Macroeconomic Theory Prof. M. El-Sakka CBA. Kuwait University Macroeconomic Theory Chapter 3 Inflation, Unemployment and Monetary Rules.

Macroeconomic Theory Macroeconomic Theory Prof. M. El-Sakka Prof. M. El-Sakka CBA. Kuwait University CBA. Kuwait University

Macroeconomic TheoryMacroeconomic Theory

Chapter 3 Chapter 3 Inflation, Unemployment and Inflation, Unemployment and

Monetary RulesMonetary Rules


Central banks are now typically viewed as operating through Central banks are now typically viewed as operating through adjusting adjusting r r in order to keep the economy close to its in order to keep the economy close to its inflation inflation target at the eq level of output. target at the eq level of output.

Inflation is constant at eq output. If IS shifts to the RHS → higher Inflation is constant at eq output. If IS shifts to the RHS → higher inflation. This will be incorporated in future wage and price inflation. This will be incorporated in future wage and price setting which will be squeezed out of the economy by a period of setting which will be squeezed out of the economy by a period of above eq unemp. above eq unemp.

Central banks aim is to minimize the cost of shocks to the Central banks aim is to minimize the cost of shocks to the economy in terms of higher inflation and unemployment. It will economy in terms of higher inflation and unemployment. It will raise raise rr to guide the economy back toward target inflation and eq to guide the economy back toward target inflation and eq unemp. This behavior is known as “unemp. This behavior is known as “reaction functionreaction function”, or ”, or ““monetary policy rulemonetary policy rule”. ”.

By combining PC (Phillips Curve), IS and monetary rule we have By combining PC (Phillips Curve), IS and monetary rule we have the 3 equation model the 3 equation model IS-PC-MRIS-PC-MR. .


Inflation and Phillips curvesInflation and Phillips curves Inflation is the rate of change in prices: Inflation is the rate of change in prices:

ππ = P-P = P-P-1-1/P/P-1-1

Policy makers are concerned about Policy makers are concerned about ππ. . 1.1. High inflation tends to be volatile and creates High inflation tends to be volatile and creates uncertaintyuncertainty

2.2. Inflation undermines the way Inflation undermines the way PP convey information. convey information.

3.3. It is costly to bring inflation down, as It is costly to bring inflation down, as unemp willunemp will ↑↑.. Inflation inertiaInflation inertia In the standard model inflation depends onIn the standard model inflation depends on

Past inflation Past inflation ππ-1-1

The gape between current unemp. and the ERU. The gape between current unemp. and the ERU.

interpretations of the interpretations of the ππ-1-1..

1.1. Wage setters expect inflation this period to continue as it is in the last period. Wage setters expect inflation this period to continue as it is in the last period. This is “This is “adaptive expectationsadaptive expectations””

ππEE= = ππEE-1-1 + a( + a(ππ-1-1- - ππEE

-1-1),), 0 1 Adaptive expectations 0 1 Adaptive expectations

Expected Expected ππ equals last period equals last period ππEE plus a correction term ( plus a correction term (forecast errorforecast error))

a


If forecast errors are fully corrected If forecast errors are fully corrected a=1a=1 and and ππEE= = ππEE-1-1 (simple (simple

adaptive expectations). adaptive expectations). This is an This is an implausibleimplausible way to form expectations. Why we look way to form expectations. Why we look

entirely to the past.entirely to the past.

2.2. Anther realistic interpretation of why we include past inflation is Anther realistic interpretation of why we include past inflation is inertiainertia that characterize the wage and price setting. Wage setters that characterize the wage and price setting. Wage setters incorporate past inflation in order to make up for any erosion in incorporate past inflation in order to make up for any erosion in living standards taken place since last wage round. Wage setters living standards taken place since last wage round. Wage setters are assumed are assumed not to be able to expected future changesnot to be able to expected future changes in their in their current bargain.current bargain.

We denote inflation inertia using the lagged inflation We denote inflation inertia using the lagged inflation ππll

ππ = = ππ-1-1 + a (y-ye) + a (y-ye)

i.e., current inflation equals inflation inertia plus output gap. i.e., current inflation equals inflation inertia plus output gap. (this is (this is expectations augmented PCexpectations augmented PC).).


Deriving Phillips curvesDeriving Phillips curves We have seen that at eq We have seen that at eq WSWS and and PSPS curves cross at a curves cross at a uniqueunique unemp rateunemp rate at at

which the labor market is in eq and there is no incentive for wage and price which the labor market is in eq and there is no incentive for wage and price setters to change their behavior. setters to change their behavior.

If inflation is 4% and unemp is at the If inflation is 4% and unemp is at the ERUERU. In fig 3.1 emp is . In fig 3.1 emp is EE11 and and ww is is ww11. to . to

keep keep ww constant at constant at ww11, wage setters require a money wage rise that will make , wage setters require a money wage rise that will make

up for. Since prices have risen by 4%, up for. Since prices have risen by 4%, WW will rise by 4%. will rise by 4%. Firms set prices according to their pricing rule. Since Firms set prices according to their pricing rule. Since

P=(1+P=(1+μμhathat) . W/) . W/λλ

ΔΔP/P = P/P = ΔΔW/W - W/W - ΔλΔλ//λλ When average productivity of labor When average productivity of labor λλ is constant is constant

ΔΔP/P = P/P = ΔΔW/WW/W See the following table and figure 3.1. Results of the table can be illustrated See the following table and figure 3.1. Results of the table can be illustrated

using a Phillips curve diagram. using a Phillips curve diagram.


Figure 3.1Figure 3.1


Constant, rising and falling inflationConstant, rising and falling inflation

Inflation (% per year) and employment period employment Lagged

π gap Wage

inflation Price

inflation 0 E1 4 0 4 4

Case 1: Constant inflation 1 E1 4 0 4 4 2 E1 4 0 4 4 3 E1 4 0 4 4

Case 2: Rising inflation 1 E2 4 2 6 6 2 E2 6 2 8 8 3 E2 8 2 10 10

Case 3: Falling inflation 1 E3 4 -2 2 2 2 E3 2 -2 0 0 3 E3 0 -2 -2 -2


In reality there is no In reality there is no one for oneone for one relationship between a rise in relationship between a rise in yy and a fall in and a fall in unempunemp. This is due to:. This is due to:1.1. Labor hoardingLabor hoarding

2.2. Economically inactive laborEconomically inactive labor

A change in A change in yy by 1% tends to be associated with a change in by 1% tends to be associated with a change in unemp by less than 0.5% (Okun’s law).unemp by less than 0.5% (Okun’s law).

Using the data in table 3.1 we can plot the other Phillips curves Using the data in table 3.1 we can plot the other Phillips curves as they are shown in fig 3.2.as they are shown in fig 3.2.

Each Phillips curve is defined by two characteristics:Each Phillips curve is defined by two characteristics:1.1. The lagged inflation The lagged inflation rate which is equal to past inflation and fixes the rate which is equal to past inflation and fixes the

height of PC on a vertical line above the level of output associated with height of PC on a vertical line above the level of output associated with ERU.ERU.

2.2. The slope of WS The slope of WS curve, which fixes its slope. PC will be steeper if WS curve, which fixes its slope. PC will be steeper if WS curve is steeper and vice versa.curve is steeper and vice versa.


W increases W increases by lagged inflation plus an amount to close the gape by lagged inflation plus an amount to close the gape between existing real wage (on between existing real wage (on PSPS curve) and the curve) and the ww on the on the WSWS curve. The percentage gap is a function of curve. The percentage gap is a function of yy and and yeye. So for . So for simplicity: simplicity:

ππ = = ππll + a (y-ye) + a (y-ye)

ππ = = ππ-1-1 + a (y-ye) + a (y-ye)

ππ = inflation inertia + output gape. = inflation inertia + output gape. aa is a positive constant. The is a positive constant. The yy deviation is approximately equal to deviation is approximately equal to

((y – yey – ye). If ). If (y-ye)(y-ye) is positive inflation will be higher than last is positive inflation will be higher than last period, And if period, And if (y-ye)(y-ye) is negative, inflation will fall below last is negative, inflation will fall below last period, finally if period, finally if (y=ye)(y=ye) inflation is constant. inflation is constant.

Hence the PC shifts up or down whenever lagged inflation Hence the PC shifts up or down whenever lagged inflation changes and that its slope depends on changes and that its slope depends on aa, which in turn reflects the , which in turn reflects the slope of the WS curve.slope of the WS curve.


Deriving the Phillips Curves fig 3.2Deriving the Phillips Curves fig 3.2


Phillips’ original curvePhillips’ original curve If the economy is affected by If the economy is affected by random shocksrandom shocks to AD, the economy would to AD, the economy would

be observed at the points shown in fig 3.3. this is one way to present the be observed at the points shown in fig 3.3. this is one way to present the original PC using data for the UK between 1861-1957. fig 3.4 is a original PC using data for the UK between 1861-1957. fig 3.4 is a reproduction for the period 1861-1913reproduction for the period 1861-1913

Phillips original curve may exist but it cannot be exploitedPhillips original curve may exist but it cannot be exploited Can the govt use policy to shift the economy from its customary position Can the govt use policy to shift the economy from its customary position

to a higher level (from to a higher level (from A to BA to B in fig 3.3). in fig 3.3). Suppose that the govt increases MS,Suppose that the govt increases MS, i i falls, and falls, and yy increases. Unlike the increases. Unlike the

original PC we have quite different situation: the govt is seeking to keep original PC we have quite different situation: the govt is seeking to keep yy at at y2y2 to lower unemployment even with inflation. The tendency of the to lower unemployment even with inflation. The tendency of the economy to be near point B is taken in the calculations of workers. They economy to be near point B is taken in the calculations of workers. They will claim for a will claim for a WW rise by 2%, and expected inflation will rise from 0 to rise by 2%, and expected inflation will rise from 0 to 2%, the PC curve shifts up. 2%, the PC curve shifts up.






If the govt persists with its policy of holding y at If the govt persists with its policy of holding y at y2y2, PC will , PC will continue to shift up and lower unemp will be associated with ever continue to shift up and lower unemp will be associated with ever increasing inflationincreasing inflation. This is known as the . This is known as the Lucas critiqueLucas critique. .

So while the relationship estimated by Phillips seemed to suggest So while the relationship estimated by Phillips seemed to suggest the existence of the the existence of the trade offtrade off, but this , but this collapsedcollapsed as soon as the govt as soon as the govt tried to exploit it. A stable PC only existed because govt did not tried to exploit it. A stable PC only existed because govt did not systematically try to exploit. systematically try to exploit.

Hence policy makers can only choose points on the Hence policy makers can only choose points on the vertical linevertical line above above yy at the at the ERUERU, this has led to the , this has led to the vertical long run PCvertical long run PC. .


Disinflation is costlyDisinflation is costly An important implication of the An important implication of the PC (PC (ππ = = ππ-1-1 + a (y-ye)) + a (y-ye)) is that is that

disinflationdisinflation will be at a will be at a costcost ( (unemp will be higher than ERUunemp will be higher than ERU). ). Assume that inflation is high and constant, and unemp is at ERU. Assume that inflation is high and constant, and unemp is at ERU. If inflation is to be lower than last period, If inflation is to be lower than last period, uenempuenemp must be must be pushed up above pushed up above ERUERU. When unemp is above ERU, there is a . When unemp is above ERU, there is a negativenegative gap between WS curve and PSgap between WS curve and PS curve. From the PC curve. From the PC equation:equation:

ππ = = ππ-1-1 + a (y - ye), + a (y - ye),

=> (=> (ππ - - ππ-1-1) = a (y - ye),) = a (y - ye),

If (If (ππ - - ππ-1-1) < 0 (disinflation), ) < 0 (disinflation),

Then a (y - ye) < 0,Then a (y - ye) < 0,=> y < ye (higher unemp)=> y < ye (higher unemp)

Look at fig 3.5. the economy at B with high inflation 8%. The Look at fig 3.5. the economy at B with high inflation 8%. The central bank wishes to reduce inflation to target 2%. central bank wishes to reduce inflation to target 2%.


The only points on the curve with inflation below 8% are to the The only points on the curve with inflation below 8% are to the left of B, i.e. left of B, i.e. higher unemphigher unemp. Disinflation is . Disinflation is costlycostly. .

The The PC (PC (ππll = 8), = 8), assume that the CB has chosen to raise unemp to assume that the CB has chosen to raise unemp to FF. Inflation falls to 6%, and a new . Inflation falls to 6%, and a new PC (PC (ππll = 6) = 6) arises. The CB can arises. The CB can then chose a point on then chose a point on PC (PC (ππll = 6), = 6), F’.F’. This leads to a downward This leads to a downward shift in the PC (not shown), eventually the objective of 2% shift in the PC (not shown), eventually the objective of 2% inflation is achieved and the economy remains at the ERU. inflation is achieved and the economy remains at the ERU.




Disinflation and central bank preferencesDisinflation and central bank preferences Which point along the PC curve the central bank would choose Which point along the PC curve the central bank would choose

when implementing disinflation. Given inflation target 2%, at one when implementing disinflation. Given inflation target 2%, at one extreme the extreme the CBCB could choose point could choose point CC on fig 3.6. although this on fig 3.6. although this brings down inflation to target in the next period, but the cost is a brings down inflation to target in the next period, but the cost is a steep steep rise in unemploymentrise in unemployment (low output at C). The PC shifts to PC (low output at C). The PC shifts to PC ((ππll = 2) = 2) and the CB safely cut and the CB safely cut ii to stabilize to stabilize yy at at yeye. The economy . The economy would move from would move from B to C to AB to C to A. .

A less harsh point for the CB is to choose A less harsh point for the CB is to choose point Fpoint F. the fall in . the fall in inflation and the rise in unemp will be less than if C is chosen. As inflation and the rise in unemp will be less than if C is chosen. As the CB is willing to sacrifice a rise in unemp to get a given the CB is willing to sacrifice a rise in unemp to get a given reduction in inflation we will move along the PC from B to C. reduction in inflation we will move along the PC from B to C. inflation aversion rises as the CB chooses a point closer to C. inflation aversion rises as the CB chooses a point closer to C.


The CB preference between a deviation of inflation from The CB preference between a deviation of inflation from ππTT or or unemp from ERU can be represented with unemp from ERU can be represented with indifference curvesindifference curves as as shown in fig 3.6. indifference curves of the CB of the more shown in fig 3.6. indifference curves of the CB of the more inflation averse CB are inflation averse CB are flatter flatter than the less inflation aversethan the less inflation averse. .

The more inflation averse CB chooses point The more inflation averse CB chooses point DD because it is willing because it is willing to sacrifice a bigger increase in unemp to get inflation lower more, to sacrifice a bigger increase in unemp to get inflation lower more, and the other one chooses and the other one chooses FF on PC( on PC(ππll = 8 = 8). As the PC shifts down, ). As the PC shifts down, the CB chooses its preferred position where the indifference curve the CB chooses its preferred position where the indifference curve is tangential to the new PC. In this way the economy adjusts to is tangential to the new PC. In this way the economy adjusts to point point AA. .

The inflation averse CB guides the economy down the path from The inflation averse CB guides the economy down the path from D to AD to A. the less inflation averse CB guides the economy down the . the less inflation averse CB guides the economy down the path from path from F to AF to A. since the most preferred position is with . since the most preferred position is with ππ==ππTT and and y=ye,y=ye, the indifference curves shrink to a point at the indifference curves shrink to a point at AA. .



Inflation averse

Less Inflation less averse


Costless disinflation and rational expectationsCostless disinflation and rational expectations If the influence of the If the influence of the past on wage is absentpast on wage is absent, it would be possible , it would be possible

for the economy to jump from B to A in fig 3.5 without any rise in for the economy to jump from B to A in fig 3.5 without any rise in unemp. unemp.

Additional assumptions to eliminate the Additional assumptions to eliminate the cost of disinflation: cost of disinflation: 1.1. Inflation inertia is absent. No nominal rigidities in the economy in Inflation inertia is absent. No nominal rigidities in the economy in

wage or price setting behavior or institutional inertia, and wage or price setting behavior or institutional inertia, and adaptive expectations play no role in WS. Instead rational adaptive expectations play no role in WS. Instead rational expectations hypothesis holds. Hence we have expectations hypothesis holds. Hence we have

ππ = = ππEE + a (y-ye) + ɛ (ɛ is a random shock term) + a (y-ye) + ɛ (ɛ is a random shock term)2.2. When the CB announces a low inflation target When the CB announces a low inflation target ππTT it is believed by it is believed by

market participants, or CB policy announcement is market participants, or CB policy announcement is crediblecredible. . ππ = = ππTT + ɛ + ɛ

3.3. Inflation remains at the target, apart form unforeseen shocks Inflation remains at the target, apart form unforeseen shocks ɛɛ. .


Rational expectationsRational expectations of inflation mean the only difference of inflation mean the only difference between expected and actual inflation is something between expected and actual inflation is something randomrandom: : agents do not make agents do not make systematic errorssystematic errors, or agents subjective equal , or agents subjective equal objective expectations given all information is available at the objective expectations given all information is available at the time of forming expectations. The rational expectations time of forming expectations. The rational expectations hypothesis means that hypothesis means that

ππEE = E = Eππ = E( = E(ππTT + ɛ) = + ɛ) = ππTT + Eɛ = + Eɛ = ππTT ππEE = = ππT T (rational expectations of inflation)(rational expectations of inflation)

E is the E is the objectiveobjective expected value and the PC is now expected value and the PC is nowππ = = ππTT + a (y-ye) + ɛ + a (y-ye) + ɛ (PC; rational expectations). Rearrange:(PC; rational expectations). Rearrange:y-ye = 1/a(y-ye = 1/a(ππ - - ππTT - ɛ) - ɛ) = 1/a(= 1/a(ππ - - ππEE))

Hence y=ye + 1/a(Hence y=ye + 1/a(ππ - - ππEE), (), (ππ – – ππEE)) inflation surprise inflation surprisey=ye+y=ye+ζζ (Lucas surprise supply equation)(Lucas surprise supply equation)

ζζ (ksi is a random error) (ksi is a random error)


Output only deviates from eq when there is a Output only deviates from eq when there is a surprise to inflationsurprise to inflation. . Surprise or unanticipated inflation is normally interpreted as Surprise or unanticipated inflation is normally interpreted as pushing output from eqpushing output from eq, as firms will find it difficult to know , as firms will find it difficult to know whether there is a rise in inflation in general, or in its product whether there is a rise in inflation in general, or in its product relative to the general price level. It will not be possible for firms relative to the general price level. It will not be possible for firms to distinguish with certainty between the general and the relative to distinguish with certainty between the general and the relative price change.price change.

In a world of rational expectations, and In a world of rational expectations, and crediblecredible inflation target, inflation target, random shocks to inflation (random shocks to inflation (surprisessurprises) will lead output to ) will lead output to deviatedeviate from its eq level, there will not even be temporary movements from its eq level, there will not even be temporary movements along the PC in response to announced changes in govt policy. along the PC in response to announced changes in govt policy. Disinflation will Disinflation will not be costlynot be costly..

The distinction between the two approaches should be noted:The distinction between the two approaches should be noted: When using When using inertiainertia augmented PC, causality goes from a augmented PC, causality goes from a

deviation in output from its eq to a change in inflation relative to deviation in output from its eq to a change in inflation relative to lagged inflation.lagged inflation.


ΔΔAD → AD → ΔΔy relative to ye → y relative to ye → ΔπΔπ relative to relative to ππ-1-1

In the Lucas surprise supply eq causality goes from a deviation in In the Lucas surprise supply eq causality goes from a deviation in inflation from its expected value to a change in output relative to inflation from its expected value to a change in output relative to eq.eq.

ΔπΔπ relative to relative to ππE E → → ΔΔy relative to yey relative to ye The Lucas supply equation highlights that systematic monetary The Lucas supply equation highlights that systematic monetary

policy is policy is ineffectiveineffective in altering the level of economic activity, and in altering the level of economic activity, and there is no need for it because the economy returns directly to eq there is no need for it because the economy returns directly to eq once a shock to inflation has disappearedonce a shock to inflation has disappeared (strong assumptions). (strong assumptions).


The 3 equation model: IS-PC-MR The 3 equation model: IS-PC-MR (1) The (1) The ISIS equation: simplify the IS equation to be: equation: simplify the IS equation to be:

y=A-ary=A-ar IS EquationIS Equation

We will be interested in We will be interested in rr that equates that equates yy to to yeye

ye = A – arye = A – arss Stabilizing interest rate Stabilizing interest rate

rrss changes whenever changes whenever AA or or yeye changes. changes.

y-ye = -a(r - ry-ye = -a(r - rss)) (IS, output gap form)(IS, output gap form)

This eq makes it clear that output will deviate from eq to the This eq makes it clear that output will deviate from eq to the extent that the extent that the rr differs from the stabilizing differs from the stabilizing rrss. The CB is going to . The CB is going to

choose choose rr so as to so as to influence output gapinfluence output gap as it seeks to achieve its as it seeks to achieve its stabilization objective. stabilization objective. InstantaneousInstantaneous change in change in yy can’t be can’t be achieved by altering achieved by altering rr, it takes time for , it takes time for rr changes to feed through changes to feed through to affect I and to affect I and yy. .


(2) the inertia-augmented (2) the inertia-augmented Phillips curvePhillips curve equation equation

ππ = = ππ-1-1 + a (y-ye) + a (y-ye) (PC) (PC) (3) The third eq the (3) The third eq the MRMR is deviated from the CB’s output is deviated from the CB’s output

inflation tradeoff. This can be written as:inflation tradeoff. This can be written as:y-ye = -b(y-ye = -b(ππ – – ππTT) (MR) ) (MR)

This equation shows the combination of This equation shows the combination of yy and and ππ that the CB will that the CB will choose given the PC it faces. Whenchoose given the PC it faces. When ππ is high, it will choose to is high, it will choose to reduce reduce ADAD (by raising (by raising rr), see fig. 3.6. a higher ), see fig. 3.6. a higher bb is associated with is associated with a move inflation-averse central bank.a move inflation-averse central bank.

To construct the To construct the MRMR line simply take a PC to find the CB line simply take a PC to find the CB best best output inflation combinationoutput inflation combination along the PC. Find the along the PC. Find the tangencytangency between the CB indifference curves and the relevant PC between the CB indifference curves and the relevant PC constraint it faces. At each point of tangency the MR equation will constraint it faces. At each point of tangency the MR equation will hold. Note also that the hold. Note also that the MRMR line will go through line will go through y=yey=ye and and ππ = = ππee. .

In fig 3.6 the MR is found by joining up points D, D’ and A. In fig 3.6 the MR is found by joining up points D, D’ and A.


For the less inflation averse CB by joining points For the less inflation averse CB by joining points F, F’ and AF, F’ and A.. Whenever the economy shifted away from the Whenever the economy shifted away from the (ye, (ye, ππTT), ), by a by a shockshock, ,

the CB will use a change in the CB will use a change in rr to get the economy onto the to get the economy onto the MRMR line, line, once on the line, it must continue to adjust once on the line, it must continue to adjust rr until the economy until the economy returns toreturns to (ye, (ye, ππTT)). Look at fig 3.7. at point . Look at fig 3.7. at point BB inflation rise to 6%, inflation rise to 6%, to get inflation back to target, to get inflation back to target, yy is going to be below eq. the is going to be below eq. the MRMR shows that shows that the the CB will choose point CB will choose point FF by raising by raising rr, AD falls below , AD falls below yeye, and adjusts back to point , and adjusts back to point ZZ. .

If inflation falls below the target at point If inflation falls below the target at point B’,B’, the CB prefers point the CB prefers point GG, , yy goes above its eq to push inflation up to 2% until point goes above its eq to push inflation up to 2% until point Z Z. .

The CB is going from chosen The CB is going from chosen yy on the MR line to the IS curve to on the MR line to the IS curve to see see rr that CB must set. that CB must set.




An inflation shockAn inflation shock Look at fig 3.8, the top diagram is the IS and the MR and PC in Look at fig 3.8, the top diagram is the IS and the MR and PC in

the bottom diagram. Starting at point the bottom diagram. Starting at point AA with with y=yey=ye and and ππTT is 2%. is 2%. We assume that there is an inflationary shock to the economy, We assume that there is an inflationary shock to the economy, which pushes inflation to 4%, the economy moves to point B on which pushes inflation to 4%, the economy moves to point B on PC(PC(ππll = 4), = 4), the CB choosesthe CB chooses r’r’ on the IS curve (point on the IS curve (point C’C’) to achieve ) to achieve point C on point C on PC(PC(ππll = 4). = 4). In the next period the PC shifts down as a In the next period the PC shifts down as a result of result of falling inflationfalling inflation, the new , the new PC(PC(ππll = 3). = 3).

The economy is guided down the The economy is guided down the MRMR line to the south east as the line to the south east as the CB implements the CB implements the MRMR. we also see the path where the CB . we also see the path where the CB reduces reduces rr back towards stabilizing back towards stabilizing rrss. Eventually the economy . Eventually the economy

returns to eq with target inflation at Z. frequent adjustments of returns to eq with target inflation at Z. frequent adjustments of rr are required by the monetary policy rule. are required by the monetary policy rule.




A temporary demand shockA temporary demand shock See fig 3.9, if the economy starts off eq with See fig 3.9, if the economy starts off eq with ππTT is 2%, and the is 2%, and the

economy is disturbed by a temporary AD shock. The IS that economy is disturbed by a temporary AD shock. The IS that reflects the shock is reflects the shock is IS’IS’ and remains IS’ for only one period. and remains IS’ for only one period. yy is is pushed up pushed up y’>yey’>ye. Inflation rise above target (to 4%), i.e. PC(. Inflation rise above target (to 4%), i.e. PC(ππll = = 44), along which the CB must choose its preferred point ), along which the CB must choose its preferred point CC. by . by going vertically up to point going vertically up to point C’C’ in the IS diagram. The CB can in the IS diagram. The CB can work out that the appropriate r is work out that the appropriate r is r’.r’. The subsequent adjustment The subsequent adjustment path down the MR line to point Z is exactly the same as the case path down the MR line to point Z is exactly the same as the case of the inflation shock. of the inflation shock.

The economy is shifted from A to B as a result of AD shock. The economy is shifted from A to B as a result of AD shock. Inflation is above target, which eliminated by pushing output Inflation is above target, which eliminated by pushing output below equilibrium. The CB raises below equilibrium. The CB raises rr in response to AD shock to in response to AD shock to depress interest sensitive demand and reduce output. depress interest sensitive demand and reduce output.




A permanent demand shockA permanent demand shock The IS shifts permanently to IS’. See fig.3.10 The economy starts The IS shifts permanently to IS’. See fig.3.10 The economy starts

at eq with inflation target 2%. The initial stabilizing r is at eq with inflation target 2%. The initial stabilizing r is rsrs. The . The IS shifts rightwards to IS’. Output goes up to IS shifts rightwards to IS’. Output goes up to y’:y’: the economy is at the economy is at point B on the PC diagram and at point B on the PC diagram and at B’B’ in the IS diagram. in the IS diagram. Because Because the IS shock is permanent, the stabilizing interest has risen to the IS shock is permanent, the stabilizing interest has risen to r’r’ss. .

with higher exogenous demand, a higher with higher exogenous demand, a higher rr is required to dampen is required to dampen AD so that AD so that y=yey=ye. .

In order to get the economy onto the MR line at point C, the CB In order to get the economy onto the MR line at point C, the CB has to set r at has to set r at r’,r’, considerably higher than was necessary in the considerably higher than was necessary in the case of the temporary demand shock. Once the economy is at case of the temporary demand shock. Once the economy is at points points CC and and C’,C’, adjustment along MR and IS’ takes place in the adjustment along MR and IS’ takes place in the usual way, the new eq is Z in PC diagram and usual way, the new eq is Z in PC diagram and Z’Z’ in the IS in the IS diagram. diagram.




The MR and the real interest rateThe MR and the real interest rate See fig 3.10 again. To steer inflation back to the target the CB See fig 3.10 again. To steer inflation back to the target the CB

raises raises rr and the economy moves to and the economy moves to CC and and C’C’ which is a rise in which is a rise in rr from from rrss to to r’.r’. Contrast this with two alternatives: keeping Contrast this with two alternatives: keeping rr

unchanged and keeping the nominal interest unchanged. If unchanged and keeping the nominal interest unchanged. If rr is is unchanged at unchanged at rrss, y remains at , y remains at y’y’ above eq and inflation will above eq and inflation will

continue to rise as the PC shifts upward each period. If nominal continue to rise as the PC shifts upward each period. If nominal interest is unchanged the economy moves from interest is unchanged the economy moves from B’B’ to a point on to a point on the IS’ to the south east of point B’. The rise in inflation is the IS’ to the south east of point B’. The rise in inflation is signaled by the persistence of signaled by the persistence of yy above above yeye, reduces , reduces rr with a given with a given nominal interest and higher inflation, nominal interest and higher inflation, rr falls. ( falls. (i=r+i=r+ππEE, and r=i- , and r=i- ππEE). ). This will boast This will boast yy taking the economy further away from the taking the economy further away from the inflation target. inflation target.


Sacrifice ratios and disinflation strategiesSacrifice ratios and disinflation strategies Unemployment can be a consequence to a fall in inflation. “Unemployment can be a consequence to a fall in inflation. “Cold Cold

turkeyturkey” or “” or “shock therapyshock therapy” are applied to this strategy in ” are applied to this strategy in contrast to the contrast to the gradualistgradualist approach, disinflation takes longer. Is approach, disinflation takes longer. Is cumulative unemployment higher under cold turkey or cumulative unemployment higher under cold turkey or gradualism. gradualism.

If PCs are linear and parallel, cumulative unemployment to If PCs are linear and parallel, cumulative unemployment to reduce inflation to target is the same under both strategies, i.e., reduce inflation to target is the same under both strategies, i.e., sacrifice ratio (cumulative unemployment to achieve a given sacrifice ratio (cumulative unemployment to achieve a given reduction in inflation) is independent of the degree of inflation reduction in inflation) is independent of the degree of inflation aversion of the CB. aversion of the CB.

Assume a government operates a simple MRAssume a government operates a simple MRy-ye = -b(y-ye = -b(ππ- - ππTT),), b=toughness of response to high inflationb=toughness of response to high inflation

assume that cumulative unemployment is independent of assume that cumulative unemployment is independent of bb. this . this assumption is that inertia augmented PC is linearassumption is that inertia augmented PC is linear




ππ = = ππll + a (y-ye) + a (y-ye)

with with

ππll= = ππ-1-1 Look at figure 3.11. first assume maximum toughness so that Look at figure 3.11. first assume maximum toughness so that b=∞b=∞ the the

preference is to bring inflation back preference is to bring inflation back immediatelyimmediately. MR is horizontal (MR. MR is horizontal (MR11). If ). If

there is an upward shock to inflation i.e., there is an upward shock to inflation i.e., ππll = = ππ00 > > ππTT. . With MR1, y falls to y With MR1, y falls to y00

as the sharp rise in r takes effect. as the sharp rise in r takes effect. ππ falls from falls from ππ00 to to ππTT, , next periodnext period ππll = = ππTT, so , so

the CB can safely cutthe CB can safely cut r r back to the stabilizingback to the stabilizing r r andand y y rises back torises back to ye. ye. There is There is unemployment ofunemployment of ye-y ye-y00 for one period, after which unemployment is zero for one period, after which unemployment is zero

again: cumulative unemp is simplyagain: cumulative unemp is simply ye-y ye-y00. .

If the govt has more lenient MR (MR2), as a result of inflation shock, y is cut If the govt has more lenient MR (MR2), as a result of inflation shock, y is cut from from yeye to to yy11 so that in the first period so that in the first period ππll falls fromfalls from ππll = = ππ0 to 0 to ππll = = ππ1. 1. using using

MR2, the PC withMR2, the PC with ππll = = ππ1 1 implies thatimplies that y y rises fromrises from y1 y1 toto y2. y2. unemployment in unemployment in the second period isthe second period is (ye-y2). (ye-y2). Cumulative unemployment after 2 periods isCumulative unemployment after 2 periods is (ye- (ye-y1) + (ye – y2). y1) + (ye – y2).


The proof of the assertion that cumulative unemp does not depend on the value The proof of the assertion that cumulative unemp does not depend on the value of of bb can be seen from fig 3.11. can be seen from fig 3.11. (ye-y0) (ye-y0) is exactly is exactly (y(yAA-y0-y0) on the horizontal axis, ) on the horizontal axis,

(ye-y(ye-y22) ) is exactly is exactly (y(yBB-y-yAA). ). If we add the unemp created in each subsequent If we add the unemp created in each subsequent

period in the gradualist case to (yperiod in the gradualist case to (yAA-y-y00)+(y)+(yBB-y-yAA)+…, the total is exactly (ye-y)+…, the total is exactly (ye-y00), ),

i.e., it is equal to the cumulative unemp in the cold turkey case with b=∞.i.e., it is equal to the cumulative unemp in the cold turkey case with b=∞.

The proof depends on the linearity of the PCs. Look at figure 3.12. to see what The proof depends on the linearity of the PCs. Look at figure 3.12. to see what happens when the PC is convex we use the MR with b= ∞and PC(happens when the PC is convex we use the MR with b= ∞and PC(ππll = = ππ0). This 0). This reflects the empirical finding that inflation becomes less sensitive to a rise in reflects the empirical finding that inflation becomes less sensitive to a rise in unemp the higher unemp is. unemp the higher unemp is. This implies a reduction in y greater than the fall This implies a reduction in y greater than the fall to y0. hence cumulative unemp with a more inflation averse MR will be greater to y0. hence cumulative unemp with a more inflation averse MR will be greater with a weaker one. Hence the strategy of a very inflation averse CB of reducing with a weaker one. Hence the strategy of a very inflation averse CB of reducing inflation to the target very fast will be more costly than a gradualist one.inflation to the target very fast will be more costly than a gradualist one.

With non linear PCs the sacrifice ratio is higher for a more inflation averse With non linear PCs the sacrifice ratio is higher for a more inflation averse CB. With a linear PCs, the reduction of inflation to target has the same total CB. With a linear PCs, the reduction of inflation to target has the same total unemp cost. unemp cost.




Inflation at the medium run equilibriumInflation at the medium run equilibrium Two monetary policiesTwo monetary policies Interest rate rule (MR approach)Interest rate rule (MR approach) In the 3 eq model, as long as the CB objective is to stabilize the economy at In the 3 eq model, as long as the CB objective is to stabilize the economy at

ERU, inflation at the medium run eq is equal to the target set by the CB ERU, inflation at the medium run eq is equal to the target set by the CB ππ = = ππTT. . Since the CB is constrained to choose a point on the inertia-augmented PC, it Since the CB is constrained to choose a point on the inertia-augmented PC, it will have to raise r to set the economy on the path toward the new inflation will have to raise r to set the economy on the path toward the new inflation target. There will be a phase of costly disinflation before the new inflation is target. There will be a phase of costly disinflation before the new inflation is achieved. achieved.

Money supply rule (LM approach)Money supply rule (LM approach) MS is under the control of the CB. The growth rate of MS determines the rate MS is under the control of the CB. The growth rate of MS determines the rate

of inflation in the medium run eq. We assume the approximation holds so that:of inflation in the medium run eq. We assume the approximation holds so that:

i = r + i = r + ππEE

the medium run eq, the medium run eq, ππ = = ππEE so that so that

i = r + i = r + ππ


Next we take money market eq conditionNext we take money market eq condition

Ms/p = L(i,y)Ms/p = L(i,y)

= L(r + = L(r + ππ, y ), y ) y is determined by WS and PS curves at y is determined by WS and PS curves at yeye. The IS is fixed by AD. . The IS is fixed by AD.

Hence Hence rr associated with associated with yeye is fixed at is fixed at rrss. Since in the medium run . Since in the medium run

ππ is constant the real demand for money is constant. MS/P must is constant the real demand for money is constant. MS/P must also be constant, which requires also be constant, which requires PP to grow at the same rate of MS to grow at the same rate of MS which is under the control of CB. Assume that MS growth which is under the control of CB. Assume that MS growth γγMM is is constant atconstant at γγMMparpar (exogenous): (exogenous):

γγMMparpar = M-M-1/M-1 = M-M-1/M-1

ππ = = γγMMparpar


How the MR relates to the LM curve.How the MR relates to the LM curve. What is the relationship between MR approach and LM What is the relationship between MR approach and LM

approach. There are two key points:approach. There are two key points: First the approach to use depend on the type of M policy, if First the approach to use depend on the type of M policy, if

interest rate based MR, the correct model is the 3 eq with MR. interest rate based MR, the correct model is the 3 eq with MR. this is called an this is called an inflation targeting regime.inflation targeting regime. If the target is to set If the target is to set γγMMparpar oror M Mss

parpar. . A money supply rule requires the use of the LM A money supply rule requires the use of the LM curve approach.curve approach.

Second the LM condition does not disappear when the MR Second the LM condition does not disappear when the MR approach is being used. We need to distinguish between LM approach is being used. We need to distinguish between LM condition condition Ms/p = L(i,y)Ms/p = L(i,y) and the money supply rule, which assumes and the money supply rule, which assumes that MS is set exogenously. The LM condition must always hold that MS is set exogenously. The LM condition must always hold irrespective of whether the govt is using MS rule or MR based on irrespective of whether the govt is using MS rule or MR based on rr. otherwise . otherwise rr would not remain at desired level. The LM curve is would not remain at desired level. The LM curve is present in the background but it plays no role in fixing the present in the background but it plays no role in fixing the position of the economy position of the economy y,y, ππ or r. or r.


Inflation in the IS/LM modelInflation in the IS/LM model The IS/LM presents a different picture of policy making from the The IS/LM presents a different picture of policy making from the

3 eq model. When using MR the CB is 3 eq model. When using MR the CB is forward looking forward looking and and setting setting rr to guide the economy back to eq. by contrast using MS to guide the economy back to eq. by contrast using MS rule implies that M policy is rule implies that M policy is passivepassive..

When the economy is subjected to a shock, the new medium term When the economy is subjected to a shock, the new medium term eq will be eq will be identicalidentical in both models. However the adjustment path in both models. However the adjustment path with MS rule will be different. The CB is assumed to stick to a with MS rule will be different. The CB is assumed to stick to a constant MS growthconstant MS growth. . rr then changes as a result of interaction then changes as a result of interaction between the CB fixed money supply growth and the evolution of between the CB fixed money supply growth and the evolution of inflation. If there is a permanent AD shock, adjustment takes inflation. If there is a permanent AD shock, adjustment takes place in the IS/LM as follows:place in the IS/LM as follows:

1. A RHS shift of IS will raise 1. A RHS shift of IS will raise yy and M and Mdd. In the short run MS . In the short run MS growth and inflation are equal, and MS/P is constant. The LM growth and inflation are equal, and MS/P is constant. The LM stays fixed, there will be a sale of bonds and stays fixed, there will be a sale of bonds and rr rises. This is a rises. This is a movement along LM to its intersection with the new IS. movement along LM to its intersection with the new IS.


2. higher y leads to a rise in inflation, which reduced MS/P causes 2. higher y leads to a rise in inflation, which reduced MS/P causes the LM to shift to the left. This dampens AD. the LM to shift to the left. This dampens AD.

3. as inflation increases it must end up back to its original level in 3. as inflation increases it must end up back to its original level in the new medium run eq. the inertia in inflation implies that y will the new medium run eq. the inertia in inflation implies that y will have to fall below ye,have to fall below ye, y<ye y<ye. .

4. a spiral shaped adjustment path in the PC diagram will be 4. a spiral shaped adjustment path in the PC diagram will be traced as the economy moves first to the north east and then in a traced as the economy moves first to the north east and then in a counter-clockwise spiral back to eq. See fig 3.13. counter-clockwise spiral back to eq. See fig 3.13.








Macroeconomic Theory Prof. M. El-Sakka CBA. Kuwait University Macroeconomic Theory Chapter 3 Inflation, Unemployment and Monetary Rules.

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