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A '''monetary policy reaction function''' describes how a [[central bank]] systematically adjusts its [[Central bank#Policy instruments|policy instruments]] in response to changes in economic conditions. This function provides a framework for understanding how central banks make policy decisions based on observable economic indicators.
The '''monetary policy reaction function''' (MPRF) is the upward-sloping relationship between the [[inflation rate]] and the [[unemployment rate]]. When the [[inflation rate]] rises, a [[central bank]] wishing to fight [[inflation]] will raise [[interest rates]] to reduce output and thus increase the [[unemployment rate]].
==Examples==
The MPRF is a function of the [[Taylor rule]], the [[IS curve]], and [[Okun's law]].{{cn|date=August 2013}}
The most influential reaction function is the [[Taylor rule]], developed by economist John Taylor in 1993. The rule provides a systematic formula for setting the [[nominal interest rate]] based on four key variables: The deviation of current [[inflation rate]] from the central bank's target; The current [[inflation rate]] itself; The equilibrium [[real interest rate]]; and the [[output gap]], measured as the percentage difference between actual [[GDP]] and [[potential output]].
The MPRF has the equation:
An alternative formulation of the monetary policy reaction function was proposed by [[Ben Bernanke]] and [[Robert H. Frank]].<ref>Bernanke, Ben, and Frank, Robert. ''Principles of Economics'', 3rd edition.</ref> Their simplified version describes a positive relationship between the [[real interest rate]] and the [[inflation rate]], where central banks respond to rising inflation by increasing real interest rates:
<math>u = u_{0} + \Phi(\pi - \pi_{t})</math>
Where <math>\Phi</math> is a parameter that tells us how much unemployment rises when the [[central bank]] raises the [[real interest rate]] <math>r</math> because it thinks that [[inflation]] is too high and needs to be reduced.
where
The Slope of the MPRF is: <math>\frac{1}{\Phi}</math>
:r * = long-runcurrent target for the real interest rate<br /> ▼
The MPRF is used hand in hand with the [[Phillips Curve]] to determine the effects of [[economic policy]]. This framework illustrates [[Underemployment equilibrium|equilibrium]] levels of the [[unemployment rate]] and the [[inflation rate]] in a [[sticky-price model]].
π:r* = long-run target for the inflationreal interest rate <br />▼:g = constant term (or the slope of the MPRF)<br /> ▼
:π = actual inflation rate<br /> ▼
:π* = long-run target for the inflation rate
This linear relationship provides a more straightforward framework compared to the multi-variable Taylor rule, though it captures fewer economic factors.
== Alternative ==
Alternatively, in [[Ben Bernanke]] and [[Robert H. Frank]]'s ''Principles of Economics'' textbook, the MPRF is a model of the Fed's interest rate behavior. In its most simple form, the MPRF is an upward-sloping relationship between the real interest rate and the inflation rate. The following is an example of an MPRF from the third edition of the textbook{{full|date=August 2013}}:
r = target real interest rate (or actual real interest rate)<br />
▲r* = long-run target for the real interest rate<br />
▲g = constant term (or the slope of the MPRF)<br />
▲π = actual inflation rate<br />
▲π* = long-run target for the inflation rate
Of course, the MPRF above is just one example, and there are other examples (such as the [[Taylor rule]]) that are more complex.
The following graph shows the simple MPRF with the real interest rate on the Y-axis and the inflation rate on the X-axis.<ref>from the [http://econblog.aplia.com/2007/10/monetary-policy-reaction-function.html?showComments=false Aplia Econ Blog]</ref> Assume a 3% actual and long-run target inflation rate.
== References ==
{{Reflist}}
{{Central banks}}
[[Category:MacroeconomicsMonetary policy]]
[[Category:Monetary economics]]
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