Three Equation Model IS PC MR Monetary Macroeconomics Motivation for the Model Over the last decade many central banks have adopted the policy goal of inflation targeting in the conduct of monetary policy Monetary policy is implemented through the use of a nominal interest rate as its policy instrument Traditional macro models make monetary policy actions appear exogenous rather than reflecting the fact that most policy actions represent endogenous reaction to the economy Motivation The model we will study assumes the monetary policy authority the central bank acts systematically to minimize fluctuations of output around the full employment level natural rate and inflation around its inflation target Follows a Taylor Rule Key Assumptions of the Model 1 The inflation process is persistent slow to change In line with a wealth of empirical evidence pte pt 1 2 In terms of adjustment lags assume that it takes one year for monetary policy to affect output and a year for a change in output to affect inflation 2 years to have an impact on inflation Fed Governors Mishkin and Kroszner have given speeches recently citing studies that showing the inflationary process to be less persistent Adjustment Lags The empirical evidence is that on average it takes up to about one year in this and other industrial economies for the response to a monetary policy change to have its peak effect on demand and production and that it takes up to a further year for these activity changes to have their fullest impact on the inflation rate Bank of England 1999 The Transmission of Monetary Policy p 9 http www bankofengland co uk montrans pdf Key Assumptions of the Model 3 The central bank sets the nominal interest rate i But with assumption 1 the expected rate of inflation is given in the short run so the central bank can set the real rate r in the short run think about why Assumption 1 Real Interest rate From Assumption 1 pte pt 1 e r i p r i pt 1 The IS Curve y C I G EX IM C Consumption I Investment G Government EX Exports IM Imports EX IM Net Exports y real GDP How does a change in the real interest rate r affect spending As r C Think about why y As r I y As r EX and IM y The IS Curve shows an inverse relationship between r and y r IS y So the Central Bank can adjust r to determine y r r1 r2 r3 IS y1 y2 y3 If they know the IS curve relation y So the Central Bank can adjust r to determine y 1 If it can control the real interest rate and big AND 2 If it knows the relationship between r and y This is to say it knows the position and the shape of the IS Curve Remember the Fed controls the nominal FFR iFFR Shifts in the IS Curve We will refer to shifts in the IS curve as demand shocks For example Change in I Change in G Change in Consumer Confidence change in C Shifts in the IS Curve r C I C G I G IS0 IS1 IS2 y There is a real interest rate rs consistent with full employment ye r rs A IS ye y We will refer to rs as the stabilizing real interest rate Or the neutral real interest rate rn in Taylor equation Inflation Process 1 e 1 or e 1 2 e y ye or 3 1 y ye 1 Represents inflation inertia People look backwards in forming expectations expectations are slow to change 2 and 3 state for a given e inflation rises as y rises above full employment ye and falls as y falls below ye Question If y ye what can we say about inflation Phillips Curve I Phillips Curve e y ye or y ye VPC Vertical Phillips Curve e I 1 2 y ye 2 y ye ye y Phillips Curve e y ye Movement along the curve VPC e I 1 2 3 2 1 y2 ye y1 y When y rises above ye the output gap When y falls below ye the output gap Shifts in the Phillips Curve e y ye Inflation VPC PC e 3 PC e 2 3 T 2 ye y Figure 1 Full Employment Equilibrium The economy is at a constant inflation equilibrium output level with y ye Inflation is constant at the target rate T 2 VPC The stabilizing interest rate is rs Question According to the Taylor Rule what is the nominal FFR iffr Figure 2 Supply Shock Suppose an inflation shock supply shock takes the economy from A to B At B there is full employment with high inflation at 4 B Inflation is above the central bank target level T 2 The Fed wishes to reduce inflation to the target level of 2 What does the Phillips Curve show The Phillips Curve PC I 4 shows given last period s inflation the inflation and output trade off faced by the central bank The only points on the Phillips Curve with inflation below 4 are to the left of B i e with lower output and hence higher unemployment The Fed must create an output gap in order to reduce inflation To do this the Fed must increase the real interest rate Figure Figure 3 3How does the central bank behave The Fed chooses interest rate r at point C causing income to fall to y1 As y falls move down along the PC inflation falls to 3 why MR Question What happens to the PC over time as inflation falls Monetary Policy Reaction MR Function The Taylor Rule is an example A nominal anchor defined in terms of an inflation target provides guidance as to how the real interest rate should be adjusted in response to different shocks hitting the economy The objective is stable inflation while minimizing output fluctuations Figure 4 The Fed raises the real interest rate to slow down the economy Inflation falls to 3 As falls people adjust their expectations downward and the PC shifts down to a level consistent with 3 expected inflation With lower inflation the Fed can now adjust the interest rate downward as inflation falls The economy moves down the IS curve from C to D to A and along the MR curve from C to D to A y1 Eventually the target rate of inflation of 2 is achieved and the economy is at full employment So what happened here The MR line shows the level of output the central bank will choose given the Phillips curve constraint that it faces To implement its output choice the central bank sets the appropriate interest rate as shown in the IS diagram As inflation gradually falls the Phillips curve shifts down and the central bank chooses an output level closer to the equilibrium This traces out the path down the MR along which the economy moves back to equilibrium i e along the MR curve from C to D to A in the Phillips diagram along the IS curve from C to D to …