gla 1001 macroeconomics m , i g - university of toronto 04...1. 𝒕𝒕 𝑬𝑬 b...

GLA 1001MACROECONOMICS:

MARKETS, INSTITUTIONS AND GROWTH

LECTURE 4:MACROECONOMIC POLICY –THE DERIVATION OF THE MR CURVE

© 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)© Gustavo Indart Slide 2

AN INFLATIONARY SHOCK WITHOUTGOVERNMENT INTERVENTION


w

PSwe

WS

Ne Nπ

y

NH

2%

PC1

ye

2%4%

yH

A

B

PC2

6%

𝝅𝝅𝒕𝒕 = 𝝅𝝅𝒕𝒕𝑬𝑬 + 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆A

Suppose that 𝝅𝝅𝒕𝒕−𝟏𝟏 = 2%, so 𝝅𝝅𝒕𝒕𝑬𝑬 = 𝟐𝟐𝟐. Then at point A, 𝝅𝝅𝒕𝒕 = 2%, and the corresponding Phillips curve is PC1.

𝝅𝝅𝒕𝒕𝑬𝑬 = 𝝅𝝅𝒕𝒕−𝟏𝟏B

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, 𝝅𝝅𝒕𝒕 = 4% (point B on the PC1 curve).

Since 𝝅𝝅𝒕𝒕 = 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 people’s fear of high inflation to push for excessive anti-inflationary policies Only zero inflation is both low and stable

IS INFLATION ALWAYS “BAD”?


Orthodox economists believe that “inflation is always and everywhere a monetary phenomenon” (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?


MONEY SUPPLY AND INFLATION


Inflation is a monetary phenomenon and thus curbing inflation requires tight monetary policy (to reduce 𝒚𝒚𝑫𝑫)

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


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 (𝒚𝒚) deviates from potential output (𝒚𝒚𝒆𝒆) Inflation (𝝅𝝅) deviates from the chosen target (𝝅𝝅𝑻𝑻)

INFLATION TARGETING: THE NEWCONSENSUS MODEL


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?


CANADA: INFLATION AND DEFLATIONJANUARY 1962 TO NOVEMBER 2018


Source: Trading Economics / Statistics Canada.

December 1992:Target 3%

December 1995:Target 2%

THE BANK OF CANADA


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 “consult regularly on monetary policy”

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?


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


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


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 bank’s best response to the shock

OBJECTIVE OF THE CENTRAL BANK


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 it’s important to have an adequate degree of operational independence in the conduct of monetary policy

SUMMARY OF MODERN INFLATION-TARGETING CENTRAL BANK


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)


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 maker’s 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 bank’s loss function subject to the Phillips curve constraint This is the MR curve

HOW TO DERIVE A MONETARYPOLICY RULE


Assumption: The central bank minimizes the deviations from the inflation target and equilibrium output This defines the central bank’s preferences

The central bank minimizes the following loss function:

𝑳𝑳 = (𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆)𝟐𝟐 + 𝜷𝜷(𝝅𝝅𝒕𝒕 − 𝝅𝝅𝑻𝑻)𝟐𝟐

where 𝜷𝜷 reflects the central bank’s relative degree of inflation aversion

Therefore, the central bank is worse off the further away: Inflation (𝝅𝝅𝒕𝒕) is from its target level (𝝅𝝅𝑻𝑻) Output (𝒚𝒚𝒕𝒕) is from its equilibrium level (𝒚𝒚𝒆𝒆)

THE CENTRAL BANK PREFERENCES


CENTRAL BANK LOSS FUNCTION


b) Inflation averse: β>1a) Balanced: β=1 c) Unemployment averse: β<1

π π π

yyy

πT πT πT

yeyeye

Declining utility

Note: Loss is zero at the bliss point. Utility declines (i.e., loss increases) with distance from the bliss point.

𝑳𝑳 = (𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆)𝟐𝟐 + 𝜷𝜷(𝝅𝝅𝒕𝒕 − 𝝅𝝅𝑻𝑻)𝟐𝟐

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:

𝝅𝝅𝒕𝒕𝑬𝑬 = 𝝅𝝅𝒕𝒕−𝟏𝟏

In this case, the adaptive expectations Phillips curve is:

𝝅𝝅𝒕𝒕 = 𝝅𝝅𝒕𝒕−𝟏𝟏 + 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆

The Phillips curve represents a constraint for the central bank It can only choose a point on the Phillips curve

THE PHILLIPS CURVE CONSTRAINT


THE CENTRAL BANK LOSS MINIMIZATION


π

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(𝜋𝜋𝐸𝐸= 2%)

For simplicity, let’s assume 𝜶𝜶 = 𝟏𝟏. Let’s also assume that initially inflation is 2% and the central bank chooses the bliss point A (its loss is zero).

𝜋𝜋𝑇𝑇 = 2

yey1


4

3

•

B

C

D

Assuming 𝜷𝜷 = 𝟏𝟏, at point Bthe loss is equal to 4. And so is it at point C.

𝑳𝑳 = (𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆)𝟐𝟐 + 𝜷𝜷(𝝅𝝅𝒕𝒕 − 𝝅𝝅𝑻𝑻)𝟐𝟐𝝅𝝅𝒕𝒕 = 𝝅𝝅𝒕𝒕−𝟏𝟏 + 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆

//

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:

𝑳𝑳 = (𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆)𝟐𝟐 + 𝜷𝜷(𝝅𝝅𝒕𝒕 − 𝝅𝝅𝑻𝑻)𝟐𝟐 (1)

subject to (the Phillips curve constraint):

𝝅𝝅𝒕𝒕 = 𝝅𝝅𝒕𝒕−𝟏𝟏 + 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 (2)

THE MATHEMATICAL DERIVATION OFTHE MR CURVE


Substituting the equation for the Phillips curve (2) into the central bank loss function (1) we get:

𝑳𝑳 = (𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆)𝟐𝟐 + 𝜷𝜷[𝝅𝝅𝒕𝒕−𝟏𝟏 + 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 − 𝝅𝝅𝑻𝑻]𝟐𝟐

And differentiating this loss function with respect to 𝒚𝒚𝒕𝒕 and making it equal to zero:

𝝏𝝏𝑳𝑳𝝏𝝏𝒚𝒚𝒕𝒕

= 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 + 𝜶𝜶𝜷𝜷 𝝅𝝅𝒕𝒕−𝟏𝟏 + 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 − 𝝅𝝅𝑻𝑻 = 𝟎𝟎

And from the Phillips curve we have that:

𝝅𝝅𝒕𝒕−𝟏𝟏 = 𝝅𝝅𝒕𝒕 − 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆

THE MATHEMATICAL DERIVATION OF THEMR CURVE (CONT’D)


𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 + 𝜶𝜶𝜷𝜷 𝝅𝝅𝒕𝒕−𝟏𝟏 + 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 − 𝝅𝝅𝑻𝑻 = 𝟎𝟎 (3)

𝝅𝝅𝒕𝒕−𝟏𝟏 = 𝝅𝝅𝒕𝒕 − 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 (4)

And substituting equation (4) into equation (3) we get:

𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 + 𝜶𝜶𝜷𝜷 𝝅𝝅𝒕𝒕 − 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 + 𝜶𝜶 𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 − 𝝅𝝅𝑻𝑻 = 𝟎𝟎

In this way we obtain the monetary rule, i.e., the equation for the MR curve:

𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆 + 𝜶𝜶𝜷𝜷 𝝅𝝅𝒕𝒕 − 𝝅𝝅𝑻𝑻 = 𝟎𝟎 or 𝝅𝝅𝒕𝒕 = 𝝅𝝅𝑻𝑻 − 𝟏𝟏𝜶𝜶𝜷𝜷

𝒚𝒚𝒕𝒕 − 𝒚𝒚𝒆𝒆

THE MATHEMATICAL DERIVATION OFTHE MR CURVE (CONT’D)


THE MR CURVE

The monetary rule shows the central bank’s 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 (𝒚𝒚𝑫𝑫) and output (y) below ye so as to reduce π towards 𝝅𝝅𝑻𝑻


𝝅𝝅𝒕𝒕 = 𝝅𝝅𝑻𝑻 −𝟏𝟏𝜶𝜶𝜷𝜷


THE GRAPHICAL DERIVATION OFTHE MR CURVE


π

y

Joining all these points of loss minimization, we graphically construct the central bank’s MR curve.

Given this constraint, the central bank minimizes its loss function.

A


There is one PC curve corresponding to each rate of inflation. Each PC curve represents the constraint faced by the central bank.

𝜋𝜋𝑇𝑇 = 2

ye


4

3


B

CD

5


••

MR

•

Assumption:𝜶𝜶 = 𝟏𝟏𝜷𝜷 = 𝟏𝟏

𝝅𝝅𝒕𝒕 = 𝝅𝝅𝑻𝑻 −𝟏𝟏𝜶𝜶𝜷𝜷


gla 1001 macroeconomics m , i g - university of toronto 04...1. 𝒕𝒕 𝑬𝑬 b...

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