macroeconomics 2 islm model

8/12/2019 Macroeconomics 2 ISLM Model

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Macroeconomics 2:Introducing the IS-MP-PC Model

Karl Whelan

School of Economics, UCD

January 21, 2013

Karl Whelan (UCD) Introducing the IS-MP-PC Model January 21, 2013 1 / 34
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Beyond IS-LM

As this is the second module in a two-module sequence, followingMacroeconomics 1, I am assuming that everyone in this class has seen the

IS-LM and AS-AD models.In the first part of this course, we are going to revisit and expand on thesemodels in a number of ways:

1 More Realistic: Rather than the traditional LM curve, we will describe

monetary policy in a way that is more consistent with how it is nowimplemented, i.e. we will assume the central bank follows a rule thatdictates how it sets nominal interest rates. We will focus on how theproperties of the monetary policy rule influence the behaviour of theeconomy.

2 Expectations: We will have a more careful treatment of the roles

played by real interest rates and inflation expectations.3 The Zero Bound: We will model the zero lower bound on interest

rates and discuss its implications for policy.

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A Model With Three Elements

Our model will have three elements to it.

1 A Phillips Curvedescribing how inflation depends on output.2 An IS Curvedescribing how output depends upon interest rates.3 A Monetary Policy Ruledescribing how the central bank sets interest

rates depending on inflation and/or output.

Putting these three elements together, I will call it the IS-MP-PC model (i.e.

The Income-Spending/Monetary Policy/Phillips Curve model).We will describe the model with equations.

We will also merge together the second two elements (the IS curve and themonetary policy rule) to give a new IS-MP curve that can be combined withthe Phillips curve to use graphs to illustrate the models properties.

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Part I

The Phillips Curve

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The Phillips Curve

What are the tradeoffs facing a central bank? A 1958 study by the LSEsA.W. Phillips seemed to provide the answer.

Phillips documented a strong negative relationship between wage inflationand unemployment: Low unemployment was associated with high inflation,presumably because tight labour markets stimulated wage inflation.

A 1960 study by MIT economists Solow and Samuelson replicated these

findings for the US and emphasised that the relationship also worked forprice inflation.

The Phillips curve tradeoff quickly became the basis for the discussion ofmacroeconomic policy.

Policy faced a tradeoff: Lower unemployment could be achieved, but only atthe cost of higher inflation.

However, Milton Friedmans 1968 presidential address to the AmericanEconomic Association produced a well-timed and influential critique of thethinking underlying the Phillips Curve.

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A. W. Phillipss Graph

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Solow and Samuelsons Description of the Phillips Curve

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The Expectations-Augmented Phillips Curve

Friedman pointed out that it was expected real wages that affected wage

bargaining.

If low unemployment means workers have strong bargaining position, thenhigh nominal wage inflation on its own is not good enough: They wantnominal wage inflation greater than price inflation.

Friedman argued that if policy-makers tried to exploit an apparent Phillipscurve tradeoff, then the public would get used to high inflation and come toexpect it. Inflation expectations would move up and the previously-existingtradeoff between inflation and output would disappear.

In particular, he put forward the idea that there was a natural rate of

unemployment and that attempts to keep unemployment below this levelcould not work in the long run.

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The Demise of the Basic Phillips Curve

Monetary and fiscal policy in the 1960s were very expansionary around theworld.

At first, the Phillips curve seemed to work: Inflation rose and unemploymentfell.

However, as the public got used to high inflation, the Phillips tradeoff gotworse. By the late 1960s inflation was still rising even though unemployment

had moved up.

This stagflation combination of high inflation and high unemployment goteven worse in the 1970s.

This was exactly what Friedman predicted would happen.

Today, the data no longer show any sign of a negative relationship betweeninflation and unemployment. If fact, the correlation is positive: The originalformulation of the Phillips curve is widely agreed to be wrong.

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The Evolution of US Inflation and Unemployment

US Inflation and Unemployment, 1955-2012

Inflation Unemployment

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

0

2

4

6

8

10

12

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The Failure of the Phillips Curve

US Inflation and Unemployment, 1955-2012

Inflation is the Four-Quarter Percentage Change in GDP Deflator

Inflation

Unemploymen

t

0.0 2.5 5.0 7.5 10.0 12.5

3

4

5

6

7

8

9

10

11

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Our Version of the Phillips Curve

Our version of the Phillips curve is as follows:

t=et + (yt y

t) +

t

Here represents inflation and by twe mean inflation at time t.

The equation states that inflation depends on three factors.

1 Inflation Expectations: This is given by the et term which represents thepublics inflation expectations at time t. We have put a time subscript onthis variable because the publics expectations may change over time. Notethat a 1 point increase in inflation expectations raises inflation by exactly

one point this is because we are assuming that people bargain over realwages and higher expected inflation translates one-for-one into their wagebargaining, which in turn is passed into price inflation.

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t=et + (yt

y

t) +

t



2 The Output Gap: This is given by (yt y

t). It is the gap between GDP attime t, as represented by ytand what we will term the natural level ofoutput, which we term yt. This is the level of output at time tthat wouldbe consistent with unemployment equalling its natural rate. We wouldexpect this natural level of output to gradually increase over time asproductivity levels improve. The coefficient (pronounced gamma)describes exactly how much inflation is generated by a 1 percent increase inthe gap between output and its natural rate.



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t

=et

+ (yt

yt

) + t



3 Inflationary Shocks: No model in economics is perfect. So while inflationexpectations and the output gap may be key drivers of inflation, they wontcapture all the factors that influence inflation at any time. For example,supply shocks like a temporary increase in the price of imported oil candrive up inflation for a while. To capture these kinds of temporary factors,

we include an inflationary shock term,

t . The superscript indicatesthat this is the inflationary shock (this will distinguish it from the outputshock that we will also add to the model) and the tsubscript indicates thatthese shocks change over time.

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The Phillips Curve Graph with t = 0



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The Phillips Curve as we move from t= 0 to t >0

(An Aggregate Supply Shock)

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The Phillips Curve as we move from et = 1 to et = 2

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Part II

The IS-MP Curve


R l I R d h IS C
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Real Interest Rates and the IS Curve

The second element of the model is one that should be familiar to you: AnIS curve relating output to interest rates. The higher interest rates are, the

lower output is.I want to stress, however, that the IS relationship is between output andreal interest rates, not nominal rates. Real interest rates adjust theheadline (nominal) interest rate by subtracting off inflation.

Suppose I told you the interest rate was 10 percent. Is this a high interest

rate? The answer is that it really depends on inflation.

Consider the decision to save. If the interest rate if 5% but inflation is 2%,then youll be able to buy 3% more stuff next year because you saved andsaving seems like a good idea. In constrast, if the interest rate if 5% butinflation is 8%, then youll be able to buy 3% less stuff next year even

though you have saved your money and earned interest.

Similar point applies to firms. If inflation is 10%, then a firm can expectthat its prices (and profits) will be increasing by that much over the nextyear and a 10% interest rate wont seem so high. But if prices are falling,then a 10% interest rate on borrowings will seem very high.


O V i f h IS C
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Our Version of the IS Curve

Our version of the IS curve will be the following:

yt=y

t

(it

t

r

) + y

t

Expressed in words, this equation states that the gap between output and itsnatural rate yt y

t depends on two factors:

1 The Real Interest Rate:

The nominal interest rate at time t is represented by it, so the real

interest rate is it t. The equation has been constructed in a particular way so that it

explicitly defines the real interest rate at which output will, on average,

equal its natural rate.T This is denoted by r. This rate can be termed the natural rate of interest. When

y

t = 0,

then a real interest rate of r will imply yt =y

t .


O V i f th IS C
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Our Version of the IS Curve

Our version of the IS curve will be the following:

yt=y

t

(it

t

r

) + y

t

Expressed in words, this equation states that the gap between output and itsnatural rate yt y

t depends on two factors:

2 Aggregate Demand Shocks, y

t:

Many other factors beyond the real interest rate influence aggregate

spending decisions. These include fiscal policy, asset prices and consumer and business

sentiment. We will model all of these factors as temporary deviations from zero of

an aggregate demand shock,

y

t . Note that this shock has a superscript yto distinguish it from the

aggregate supply shock t that moves the Phillips curve up and

down.


M t P li Th LM C A h
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Monetary Policy: The LM Curve Approach

We has described how inflation depends on output and how output dependson interest rates. Can complete the model by describing how interest rates

are determined.Traditionally, this is where the LM curve is introduced. Links demand for thereal money stock with nominal interest rates and output:

mt

pt= it+ yt

This can be re-arranged to give a positive relationship between output andinterest rates:

yt=1

mt

pt + it

Combined with the negative relationship between these variables in the IS

curve to determine unique values for output and interest rates. Illustrated ina graph with an upward-sloping LM curve and a downward-sloping IS curve.Monetary policy described as central bank adjusting the money supply mt ina way that sets the position of the LM curve.

The determination of prices is then described separately in an AS-AD model.


Mo eta Polic O A oach
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Monetary Policy: Our Approach

Instead of the LM curve approach, we will model monetary policy byassuming that the central bank sets nominal interest rates according to a

particular rule. There are two reasons for this appraoch.

1 Realism: In practice, no modern central bank implements its monetarypolicy by setting a specified level of the monetary base. Instead, theyset short-term interest rates to equal to some target level. The supplyof base money ends up being whatever emerges from enforcing the

interest rate target. This makes the LM curve (and the money supply)of secondary interest when thinking about core macroeconomic issues.

2 Simplicity: The traditional approach uses a separate AS-AD model todescribe the determination of prices (and thus, implicitly, inflation).However, the reality is that rather than being determined independently

of inflation, most modern central banks set interest rates with a veryclose eye on inflationary developments. In simplifying the determinationof output, inflation and interest rates down to a single model, thisapproach is also simpler than one that requires two different sets ofgraphs.


The Monetary Policy Rule
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The Monetary Policy Rule

We first consider a monetary policy rule of the form:

it=r + + (t

)

The central bank adjusts the nominal interest rate, it, upwards wheninflation, t, goes up and downwards when inflation goes down (we areassuming that >0) and it does so in a way that means when inflationequals a target level, , chosen by the central bank, real interest rates will

be equal to their natural level.Note what the nominal interest rate will be if inflation equals its target level(i.e. t=

). The nominal interest rate will be it=r + . In this case,

the real interest rate will be it t=r.

Think about why a rule of this form might be a good idea. Suppose the

central bank has a target interest rate of

that it wants to achieve. Ideally,the public will understand and set et =

.

If that can be achieved, then the Phillips curve tells us that, on average,inflation will equal provided we have yt=y

t. And the IS curve tells usthat, on average, we will have yt=y

t when it t=r.


The Full Model
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The Full Model

Thats the model. It consists of three equations.

1 The Phillips curve:

t=et + (yt y

t) +

t

2 The IS curve:yt=y

t (it t r) + yt

3 The monetary policy rule:

it=r

+

+ (t

)

I had promised a graphical representation of this model. However, this is asystem of three variables which makes it hard to express on a graph withtwo axes.

To make the model easier to analyse using graphs, we are going to reduce itdown to a system with two main variables (inflation and output).

We can do this because the monetary policy rule makes interest rates are afunction of inflation, so we can substitute this rule into the IS curve to get anew relationship between output and inflation that we will call the IS-MPcurve.


The IS MP Curve
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The IS-MP Curve

If we replace the term itin the IS curve with the formula from the monetary

policy rule, we get

yt=y

t [r + + (t

)] + (t+r) + yt

Now multiply out the terms in this equation to get

yt=y

t r

(t ) + t+ r

+ yt

Canceling terms and re-arranging, this simplifies to

yt=y

t ( 1) (t ) + yt

This is the IS-MP curve. It combines the information in the IS curve and theMP curve into one relationship.


The IS MP Curve Graph
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The IS-MP Curve Graph

The IS-MP curve is

yt=y

t

(

1) (t

) + y

t

How this curve looks in a graph depends especially on the value of, theparameter that describes how the central bank reacts to inflation.

An extra unit of inflation implies a change of ( 1) in output. Is this

positive or negative? Well we are assuming that >0 so this combinedcoefficient will be negative if 1> 0, i.e. the IS-MP curve will slopedownwards if >1 and upwards if 1then an increase in inflation leads to higher real interest rates and, via the IScurve relation, to lower output.

For now, we will assume that >1 so that we have a downward-slopingIS-MP curve but we will revisit this later.


The IS-MP Curve with y = 0
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The IS-MP Curve with t = 0


The IS-MP Curve as we move from yt = 0 to yt > 0
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The IS MP Curve as we move from t= 0 to t >0

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Part III

Putting the Pieces Together


The IS-MP-PC Model Graph
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The IS MP PC Model Graph

We can now illustrate the full model in a single graph.

The graph features one curve that slopes upwards (the Phillips curve) andone that slopes downwards (the IS-MP curve provided we assume that >1.)

The next figure provides the simplest possible example of the graph. This is

the case where both the temporary shocks,

t and

y

tequal zero and thepublics expectation of inflation is equal to the central banks inflation target.

Note that I have labelled the PC and IS-MP curves to explicitly indicatewhat the expected and target rates of inflation are and it will be a good ideafor you to do the same when answering questions about this model.

In the next set of notes, we will analyse this model in depth, examining whathappens when various types of events occur and focusing carefully on howinflation expectations change over time.


Expected Inflation Equals the Inflation Target
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Expected Inflation Equals the Inflation Target


A More Complicated Monetary Policy Rule
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p y y

In a famous 1993 paper, economist John Taylor argued for a monetarypolicy rule in which the central bank adjusted interest rates in response toboth inflation and the gap between output and an estimated trend.

Within our model structure, we can amend our monetary policy rule to bemore like this Taylor rule as follows:

it=r + + (t

) + y(yt y

t)

Substituting this into the IS curve, we getyt=y

t [r + + (t

) + y(yt y

t)] + (t+r) + yt

This can be re-arranged to give

yt y

t = ( 1)

1 + y(t

) + 1

1 + yy

t

This shows that broadening the monetary policy rule to incorporate interestrates responding to the output gap doesnt change the essential form of theIS-MP curve. As long as >1, the curve slopes downwards and featurest=

when yt=y

t and there are no inflationary shocks.


Things to Understand From This Topic
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g p

1 The evidence on the Phillips curve.

2

The Phillips curve that features in our model and how to draw it.3 Why real interest rates are what matters for aggregage demand.

4 The IS curve that features in our model.

5 The monetary policy that features in our model.

6 How to derive the IS-MP curve.

7 What determines the slope of the IS-MP curve.

8 How the IS-MP curve changes when the monetary policy rule takes the formof a Taylor rule.

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macroeconomics 2 islm model

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