improve monetary policy by making it easier to hit short-term interest rate targets. However, the Fed didn't have the authority to pay this kind of interest until 2008.

This new policy is especially important now that the Fed has been holding more than $1 trillion dollars in total reserves from depository institutions for the past three years. Total reserve balances held at the Fed include required reserves and any excess reserves that depository institutions choose to hold on top of the required reserves.

In the United States, paying interest on reserve balances was designed to broaden the scope of the Fed's lending programs to address conditions in credit markets while maintaining the federal funds rate close to the target established by the Federal Open Market Committee (FOMC), the Fed's monetary policy decisionmakers.

Globally, a number of central banks have the authority to pay interest on reserves held against deposits. For example, the Bank of England has paid interest on reserves since 2009, and the European Central Bank has had this authority from its inception in 1999.
Interest on reserves adopted by the U.S. Congress in 2006
Before the crisis, Congress passed the Financial Services Regulatory Relief Act of 2006 authorizing the Federal Reserve to begin paying interest on reserves held against certain types of deposit liabilities. The legislation was supposed to go into effect beginning October 1, 2011. However, during the financial crisis, the effective date was moved up by three years through the Emergency Economic Stabilization Act of 2008. This was important for monetary policy because the Federal Reserve's various liquidity facilities initiated during the financial crisis caused upward pressure on excess reserves and placed downward pressure on the Federal funds rate. To counteract these pressures, on October 6, 2008, the Federal Reserve Board announced that it would begin paying interest on depository institutions' reserve balances.

In the rest of this response, I will focus on the details of these interest rate payments and discuss why they were implemented.
Required and excess reserves before and after the crisis
Under the 2006 Act, Federal Reserve Banks were directed to

...pay interest on required reserve balances (that is, balances held to satisfy depository institutions' reserve requirements) and on excess balances (balances held in excess of required reserve balances and clearing balances).

In 2007, required reserves averaged $43 billion, while excess reserves averaged only $1.9 billion. This relationship was typical for the past 50 years when the Fed did not pay interest on reserves with only two exceptions. Those occurred when the Fed provided unusual levels of reserves to depository institutions in September 2001 following the terrorist attacks and in August 2007 at the onset of the global financial crisis. Other than those two months, excess reserves were less than 10% of total reserve holdings, because depository institutions had an incentive to minimize noninterest-bearing excess reserves held at the Fed.

The failure of high profile U.S. financial institutions in September 2008 caused a great degree of instability in the financial system. Consistent with its role as a lender of last resort, the Fed provided unprecedented amounts of liquidity to the financial system. Once the Fed was authorized to pay interest on reserves, the relationship between the levels of required reserves and excess reserves changed dramatically. For example, required reserves averaged almost $100 billion during the first six months of 2012, while excess reserves averaged $1.5 trillion! As shown in Figure 1, since September 2008, the vast majority of total reserves (blue line) held at the Fed belong to the excess reserves category (black line), while required reserves for all depository institutions (red line) have remained relatively stable.
Figure 1. The Close Historical Relationship between Total and
Required Reserves Ended during the Financial Crisis.
Paying interest on reserves gives policymakers more control over the federal funds rate
The Fed's new authority gave policymakers another tool to use during the financial crisis. Paying interest on reserves allowed the Fed to increase the level of reserves and still maintain control of the federal funds rate. As the Board's website states, "Paying interest on excess balances should help to establish a lower bound on the federal funds rate." The Board's October 6, 2008, Press Release described the new policy this way:

The payment of interest on excess reserves will permit the Federal Reserve to expand its balance sheet as necessary to provide the liquidity necessary to support financial stability while implementing the monetary policy that is appropriate in light of the System's macroeconomic objectives of maximum employment and price stability.

This was compelling in the months after September 2008, as the financial crisis deepened, Fed lending from the discount window soared, lending from the newly created liquidity facilities spiked, and excess reserves climbed into the hundreds of billions of dollars range, far exceeding depositories' required reserves.

In this situation, the Federal Reserve Bank of New York said that the Open Market Desk

...encountered difficulty achieving the operating target for the federal funds rate set by the FOMC, because the expansion of the Federal Reserve's various liquidity facilities has caused a large increase in excess balances. The expansion of excess reserves in turn has placed extraordinary downward pressure on the overnight federal funds rate. Paying interest on excess reserveswill better enable the Desk to achieve the target for the federal funds rate.

Interest on Reserves will play an import role in the Fed's 'exit strategy' as well
Essentially, paying interest on reserves allows the Fed to place a floor on the federal funds rate, since depository institutions have little incentive to lend in the overnight interbank federal funds market at rates below the interest rate on excess reserves. This allows the Desk to keep the federal funds rate closer to the FOMC's target rate than it would have been able to otherwise.

Finally, the Fed can change the rate for interest on reserves to adjust the incentives for depository institutions to hold reserves to a level that is appropriate for monetary policy. This also provides an important "exit strategy" tool, which will allow the Fed to better control the level of excess reserves when it begins to remove monetary policy stimulus.

What is the interest rate on reserve balances?

When interest on reserves was first implemented, the Federal Reserve Board used a formula that set the rate paid on required reserves above the rate on excess reserve balances. However, in late 2008 the Board released a series of press releases (See Related Press Releases) announcing adjustments to this formula. Since January 2009, the monthly average interest rate on both required reserve and excess reserve balances has been 25 basis points, or 0.25% at an annual rate, in keeping with the federal funds target range of 0 to 25 basis points during this period (see Figure 2).
Figure 2. History of the Federal Funds Target Interest Rate and
Interest Rates on Required Reserves and Excess Reserves Date of publication: First Quarter 2013 Resources
For more information on these rates please visit the Board's website, Interest on Required Balances and Excess Reserves.

Amstad, Marlene, and Antoine Martin. 2011. "Monetary Policy Implementation: Common Goals but Different Practices." Current Issues in Economics and Finance 7(7), Federal Reserve Bank of New York.

Bernanke, Ben. 2010. "Federal Reserve's Exit Strategy." Testimony before the Committee on Financial Services, U.S. House of Representatives, Washington, D.C., February 10.

Board of Governors of the Federal Reserve System. 2008. "Press Release," October 6.

Board of Governors of the Federal Reserve System. 2011. "Credit and Liquidity Programs and the Balance Sheet." Website, accessed January 2013.

Board of Governors of the Federal Reserve System. 2013a. "Aggregate Reserves of Depository Institutions and the Monetary Base." H.3 Release, website, accessed January 2013.

Board of Governors of the Federal Reserve System. 2013b. "Interest on Required Balances and Excess Reserves." Website, accessed January 2013.

Board of Governors of the Federal Reserve System. 2013c. "Reserve Requirements." Website, accessed January 2013.

Bowman, David, Etienne Gagnon, and Mike Leahy. 2010. "Interest on Excess Reserves as a Monetary Policy Instrument: The Experience of Foreign Central Banks." International Financial Discussion Papers 996, pp. 11-14, Board of Governors of the Federal Reserve System.

Bullard, James. 2011. "The Fed's Emergency Liquidity Facilities: Why They Were Necessary." The Regional Economist (January), Federal Reserve Bank of St. Louis.

Federal Reserve Bank of New York. 2013. "FAQs about Interest on Reserves and the Implementation of Monetary Policy." Website, accessed January 2013.

Gage, Caroline Salas, and Liz Capo McCormick. "Fed Weighs Cutting Interest on Banks' Reserves after ECB Move." Bloomberg.com, July 30.

Goodfriend, Marvin. 2002. "Interest on Reserves and Monetary Policy." FRBNY Economic Policy Review (May), Federal Reserve Bank of New York.
Data and Resources on Reserves
Walter, John R., and Renee Haltom. 2009. "The Effect of Interest on Reserves on Monetary Policy." Economic Brief EB09-12, Federal Reserve Bank of Richmond, December.

For current data on the level of reserves please see the Federal Reserve Board's weekly H.3 Release, Aggregate Reserves of Depository Institutions and the Monetary Base.
End Notes
For information on the reserves that depository institutions (including commercial banks, savings institutions, credit unions, and foreign agencies and branches) are required to hold by the Federal Reserve System, please link to "Reserves."

1. See the Board of Governors website for a description of reserve requirements and how they are calculated. Goodfriend (2002) and Walter and Haltom (2009) provide some insights into this policy issue.

2. Amstad and Martin (2011). For additional detail on the Bank of England's (and several other central banks) policy of paying interest on reserves, see Bowman, Gagnon, and Leahy 2010.

. The gray bar represents the 2007-2009 recession as defined by the National Bureau of Economic Research (NBER). See Dr. Econ, June 2003, "Which organization determines whether the U.S. economy is in a recession" or Dr. Econ, January 2008, "How many recessions have occurred in the U.S. economy?" or the National Bureau of Economic Research.

. Note that some nonbank institutions, for example government-sponsored enterprises (GSEs), still hold deposits at the Fed that do not earn interest. These institutions may be willing to engage in transactions below the rate for interest on reserves, explaining why the federal funds rate may still drop below that rate at times.

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Why did the Federal Reserve start paying interest on reserve balances held on deposit at the Fed? Does the Fed pay interest on required reserves, excess reserves, or both? What interest rate does the Fed pay?

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Four decades ago, Milton Friedman recommended that central banks like the Federal Reserve pay interest to depository institutions on the reserves they are required to hold against their deposit liabilities. This proposal was intended to improve monetary policy by making it easier to hit short-term interest rate targets.

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The Taylor Rule is an interest rate forecasting model invented by famed economist John Taylor in 1992 and outlined in his 1993 study, " Discretion Versus Policy Rules in Practice." It suggests how central banks should change interest rates to account for inflation and other economic conditions.

The Taylor Rule suggests that the Federal Reserve should raise rates when inflation is above target or when gross domestic product (GDP) growth is too high and above potential. It also suggests that the Fed should lower rates when inflation is below the target level or when GDP growth is too slow and below potential.

The Taylor Rule Background

Taylor operated in the early 1990s with credible assumptions that the Federal Reserve determined future interest rates based on the rational expectations theory of macroeconomics. This is a backward-looking model that assumes if workers, consumers, and firms have positive expectations for the future of the economy, then interest rates don't need an adjustment.

Taylor noted that the problem with this model is not only that it is backward-looking, but it also doesn't take into account long-term economic prospects. This situation brought rise to the Taylor Rule.

Since its inception, the Taylor Rule has served not only as a gauge of interest rates, inflation, and output levels, but also as a guide to gauge proper levels of the money supply.

The Taylor Rule Formula

I = nominal fed funds rate
R* = real federal funds rate (usually 2%)
PI = rate of inflation
P* = target inflation rate
Y = logarithm of real output
Y* = logarithm of potential output

The product of the Taylor Rule is three numbers: an interest rate, an inflation rate and a GDP rate, all based on an equilibrium rate to gauge the proper balance for an interest rate forecast by monetary authorities.

This formula suggests that the difference between a nominal interest rate and a real interest rate is inflation. Real interest rates account for inflation while nominal rates do not. To compare rates of inflation, one must look at the factors that drive it.

Three Factors That Drive Inflation

Prices and inflation are driven by three factors: the consumer price index (CPI), producer prices, and the employment index. Most nations in the modern day look at the consumer price index as a whole rather than look at core CPI. This method allows an observer to look at the total picture of an economy in terms of prices and inflation since core CPI excludes food and energy prices.

Rising prices mean higher inflation, so Taylor recommends factoring the rate of inflation over one year (or four quarters) for a comprehensive picture.

He recommends the real interest rate should be 1.5 times the inflation rate. This is based on the assumption of an equilibrium rate that factors the real inflation rate against the expected inflation rate. Taylor calls this the equilibrium, a 2% steady state, equal to a rate of about 2%. But that's only part of the equation-output must be factored in as well.

To properly gauge inflation and price levels, apply a moving average of the various price levels to determine a trend and to smooth out fluctuations. Perform the same functions on a monthly interest rate chart. Follow the fed funds rate to determine trends.

Determining Total Economic Output

The total output of an economy can be determined by productivity, labor force participation, and changes in employment. For the Taylor Rule calculation, we look at real output against potential output.

The Taylor Rule looks at GDP in terms of real and nominal GDP, or what Taylor calls actual and trend GDP. It factors in the GDP deflater, which measures prices of all goods produced domestically. We do this by dividing nominal GDP by real GDP and multiplying this figure by 100.

The answer is the figure for real GDP. We are deflating nominal GDP into a true number to fully measure total output of an economy.

When inflation is on target and GDP is growing at its potential, rates are said to be neutral. This model aims to stabilize the economy in the short term and to stabilize inflation over the long term.

The Taylor Rule and Asset Bubbles

Some people thought the central bank was to blame-at least partly-for the housing crisis in 2007-2008. They assert that interest rates were kept too low in the years following the dot-com bubble and leading up to the housing market crash in 2008.

This is what causes asset bubbles, so interest rates must eventually be raised to balance inflation and output levels. A further problem of asset bubbles is money supply levels rise far higher than is needed to balance an economy suffering from inflation and output imbalances.

Had the central bank followed the Taylor rule during this time, which indicated the interest rate should be much higher, the bubble may have been smaller, as less people would have been incentivized to buy homes.

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The Taylor Rule: An Economic Model for Monetary Policy

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The Taylor Rule is an interest rate forecasting model invented by famed economist John Taylor in 1992 and outlined in his 1993 study, " Discretion Versus Policy Rules in Practice." It suggests how central banks should change interest rates to account for inflation and other economic conditions.

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Stanford economist John Taylor's many contributions to monetary economics include his introduction of what has become known as the Taylor rule (as named by others, not by John). The Taylor rule is a simple equation-essentially, a rule of thumb-that is intended to describe the interest rate decisions of the Federal Reserve's Federal Open Market Committee (FOMC).

The Taylor rule is a valuable descriptive device. However, John has argued that his rule should prescribe as well as describe-that is, he believes that it (or a similar rule) should be a benchmark for monetary policy. Starting from that premise, John has been quite critical of the Fed's policies of the past dozen years or so. He repeated some of his criticisms at a recent IMF conference in which we both participated. In short, John believes that the Fed has not followed the prescriptions of the Taylor rule sufficiently closely, and that this supposed failure has led to very poor policy outcomes. In this post I will explain why I disagree with a number of John's claims.

Taylor Rule Basics

I'll begin with some Taylor rule basics. Historically, the FOMC has set monetary policy by raising or lowering its target for the federal funds rate, the interest rate at which banks make overnight loans to each other. The Taylor rule, which John introduced in a 1993 paper, is a numerical formula that relates the FOMC's target for the federal funds rate to the current state of the economy. Here's the formula:

where

r = the federal funds rate

p = the rate of inflation

y = the percent deviation of real GDP from a target

Normally, the Fed's "target" for real GDP is potential output, the amount the economy can sustainably produce when capital and labor are fully employed. With that assumption, the variable y in the Taylor rule can be interpreted as the excess of actual GDP over potential output, also known as the output gap.

To put the equation into words, the (original) Taylor rule predicts that the FOMC will raise the federal funds rate (tighten monetary policy) by one-half percentage point:

(1) for each percentage point that inflation rises relative to the Fed's target, assumed to be 2 percent; or

(2) for each percentage point that that output rises relative to its potential.

The Taylor rule also predicts that when inflation is at target and output is at potential (the output gap is zero), the FOMC will set the real federal funds rate at 2 percent-about its historical average. In his 1993 paper, John showed that the rule described FOMC behavior over the previous half dozen years or so quite well.

Taylor's Critique of Fed Policy

The Taylor rule provides a nice, simple description of how monetary policy has been made in the past. But what does it say about how monetary policy should be made?

Originally, John did not seem to believe that his eponymous rule should be more than a general guideline. Indeed, in his 1993 article, he took pains to point out that a simple mechanical rule could not take into account the many factors that policymakers must consider in practice. (See my IMF remarks for a relevant passage from Taylor 1993. See also Taylor 1999.) I believe that John's original view was sensible. As a policymaker I often referred to various policy rules, including variants of the Taylor rule. However, it seemed to me self-evident that such rules could not incorporate all the relevant considerations for making policy in a complex, dynamic economy.

Lately, though, John has taken a much more prescriptive view, essentially arguing that policy should hew closely to the Taylor rule (or a similar rule) virtually all the time, and that even relatively small deviations from the rule can have enormous costs. He has made two specific claims, see for example here and here:

First, John argues that the FOMC kept interest rates much lower than prescribed by the Taylor rule during 2003-2005, and that this deviation was a major source of the housing bubble and other financial excesses.

Second, he asserts that the Fed's monetary policy since the financial crisis has not been sufficiently rule-like, and that policy has been too easy. He says that, if the FOMC had been following the Taylor rule, it would have ended its policy of near-zero interest rates several years ago. He blames much of the disappointing recovery on the Fed's putative deviations from the Taylor rule.

The basis of John's claims is findings like those of Figure 1 below, which is my update of the original Taylor rule for the period 1993 to the present. To construct Figure 1, I followed Taylor's original paper and measured inflation using the GDP deflator (more on this in a moment). To measure the output gap, for the period through 2009 I used estimates prepared by Federal Reserve staff for FOMC meetings, which are disclosed after a five year lag. For 2010 through the present, for which Fed staff estimates of the output gap are not yet publicly available, I used estimates produced and published by the Congressional Budget Office. Importantly, for all figures in this post, I used only data that were known to policymakers at the time they made their decisions. Because initial data are often substantially revised, using real-time data is essential for evaluating policy choices. (See my note for more information about data sources and this file for the data itself).

As you can see, the figure shows the actual fed funds rate falling below the Taylor rule prescription both in 2003-2005 and since about 2011. That is, if the Taylor rule shown in Figure 1 is the benchmark, then monetary policy was at least somewhat "too easy" in both those periods.

I responded to assertions similar to John's first claim, that too-easy money caused the US housing bubble, in a 2010 speech. Briefly, I argued there that the Fed's interest-rate policies in 2003-2005 can't explain the size, timing, or global nature of the housing bubble. I won't repeat those points here. Instead, I want here to address John's critique on its own grounds, by examining whether it's really true that-relative to a plausible Taylor rule benchmark-US monetary policy was too easy during 2003-2005 and in the period since the crisis.

A Modified Taylor Rule

To check the robustness of John's claims, I calculated the policy predictions of a Taylor-type rule that was modified in two ways that seem sensible to me.

First, I changed the measure of inflation used in the Taylor rule. In his 1993 paper, John chose to measure inflation using a price index known as the GDP deflator (I used that measure of inflation in constructing Figure 1 above). However, when talking about inflation, economists (and the FOMC) usually mean the rate of increase of consumer prices. The GDP deflator incorporates not only the prices of domestically produced consumer goods and services, but also other categories of prices, such as the prices of capital goods and the imputed prices of government spending (on defense, for example). It also excludes the prices of imports, including imported consumer goods.

In practice, the FOMC has long been clear that its preferred measure of inflation is the rate of change in consumer prices, as reflected specifically in the deflator for personal consumption expenditures (PCE). The FOMC targets overall PCE inflation, but has typically viewed core PCE inflation (which excludes volatile food and energy prices) as a better measure of the medium-term inflation trend and thus as a better predictor of future inflation. Accordingly, I define inflation for the purposes of my modified Taylor rule as core PCE inflation. ¹

Second, it's important to consider how policy responds, quantitatively, to changes in inflation and the output gap. The original Taylor rule assumes that the funds rate responds by a half-percentage point to a one percentage point change in either inflation or the output gap (that is, the coefficient on both variables is 0.5). In principle, the relative weights on the output gap and inflation should depend on, among other things, the extent to which policymakers are willing to accept greater variability in inflation in exchange for greater stability in output. Some research subsequent to John's original paper, summarized by Taylor (1999), found a case for allowing a larger response of the funds rate to the output gap (specifically, a coefficient of 1.0 rather than 0.5). In my experience, the FOMC paid closer attention to variants of the Taylor rule that include the higher output gap coefficient. For example, Janet Yellen has suggested that the FOMC's "balanced approach" in responding to inflation and unemployment is more consistent with a coefficient on the output gap of 1.0, rather than 0.5. In my modified Taylor rule I assumed the higher coefficient on the output gap.

Figure 2 below shows the predictions for the federal funds rate of my preferred version of the Taylor rule, which measures inflation using the core PCE deflator and assumes that the weight on the output gap is 1.0 rather than 0.5.

As you can see in the figure, the predictions of my updated Taylor rule (green line) and actual Fed policy (dashed black line) are generally quite close over the past two decades (the green line starts in 1996 because real-time data for the core PCE deflator are not available before then). In particular, it is no longer the case that the actual funds rate falls below the predictions of the rule in 2003-2005.

As for the period since the financial crisis, the modified Taylor rule in Figure 2 suggests that the "right" funds rate was quite negative, at least until very recently. If the Taylor rule predicts a sharply negative funds rate, which of course is not feasible, then it seems sensible for the FOMC to have done what it did: keep the funds rate close to zero (about as low as it can go) while looking for other tools (like purchases of securities) to achieve further monetary ease. ²

As John points out, the US recovery has been disappointing. But attributing that to Fed policy is a stretch. The financial crisis of 2007-2009 was the worst at least since the Depression, and it left deep scars on the economy. The recovery faced other headwinds, such as tight fiscal policy from 2010 on and the resurgence of financial problems in Europe. Compared to other industrial countries, the US has enjoyed a relatively strong recovery from the Great Recession.

In short, Figure 2 argues against Taylor's two criticisms, on their own terms. Relative to a modified but plausible Taylor rule, monetary policy since the early 1990s seems reasonable and consistent.

It could be argued, of course, that my two modifications of the original Taylor rule are not reasonable. Frankly, I don't think there is much of a case for not employing real-time data or for using the GDP deflator to measure inflation rather than using overall or core PCE inflation. With respect to the choice of the weight on the output gap, the research on Taylor rules does not provide much basis for choosing between 0.5 and 1.0. However, the choice of 1.0 seems best to describe the FOMC's efforts to support job growth while also keeping inflation close to target in the medium term.

I also note an odd feature of the Taylor rules I estimated with the original coefficient of 0.5 on the output gap. No matter what inflation measure is chosen, such rules tend to imply that Fed policy was too tight in the 1990s, as well as too easy in 2003-2005. (You can see this result for the GDP deflator in Figure 1. It's also true if overall PCE inflation is used as the inflation measure.) If easy money is an important cause of bubbles, how can the large gains in the stock market in the 1990s be reconciled with monetary policy that appears if anything too tight?

Monetary Policy: Systematic, Not Automatic

I've shown that US monetary policy since the early 1990s is pretty well described by a modified Taylor rule. Does that mean that the Fed should dispense with its elaborate deliberations and simply follow that rule in the future? In particular, would it make sense, as Taylor proposes, for the FOMC to state in advance its rule for changing interest rates?

No. Monetary policy should be systematic, not automatic. The simplicity of the Taylor rule disguises the complexity of the underlying judgments that FOMC members must continually make if they are to make good policy decisions. Here are just a few examples (not an exhaustive list):

The Taylor rule assumes that policymakers know, and can agree on, the size of the output gap. In fact, as current debates about the amount of slack in the labor market attest, measuring the output gap is very difficult and FOMC members typically have different judgments. It would be neither feasible nor desirable to try to force the FOMC to agree on the size of the output gap at a point in time.

The Taylor rule also assumes that the equilibrium federal funds rate (the rate when inflation is at target and the output gap is zero) is fixed, at 2 percent in real terms (or about 4 percent in nominal terms). In principle, if that equilibrium rate were to change, then Taylor rule projections would have to be adjusted. As noted in footnote 2, both FOMC participants and the markets apparently see the equilibrium funds rate as lower than standard Taylor rules assume. But again, there is plenty of disagreement, and forcing the FOMC to agree on one value would risk closing off important debates.

The Taylor rule provides no guidance about what to do when the predicted rate is negative, as has been the case for almost the entire period since the crisis.

There is no agreement on what the Taylor rule weights on inflation and the output gap should be, except with respect to their signs. The optimal weights would respond not only to changes in preferences of policymakers, but also to changes in the structure of the economy and the channels of monetary policy transmission.

I don't think we'll be replacing the FOMC with robots anytime soon. I certainly hope not.

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The Taylor Rule: A benchmark for monetary policy?

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Stanford economist John Taylor's many contributions to monetary economics include his introduction of what has become known as the Taylor rule (as named by others, not by John). The Taylor rule is a simple equation-essentially, a rule of thumb-that is intended to describe the interest rate decisions of the Federal Reserve's Federal Open Market Committee (FOMC).

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Following A Modernized Version of the Taylor Rule Part 1

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Academic research on monetary policy rules is voluminous. One of the most famous rules was published in 1993 by John Taylor, a well-known academic economist from Stanford University. The eponymous Taylor rule, and its many variants, is followed widely by financial market participants, economists, and those in monetary policymaking circles. ¹ In its basic form, the Taylor rule states that the monetary authority (e.g., the Federal Reserve) should set its policy rate in the following manner:

where i is the nominal federal funds interest rate; r* is the equilibrium real interest rate; π is the current inflation rate, measured from a year earlier; y is real gross domestic product (GDP) and y* is real potential GDP, the difference between the two being the output gap; and π* is the Fed's inflation target, which is currently 2 percent for the personal consumption expenditures price index. ²

Three key principles are embedded in the Taylor rule. First, the Fed should raise its federal funds target rate proportionally more when inflation increases. This is known as the Taylor principle. Second, the interest rate should be adjusted in response to the output gap, a measure of "slack" in the economy. This is known as the Phillips relationship, whereby inflation decreases (increases) if real GDP decreases (increases) relative to real potential GDP. In Taylor's original specification, the coefficients on the output and inflation gaps, α and β, respectively, were each 0.5. Third, Taylor stipulated that the equilibrium real interest rate, r*, should be fixed over time at 2 percent. Although Taylor believes that r* should remain invariant over time, other policymakers have instead adopted the position that r* is time varying and depends importantly on the underlying growth rate of the economy and other factors, such as the demand for risk-free Treasury securities (i.e., "safe assets"). ³

To illustrate the Taylor principle noted above, the figure shows how the Taylor rule would evolve under higher- and lower-inflation scenarios between now and the end of 2020. In the former, inflation would increase by 12.5 basis points per quarter (0.5 percentage points per year) from the third quarter of 2018 to the fourth quarter of 2020. In the latter, inflation would slow by 12.5 basis points per quarter. Each scenario assumes that the output gap remains constant at the value that prevailed in the third quarter of 2018. As expected, under the higher-inflation scenario, the rule indicates that the Federal Open Market Committee should continue to raise its target rate. It indicates the opposite if inflation were to slow-again, under the assumption of an unchanged output gap.

Interestingly, the figure also shows that during the current expansion, the actual federal funds target rate has been consistently below the rate suggested by the Taylor rule. Using actual data through the third quarter of 2018, the actual federal funds target rate is 1.88 percent, while the rule indicates that the rate should be about 4.75 percent. ⁴

The large discrepancy between the actual federal funds target rate and the rate indicated by the Taylor rule using current data suggests that the Federal Open Market Committee may be following a different version of the Taylor rule. In a recent speech, Federal Reserve Bank of St. Louis President James Bullard presented an alternative-"modernized"-version of the Taylor rule. Part 2 of this Economic Synopses essay will assess whether the actual federal funds target rate more closely hews to the version described by Bullard.
Notes References

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Is the Fed Following a "Modernized" Version of the Taylor Rule? Part 1

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Academic research on monetary policy rules is voluminous. One of the most famous rules was published in 1993 by John Taylor, a well-known academic economist from Stanford University. The eponymous Taylor rule, and its many variants, is followed widely by financial market participants, economists, and those in monetary policymaking circles.

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Following a Modernized Version of the Taylor Rule Part 2

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As noted in Part 1 of this two-part Economic Synopses essay, the Taylor rule is widely used in academic research on monetary policy rules. ¹ This rule, and its many variants, is also followed widely among financial market participants, economists, and those in monetary policymaking circles.

In a recent speech, Federal Reserve Bank of St. Louis President James Bullard presented an alternative version of the Taylor rule that reflects three developments that today's monetary policymakers routinely confront. First, the economy has entered an economic regime of low interest rates that reflects, importantly, weak productivity growth and a strong demand for safe assets. ² Second, the Fed appears to have successfully engineered a regime of low and relatively stable inflation expectations that are anchored near the Fed's inflation target. Third, the Phillips relationship that posits a negative relationship between inflation and the current level of the unemployment rate and a measure of the "natural rate" has all but disappeared. ³ Accordingly, this development means falling levels of the unemployment rate relative to its natural rate will have a very small effect on inflation.

Given these developments, Bullard proposes an alternative, what he terms a "modernized" version, of the Taylor rule:

Bullard's modernized version of the Taylor rule embeds several changes from Taylor's original specification. ⁴ First, there is a one-quarter lag of the federal funds target rate ( i₋₁) with a fixed coefficient of ρ. This "smoothing" parameter is used by many in the policy rule literature. In this case, Bullard assigns ρ a value of 0.85. This assignment means that the past period's policy rate is extraordinarily important for setting the current period's policy rate. Second, the output and inflation gaps remain in the policy function, but they are measured a bit differently. The output gap ( u) is instead measured as the difference between the current unemployment rate and the Congressional Budget Office's natural rate of unemployment. The inflation gap ( π) is measured as the difference between a market-based measure of inflation expectations and the Fed's inflation target. Specifically, inflation expectations are measured as the difference between the nominal yield on a 5-year (5Y) Treasury security and the yield on an inflation-adjusted (real) 5Y Treasury inflation-protected security (TIPS). ⁵ This difference is sometimes called the breakeven inflation (BEI) rate. Third, r* now varies over time instead of being set at a fixed 2 percent. In this case, r* is measured as the trend interest rate estimated from a Hodrick-Prescott filter of the 1-year nominal constant maturity Treasury yield less the four-quarter change in the Federal Reserve Bank of Dallas's trimmed mean measure of the personal consumption expenditures (PCE) inflation rate. Fourth, the current inflation rate, π, is replaced by the Federal Open Market Committee's (FOMC's) inflation target ( π*), which is set at 2 percent. Finally, Bullard reduces the coefficient on the unemployment rate gap ( ϕ) to 0.1, to reflect the flatness of the Phillips curve. The coefficient on the inflation gap ( ϕ) is equal to 1.5 and consistent with the 1993 Taylor rule. Since ρ equals 0.85, this value means that the rule is very inertial in setting policy-that is, the past period's federal funds target rate is important for setting the current period's target rate.

The figure plots five versions of Bullard's modernized Taylor rule that are based on five different measures of inflation expectations. Four of the five measures of inflation expectations are market-based measures calculated as the difference between the yield on a nominal Treasury security and the yield on a TIPS. The first market-based measure is Bullard's preferred measure: the 5Y BEI less 30 basis points (the adjusted 5Y BEI). The second is the market's predicted average inflation rate over the next five years without this adjustment: the 5Y BEI. The third market-based measure is the inflation rate that is expected to prevail over the five-year period beginning five years from today: the 5Y, 5Y forward BEI (5Y5Y BEI). The fourth market-based measure is the average inflation rate that is expected to prevail over the next 10 years: the 10Y BEI. The final inflation expectations measure is based on the Federal Reserve Bank of Philadelphia's quarterly Survey of Professional Forecasters. Specifically, each participant in the survey is asked to forecast the average PCE price index inflation rate expected over the next 10 years. ⁶

The figure also plots the federal funds rate calculated from the 1993 Taylor rule, as described above and plotted in Part 1 of this Economic Synopses essay. To see how these two rules differ in their policy prescriptions, consider the prescription for the fourth quarter of 2015, when the FOMC lifted its federal funds target rate for the first time in a decade. The 1993 Taylor rule indicated that the rate should be set at 0.88 percent. The average of the five rules cited above was 0.12 percent, which was pretty close to the actual average of 0.16 percent. Over the next four quarters, real GDP growth remained close to 2 percent, the unemployment rate fell from 5 percent to 4.7 percent, and inflation increased from 1.6 percent to 2 percent. In the fourth quarter of 2016, the 1993 Taylor rule indicated that the target rate should be 2.9 percent, while the average of the five modernized Taylor rules was 0.46 percent. The actual target rate in the fourth quarter of 2016 was 0.42 percent. A key difference between the two rules during this period is that the 1993 Taylor rule assumes a fixed r* equal to 2 percent. In the modernized rule, r* was equal to -1.12 percent in the fourth quarter of 2015 and then -0.72 percent four quarters later.

Visual evidence from the figure suggests that the FOMC has been-more or less-following Bullard's version of the Taylor rule during this expansion rather than the 1993 Taylor rule. With most measures of inflation expectations converging to around 2 percent in the fourth quarter of 2018, the recommended FOMC interest rate targets from the modernized Taylor rules have effectively converged to slightly less than 2 percent: From 1.84 percent using the adjusted 5Y BEI measure of inflation expectations to 1.99 percent using the 5Y5Y BEI measure of inflation expectations. On balance, then, using available 2018 fourth-quarter values, this framework suggests policy is modestly "tight" based on the current federal funds target range of 2.25 percent to 2.5 percent. ⁷

If inflation expectations remain anchored at close to 2 percent and the unemployment rate remains close to its current level or even falls a bit further, then the rule stipulates that the only reason to raise rates would be if r* increases.
Notes References

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Is the Fed Following a "Modernized" Version of the Taylor Rule? Part 2

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As noted in Part 1 of this two-part Economic Synopses essay, the Taylor rule is widely used in academic research on monetary policy rules. 1 This rule, and its many variants, is also followed widely among financial market participants, economists, and those in monetary policymaking circles.

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How the Fed worked before the Great Recession

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How the Fed worked before the Great Recession

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How the Federal Reserve Worked: Before the Great Recession

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How the Fed worked after the Great Recession

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How the Fed worked after the Great Recession

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How the Federal Reserve Works: After the Great Recession

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How the Fed Works: After the Great Recession Practice Questions

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How the Fed Worked Before the Great Recession Practice Questions

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Monetary Policy: The Best Case Scenario Practice Questions

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Monetary Policy: The Negative Real Shock Dilemma

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Monetary Policy: The Negative Real Shock Dilemma Practice Questions

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The Taylor Rule is a model used to forecast interest rates. Created by famed economist John Taylor in 1992, it suggests how the central bank should change interest rates to account for inflation and other economic conditions.According to the Taylor Rule, the Federal Reserve should raise interest rates when inflation is above target, or when GDP growth is too high. The Fed should lower rates when inflation is below the target level, or when GDP growth is too slow. The Taylor Rule aims to stabilize the economy in the short term, and stabilize inflation over the long term. The Taylor Rule looks like this: i = r* + pi + 0.5 (pi-pi*) = 0.5 (y-y*) Where i is the nominal federal funds rate, r asterisk is the real federal funds rate, pi is the rate of inflation, p asterisk is the target inflation rate, y is a logarithm of real output, and y asterisk is a logarithm of potential output. The Taylor Rule comes up with an interest rate, an inflation rate and a GDP rate that are all based on the one rate that should determine the correct balance for interest rate forecasts. Essentially, the equation says that the difference between a nominal and real interest rate is inflation. Real interest rates account for inflation; nominal rates do not. If, for example, the nominal interest rate on a three-year deposit is 4% and inflation over the three years is 3%, then the real interest rate is 1%. Taylor recommended the real interest rate should be 1.5 times the inflation rate.

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The Taylor Rule: Calculating Monetary Policy

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The Taylor Rule is a model used to forecast interest rates. Created by famed economist John Taylor in 1992, it suggests how the central bank should change interest rates to account for inflation and other economic conditions.According to the Taylor Rule, the Federal Reserve should raise interest rates when inflation is above target, or when GDP growth is too high.

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The Taylor rule is an interest rate forecasting model invented and perfected by famed economist John Taylor in 1992 and outlined in his landmark 1993 study, "Discretion Vs. Policy Rules in Practice."

Taylor operated in the early 1990s with credible assumptions that the Federal Reserve determined future interest rates based on the rational expectations theory of macroeconomics. This is a backward-looking model that assumes if workers, consumers and firms have positive expectations for the future of the economy, interest rates don't need an adjustment. The problem with this model is not only that it is backward-looking, but it also doesn't take into account long-term economic prospects.

The Phillips curve was the last discredited rational expectations theory model that attempted to forecast the tradeoff between inflation and employment. The problem again was while short-term expectation may have been correct, long-term assumptions based on these models are difficult, and how can adjustments be made to an economy if the interest rate action taken was wrong? Here, monetary policy was based more on discretion than concrete rules. What economists found was they couldn't imply monetary expectations based on rational expectation theories any longer, particularly when an economy didn't grow or stagflation was the result of a recent interest rate change. This situation brought rise to the Taylor rule.

The formula used for the Taylor rule looks like this:
i= r* + pi + 0.5 (pi-pi*) + 0.5 ( y-y*)
i = nominal fed funds rate
r* = real federal funds rate (usually 2%)
pi = rate of inflation
p* = target inflation rate
Y = logarithm of real output
y* = logarithm of potential output

What this equation says is the difference between a nominal and real interest rate is inflation. Real interest rates are factored for inflation while nominal rates are not. Here we are looking at possible targets of interest rates, but this can't be accomplished in isolation without looking at inflation. To compare rates of inflation or non-inflation, one must look at the total picture of an economy in terms of prices.

Prices and inflation are driven by three factors: the consumer price index, producer prices and the employment index. Most nations in the modern day look at the consumer price index as a whole rather than look at core CPI. Taylor recommends this method, as core CPI excludes food and energy prices. This method allows an observer to look at the total picture of an economy in terms of prices and inflation. Rising prices means higher inflation, so Taylor recommends factoring the rate of inflation over one year (or four quarters) for a comprehensive picture. (For related reading, see: Why The Consumer Price Index Is Controversial.)

Taylor recommends the real interest rate should be 1.5 times the inflation rate. This is based on the assumption of an equilibrium rate that factors the real inflation rate against the expected inflation rate. Taylor calls this the equilibrium, a 2% steady state, equal to a rate of about 2%. Another way to look at this is the coefficients on the deviation of real GDP from trend GDP and the inflation rate. Both methods are about the same for forecasting purposes. But that's only half of the equation-output must be factored in as well.

The total output picture of an economy is determined by productivity, labor force participation and changes in employment. For the equation, we look at real output against potential output. We must look at GDP in terms of real and nominal GDP, or, to use the words of John Taylor, actual vs. trend GDP. To do this, we must factor in the GDP deflater, which measures prices of all goods produced domestically. We do this by dividing nominal GDP by real GDP and multiplying this figure by 100. The answer is the figure for real GDP. We are deflating nominal GDP into a true number to fully measure total output of an economy. (For more, see: What Is GDP and Why Is It So Important?)

The product of the Taylor rule is three numbers: an interest rate, an inflation rate and a GDP rate, all based on an equilibrium rate to gauge the proper balance for an interest rate forecast by monetary authorities.

The rule for policymakers is this: The Federal Reserve should raise rates when inflation is above target or when GDP growth is too high and above potential. The Fed should lower rates when inflation is below the target level or when GDP growth is too slow and below potential. When inflation is on target and GDP is growing at its potential, rates are said to be neutral. This model aims to stabilize the economy in the short term and to stabilize inflation over the long term. To properly gauge inflation and price levels, apply a moving average of the various price levels to determine a trend and to smooth out fluctuations. Perform the same functions on a monthly interest rate chart. Follow the fed funds rate to determine trends.

While the Taylor rule has served economies in good economic times, it can also serve as a gauge for bad economic times. Suppose a central bank held interest rates too low for too long. This is what causes asset bubbles, so interest rates must eventually be raised to balance inflation and output levels. A further problem of asset bubbles is money supply levels rise far higher than is needed to balance an economy suffering from inflation and output imbalances. Many thought the central bank was to blame-at least partly-for the housing crisis in 2007-2008. The reasoning is interest was kept too low in the years following the dot-com bubble and leading up to the housing market crash in 2008 (see chart). Had the central bank followed the Taylor rule during this time, which indicated the interest rate should be much higher, the bubble may have been smaller, as less people would have been incentivized to buy homes. Taylor himself has argued the crisis would have been significantly smaller if the central bank had followed rules-based monetary policy.
Source: The Brookings Institution
The Taylor rule has held many central banks around the world in good stead since its inception in 1993. It has served not only as a gauge of interest rates, inflation and output levels, but also as a guide to gauge proper levels of the money supply, since money supply levels and inflation meld together to form a perfect economy. It allows us to understand money vs. prices to determine a proper balance, which is important because inflation can erode the purchasing power of the dollar if it's not leveled properly. (To learn more, see: Economics Basics Tutorial.)

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The Taylor Rule: An Economic Model for Monetary Policy

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The Taylor rule is an interest rate forecasting model invented and perfected by famed economist John Taylor in 1992 and outlined in his landmark 1993 study, "Discretion Vs. Policy Rules in Practice." Taylor operated in the early 1990s with credible assumptions that the Federal Reserve determined future interest rates based on the rational expectations theory of macroeconomics.

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Interview with John Taylor

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145 – George Selgin on *Floored!* by Macro Musings

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George Selgin is the director of the Cato Institute’s Center for Monetary and Financial Alternatives, professor emeritus of economics at the University of Georgia, and a returning guest to show.  For this special live episode, George joins Macro Musings to talk about his new book, *Floored: How a Misguided Fed Experiment Deepened and Prolonged the Great Recession.* David and George also discuss the liquidity coverage ratio, the Fed’s transition from a corridor to a floor system, and the arguments for and against such an operating system. 

Transcript for the episode: https://www.mercatus.org/bridge/podcasts/02252019/floors-and-corridors 

George’s Twitter: @GeorgeSelgin 
George’s Cato Institute profile: https://www.cato.org/people/george-selgin 

Related Links: 

*The Fed Marches On* by George Selgin 
https://www.alt-m.org/2019/01/31/the-fed-marches-on/ 

*Balance Sheet News* blog post by Stephen Williamson  http://newmonetarism.blogspot.com/2019/02/balance-sheet-news_21.html 

David Beckworth’s Twitter thread on the Fed’s decision to stick with a floor system: https://twitter.com/DavidBeckworth/status/1098956723501576192 

David’s blog: macromarketmusings.blogspot.com 
David’s Twitter: @DavidBeckworth

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First, let's introduce some of the monetary policy terms we'll be using here:

Federal Open Market Committee (FOMC): The seven members of the Board of Governors; the president of the Federal Reserve Bank of New York; and, on a rotating basis, the presidents of four other Reserve Banks. Nonvoting Reserve Bank presidents also participate in deliberations and discussion.

Federal funds rate (FFR): The interest rate at which depository institutions and Federal Home Loan Banks borrow and lend reserve balances to each other overnight.

Interest on reserve balances (IORB): Interest paid on reserves that banks hold in their accounts at a Federal Reserve Bank.

Overnight reverse repurchase agreement (ON RRP): An overnight transaction in which the Federal Reserve sells a security to an eligible counterparty and simultaneously agrees to buy the security back the next day.

The FOMC sets the stance of monetary policy by adjusting the target range for the FFR. To ensure the target range is transmitted to market interest rates, the FOMC uses the IORB as the primary tool and the ON RRP facility as the supplemental tool. The graph above shows that the Fed has successfully transmitted its desired policy stance to financial markets: The effective FFR has been within the upper and lower limits of the target range set by the FOMC-that is, the blue line stayed between the red and green lines.

Let's look at these two "administered" rates* that the FOMC has used to steer the FFR within the target range:

1. Banks earn interest on reserve balances (IORB) on the funds they place in their reserve accounts at the Fed. Because the IORB rate serves as a reservation rate for banks, and banks can arbitrage the difference between IORB and other short-term rates, it is an effective tool for guiding the FFR.**

2. The Fed offers a broad set of large financial institutions the opportunity to deposit funds at the Fed overnight (with a security held as collateral) in the overnight reverse repurchase agreement (ON RRP) facility. Many of these financial institutions do not have access to interest on reserves. The Fed announces the capacity of the facility and an offering rate. Institutions then place bids that include the amount of their deposit and the minimum interest rate they would receive from the Fed. As long as the total amount of funds that institutions bid is less than the Fed's set capacity, institutions' full bid amounts are placed in the facility and the funds earn the ON RRP offering rate. However, if there is more demand than capacity, the Fed sorts the bids by their rates, lowest to highest, and awards funds to institutions in that order. The bid rate for the last institution to be accepted into the facility (once capacity is reached) becomes the award rate for all institutions. The Fed has set a large capacity, though, and the ON RRP offering rate has been the award rate in all auctions to date. As with the IORB rate, institutions use the ON RRP offering rate to help them arbitrage other short-term rates. Because it is set below the IORB rate, it serves as a supplementary rate and acts like a floor for the FFR.

The graph above shows the Fed's new implementation tools in action. After the Great Financial Crisis, the Fed held the target range for the FFR at 0 to 25 basis points until December 16, 2015 (a date known as "liftoff"). Since then, the FOMC has adjusted the target range up and down several times, including a recent return to the range of 0 to 25 basis points on March 15, 2020, in response to the economic effects of the COVID-19 pandemic. When the FOMC moved the target range, the administered rates were also adjusted, and the FFR (green line) moved simultaneously.

The Fed determined the appropriate IORB rate (red line) and ON RRP offering (and, hence, award) rate (blue line) to keep the FFR in the target range. Over time, the administered rates have been adjusted relative to the range and relative to each other over time. The settings of the Fed's administered rates are always determined to keep the FFR within the target range. For example, at liftoff, the IORB rate was set at the top of the range and the ON RRP offering (award) rate at the bottom of the range. But, over time, as market pressures moved the FFR toward the top of the target range, the Fed moved the IORB rate a bit lower and within the target range. This is visible in the next graph: Before June 16, 2018, the IROB rate (labeled as "interest rate on excess reserves") is not visible because it lies beneath the upper limit of the federal funds target range. As the Fed lowered the IORB rate to move the FFR toward the middle of the target range, the IORB rate becomes visible and the FFR moves down in the range. The Fed has made two similar adjustments, moving the IORB rate lower relative to the upper limit of the target range. The ON RRP offering rate, acting as a floor, has remained at the bottom of the range over most of this period, with the award rate being a touch below the lower limit a few times.

The Fed's toolbox includes two other tools that support effective policy implementation. The discount rate acts a ceiling for the FFR because banks should not be willing to pay more for funds than the rate at which they can borrow from Fed. And, the Fed conducts open market operations - while no longer the primary tool for adjusting the FFR, the Fed uses open market operations periodically to ensure that the reserves in the banking system remain ample.

For more information, see The Fed's New Monetary Policy Tools.

*An "administered" rate is an interest rate set by a central authority, such as the Fed, as opposed to an interest rate determined in a market.

**These data are listed in FRED as "interest rate on excess reserves." Since the Fed decided to reduce reserve requirements to zero percent, it has indicated it may change the name to better reflect current use of the tool.

How this graph was created: First graph: Search for and select "Federal Funds Target Range - Upper Limit," "Federal Funds Rate - Lower Limit," and "Effective Federal Funds Rate (daily)" and click "Add to Graph." From the "Edit Graph" panel, use the "Add Line" option to search for "Interest Rate on Excess Reserves" and then select "Add data series." Adjust the date range to January 1, 2015, to the current date. Second graph: Search for and select "Overnight Reverse Repurchase Agreements Award Rate: Treasury Securities Sold by the Federal Reserve in the Temporary Open Market Operations," "Interest Rate on Excess Reserves," and "Effective Federal Funds Rate (daily)." Adjust the date range to January 1, 2015, to the current date. Third graph: Start with the second graph, search for and select "Federal Funds Target Range - Upper Limit," and "Federal Funds Rate - Lower Limit" and "Effective Federal Funds Rate (daily)." Adjust the date range to January 1, 2018, to June 30, 2020. In all cases, adjust the colors to your liking with the color palette in the "Edit Graph" panel's "Format" tab.

Suggested by Scott Wolla and Jane Ihrig.

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Visualizing the Fed's new monetary policy tools

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First, let's introduce some of the monetary policy terms we'll be using here: Federal Open Market Committee (FOMC): The seven members of the Board of Governors; the president of the Federal Reserve Bank of New York; and, on a rotating basis, the presidents of four other Reserve Banks.