# Taylor rule

Taylor rule | |
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## Taylor Rule - Introduction

**John B. Taylor** is a professor at Stanford University. He has been involved in economic policy since 2001 as Under Secretary of the US Treasury. He is recognised as one of the leading economists to date and for his position in the **New-Keynesian** wave. His observations and work aim to better understand the economy, in order to better appropriate systems and therefore by extension, make the best possible empirical decisions. It is in this context that the Taylor rule was conceived.

**The Taylor rule is a pragmatic rule of conduct** (based on previous experiences) according to which the interest rate should be adjusted by the monetary authorities over the cycle to a level equal to the equilibrium interest rate (which depends on potential growth), plus fifty percent of the inflation gap (actual inflation minus target inflation), plus fifty percent of the output gap.

• The Taylor rule roughly reflects the average behavior of most central banks in the recent past and thus indicates whether monetary policy is more or less accommodating or restrictive, taking into account the position in the cycle.

## Analysis & Construction of the rule

The rule therefore allows the stance of monetary policy to be assessed in the light of fundamental economic conditions by comparing the calculated rate with the market rate.
In **macroeconomic mathematics**, the equation generally takes the following form :

**nominal interest rate resulting from monetary policy = r + pt + 0.5 (pt-p*) + 0.5 (y - y*)**

• r: the neutral real interest rate

• pt : the inflation rate of period t

• pt - p* : difference between observed inflation and the inflation rate targeted by the central bank as an objective

• yt-y*: Called the **OUTGAP**, it is the difference between the *observed growth rate* and *the trend growth rate* of the economy

The output gap is the difference between actual and potential growth. A large output gap is a sign of slack in the economy, and therefore moderates (all else being equal) inflation. It is implicitly assumed that central bankers are keen to reduce the output gap to zero.

Taylor reproduces the behavior of US interest rates during the 1980s using a simple rule with two targets: an inflation target and an activity target. He shows, using rational expectations models, that such rules can be optimal in the sense that they minimize the volatility of GDP and prices. The rule he chooses to illustrate his point will later bear his name. It may be useful to examine each of its variables.

- The real short-term interest rate defined by the Taylor rule is "appropriate to the economic situation". This rule is primarily based on historical regularity: it faithfully reproduces past developments in Fed Funds rates based on the two variables, prices and GDP. However, it does not a priori predict their future evolution (change of target, for example).

- The Taylor rule, by taking account of actual inflation and activity, makes it possible to reconcile the central banker's short and medium-term objectives. Indeed, short-term inflationary pressures arise from the mismatch between demand and potential supply. It is therefore not paradoxical that a central bank targeting inflation also incorporates variations in the output gap into its reaction function.

- By choosing the coefficients also for their simplicity (0.5), the author has given this rule obvious pedagogical virtues: it is simple to interpret and easy to remember. In fact, it is widely used, especially by bank economists.

The Taylor rate can then be interpreted as an interest rate allowing GDP and inflation to return to their target values. It has no normative value, but represents a reference value. The difference between the policy rate of the monetary authorities and the Taylor rate is used to characterize a monetary policy: an accommodating (respectively restrictive) monetary policy is characterized by rates below (respectively above) the Taylor rate.

This type of rule has good stabilizing properties provided that it respects the Taylor principle according to which the weight attributed by central bankers to price stabilization must be greater than unity. This condition implies that the appearance of higher inflation is immediately compensated by a more than proportional increase in the nominal interest rate, which in turn leads to an increase in the real short-term interest rate, which in turn is supposed to reduce inflationary pressures.

## A flawed indicator

However, this rule has serious limitations, and one of the main ones is the requirement that households have rational expectations.

**John Cochrane**, a researcher who has strongly challenged Taylor's approach, argues that the expression of a rational expectations equilibrium cannot stabilize an inflation rate.
His position can be highlighted with this quote in 2007.

“I argue that the Taylor principle, in the context of new-Keynesian models, does not, in fact, determine inflation or the price level. Nothing in economics rules out explosive or “non-local” nominal paths. Transversality conditions can rule out real explosions, but not nominal ones”. ^{[1]}.

## References

*Bennett T. McCallum (2008). https://www.nber.org/system/files/working_papers/w14534/w14534.pdf Journal of Monetary Economics, 3-4.**Sharon Kozicki (1999). https://www.kansascityfed.org/documents/1182/1999-How%20Useful%20Are%20Taylor%20Rules%20for%20Monetary%20Policy%3F.pdf Economic Review-Federal Reserve Bank of Kansas, 2-7.**Athanasios Orphanides (2007-2018) https://www.federalreserve.gov/PubS/feds/2007/200718/200718pap.pdf Monetary economics, 3-5..*

**Author:** Piotr CEDRO

- ↑ Cochrane (2007)