exchange rate in small macro models

8/7/2019 Exchange Rate in Small Macro Models

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DOFIN Finan e Interna ionale

Exchange Rate in Small Macro

Models


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Outline Recall different transmission mechanisms

A basic (open-economy) model Examine transmission mechanism in such model

Think about different transmission mechanisms=> Consider extensions to the model that maybe relevant

for your anal ysis

Data and estimation problems and other difficulties


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The transmission mechanismA definition:

How changes in the policy variable affectinflation and output

We are interested in: The channels (economic relationships) of themonetary transmission mechanism

How quickly they work How large are the effects


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Caveats i) The relative importance of the differentchannels is not constant: either across countries,across time or in response to different circumstances ;

hence variable lags .ii) Changes in policy can change the transmission

mechanism itself : the Luca s critique .


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Sticky prices

An important issue is the speed with whichnominal variables readjust in response to

changes in fundamentalsi.e. how sticky are prices

The stickier the prices the more monetarypolicy acts through the real economy in theshort run

In low inflation countries price-setters mayhave less incentive to change prices.

Therefore prices may be stickier


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Flexible-price world

If prices immediately adjusted fully monetary

policy would be relatively simple:by controlling the money supply we could control

the price level and thus inflationthe classical dichotomy would hold: nominal

variables would not affect real variables

But we dont live in a flexible-price world


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Common types of transmissionmechanism

Interest rate channel Exchange rate channel

Other asset effect channel (monetarist view) Credit channel

Expectations

Throughout assume prices are sticky


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Interest rate channel/Intertemporalsubstitution

The basic Keynesian channel

M i I (C ) Y

Expand money, reducing rates, lowering cost of

borrowing for firms (and consumers) leading to anincrease in investment (and consumption) andtherefore output


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Exchange rate channel - NetExports channel

Takes the following form

M i E NX Y

Expand money supply, the interest rate decreases,

domestic deposits (strength depends on the risk premia) become less desirable, exchange ratedepreciat es, leading to an increase in the current

account and thus to output


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Monetarist/Other Asset Pricechannel

Changes to money lead to interest rate changes

affecting asset prices other than the exchange rateTrue monetarist view considers any asset pricechangeThese affect investment and consumption


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Monetarist - Investment channelInvestment channel (Tobins q)

M Pe q I Y

Money increases, agents hold too much and use someto purchase other assets and their price rise. Thisraises the value of firms and increases q therebyincreasing investment. Higher investment leads tohigher output


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Monetarist - Consumption andstock market

Channel works through wealth effects

M Pe wealth C Y

An increase in money implies that consumers holdtoo much and purchase assets. Wealth increases andso does consumption. The increase in consumptionleads to an increase in outputRecent research suggests wealth effect might be low!


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Monetarist - Consumption,Housing channel

Channel works through wealth effects

M i Hd Hp wealth C Y

An increase in money leads to lower interest rates.Housing demand increases and house pricesincrease. Wealth increases and so does consumption.

The increase in consumption leads to an increase inoutput


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Credit ChannelTwo types: bank lending and balance-sheet

Bank lending important for small firms andconsumers who cannot raise their own funds

Balance-sheet channel based on the principle thathealthier balance-sheets lead to more generous

borrowing conditions; emphasis on informationalasymmetries


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Credit channel - Balance sheetThere are many ways in which this channel can work

M Pe Adverse Selection Moral hazard lending I (C ) Y

Firms: Money increases, asset prices increase, firmsnet worth and balance sheet increase, less risk tolend to firm and therefore lending increases leadingto increase in output


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Credit Channel - Balance sheet

Consumers: Money increases, asset prices increase,wealth increases (both through stock market or housing) thus improving the consumers balance

sheet leading to a reduction in adverse selection andmoral hazard and banks willing to lend more leadingto an increase in consumption and therefore output.


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Credit Channel

Another reason the credit channel is important is thatincreases in interest rates may increase firms and

consumers financial distress. This is an importantpoint in terms of financial stability. With firms andconsumers not able to repay debt, banks position

worsens


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ExpectationsExpectations about the future stance of policyimportantAll variables that have intertemporal implicationsaffected by agents beliefs and how the CB will reactto themImpacts expectations on markets as well as on

investment and consumption decisions


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What to look out in your country?

Openness to international trade and capital(exchange rate channel)Financial developments (interest, monetary,expectational and credit channels)

Financial situation of firms and households (creditchannels)Other economic developments (choosing to joinEMU, adoption of inflation targeting, structuralreforms)


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Size and openness of economy

Determines the size of the exchange rate channel and

how the authorities are able to affect interest ratesExchange rate pass-through important


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Structure of financial systemIs it based primarily on banks or does it comprise anumber of institutions?

Are the banks public or private?Monetary policy is able to affect interest rates morequickly and transparently if the market is diversifiedConsumption and investment will respond more torates if market liberalised and agents can borrow(credit channel)Exchange rate channel not important if notliberalised - role of capital controls


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The transmission mechanism asequations...

UIP UIPpolicy rule policy rulePrice equationWage equation Phillips curvelabour supply

Domestic demandexports, imports IS curve

GDP identity


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IS Curve: Closed Economy Basic Equation obtained from the solution to the

consumers problem plus some assumptions Standard IS curve (based on log-linear Euler

equation) is:

yt =a*E t yt+1 - c*E t (i t - t+1 ) a, c>0

y is output gap, i is the nominal interest rate, isCPI inflation

Note forward-looking behaviour and expectations


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IS Curve - Extensions

Open-economy:yt =a*E t yt+1 - c*E t (it - t+1 )+ d*e t d>0

e is the real exchange rate. Definitional issuesexamined later

Habits/Adjustment costs/Sticky Information :yt =a*E t yt+1 +b* y t-1 - c*E t (it - t+1 )+d*e t

(+u* E t yt+2 +v* y t-2 +)ie lags and leads of the gap


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IS curve - extensions Money:

yt =a*E t yt+1 +b* y t-1 -c*E t (i t - t+1 )+d*e t +f*M t

Motivation: Money in utility function, proxies for errors in output gap, some kind of balance sheet effectproxy, monetarist view of the transmission mechanism


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IS Curve - Extensions Financial liberalisation:

yt =a*E t yt+1 +b* y t-1 - c*E t (i t - t+1 )+d*e t (+f*M t )+z*E t [(ilending t - t+1 )-(i t - t+1 )]

Balance Sheet effect:yt =a*E t yt+1 +b* y t-1 - c*E t (ilending t - t+1 )+d*e t

(+f*M t )E t (ilending t - t+1 ) = + E t (i t - t+1 ) - *NFW t - * NFW t


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IS Curve - Extensions Other variables include:

EA GDP terms of trade, share prices in the domestic economy, Industrial production in other countries (say

OECD)

Price of oil (if oil producing economy) Governments fiscal position


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Phillips CurveEquation obtained from the solution to a companyspricing problem plus some assumptions

Inflation definition: t = w*td+(1- w) tf Standard Philips curve is:

t =+g *

E t t+1 + j* y t or

t = + g*E

t

t+1+ j* mc

t ie we can use the output gap or the marginal cost(mc) of firms


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Phillips Curve - Extensions

Open Economy:

t = + g*E t t+1 + j* y t + k* e t Sticky Information:

t = + g*E t t+1 + h* t-1 + j* y t + * y t-1 + k* e t Note we can use the marginal cost version in both

equations Also note possible coefficient restrictions why?


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Phillips Curve - ExtensionsError correction terms:

t = + g*E t t+1 + j* y t + k* e t - (p t-1- pm t-1- ulc t-1)We could consider other error correction terms. Herewe have import prices and unit labour costs

Other terms:Import prices (dynamics)

Oil pricesExpectational terms for disinflation paths


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Exchange rate

Definition of exchange rate normally used:

imported goods prices relative to the aggregateCPI

UIP (Normally used):E t et+1 =R t - R t * + risk premium t

UIP with lags:E t et+1 = * et + R t - Rt * + risk premium t


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Exchange rate

The risk premium can be proxied through spreads

of external treasuries to domestic bonds Other variables in the exchange rate equation

include terms of trade, Net foreign assets, currentaccount balance


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Curs nominal (EUR), index 2005=100

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CZK HUF PLN RON

Curs nominal bilateral (fa de EUR) indice cu baza anul 2005


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Curs real bilateral (fa de EUR) indice cu baza anul 2005, calculatutiliznd HICP

Curs real (EUR), HICP, index 2005=100

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CZK HUF PLN RON


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Curs real EURRON indice cu baza anul 2005, calculat utilizndHICP, IPP, deflatorul PIB i deflatorul exporturilor

Curs real EURRON, index 2005=100

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Defl exp Defl PIB PPI HICP


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Curs real EURCZK, index 2005=100

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Defl exp Defl PIB PPI HICP

Curs real EURCZK indice cu baza anul 2005, calculat utilizndHICP, IPP, deflatorul PIB i deflatorul exporturilor


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Interest Rate RulesDerived from the policy makers optimisationproblem (minimise a loss function comprisingdeviations of inflation from target, the output gap,

the interest rate and the exchange rate):it =l* y t +n* t +o* i t-1+u*e t

It is possible to add lags of these variablesOther variables could be ECM terms, moneyvariables, switching regimes


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Other issues of importance?

Euroization

economy Declining (trending) inflation rate Changing policy reaction functions (changing

policy regimes) Measurement of the output gap

Econometric issues


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Euroisation economy Most assets and liabilities are denominated in euro

(normally liabilities)

If the economy has a fixed exchange rate thecentral banks policy function will be a function of the exchange rate

If the economy has a floating exchange rate wemay have to introduce balance sheet and wealtheffects, model the banking systems, introduce EU variables (if the conomy is euroised )

We may need to think about bubbles

T di i fl i


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Trending inflation

We can introduce a time trend We can investigate the role of using different

inflation targets to achieve a lower inflation rate

Ch i li i


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Changing policy regime

May need to consider switching type models: it

will necessitate to change most of the equations inthe model

Could use dummy variables instead of switchingmodel


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Output gap measurements Linear trends (with breaks) often used HP filters Could try Beveridge-Nelson decompositions The Kalman filter to obtain potential output Other types of filters


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Summary

We have considered a number of transmissionmechanisms These will lead to different models We wish to consider small models comprising an

IS curve, a Phillips Curve, an exchange rate

equation and a policy rule Other issues may be important (econometrics,

measurement of variables)


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Appendix: Derivation of some

of the equations of interest


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Building the model: IS curve


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Building the model: IS curve Consumption comprises domestic and foreign goods:

(2)

is the elasticity of substitution between domestic and foreigngoods, is the share of domestic consumption allocated to importedgoods. Disaggregating further:

(3)

is the price elasticity of demand faced by eachmonopolist. Goods with (j)s, are quantities of domestic and

foreign goods purchased by individuals

( ) ( )( ) ( )( )[ ]( ) /1/1/1/1/11 += f t ht t C C C

( ) ( ) f hidjjC C it it ,,)(

1/1

0

/1 ==



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Building the model: IS curve The budget constraint faced by individuals is given

(4)

where

(5)

denotes total consumption expenditure, P are prices, F is thestochastic discount factor, B are bonds, TR are transfers and is thetax rate

[ ]( ) t t t ht ht

t t t t t t

TRBjM jY jP

BF E jM jS

+++++

++

)()()(1

)()(

1

11,

[ ] +=1

0

)()()()()( djjC jP jC jP jS f t f

t ht

ht t



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Building the model: IS curveThe consumer faces two problems: an intertemporal problemdeciding how much to consume today vs tomorrow, howmuch of the individual goods to consume each period

Demand for domestic and foreign goods is given by

(6)

where

(7)

f hiC P

jP jC it it

i

t it ,,)()( ==

( )

( )

f hidjjP P it it ,,)(

1/11

0

1 ==



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Building the model: IS curve Using the definition of consumption (2), (6) can be

written as(8)

where(9)

The budget constraint is now

(10)

( )( ) ( )[ ]

+=1

1

11

1 f t ht t P P P

( ) f hiC P P C t t

i

t it ,,1 ==

[ ]( ) t t t ht

ht

t t t t t t t

TRBjM jY jP

BF E jM C P

+++++

++

)()()(1

)(

1

11,



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Building the model: IS curve The inter-temporal decision is given by

(11)

And the decision to hold money balances is givenby

(12)

[ ]( )( )= +

++

1

11,

t

t

t c

t ct t t t P

P C u

C uE F E

( )

( )+

=

++ 11

1

t

t

t ct

t t

t

mt c

P

P C uE

P P

M

hC u



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Building the model: IS curve Let total output produced in the economy be the

sum of goods sold in the domestic and foreign

markets

(13) Foreigners will also have an Euler type equation

for domestic goods(14)

( ) *1 ht ht t C C Y +=

[ ] ( )( )

=++

++

11

11, *

**

*

t

t

t

t

t c

t ct t t t S

S P P

C uC u

E F E


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Building the model: the Phillips Curve


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In equilibrium, each consumer-producer that choosesa new price in period t will choose the same new price

and the same level of output. The aggregate price of domestic goods obeys

Using this expression plus the results from the

optimisation problem and log-linearising around thesteady-state yields

( ) ( )( )[ ]

+= 1

1

)(11 jP pp ht ht ht



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The Phillips Curve

t qt xht t

ht qxE ++= +1

Building the model: UIP


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Building the model: UIP

UIP is imposed

[ ] t t t t t ssE ii += +1*

Building the model: Policy function


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Building the model: Policy function

The policy rule is the result of loss functionminimisation problem for the monetary authorities

( ){ }+=

=0

22

**min

t T t t t xbaE L

exchange rate in small macro models

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