Editing Taylor rule (section)

==Equation==
According to Taylor's original version of the rule, the [[real interest rate|real]] policy interest rate should respond to divergences of actual inflation rates from target inflation rates and of actual [[Gross Domestic Product]] (GDP) from potential GDP:

:<math>i_t = \pi_t + r_t^* + a_\pi ( \pi_t - \pi_t^* ) + a_y \cdot 100 ( Y_t - \bar Y_t )/ \bar Y_t.</math>

In this equation, <math>i_t</math> is the target short-term [[nominal interest rate|nominal]] policy interest rate (e.g. the [[federal funds rate]] in the US, the [[Official bank rate|Bank of England base rate]] in the UK), <math>\pi_t</math> is the rate of [[inflation]] as measured by the [[GDP deflator]], <math>\pi^*_t</math> is the desired rate of inflation, <math>r_t^*</math> is the assumed natural/equilibrium interest rate,<ref>{{Cite periodical |last1=Lopez-Salido |first1=David |last2=Sanz-Maldonado |first2=Gerardo |last3=Schippits |first3=Carly |last4=Wei |first4=Min |date=2020-06-19 |title=Measuring the Natural Rate of Interest: The Role of Inflation Expectations |periodical=FEDS Notes |url=https://www.federalreserve.gov/econres/notes/feds-notes/measuring-the-natural-rate-of-interest-the-role-of-inflation-expectations-20200619.html |language=en}}</ref> <math>Y_t</math> is the actual [[Gross Domestic Product|GDP]], and <math>\bar Y_t</math> is the [[potential output]], as determined by a linear trend. <math>100(Y_t - \bar Y_t)/ \bar Y_t</math> is the [[output gap]], in percentage points.

Because of <math>i_t - \pi_t = \mbox{real policy interest rate}</math>,
: <math>\begin{align}
  \mbox{Desired real policy interest rate} &= \mbox{equilibrium real interest rate} \\
  &+ a_{\pi} \times \mbox{difference from the inflation target} \\
  &+ a_y \times \mbox{output gap} \\
  \end{align}
</math>
In this equation, both <math>a_{\pi}</math> and <math>a_y</math> should be positive (as a rough rule of thumb, Taylor's 1993 paper proposed setting <math>a_{\pi}=a_y=0.5</math>).<ref>{{cite book|first=Athanasios |last=Orphanides |year=2008|chapter=Taylor rules equation (7)|title=[[The New Palgrave Dictionary of Economics]] |edition=2|volume= 8 |pages=2000–2004 |chapter-url=http://www.dictionaryofeconomics.com/article?id=pde2008_T000215&q=taylor%20rules&topicid=&result_number=1 }}{{dead link|date=November 2022}}</ref> That is, the rule produces a relatively high real interest rate (a "tight" monetary policy) when inflation is above its target or when output is above its [[full employment|full-employment]] level, in order to reduce inflationary pressure. It recommends a relatively low real interest rate ("easy" monetary policy) in the opposite situation, to stimulate output. In this way, the Taylor rule is inherently counter-cyclical, as it prescribes policy actions that lean against the direction of economic fluctuations. Sometimes monetary policy goals may conflict, as in the case of stagflation, when inflation is above its target with a substantial output gap. In such a situation, a Taylor rule specifies the relative weights given to reducing inflation versus increasing output.