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Small Open Economy
Lawrence ChristianoMarch, 2014, Bank of Korea
Department of Economics, Northwestern University
Outline
Simple Closed Economy Model
Extend Model to Open EconomyI Equilibrium conditionsI Indicate complications to bring the model to the data.I Similar in spirit to Ramses I model
F Adolfson-Laséen-Lindé-Villan at Swedish Riksbank
Brief Discussion of Introducing Financial FrictionsI Christiano-Trabandt-Walentin (CTW) Model, Ramses II model.
F Based on Christiano-Motto-Rostagno (‘Risk Shocks’)
I Mihai Copaciu of Romanian Central Bank.
Application:I will US ‘lift o§’ act like a locomotive to rest of world economy, or willit be a problem (especially for EME’s)?
Simple Closed Economy Model
Results from closed economy modelI Household preferences:
E0•
Ât=0
bt{
u (Ct )− exp (tt )
N1+jt1+ j
!, u (Ct ) ≡ logCt
I Aggregate resources and household intertemporal optimization:
Yt = p∗t AtNt , uc ,t = bEtuc ,t+1Rt
pt+1
I Law of motion of price distortion:
p∗t =
0
@(1− q)
1− q (pt )
#−1
1− q
! ##−1
+qp#
tp∗t−1
1
A−1
(1)
Simple Closed Economy ModelEquilibrium conditions associated with price setting:
YtCt+ Etp#−1
t+1bqFt+1 = Ft (2)
Ft
'1− qp#−1
t
1− q
( 11−#
= Kt (3)
#
#− 1(1− n)
=WtPt
by household optimizationz }| {exp (tt )N
jt
uc ,t×1At
YtCt
+Etbqp#t+1Kt+1 = Kt (4)
note: in simple closed economy model, Yt = Ct , but this is not so inopen economy. For a derivation in the simple closed economy, see,e.g., http://faculty.wcas.northwestern.edu/~lchrist/d16/d1614/Labor_market_handout.pdf
Extensions to Small Open Economy
Outline:I the equilibrium conditions of the open economy modelI system jumps from 6 equations in basic model to 16 equations in 16variables!
Extensions to Small Open Economy: 16 variables
rate of depreciation, exports, real foreign assets, terms of trade, real exchange ratez }| {st , xt , aft , p
xt , qt
price of domestic consumption (now, c is a composite of domestically produced goods & imports)z}|{pct
price of importsz}|{pmt
consumption price inflationz}|{pct
reduced form object to (i) achieve technical objective, (ii) adjust UIP implicationz}|{Ft
closed economy variablesz }| {Rt ,pt ,Nt , ct ,Kt ,Ft , p∗t
Extensions to Small Open Economy- Outline
After describing 16 equilibrium conditions:I compute the steady stateI the ‘uncovered interest parity puzzle’, and the role of Ft in addressingthe puzzle.
I summary of the endogenous and exogenous variables of the model, aswell as the equations.
I several computational experiments to illustrate the properties of themodel.
Modifications to Simple Model to Create Open Economy
Unchanged:I household preferencesI production of (domestic) homogeneous good, Yt (= Atp∗t Nt )I three Calvo price friction equations
Changes:I household budget constraint includes opportunity to acquire foreignassets/liabilities.
I intertemporal Euler equation changed as a reduced formaccommodation of evidence on uncovered interest parity.
I Yt = Ct no longer true.I introduce exports, imports, balance of payments.I exchange rate,
St = domestic currency price of one unit of foreign currencySt =
domestic moneyforeign money
Monetary Policy: two approaches
Taylor rule
log-RtR
.= rR log
-Rt−1R
.+ (1− rR )Et [rp log
-pct+1pc
.(5)
+ry log-yt+1y
.] + #R ,t
where (could also add exchange rate, real exchange rate and otherthings):
pc ~target consumer price inflation
#R ,t ~iid, mean zero monetary policy shock
yt ~Yt/AtRt ~‘risk free’ nominal rate of interest
#R ,t ~mean zero monetary policy shock.
Monetary Policy: two approaches
Second approach (Norges Bank, Riksbank)I Solve a type of Ramsey problem in which preferences correspond topreferences of monetary policy committee:
Et•
Âj=0
bj{/100
hpct pct−1pct−2pct−3 − (p
c )4i22
+ ly
-100 log
-yty
..2
+lDR (400 [Rt − Rt−1 ])2 + ls (St − S)
2}
straightforward to implement in Dynare.
We will stress first approach.
Household Budget Constraint
‘Uses of funds less than or equal to sources of funds’
StAft+1 + PtCt + Bt+1
≤ BtRt−1 + SthFt−1Rft−1
iAft +WtNt + transfers and profitst
Domestic bonds
Bt ~beginning of period t stock of loans
Rt ~rate of return on bonds
Foreign assets
Aft ~beginning-of-period t net stock of foreign assets
(liabilities, if negative) held by domestic residents.
FtRft ~rate of return on Aft
Ft ~premium on foreign asset returns
Household Intertemporal First Order Conditions: ForeignAssets
Optimality of foreign asset choice (verify this by solving Lagrangianrepresentation of household problem)
utility cost of 1 unit of foreign currency=St units of domestic currency, St/Pct units of Ctz }| {uc ,tStPct
= bEt
conversion into utility unitsz }| {uc ,t+1
×
quantity of domestic cons. goods purchased from the payo§ of 1 unit of foreign currencyz }| {
St+1
foreign currency payo§ next period from one unit of foreign currency todayz }| {Rft Ft
Pct+1
Household Intertemporal First Order Conditions: ForeignAssets
First order condition:
StPct Ct
= bEtSt+1Rft Ft
Pct+1Ct+1
Scaling:
1ct= bEt
st+1Rft Ft
pct+1ct+1 exp (Dat+1), st ≡
StSt−1
, ct =CtAt. (6)
Technology:at ≡ log (At ) , Dat = at − at−1.
Household Intertemporal First Order Conditions: DomesticAssets
First order condition:
1Pct Ct
= bEtRt
Pct+1Ct+1
Scaling:1ct= bEt
Rtpct+1ct+1 exp (Dat+1)
. (7)
Final Domestic Consumption Goods
Produced by representative, competitive firm using:
Ct =
"
(1−wc )1
hc
/Cdt2 hc−1
hc +w1
hcc (Cmt )
hc−1hc
# hchc−1
where
Cdt ~ domestic homogeneous output good, price PtCmt ~ imported good, price Pmt
5≡ StPft
6
Ct ~ final consumption good, Pcthc ~ elasticity of substitution, domestic and foreign goods.
Final Domestic Consumption Goods
Profit maximization by representative firm:
maxPct Ct − Pmt C
mt − PtC
dt ,
subject to production function.
First order conditions associated with maximization:
Cmt : Pct
=/
wcCtCmt
2 1hc
z }| {dCtdCmt
= Pmt , Cdt : Pct
=
-(1−wc )
CtCdt
. 1hc
z}|{dCtdCdt
= Pt
so that the demand functions are:
Cmt = wc
-PctPmt
.hcCt , Cdt = (1−wc )
-PctPt
.hcCt .
Price Function
Substituting demand functions back into the production function:
Ct = [(1−wc )1
hc
-Ct
-PctPt
.hc(1−wc )
. hc−1hc
+w1
hcc
-wc
-PctPmt
.hcCt
. hc−1hc
]hc
hc−1 ,
or
pct =h(1−wc ) +wc (pmt )
1−hci 11−hc
,(8)
where
pct ≡PctPt, pmt ≡
PmtPt.
Real Exchange Rate and Consumption Price Inflation
Real Exchange Rate:
pmt =PctPct
PmtPt
= pct ×
≡ St Pft
Pct, real exchange ratez}|{qt (9)
Consumption good inflation and homogeneous good inflation:
pct ≡PctPct−1
=Ptpct
Pt−1pct−1= pt
"(1−wc ) +wc (pmt )
1−hc
(1−wc ) +wc5pmt−1
61−hc
# 11−hc
(10)
Exports
Foreign demand for domestic goods:
Xt =-PxtPft
.−hfY ft = (p
xt )−hf Y ft ,
terms of tradez}|{pxt =
PxtPft
Y ft ~ foreign outputPft ~ foreign currency price of foreign goodPxt ~ foreign currency price of export good
Scaling by Atxt = (pxt )
−hf y ft (11)
Rate of Depreciation, Inflation...
Competition: Price of export equals marginal cost:
StPxt = Pt .
Scaling:
1 =StPxtPt
=Pct StP
ft P
xt
PtPct Pft
= qtpxt pct (12)
Also,
qtqt−1
= stpftpct, st ≡
StSt−1
, pft ≡PftPft−1
(13)
Homogeneous Goods Market Clearing
Clearing in domestic homogeneous goods market:
output of domestic homogeneous good, Yt= uses of domestic homogeneous goods
=
goods used in production of final consumption, Ctz}|{Cdt +
exportsz}|{Xt +
governmentz}|{Gt
= (1−wc ) (pct )hc Ct + Xt + Gt .
Aggregate Employment and Uses of Homogeneous Goods
Substituting out in previous expression for Yt :
Atp∗t Nt = (1−wc ) (pct )hc Ct + Xt + Gt ,
or,p∗t Nt = (1−wc ) (pct )
hc ct + xt + gt , (14)
ct ≡CtAt, xt ≡
XtAt, gt ≡
GtAt.
Balance of Payments
equality of international flows relating to trade in goods and infinancial assets:
acquisition of new net foreign assets, in domestic currency unitsz }| {StAft+1
+ expenses on importst
= receipts from exportst +
receipts from existing stock of net foreign assetsz }| {StRft−1Ft−1Aft
Balance of Payments, the Pieces
Exports and imports:
expenses on importst = StPft wc
-pctpmt
.hc
Ct
receipts from exportst = StPxt Xt .
Balance of payments:
StAft+1 + StPft wc
-pctpmt
.hcCt
= StPxt Xt + StRft−1Ft−1Aft .
Balance of Payments, Scaling
Scaling by PtAt :
StAft+1PtAt
+StPftPt
wc
-pctpmt
.hcct
=StPxtPt
xt +StRft−1Ft−1Aft
PtAt,
or,
aft + pmt wc
-pctpmt
.hcct = pct qtp
xt xt +
stRft−1Ft−1aft−1pt exp (Dat )
, (15)
where aft is ‘scaled, homogeneous goods value of net foreign assets’:
aft =StAft+1PtAt
.
Risk Term
Ft = F/aft ,R
ft ,Rt , ft
2= (16)
exp/−fa
/aft − a
2+ fs
/Rt − Rft −
/R − Rf
22+ ft
2
fa > 0, small and not important for dynamics
fs > 0, important
ft ~mean zero, iid.
Discussion of fa.I fa > 0 implies (i) if a
ft > a, then return on foreign assets low and
aft #; (ii) if aft < a, then return on foreign assets high and aft "I implication: fa > 0 is a force that drives a
ft ! a in steady state,
independent of initial conditions.I logic is same as reason why steady state stock of capital in neoclassicalgrowth model is unique, independent of initial conditions.
I in practice, put in a tiny value of fa, so that its only e§ect is to pindown aft in steady state and it does not a§ect dynamics (seeSchmitt-Grohe and Uribe).
Risk Term
Discussion of ft :I Captures, informally, the possibility that there is a shock to therequired return on domestic assets.
F When ft > 0, ‘capital outflow shock’, people stop liking domesticassets
F When ft < 0, ‘safe haven shock’, people love domestic assets (e.g.,Swiss Franc in recent years).
Discussion of fs :I fs reduced form fix for the model.I With fs = 0, model implies Uncovered Interest Parity (UIP), whichdoes not hold in the data.
I to better explain this, it is convenient to first solve for the model’ssteady state.
Steady State
household intertemporal e¢ciency conditions:
1 = bsRf
pc exp (Da)(6)
1 = bR
pc exp (Da)(7)
assumption about foreign households:
pft ≡PftPft−1
(exogenous)
1 = bRf
pf exp (Da)
Steady State
Taylor rule implies: pc = pc , (5).
Additional steady state equations:
p ≡PtPt−1
= pc (inflation target) (10)
p∗ =1−qp#
1−q/1−q(p)#−1
1−q
2 ##−1, (no distortion if pc = 1) (1)
s =pc
pf, (13)
R =p exp (Da)
b(7)
Rf = R/s ((6),(7))
Steady State, Potentially Iterative Part
Rest of the algorithm solves a single non-linear equation in a singleunknown, j.
Set j = pcq
pm = j (9) and px =1j(12)
pc =h(1−wc ) +wc (pm)
1−hci 11−hc (8)
q =j
pc
Steady State, Potentially Iterative Part...Let
g = hg y , a = hay .
Then,
0 = pmwc
-pc
pm
.hcc − pcqpx x −
-sRf
p exp (Da)− 1.
hap∗N (15)
0 = (1−wc ) (pc )hc c + x −
/1− hg
2Np∗ (14)
F =p∗N
c (1− p#−1bq)(2)
K = F'1− qp#−1
1− q
( 11−#
(3)
0 =#
#− 1(1− n)N1+jp∗ + (bqp# − 1)K (4),
These five equations involve the five unknowns: c ,N,F ,K , x . Solvethese. Adjust j until (11) is satisfied. In practice, we simply setj = 1 and used (11) to solve for y f .
Uncovered Interest Parity Algebrasubtract equations (6) and (7):
Et
'Rt − st+1Rft Ft
ct+1pct+1 exp (Dat+1)
(= 0.
I totally di§erent object in square brackets and evaluate in steady state:
dRt − st+1Rft Ft
ct+1pct+1 exp (Dat+1)
=dRt
cpc exp (Da)
−1
cpc exp (Da)
hsRf dFt + sdRft + R
f dst+1i
−R − sRf
[cpc exp (Da)]2d7ct+1pct+1 exp (Dat+1)
8
=1
bc
nRt −
hFt + Rft + st+1
io
wherext ≡ (xt − x) /x = dxt/x .
Uncovered Interest Parity, Linearized RepresentationThen,
Et
'Rt − st+1Rft Ft
ct+1pct+1 exp (Dat+1)
(= 0,
is, to a first approximation,
Et
'1
bc
nRt −
hFt + R ft + st+1
io(= 0
or,Rt = Et st+1 + R ft + Ft .
Conclude, using dxtx ' log (xt/x) , logF = 0 :
logRt − logR = Et [log st+1 − log (s)] + logRft − logRf + logFt
or, using logRf = logR − log s, definition of st+1, rt ≡ logRt ,r ft ≡ logRft
Et log St+1 − log St = rt − r ft + logFt
Uncovered Interest Parity
Under UIP, Ft = 0 :I rt > r ft ! must be an anticipated depreciation (instantaneousappreciation) of the currency for people to be happy holding theexisting stock of net foreign assets
Consider regression relation:
log St+1 − log St = b0 + b1
/rt − r ft
2+ ut .
I Under UIP (and, rational expectations), b0 = 0, b1 = 1.
When Ft 6= 0:
b1 =cov
5log St+1 − log St , rt − r ft
6
var5rt − r ft
6 = 1− fs ,
UIP Puzzle
In data,
b1 ' −.75, so UIP rejected (that’s the UIP puzzle)
Note:fs = 1.75! b1 = −0.75.
because
b1 =cov
5log St+1 − log St , rt − r ft
6
var5rt − r ft
6 = 1− fs ,
Another way to see UIP puzzle is from VAR impulse responses byEichenbaum and Evans (QJE, 1992)
I Data: rt " after monetary policy shock ! log St+j falls slowly forj = 1, 2, 3, ... .
I UIP theory: rt " after monetary policy shock ! log St+1 − log St ".
Intuition Behind UIP Puzzle
UIP puzzle: rt " and expected appreciation of the currency represents adouble-boost to the return on domestic assets. On the face of it, itappears that there is an irresistible profit opportunity. Why doesn’t thedouble-boost to domestic returns launch an avalanche of pressure to buythe domestic currency? In standard models, this pressure produces agreater instantaneous appreciation in the exchange rate, until the familiarUIP overshooting result emerges - the pressure to buy the currency leadsto such a large appreciation, that expectations of depreciation emerge. Inthis way, UIP leads to the counterfactual prediction that a higher rt will befollowed (after an instantaneous appreciation) by a period of time duringwhich the currency depreciates.
Intuition Behind ‘Resolution’ of Puzzle
Model’s resolution of the UIP puzzle: when rt " the return required forpeople to hold domestic bonds rises. This is why the double-boost todomestic returns does not create an appetite to buy large amounts ofdomestic assets. Possibly this is a reduced form way to capture the notionthat increases in rt make the domestic economy more risky. (However, theprecise mechanism by which the domestic required return rises - earningson foreign assets go up - may be di¢cult to interpret. An alternativespecification was explored, with risk-premia a§ecting domestic bonds, butthis resulted in indeterminacy problems.)
Dynamics
16 equations: price setting, (1),(2),(3),(4); monetary policy rule, (5);household intertemporal Euler equations (6),(7); relative priceequations (8),(9),(10),(12),(13); aggregate resource condition, (14);balance of payments, (15); risk term, (16); demand for exports (11).
16 endogenous variables: pct , pmt , qt ,Rt ,pt ,p
ct , p
xt ,Nt , p
∗t , a
ft ,Ft ,
st , xt , ct ,Kt ,Ft .
exogenous variables: Rft , yft , ft , gt , #R ,t , Dat , tt , pft .
I for the purpose of numerical calculations, these were modeled asindependent scalar AR(1) processes.
Extensions to Small Open Economy...
the model was solved in the manner described above:- compute the steady state using the formulas described above- log-linearize the 16 equations about steady state- solve the log-linearized system- these calculations were made easy by implementing them in Dynare.
Parameter Values
Numerical examples: Parameter values:
pf = pc = 1.005 fa = 0.03 b = 1.03−1/4
q = 3/4 j = 1 # = 61− n = #−1
# hc = 5 wc = 0.4hg = 0.3 ha = 0 hf = 1.5rR = 0.9 rp = 1.5 ry = 0.15
Modifying UIP
iid shock, 0.01, to #R ,t .
I fs = 0! after instantaneous appreciation, positive #R ,t shockfollowed by depreciation.
I for higher fs , shock followed by appreciation.I long run appreciation is increasing function of persistence of rR .
Impact of Modifications to UIP
We now consider a monetary policy shock, #R ,t = 0.01. According to (5), impliesa four percentage point (at an annual rate) policy-induced jump in Rt .The dynamic e§ects are displayed in the following figure, for fs = 0, fs = 1.75
Note: (i) appreciation smaller, though more drawn out, when fs is big; (ii) smaller appreciation results in smaller drop in net
exports, so less of a drop in demand, so less fall in output and inflation; (iii) smaller drop in net exports results in smaller drop in
real foreign assets.
Capital Outflow Shock
Consider now a domestic economy risk premium shock, a jump in theinnovation to ft equal to 0.01.
With the reduced interest in domestic assets, (i) the currency depreciates,(ii) net exports rise, (iii) hours and output rise, (iv) the upward pressure oncosts associated with higher output leads to a rise in prices.
Question Confronting Many Emerging Market Economies..
At some point, the Fed will implement its ‘exit strategy’ and raise USinterest rates (300-350 basis points?).
In the past, when Fed raised rates sharply (e.g., 1982 Volckerdisinflation, 1994 run-up in interest rates), hit the rest of world like abrick:
I Chilean crisis of 1982, Mexican default of August 1982. Mexican crisisof 1994.
Will the US ‘exit strategy’ inflict financial crises around the world,especially in emerging market economies?
I Summer 2013 ‘taper episode’ makes people worry about this possibility.
I’ll call the above possibility the BIS scenario.
BIS Scenario
Low US interest rates since 2008 have encouraged‘excessive’accumulation of debt in the world.
This has particularly a§ected emerging market economies in AsiaandLatin America.
Currency Mismatch Problem May Be Understated..
(Hyun Shin, ‘The Second Phase of Global Liquidity. . . ’, November, 2013)
Many emerging market borrowers issue dollar-denominated debtthrough foreign subsidiaries (say in the UK).
I By the usual definition (based on the residence of the issuer), thebonds are a liability of the UK entity.
But, it’s the consolidated balance sheet that matters to the emergingmarket firm.
I So, the debt issued via a foreign subsidiary could make the emergingmarket firm vulnerable to currency mismatch problems.
Hyun Shin argues:• Amount of dollar denominated debt from emerging market firms may begreatly understated.
• This is suggested by evidence that foreign currency debt by nationalitycan be much larger than foreign debt by the usual residency definition.
Shin conjectures that distinction between external debt according tonationality and residence helps to resolve the ‘taper’ puzzle:
I convulsions in emerging markets during taper episode in summer 2013seem inconsistent with apparently small net external debt position(measured in residence terms) of firms in emerging markets.
Less surprising if external debt position is in fact much bigger.
BIS Scenario
US raises interest rates.
Emerging market exchange rates depreciate.
Financial health of emerging market firms compromised.
They cut back on investment activity. . . .recessions start.
Runs on emerging market banks known to be have made loans tonow-questionable emerging market non-financial firms.
And so on. . .
Locomotive Scenario
Previous episodes of US interest rate hikes may be playing too big arole in the pessimistic outlook.
The circumstances in which the US raises interest rates may make adi§erence.
I In present circumstances, Fed has (credibly, I think) committed to onlyraise rates until well after the US economy has returned to health.
I Under these circumstances, interest rate hikes occur when the US isfirmly in the position of a locomotive, pulling the rest of the worldeconomy forward in its wake.
Which Will it Be: BIS or Locomotive Scenario?
Need a model to think about this question.
Build in the BIS-type factors that raise concerns about the worldeconomy.
Accurately capture the degree of foreign currency indebtedness offinancial and nonfinancial firms (i.e., avoid the biases that Hyun Shinis concerned about).
I Build in the nature of the constraints that cause firms to pull backwhen their net worth contracts with exchange rate depreciation.
I Build in the ‘locomotive’ scenario:
F Carefully model ‘forward guidance’ — Fed commitment to keep interestrates low even after the US economy has begun to strengthen.
A Model
Mihai Copaciu (Romanian Central Bank)I Constructs small open economy models in which investment issustained by purchases of entrepreneurs, who earn their revenues indomestic currency units.
I Entrepreneurs need financing, and the amount of financing they canget is partially a function of their accumulated net worth.
I Some of the financing is obtained from abroad.I When the currency depreciates, entrepreneurs that borrowed abroadmake capital losses and their net worth su§ers.
I They are forced to cut back on expenditures, so that investmentcrashes, bringing down the economy.
I Same model also contains the usual features that imply an expansion inthe US acts as a locomotive on the rest of the world.
DSGE Models Can Play a Useful Role in Discussions aboutFed ‘Exit Strategy’
New Keynesian Open Economy Models can Capture Two CompetingViews.
Potential for US take-o§ to:I be a locomotive.I cause a loss of net worth by foreign firms/financial institutions andforce a cut-back in foreign investment (‘BIS scenario’).
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