Foreign Exchange Rates Nominal Exchange Rate Real Exchange Rate PPP.
Exchange Rate in Small Macro Models
Transcript of 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 ==
Building the model: IS curve
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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
Building the model: IS curve
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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 ==
Building the model: IS curve
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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,
Building the model: IS curve
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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
Building the model: IS curve
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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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Building the model: the Phillips Curve
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
Building the model: the Phillips Curve
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Building the model: the Phillips Curve
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