GLA 1001MACROECONOMICS:
MARKETS, INSTITUTIONS AND GROWTH
LECTURE 4:MACROECONOMIC POLICY βTHE DERIVATION OF THE MR CURVE
Β© Gustavo Indart Slide 1
THE NEED FOR ECONOMIC POLICY
We have defined both the WS curve and the PS curve: The WS curve refers to the real wage that workers
expect to secure The PS curve refers to the real wage that profit-
maximizing firms are prepared to pay
In the absence of a policy maker, a gap between the WScurve and the PS curve will generate ever-increasing inflation
This incompatibility could be resolved in two ways: By supply-side institutional changes or policies (to shift
the WS curve down or the PS curve up) By demand-management policies (to reduce
employment and output)Β© Gustavo Indart Slide 2
AN INFLATIONARY SHOCK WITHOUTGOVERNMENT INTERVENTION
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w
PSwe
WS
Ne NΟ
y
NH
2%
PC1
ye
2%4%
yH
A
B
PC2
6%
π π ππ = π π πππ¬π¬ + πΆπΆ ππππ β ππππA
Suppose that π π ππβππ = 2%, so π π πππ¬π¬ = πππ. Then at point A, π π ππ = 2%, and the corresponding Phillips curve is PC1.
π π πππ¬π¬ = π π ππβππB
Suppose N increases to NH (and y to yH) in period t and that in the next wage round wages increase by an additional 2% (i.e., by a total of 4%). Therefore, π π ππ = 4% (point B on the PC1 curve).
Since π π ππ = 4% in period t, the PC curve shifts up to PC2 in period t+1. This process is repeated period after period and an inflation spiral develops.
PC3
8%
What are the main costs of inflation? Who bears these costs? It erodes the value of money By creating greater uncertainty, it reduces investment
The costs of hyperinflation are undisputable For example, Germany (1920s), Hungary (1945),
Argentina (1980s), Zimbabwe (2008), Venezuela (2018)
Mainstream economists have exploited peopleβs fear of high inflation to push for excessive anti-inflationary policies Only zero inflation is both low and stable
IS INFLATION ALWAYS βBADβ?
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Orthodox economists believe that βinflation is always and everywhere a monetary phenomenonβ (Friedman) Too much money chasing too few goods Inflation is the result of excessive demand due to too
much money in the economy The solution then is to implement contractionary
monetary policy
Post-Keynesian economists believe that inflation is not demand-determined but rather the result of cost considerations Therefore, contractionary monetary policy will not have
the desired effects
WHAT ARE THE CAUSE OF INFLATION?
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MONEY SUPPLY AND INFLATION
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Inflation is a monetary phenomenon and thus curbing inflation requires tight monetary policy (to reduce πππ«π«)
The view that monetary policy should be used to curb inflation is based on three main hypotheses: Central banks control the money supply Money supply is an intermediate target Dichotomy between monetary and real analyses
The first hypothesis has more recently been replaced by a more realistic one: Central banks cannot control the money supply They control instead the short-term rate of interest
ORTHODOX VIEW OF INFLATION
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In the 1990s, the Bank of Canada officially adopted a policy of inflation targeting
This new measure is part of the New Consensus model, which consists of three main relationships: A negative relationship between interest rates and
investment (an IS curve) neutral rate of interest A positive relationship between the output gap and
inflation (a Philips curve) A Taylor rule where the central bank should change the
rate of interest whenever: Output (ππ) deviates from potential output (ππππ) Inflation (π π ) deviates from the chosen target (π π π»π»)
INFLATION TARGETING: THE NEWCONSENSUS MODEL
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Inflation targeting was adopted when inflation was already on the way down This period corresponds to a general decrease in real
wages
What explains that inflation decreased to very low levels in both developed countries and emerging markets?
The explanation is provided by the greater globalization of the economy: Globalization of the economy facilitates the location of
production in low wage countries Trade liberalization allows the imports of lower price
consumption and other goods
IS INFLATION TARGETING RESPONSIBLEFOR BRINGING DOWN INFLATION?
Β© Gustavo Indart Slide 9
CANADA: INFLATION AND DEFLATIONJANUARY 1962 TO NOVEMBER 2018
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Source: Trading Economics / Statistics Canada.
December 1992:Target 3%
December 1995:Target 2%
THE BANK OF CANADA
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The Bank of Canada was established in order to: regulate credit and currency; control and protect the external value of the currency; mitigate fluctuations in the general level of production,
trade, prices and employment; and generally promote the economic and financial welfare of Canada.
It is managed by a Board of Directors composed of a Governor, a Deputy Governor and twelve independentdirectors (plus the Deputy Minister of Finance)
The Minister of Finance and the Governor should βconsult regularly on monetary policyβ
The Bank of Canada is instructed by the government to conduct monetary policy Therefore, there is no absolute independence
The government states some specific macroeconomic objective such as inflation targeting, but the Bank of Canada decides how to achieve this objective Therefore, there is instrumental independence
The Bank of Canada can decide on its own when to change the rate of interest as a matter of monetary policy
HOW INDEPENDENT IS THE BANKOF CANADA?
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There is a lag as long as two years for the full impact of changes in monetary policy to take effect The central bank can look at the long run and not at
the next election
The central bank can make decision which would be politically unpopular Price stability as an at all times main objective could be
politically unpopular
It leads to greater public confidence in dealing with the financial market
This is a technical matter that must be entrusted to managers who can be held accountable
ARGUMENTS IN SUPPORT OFINDEPENDENT CENTRAL BANKS
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Aggregate demand determines the level of output and employment
Supply-side structural features determine equilibrium rate of unemployment at which inflation is constant
Three possible policy situations: If rate of unemployment is at equilibrium, inflation is
constant and central bank would do nothing If rate of unemployment is below equilibrium, inflation
is rising and central bank would increase interest rate If rate of unemployment is above equilibrium, inflation
is falling and central bank would decrease interest rate
ROLE OF THE CENTRAL BANK INSTABILIZATION
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The central bank has a double objective: to keep the economy at equilibrium output and inflation at its target
By increasing inflation above its target, an unforeseen boommay prevent the central bank from achieving its target
The central bank translates its objectives into monetary policy through the use of a monetary policy rule The MR curve relates the rate of interest to both
output and inflation
The MR curve illustrates the central bankβs best response to the shock
OBJECTIVE OF THE CENTRAL BANK
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Monetary policy affects output and employment in the short term
Monetary policy affects prices only in the medium term
Because of lags, policy has to be forward-looking
But future is uncertain, as is the impact of policy changes
Expectations matter, so giving people some idea of what you are trying to do, and acting consistently, is useful
Orthodox economists believe that itβs important to have an adequate degree of operational independence in the conduct of monetary policy
SUMMARY OF MODERN INFLATION-TARGETING CENTRAL BANK
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Now we are adding the policy maker to the model, so we will have three relationships or curves: The IS curve relating the rate of interest to output The PC curve relating output to inflation The MR curve relating the rate of interest to inflation
The MR curve (or monetary policy rule) determines the output gap the central bank should set in order to stabilize the economy after an economic shock
The MR curve shows the path along which the central bank seeks to guide the economy back to target inflation
THE NEW CONSENSUS MODEL (A.K.A THE3-EQUATION MODEL)
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First: We define central bank preferences in terms of a lossfunction capturing costs of being away from inflation target and equilibrium output It produces policy makerβs indifference curves
Second: We define the constraint faced by policy makers from the supply-side of the economy This is the Phillips curve
Third: We derive the (best response) monetary rule by minimizing the central bankβs loss function subject to the Phillips curve constraint This is the MR curve
HOW TO DERIVE A MONETARYPOLICY RULE
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Assumption: The central bank minimizes the deviations from the inflation target and equilibrium output This defines the central bankβs preferences
The central bank minimizes the following loss function:
π³π³ = (ππππ β ππππ)ππ + π·π·(π π ππ β π π π»π»)ππ
where π·π· reflects the central bankβs relative degree of inflation aversion
Therefore, the central bank is worse off the further away: Inflation (π π ππ) is from its target level (π π π»π») Output (ππππ) is from its equilibrium level (ππππ)
THE CENTRAL BANK PREFERENCES
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CENTRAL BANK LOSS FUNCTION
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b) Inflation averse: Ξ²>1a) Balanced: Ξ²=1 c) Unemployment averse: Ξ²<1
Ο Ο Ο
yyy
ΟT ΟT ΟT
yeyeye
Declining utility
Note: Loss is zero at the bliss point. Utility declines (i.e., loss increases) with distance from the bliss point.
π³π³ = (ππππ β ππππ)ππ + π·π·(π π ππ β π π π»π»)ππ
We are assuming that expectations are adaptive, that is, they are formed based on the past behaviour of the variable For instance, the expected rate of inflation could be equal
to the previous period rate of inflation:
π π πππ¬π¬ = π π ππβππ
In this case, the adaptive expectations Phillips curve is:
π π ππ = π π ππβππ + πΆπΆ ππππ β ππππ
The Phillips curve represents a constraint for the central bank It can only choose a point on the Phillips curve
THE PHILLIPS CURVE CONSTRAINT
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THE CENTRAL BANK LOSS MINIMIZATION
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Ο
y Given the new constraint, the central bank minimizes its loss at point D.
Suppose there is an inflationary shock and inflation rises to 4% and the PC curve shifts up.
A
PC(πππΈπΈ= 2%)
For simplicity, letβs assume πΆπΆ = ππ. Letβs also assume that initially inflation is 2% and the central bank chooses the bliss point A (its loss is zero).
ππππ = 2
yey1
PC(πππΈπΈ= 4%)
4
3
β’
B
C
D
Assuming π·π· = ππ, at point Bthe loss is equal to 4. And so is it at point C.
π³π³ = (ππππ β ππππ)ππ + π·π·(π π ππ β π π π»π»)πππ π ππ = π π ππβππ + πΆπΆ ππππ β ππππ
//
Assumptions: By choosing the rate of interest in period t, the central bank
affects output and thus also inflation in period t+1 At time t, the central bank is only concerned with what will
happen in period t+1
The central bank minimizes its loss function:
π³π³ = (ππππ β ππππ)ππ + π·π·(π π ππ β π π π»π»)ππ (1)
subject to (the Phillips curve constraint):
π π ππ = π π ππβππ + πΆπΆ ππππ β ππππ (2)
THE MATHEMATICAL DERIVATION OFTHE MR CURVE
Β© Gustavo Indart Slide 23
Substituting the equation for the Phillips curve (2) into the central bank loss function (1) we get:
π³π³ = (ππππ β ππππ)ππ + π·π·[π π ππβππ + πΆπΆ ππππ β ππππ β π π π»π»]ππ
And differentiating this loss function with respect to ππππ and making it equal to zero:
πππ³π³ππππππ
= ππππ β ππππ + πΆπΆπ·π· π π ππβππ + πΆπΆ ππππ β ππππ β π π π»π» = ππ
And from the Phillips curve we have that:
π π ππβππ = π π ππ β πΆπΆ ππππ β ππππ
THE MATHEMATICAL DERIVATION OF THEMR CURVE (CONTβD)
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ππππ β ππππ + πΆπΆπ·π· π π ππβππ + πΆπΆ ππππ β ππππ β π π π»π» = ππ (3)
π π ππβππ = π π ππ β πΆπΆ ππππ β ππππ (4)
And substituting equation (4) into equation (3) we get:
ππππ β ππππ + πΆπΆπ·π· π π ππ β πΆπΆ ππππ β ππππ + πΆπΆ ππππ β ππππ β π π π»π» = ππ
In this way we obtain the monetary rule, i.e., the equation for the MR curve:
ππππ β ππππ + πΆπΆπ·π· π π ππ β π π π»π» = ππ or π π ππ = π π π»π» β πππΆπΆπ·π·
ππππ β ππππ
THE MATHEMATICAL DERIVATION OFTHE MR CURVE (CONTβD)
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THE MR CURVE
The monetary rule shows the central bankβs best response to a shock
The monetary rule shows the inverse relationship between the inflation rate and output (or the output gap)
The central bank chooses the level of output directly (and the inflation rate indirectly) to maximize its utility (i.e., minimizeits loss)
The MR curve has a negative slope, which means that the central bank must keep aggregate demand (πππ«π«) and output (y) below ye so as to reduce Ο towards π π π»π»
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π π ππ = π π π»π» βπππΆπΆπ·π·
ππππ β ππππ
THE GRAPHICAL DERIVATION OFTHE MR CURVE
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Ο
y
Joining all these points of loss minimization, we graphically construct the central bankβs MR curve.
Given this constraint, the central bank minimizes its loss function.
A
PC(πππΈπΈ= 2%)
There is one PC curve corresponding to each rate of inflation. Each PC curve represents the constraint faced by the central bank.
ππππ = 2
ye
PC(πππΈπΈ= 4%)
4
3
PC(πππΈπΈ= 3%)
B
CD
5
PC(πππΈπΈ= 5%)
β’β’
MR
β’
Assumption:πΆπΆ = πππ·π· = ππ
π π ππ = π π π»π» βπππΆπΆπ·π·
ππππ β ππππ