Download This PDF is a selection from a published volume from... Economic Research Volume Title: NBER International Seminar on Macroeconomics 2007

This PDF is a selection from a published volume from the National Bureau of
Economic Research
Volume Title: NBER International Seminar on Macroeconomics 2007
Volume Author/Editor: Richard Clarida and Francesco Giavazzi, organizers
Volume Publisher: University of Chicago Press
ISSN: 1932-8796
Volume URL: http://www.nber.org/books/clar07-1
Conference Date: June 15-16, 2007
Publication Date: January 2009
Chapter Title: Capital Flows and Asset Prices
Chapter Author: Kosuke Aoki, Gianluca Benigno, Nobuhiro Kiyotaki
Chapter URL: http://www.nber.org/chapters/c3006
Chapter pages in book: (175 - 216)
4
Capital Flows and Asset Prices
Kosuke Aoki, LondonSchoolof Economics
Gianluca Benigno, LondonSchoolof Economics
Nobuhiro Kiyotaki, PrincetonUniversityandNBER
4.1 Introduction
After liberalizing internationaltransaction of financial assets, many
countries experience large swings in the value of fixed assets, the
amounts of foreign and domestic credits, and aggregate economic activities. This is true for both industrialand emerging marketcountries
alike. Notable examples in recentdecades include LatinAmericafrom
the late 1970s,the Nordic countriesin the late 1980sto the early 1990s,
and East Asia from the mid-1990s.The standard theory interpretsthe
liberalizationof internationalfinancialtransaction(capitalaccountsliberalization)as liberalizationof a particulartrade- tradebetweenpresent
goods and claims to futuregoods- which should bring similarbenefits
as liberalizationof trade of regulargoods. These volatile swings, however, raise concernsabout the potential costs of capital accountliberalization.
In a recent book, Obstfeld and Taylor(2004) analyze the flows and
ebbs of internationalfinancialtransactionssince the late nineteenthcentury,and show thatuneven capitalaccountliberalizationin the last four
decades brought mixed blessings to different countries. Prasad et al.
(2006) summarize previous theoretical and empirical studies to conclude that thereis no robustrelationshipbetween capitalaccountliberalization and economic growth, and that the benefits appear to dominate with strongdomesticfinancialinstitution,while the costs appearto
outweigh the benefitswith weak institution.1
How does the adjustmentto capital account liberalizationdepend
upon the degree of development of domestic financialinstitution?Why
may the economy with an underdeveloped financialsystem be vulnerable to shocks to foreignand domestic finance?
In orderto answerthese questionstheoretically,we single out the pos-
176
Aoki, Benigno, and Kiyotaki
sibility of default as a distinguishing featureof financialtransactiontradebetween presentgoods and claimsto futurereturns.Forthe claims
to future returns,we focus on private debt or equity, and will not address important related issues of sovereign debts, and government
guarantee of private debts, nor internationalflow of technology and
managerialcapital (foreigndirectinvestment).Withthis focus, we constructa model of small open economy in which it is difficultto enforce
debtors to repay their debt unless it is secured by the collateral.Entrepreneursuse fixed asset (land) and working capital to produce output
in the following period. At each date, some entrepreneursare productive while others are not. Here, the fixed asset is factorof productionas
well as collateralfor loan. The borrower'scredit limit is affectedby the
price of fixed asset, while the asset price is affectedby creditlimits. The
interactionbetween credit limits and the asset price turns out to be a
propagationmechanism that may generate large swings in aggregate
economics activities.
In addition to fixed asset, some fractionof futureoutput becomes collateralfor domestic loans, like projectfinance, or equity. The extent to
which futureoutput becomes collateraldepends upon both the technology and the quality of institution,which affectsthe development of domestic financialsystem. We show that, if the domestic financialsystem
is underdeveloped, it fails to transferenough purchasingpower from
savers (typicallyunproductiveentrepreneurs)to investing agents (productive entrepreneurs).Some funds are allocated to unproductiveentrepreneurswith inferiortechnology,resulting in low total factorproductivity (TFP)of the economy. The domestic interest rate earned by
savers remains low - the symptom of financial suppression, and the
domestic wage and user cost of fixed asset remain low - which is the
symptom of cost suppression.
Moreover,we considerthe extentto which assets and projectsbecome
collateralfor foreign loan is restrictedcomparedto domestic loans, because the foreigncreditorsgenerallyhave more difficultiesin enforcing
debts in a differentcountry.If the collateralconstrainton foreign borrowing is significantlytighterthan the one on the domestic borrowing,
then the domestic credit market can be segmented from the internationalcreditmarketwith distinctivelyhigherdomesticinterestratethan
foreign interestrate.
We show that the adjustmentof the economy following capital account liberalizationdepends upon the degree of developmentof the domestic financialsystem and the importanceof collateralizablefixed as-
CapitalFlows and Asset Prices
177
set in production,and the resulting relative severities of financialsuppression and cost suppression.
Whenthe domesticfinancialsystem is poor,the cost suppressionis severe with low TFPunder autarky.Due to low productioncosts, even the
unproductiveentrepreneurenjoys high rate of returns on production,
which results in relatively high domestic real interest rate. Then, after
liberalizationthere will be capital inflows toward both productive and
unproductive entrepreneurs.The initial boom is amplified by the increasein asset price that furtherloosens the borrowingconstraints.But
when the domesticfinancialsystem is poor,the boom is not sustainable:
the initial expansion of borrowing is offset by the eventual rise of production costs, and falls in the share of production of productive entrepreneursand TFP.
For the intermediatelevel of domestic financialdevelopment, financial suppressionis the dominant symptom under autarky,with the domestic interestratebeing lower than the foreign interestrate.After liberalization,there is capital outflow. The asset price falls because of the
higherinterestrateand anticipationof recession.This hurts the productive entrepreneurswith debt leverage more than the unproductiveentrepreneurs,and their share of production drops. The TFP,aggregate
output,employment,and wage rateall fall. Despite the initialrecession,
eventuallyproductiveentrepreneurswho will benefitfromcheapercost
of productionwill takeover productionof unproductiveentrepreneurs.
In the long run, the economy will recoverwith leanerand more efficient
productionwith higher TFP.
In order to address the question of why the economy with underdeveloped financialsystem is vulnerable to shocks after capital account
liberalization,we do two experiments:the firstis a shock to domestic finance, an unanticipatedfall in the fractionof future output usable as
collateralfor domestic loans. This is meant to capturean aspect of domestic banking crisis. The second is a shock to externalborrowing, an
unanticipatedincreasein the foreigninterestrate.Weshow thatboth the
domestic shock and the externalshock generatefalls in the asset price,
simultaneouscontractionsof domestic and foreign credit, endogenous
falls in TFP,and recession- a twin crises- in the short run. In the long
run, however, we find that, only if the domestic financialsystem takes
time to recover,the economy continuesto sufferfromlow TFPand stagnation.
Thereis an extensive literatureon the implicationsof credit frictions,
both domesticand international,on internationalcapitalflows and cap-
178
Aoki, Benigno,and Kiyotaki
ital account liberalization.While the basic structureof our chapter is
built upon Aoki, Benigno,and Kiyotaki(2006)to incorporatethe role of
asset prices in the adjustmentfollowing capital account liberalization,
our chaptercan be relatedto the following three strandsof literature.
The first strand of literaturefocuses on the direction of capital flow
under credit frictions.Gertlerand Rogoff (1990)constructa model of
North-Southlending under moral hazard.In their model, since agency
problem becomes less severe as a country'snet worth becomes larger,
capitalcan go from the poor South to the richerNorth.2
The second is on the implicationsof internationalcapitalflows on economic volatility.Aghion, Bacchetta,and Banerjee(2004)show thatcountries with an intermediatelevel of financialdevelopment are more unstablethanvery developed or very underdevelopedcountries.Mendoza
(2006)constructsa small open realbusiness cycle (RBC)model with collateralconstraintto analyze the role of asset prices on the sudden stops.
Although the propagationmechanism though the interactionbetween
the asset price and creditlimit is similarto ours, as is analyzedby Kiyotakiand Moore(1997),TFPmoves exogenouslyin Mendoza(2006),while
endogenously in our framework.
The third strand of literatureexamines the relationshipbetween domestic and international financial frictions. Caballero and Krishnamurthy (2001)emphasize the interactionbetween domestic and international collateral constraints for financial crises by constructing a
model where firms are subjectto liquidity shock. Since domestic collateral constraintlowers the domestic rateof returnof saving, agents tend
to undersave- they hold too little spareinternationalborrowingcapacity, which makes the economy more vulnerable to adverse shocks.
Kaminskyand Reinhart(1999)also empiricallyexamine the twin crisis:
bankingand balance-of-paymentcrisis,and found that problemsin the
banking sector typically precede a currencycrisis. While our chapter
does not explicitlymodel bankingsector,it provides a frameworkto analyze why the difficultiesof domestic financeand internationalfinance
interactwith each other throughthe asset price.
4.2 Model
4.2.1 Framework
Weconsidera small open economy with one homogeneous goods, land,
and labor.There are two types of continua of infinitely lived domestic
agents, entrepreneurs,and workers,in addition to foreigners.
179
CapitalFlowsandAssetPrices
The preferenceof the entrepreneursis describedby the expected discounted utility:
a)
^|>-'iogcsj,
where csis the consumptionat date s, and p e (0, 1) is the subjectivediscount factor,and Et is the expectations conditional on informationat
date t.
The entrepreneurhas a constantreturnsto scale productiontechnology combiningland (kt),labor (lt),and materialgoods (tnt)as inputs to
produce gross output of good (y,+1)with one period productionlag as:
"•-UHxKt^i)
-
(2)
where atis a productivityparameter,which is known at date t. Parameters k and Xrepresentthe share of land and laborin production,where
k, X,1 - k - Xg (0, 1). Materialgoods input includes both working capital and reproduciblefixed capital- noting our economy has one homogeneous goods- and gross output includes output and fixed capitalafter depreciation.At each date, some agents are productive (at= a), the
others are unproductive (at = 7), and the idiosyncraticproductivity of
each entrepreneurfollows a two-stateMarkovprocess:3
Prob{at+1= 7 1at = a) = 8, and Prob(at+l= a\at = y) = nh.
(3)
Agents can become producersor creditors.4We consider an environment in which, because the productiontechnologyis specificto the producer,only the entrepreneurwho startedthe productionhas the skill to
obtainmaximumoutput describedby the productionfunction.Despite
this skill, the produceris free to walk away from the productionand the
debt obligationbeforecompletingthe production.Besidesthe producer,
there is a lead creditorwho monitors the projectthroughout, and has
some skill to obtain 0 (< 1) fractionof maximum output, if he or she
takes over the entrepreneur'sproduction. Although the production is
divisible,thereis only one lead creditorfor each productionproject,and
only a home agent can become a lead creditor.All the other (nonlead)
outside creditors,home or foreign,cannotrecoverany amountof output
and can take over only land as collateralasset if the producer-borrower
walks away. Knowing this possibility in advance, foreign creditors(as
outside creditors)would limit the credit so that the debt repayment
of the debtor-producerdoes not exceed the value of collateral;that
(b*+1)
Aoki, Benigno,and Kiyotaki
180
where qt+1is land pricein termsof good
is, the futurevalue of land, qt+1kt,
at time t + 1 and ktis land put in collateralfor loan:
(4)
W+i^qt+iK
Similarly,the domestic lead creditorrestrictsher loan (bt+1)so that the
total sum of loans does not exceed 0 fractionof output plus the future
value of collateralland:5
&,+i+ *?+i=M,+i*,+ 6y,+r
(5)
Here, land representsfixed asset with limited supply that the outside
creditorscan recover after default, and k is the share of such asset in
gross output. We take 0 as an exogenous parameterto representthe degrees of development of the country'sfinancialinstitution.
The flow-of-fundsconstraintof the entrepreneuris given by:
c, + qt(k, *,_,) + wtlt+ mt= yt-bt-b*
+ ^ + ^,
(6)
x
rt
where wt is the real wage rate and rtis the domestic real gross interest
rate.The left-handside (LHS)of the flow-of-fundconstraintis expenditure;consumption(ct),net purchaseof land [qt(kt- kt_x)],
wage bill (zvt/,),
and materialgoods input (mt).The right-handside (RHS)is financing;
the internalfinancefrom the net worth- output minus the debt repayment to home and foreign creditors- and the external finance of the
borrowings from home and foreign creditors.6 The entrepreneur
chooses the quantities (ct,kt,/,, mt,yt+1,bt+vb*+1)to maximize the expected discounted utility subjectto the constraintsof technologyand finance (2 through6).
Next we turn to workers. Unlike the entrepreneurs,the workers do
not have productiontechnology,nor any collateralizableasset in order
to borroweitherdomesticallyor internationally.Theychoose consumption ct, labor supply /,, and domestic and foreign net borrowings (bt+1
and b*+1)
to maximize the expected discounted utility,
£,{!>-' «[c.-p(y]I
subjectto the flow of funds constraint,
rt
r
and the borrowingconstraints,
181
CapitalFlowsandAssetPrices
b,+1<0,andb*+i^0.
We assume w() is strictlyconcave. Let L be population size of workers,
and v(l) = /1+1/V(1+ l/r|) where T|> 0. The choice of laborsupply implies wt = v'(lt),and the total laborsupply becomes
Ut = Is (wt) = Lw?.
Foreignerslend to and borrowfromthe domestic agents at a constant
realgross interestrater*.Throughoutthe analysis,we assume thatthere
is no limitationon domesticlending to foreignersat this interestrate,because foreignershave enough collateral.We also assume the foreign interestrateis strictlyless than the home time preferencerate:
r*< i
(Al)
P
Let Ct,C\, and C™be aggregateconsumptionof productive entrepreneurs, unproductiveentrepreneurs,and workers,and let Bt,B\, and Bf
be aggregatequantitiesof the other quantitybtof productive entrepreneurs, unproductive entrepreneurs,and workers. Supply of land is
fixed at K.The marketclearingconditionfor land, labor,goods, and domestic creditare written as:
Kt + K\ = K,
(7)
Lt + L't= U(wt) = Lw?,
(8)
c, + c; + c? + Mt + m;
(9)
= x + y; - (B* + Bf + b*w)+ -J±iBM + B;+1+ Br+1= 0.
^
-
- ,
(10)
In the RHSof equation(9),the last two termsare the net supply of goods
by the foreignersto domestic agents. In equation (10), the debt of domestic agents to the other domestic agents should be net out in the aggregate,even though the total debts of the domestic agents need not because of the internationalborrowing and lending. (Rememberthat the
domestic creditmarketmay be segmented from the internationalcredit
market,because the home agents face the internationalborrowingconstraint.)
Thecompetitiveequilibriumis defined as a set of prices (qt,rt,wt)and
Aoki, Benigno,and Kiyotaki
182
quantitiesthat is consistent with the choice of all the individual entrepreneursand workers as well as the clearingconditions of marketsfor
land, labor,goods, and domestic credit.Becausethere are no aggregate
shocks, aside from possibly an unanticipatedexogenous shock to the
initial condition, the agents have perfect foresight of future prices and
aggregatequantitiesin the equilibrium(even though each entrepreneur
faces idiosyncraticproductivityshocks).By Walras'Law,only threeout
of four marketclearingconditionsare independent.
4.2.2 Propertiesof Equilibrium
We now describe the equilibriumof our economy. For the details of
the derivations,please see the appendix to this section.Wefirstobserve
that the domestic interestrate cannotbe lower than the foreign interest
rate:
rt> r*.
Otherwise,all of the domestic savings would go abroad,and domestic
use of land and laborwould shrinkto zero, which would contradictthe
marketclearing.
We start by describing the behavior of entrepreneurs.The international borrowing constraintimplies that, when the entrepreneurbuys
one unit of land at price qt,he can borrow up to the presentvalue of qM
with favorableforeign interest rate, and needs to finance only the difference,
from the other funds. Here utis the requireddown payment for the entrepreneurto buy a unit of land. We can also think of utas the opportunity cost- user cost- of holding land for one period.
When each entrepreneurchooses the factordemand to minimize the
cost of production,ujct+ wtlt+ mtfor a given output yt+1subjectto production function (2), the factordemand and the cost functionsatisfy:
kt:L:m=
K X
- : - : 1 - k - X, and
ut wt
Min(ufa+ wtlt+ mt)= ufwk yt+1,
at
(12)
CapitalFlows and Asset Prices
183
for the entrepreneurwith the productivityar Becausethe ratioof factor
demand are common to all the productive and unproductiveentrepreneurs, we know:
Kt: Lt:M, = - :
: 1 - k - X = K[: L[:M\.
(13)
Let Ztbe the total net worth of all the entrepreneurs:
+ k',_o- b,- b;- b*- b*\
z, = r, + y;+ <,,(*,_,
Letstbe the shareof net worth of all the productiveentrepreneurs:
5=r,
+ ,,E -s.-Bf
(i4)
The productive entrepreneurswould borrow up to the limits of international and domestic borrowing, if the rate of returns on production
[a/(uktw*)]exceeds the domestic interestrate- note that the rate of return is the inverse of unit of cost in (12):Aggregatingthe flow-of-funds
(6) acrossall the productiveentrepreneurs,we have:
utKt+ wtLt + M, <
1
,
g
(15)
ol/(u«w))
where the equalityholds if a/{uktw))> rt,and the strictlyinequalityimplies (x/(ukw))= rr The numeratorof RHSis the aggregategross saving
of the productiveentrepreneurs,becausethey save P fractionof theirnet
worth with logarithmicperiod utility function.The denominatoris the
fractionof the costs that has to be financedfrom own saving, afterborrowing 6 fractionof futureoutput from domestic creditorat the interest
rate rt.Thus, the productiveentrepreneursuse their gross saving in order to financethe gap between the total cost of production and the externalfinance.
Whilethe productiveentrepreneurshave a comparativeadvantagein
productionwith borrowing,the unproductiveentrepreneurshave comparative advantage in providing loans. So the unproductive entrepreneurs either lend to the productive entrepreneursin domestic credit
marketand/or producewith borrowingfromforeignersif the rateof returns on productionis equal to the domestic interestrate:
VI
^ rr
(16)
184
Aoki, Benigno,and Kiyotaki
This would hold with equalitywhen the unproductiveagents produce.
If (16)holds with strictinequality,the unproductiveentrepreneursspecialize in providing loans.
Concerningthe workers, they will decumulate their financialassets
until they consume all, if the domestic real interest rate is strictly less
than the time preferencerate (i.e., rt < 1/P).7 The aggregateconsumption of the workersis equal to the aggregatewages:
Bu,= B*«,= 0/ and Q = wtLs(wt).
(17)
From the behavior of the workers, the domestic credit marketequilibriumconditionbecomes Bt+1+ B't+l= 0. Togetherwith the consumption functionof the entrepreneurs,the goods marketclearingcondition
(9) can be written as:
+ M,+ M'(= pZ,+
q£ + wtV(.w,)
Bf+1rtBf+1,
where
Zt = Yt+ Y't+ qtK-B*-B*'.
(18)
Then,from the internationalborrowingconstraint,we have:
+ M, + M; < (SZr
u<K+ wtLs(wt)
(19)
If domesticinterestrateis higherthanthe foreigninterestrate,the equality holds as the internationalborrowing constraintis binding. If (19)
holds with strict inequality (with nonbinding internationalborrowing
constraint),then the domestic and foreign interest rates are equal, as
domestic credit market is perfectly integrated with the international
creditmarket.
Letxtbe the excess rateof returnsof the productiveagent over the unproductiveagent. Then
The first term in the parenthesisof RHSis the rate of returnson saving
of the productiveentrepreneurs,when they borrowup theircreditlimit.
The total net worth of the domestic agents evolve as:
(21)
Z,+1= (1 + stxt)rfiZr
Becausethe net worth of productiveentrepreneursearnsthe excess rate
of returns,the growth rate of the total net worth of the domestic agents
CapitalFlowsandAssetPrices
185
depends upon the share of productive entrepreneurs'net worth sr The
shareof productiveentrepreneursevolves as:
(l-8)(l+x,)r,pS,Z, + n8r,P(l-S,)Z,
{jU)
S'+1
(l+s,xf)rfpZ,
= (1
- 8)(1 +
xt)s,+ n8(l s,)
fT^
-*-*•>•
The denominatorof RHSof the firstequationis the totalnet worth in the
next period.Thenumeratoris the aggregatenet worth of the productive
entrepreneursin the next period, which is the sum of the net worth of
whose who continue to be productive with probability1-8 (from (3))
and the net worth of those who shift from unproductiveto be productive with probabilitynb.
The dynamic evolution of the economy is characterizedby the sequence of (qt,ut, wt,rt,Kt,K't,Lt,L\,M,, M\, Zt, st, xt, Zt+1,st+l)that satisfies (7), (8), (11), (13), (14), (15), (16), (18), (19), (20), (21), and (22) for a
given the initialland and debts of the productiveentrepreneursand foreign debt of the unproductiveentrepreneurs(Kt_vBt,B*,and B*').8
Note that,afterthe initialtotalnet worth of the entrepreneurs(Zt)and
the share of productive agents' net worth (st)are determined simultaneously with the land price (qt), the evolution of the aggregateeconomy
at future date t is described recursively as a function of the variables
(ZT,sT)along the perfectforesightequilibriumpath.
Finally,in the subsequentanalysis it would be of interestto examine
the behavior of the total factorproductivity (TFP)of the economy. We
define TFPas the ratioof total gross output over total input measure:
* _
y•*t+i +
^ v1 1+\
cyx\
w w \i-k-xJ
= ad, + 7(1 - d,)
where d, = Kt/K= Lt/Ls= Mt/(Mt+M't).Equation(23)shows thatTFPdepends on the fractionof inputs used by the productiveagents, dr
4.3 Steady State under Autarky
Beforelooking into how the economy adjuststo capitalaccountliberalization, it is useful to characterizethe steady state equilibrium of the
economy when there are no financialtransactionswith foreigners.This
Aoki, Benigno,and Kiyotaki
186
analysisenablesus to understandhow the directionof capitalflow after
liberalizationis affected by the degree of domestic financialdevelopment. Here, the home agents are not allowed to borrow from nor lend
abroad (i.e., b* = 0). Then, because the goods are homogeneous and
all land and laborare traded domestically,the economy would become
autarky.
In the steady state,all the endogenous variablesareconstant.Theuser
cost of land is now defined as the differencebetween land price and the
present value of the land price of the next period as:
u= qll - 1
(24)
J.
Letus define X = sx, the productof the shareof net worth and the extra
rate of returns of the productive agents- the importanceof extra returnsof the productiveentrepreneurs.Then,(13),(19),(21),and (22)can
be rewrittenas
k X
K:L:M = -: - :1-k-\
u w
= K:Lw^:M + M'
(25)
+ M + M' = (JZ,
qK+ w1+r>L
1 = P(l + X)r,
(26)
F(X,x) = X2 + [8(1 + n) - (1 - b)x]X- nbx = 0, and X > 0.
(28)
(27)
Togetherwith the otherequilibriumconditions (15),(16),and (20),(r,w,
q, u, x, s, X, K, L,M, M', Z) are determinedendogenously in the steady
state autarkyequilibrium.9
From the domestic credit constraint (5), the tightness of the credit
constraintdepends upon both the share of collateralizableland in production (k) and the fractionof future output usable as collateralfor domestic loan (6)- the degree of domestic financialdevelopment. In the
appendix,we show thatif the degree of domesticfinancialdevelopment
6 is below a thresholdlevel 0(k)where 6'(k) < 0, then unproductiveentrepreneurswith dominated technology continue to produce, and the
allocationof the factorsof productionare inefficientin the steady state
autarkyequilibrium.Intuitively,if the domestic financialsystem is underdeveloped (so thatthe domesticcreditconstraintis tightwith limited
share of collateralizablefixed land [k] or future output [9]), it fails to
transfer enough purchasing power from the unproductive entrepreneurs (savers) to the productive entrepreneurs(investing agents), so
CapitalFlows and Asset Prices
187
that the unproductive entrepreneurs end up employing factors of production with their inferior technology.
Figure 4.1 shows the relationship between domestic real interest rate
and the degree of domestic financial development 6 under autarky
steady state. When the degree of domestic financial development is very
high higher than 6* (k) then the economy achieves the first best allocation with no credit constraint binding. In such equilibrium, the domestic real interest rate is equal to the time preference rate, 1/(3. For
6 < 6*(k), the productive entrepreneurs face binding credit constraint (5) holds with equality. But, for 6 e [8(k), 6*(k)], only productive entrepreneurs produce (which implies efficient allocation of the factors of
production), even though the consumption of the entrepreneurs is no
longer smooth. The interest rate is now below the time preference rate
a symptom of financial suppression.
When the domestic financial system is significantly underdeveloped
with 6 < 0(k), production allocation is inefficient, the total factor productivity in (23) is low, below the productivity of the productive entre-
Figure 4.1
Steady-state interest rate under autarky
188
Aoki, Benigno, and Kiyotaki
preneursa, and closerto the productivityof the unproductiveentrepreneurs 7. Then in the steady state, the total wealth of the entrepreneurs
stays low along with the wage rate and the user cost. The real interest
rateis equal to the rateof returnon productionfor the unproductiveentrepreneurs,(16) holds with equality.BecauseTFP,wage rate,user cost
and the unit cost of productionare all increasingfunctionsof 6, the interestrateis a decreasingfunctionof 6 in the region 6 < 6(k).Intuitively,
suppression of TFPand the factorprices dominates the effect of financial suppression here: the lower 6 is, the lower is the unit cost of production for the unproductiveentrepreneur,the higher is theirrateof return on production,which is equal to the real interestratein the steady
state. Figure4.1 describessuch nonmonotonerelationshipbetween real
interestrateand the degree of domestic financialdevelopment.10
When the economy starts tradingfinancialassets with foreignersaftercapitalaccountliberalization,whetherthe economy experiencescapital inflow or outflow depends on the degree of domestic financialdevelopment, 0, for a given share of land in the production.In figure 4.2,
the world interest rate is also plotted as a horizontal line. Generally,
there are three regions. When 0 is very low, lower than 0irthen the domestic realinterestrateunder autarkyis higher thanthe foreigninterest
rate. Becauseof low TFPand low factorprices, even unproductiveentrepreneursearn relativelyhigh rate of returnon production,which is
equal to the domestic real interest rate. Then, after liberalization,both
productive and unproductive entrepreneursborrow from foreigners,
causing capitalinflow.
When the degree of domestic financialdevelopment is in intermediate region, 0 e (0,, 02),then the domestic real interestrateunder autarky
is lower than the foreign interest rate- the effect of financialsuppression dominates the suppression of factor prices. After the capital account liberalization,capitaloutflows to the foreign country.
Forhigh values of 0, 0 > 02,the domesticfinancialsystem is advanced
enough so that only productiveentrepreneursproduce and the interest
rateis high with negligible financialsuppressionunder autarky.Witha
superiordomestic financialsystem, the domestic interestrateunder autarkyis higher than the foreigninterestrate.Afterliberalization,the domestic productive entrepreneurswill attractforeign funds with their
largeborrowingcapacity.
Inwhat follows,we focus our analysison the casewith 0 e (0,0);thatis,
inefficientproductionremainsunder autarkysteady state.Thiscase is of
particularinterestbecausecapitalaccountliberalizationcan affectTFP.11
CapitalFlows and Asset Prices
189
Figure4.2
Capitalflows afterliberalization
4.4 Capital Account Liberalization
We now examine how the adjustmentto capital account liberalization
depends on the degree of development of the domestic financialinstitution, using the equationswe derived in section2.4.12In orderto illustrate
the qualitativefeaturesof the transition,we employ some numericalexamples of our model. Theparametervalues of the model are reportedin
table4.1.
4.4.1 CapitalAccount Liberalization:TheRole of Asset Price
Figure 4.3 shows the dynamics of the economy following capital account liberalization.Beforeliberalizationoccursat time 0, the economy
is at the autarkysteady state. Here we assume 0 is low ( = 0.2) and the
world interestrate is equal to 1.04.With the relativelyunderdeveloped
domestic financialsystem (low 6), the autarkyinterestrate is above the
foreign interestrate (due to a severe cost suppression), and capital ac-
Aoki, Benigno, and Kiyotaki
190
Table4.1
Parametervalues
K
0.030
X
i]
p
a
7
n
8
0.12
3.0
0.92
1.10
1.05
0.1
0.15
Notes: One period in our model corresponds to a year. Since in our model material good
- input includes both working capital and fixed capital, we set its share, 1 k X, as 0.85.
The underlying assumption is that the ratio of working capital (intermediate input) to
net output is 1, and the ratio of fixed capital to net output is 3. When the capital depreciation rate is assumed to be 0.1, then the implied share of material good input in our
model is (3 + 1)/(1 + 0.9 X 3 + 1) = 0.85. The implied ratio of land in net output is then
0.03/(0.03 + 0.12) = 0.2.
Because of our specification on utility of workers, ti represents the Frish elasticity of labor supply. It is set to 3, in line with the RBC literature (e.g., King and Rebelo [1999] assume
4). The results reported are not very sensitive to v\.
The discount factor, p, is set 0.92. One may think that this is too high as a yearly discount
rate. However, in a credit constrained economy, the steady state interest rate is lower than
the inverse of time preference rate. Indeed, our model implies that the steady state interest rate with p = 0.92 under autarky ranges from 5.5 percent to 8.1 percent depending on
the value of 0 under which unproductive agents produce.
The four parameters a, 7, n, and 8, together with k, mainly determine how likely the
inefficient production remains. We set the gap between the productivity of productive and
unproductive agents, a - 7, as 5 percentage points. Parameters n and 8 are set to 0.1 and
0.15, respectively. This implies that in the steady state the fraction of the productive agents
is equal to n/(l + n), and the expected time that an agent continues to be productive is
1/8 = 6.66 years. Finally, those parameters together imply that the unproductive agents
produce in the autarky steady state when 6 is less than 0.64.
count liberalizationcauses capitalinflow. The land (asset)price experiences a largeupward swing, becauseboth productiveand unproductive
entrepreneurscan borrow from foreigners at a cheaper interest rate
against land, as well as because the agents anticipatethat the user cost
continuesto be higher due to economicexpansion (see fig. 4.3, panel A).
As in Mendoza (2006),the asset price serves as an amplificationmechanism: the higher asset price expands the collateralvalue and creditlimits, which stimulates investment on working capital.At the same time,
the largerinvestment leads to a higher user cost for a while, which results in a higher asset price in the equilibrium.At the beginning, the internationalborrowing constraint is not binding so that the domestic
interestrate drops down to the world interestrate.
In contrastto Mendoza (2006),TFPmoves endogenously in our economy.On the one hand,the initialrisein assetpricesubstantiallyincreases
the net worth of the productive entrepreneurs,who had outstanding
debts against the unproductiveagents before the liberalization.On the
otherhand, the unproductiveentrepreneursexpand productionby borrowing from foreigners, crowding out the production of productive
Figure 4.3
Dynamicsafterliberalization:Capitalinflow (low 6):A. Interestrate;B. Efficientand inefficientinvestment
192
Aoki, Benigno,and Kiyotaki
entrepreneurs.Figure4.3, panel B shows that,when 6 is low, the crowding-out effect dominatesthe leverageeffect,and the shareof investment
of productiveentrepreneursfalls.ThenTFPdecreasesas seen in (23).
Becauseof the deteriorationof TFP,the initialboom is not sustainable.
As the country accumulatesnet foreign debt, the total net worth of the
entrepreneursdecreases.In the meantime,the internationalborrowing
constraintbecomes binding, pushing up the domestic interestrate.Output startsshrinkinguntil it converges to the new steady state value.
In order to understandhow the level of financialdevelopment interacts with asset prices, figure 4.4 shows the case 0 = 0.6;a little more developed domestic financialsystem, but still underdevelopedrelativeto
the foreign economy (6 = 0.6 < 0ain fig. 4.1 when r* = 1.04). With a
larger 6, the productive entrepreneurshave larger capacity to borrow
from domestic lenders. Initially the leverage effect dominates so that,
afterthe liberalization,the productive entrepreneursexpand theirproduction more than the unproductive entrepreneurs,which raises TFP
temporally,in contrastto figure 4.3. Comparedwith figure 4.3, the initialboom is longerwith this initialincreasein TFP,and it takeslongerfor
the internationalborrowing constraintto become binding. In the long
run, the economy stagnates because the production of productive entrepreneursis crowded out by the unproductive producers as before.
Figures4.3 and 4.4 show that, under the relativelyunderdevelopeddomestic financialsystem, even if the liberalizationcauses the temporary
boom in asset price and aggregateproduction,the liberalizationfails to
permanentlyimprove the resourceallocationand TFP.Thus, the economy will stagnate in the long run. While the long-run implicationsare
similar to those described in Aoki, Benigno, and Kiyotaki(2006),here
(i.e., with fixed land used as a collateral)the short-runadjustmentis
driven by interactionbetween the leverage effect and the degree of domestic financialdepth (see figs. 4.3 and 4.4).
In figure 4.5 we set the foreign interestrate to r* = 1.07and 6 = 0.06.
(Thiscorrespondsto the medium level of financialdevelopment in figure 4.2; 6 g (Oj,62)).Becausethe domestic financialsystem is relatively
more developed so that financial suppression relative to the foreign
economy is the majorsymptomof the home economy,underautarky,the
interestrateis lower than the foreigncounterpart.13
Then,with the liberalization, the economy experiences capital outflow and temporaryrecession. The interest rate increases to the level of foreign interest rate.
The asset price falls because the interestrate is higher and the user cost
of the asset is lower persistentlydue to recession.Theinitialfall in the asset pricehurtsthe productiveagents more thanthe unproductiveagents
Figure 4.4
Dynamicsafterliberalization:Capitalinflow (high 8):A. Interestrate;B. Efficientand inefficientinvestment
Figure 4.5
Dynamicsafterliberalization:Capitaloutflow:A. Interestrate;B. Efficientand inefficient
investment
CapitalFlowsandAssetPrices
195
because they were leveraged.As a result,the share of productionof the
productiveentrepreneursfall, and TFPdrops, which deepens the initial
recession(see fig. 4.5,panel B).However,the decreasein productioncost
in the subsequentperiods helps the productionof the productiveentrepreneursto recover.In the end, the productiveentrepreneursabsorball
the saving and the unproductiveentrepreneursstop producing. Thus,
despite the initialrecession,capitalaccountliberalizationleads to longrunefficiencyand prosperity,as is shown in Aoki,Benigno,and Kiyotaki
(2006).As before, differentlyfrom Aoki, Benigno, and Kiyotaki(2006),
the dynamicsof asset pricesthroughthe negative leverageeffecton productive entrepreneurscauses a temporarydrop in TFP.
4.4.2 WelfareImplications of Capital Account Liberalization
A naturalquestion in the debate is to what extent capitalaccountliberalizationis beneficialfor the country,and how the costs and benefitsare
distributedamong differentgroups. Toanswer this question,we examine the welfare effects on various entrepreneursand workers.14
For the entrepreneurs,we measure the welfare effect of capital account liberalizationby the average percentage change of steady state
autarkyconsumptionthatis requiredin orderto make the entrepreneur
indifferentbetween liberalizingcapital transactionsand staying in autarky.In computingthis measure,we take into accountthe effects of the
transitiondynamics from autarkyto the postliberalizationsteady state.
Formally,for each entrepreneuri, we define this measure of welfare
- as
change- called the consumptionequivalent jx1
£01 P'log W) = Eo£ P'log [(1 + iL-yc^L
t=0
(29)
*=0
where c\ is date t consumptionof entrepreneuri afterthe liberalization
at date 0, and c? is his or her date t consumptionif the autarkycontinued after date 0. We assume that at date -1, the economy is under autarkysteady state.
We know consumption c\ is proportionalto his or her net worth of
date t, z\, as:
c; = (i-p)z;
= (1 - m%r\*r\ . . . r\_v
where r\is the gross rateof returnon saving of entrepreneuri. The level
of r\is equal to rtwhen i is unproductive,and is equal to (1 4-xt)rtwhen
Aoki, Benigno,and Kiyotaki
196
i is productive at date t. Then, we can decompose the consumption
equivalent |x'into two components: the change in the initial wealth and
the change in the subsequent rates of returns between the autarky and
the postliberalization regime:
~
"
log (1 + m/)= log ( 4 ) + P Z P' (P%)j PK* P?)"1RA]?
*=o
\2o /
(30)
where zj,is the initial wealth immediately after capital account liberalization at t = 0 and zj4is the initial wealth if the autarky continued.
P=
1-8
8
nb
l-nb\
1
is the transition matrix for the productivity shift, and Rt = {log[(l + xt)rt],
log rt]f and RA = {log[(l + r4)*"4],log r4} are the vectors of the log rate
of returns for the productive and unproductive entrepreneurs in the
liberalization and in the autarky regimes, respectively. The subindex j
identifies the type of entrepreneurs (/' = 1 for productive and ; = 2 for
unproductive) at t = 0 when the liberalization occurs. Since entrepreneurs can shift from the productive to the unproductive status, for our
welfare analysis of the entrepreneurs, we will need to distinguish four
groups depending on the productivity prior and at the liberalization.
For the workers, on the other hand, we can compute the surplus of
supplying labor as:
Ct V(lt)= Wtlt ^-y/?^
= -^-w)+\
from the workers' preference, and the resulting consumption and labor
supply function. Then, we measure the welfare effect of capital account
liberalization on the worker (ix™)as the percentage change of the present value of the surplus of supplying labor as:
where wA is the wage rate under autarky.
Table 4.2 reports the welfare effect of capital account liberalization
for the cases corresponding to figures 4.3, 4.4 and 4.5. The headline of
productive-productive implies the group of entrepreneurs who were
productive at date -1 (prior to the liberalization) and continue to be
197
CapitalFlows and Asset Prices
productive at date 0 (at the liberalization). Similarly productiveunproductiveis the group who switches from productiveto unproductive fromdate-1 to date 0. Forfigure4.3 case (0 = 0.2 and r* = 1.04),with
relatively underdeveloped domestic financial system, the entrepreneurs and workers gain from the liberalization(in the first and the last
rows). All the entrepreneursgain from wealth revaluationin row (1),
while the wealth revaluationgains are particularlylarge for the entrepreneurs who were productive prior to the liberalizationdue to their
Table 4.2
Welfare analysis
2-1. theta = 0.2, r* = 1.04 : Capitalinflow (fig. 4.3)
Productive-
Productiveproductive
unproductive
Unproductiveproductive
Unproductiveunproductive
Welfare gain (ji/)
0.2931
0.2931
0.0493
0.0493
Decomposition
(1) Log wealth change
(2) Log rates of return
0.53229
0.53229
0.32342
0.32342
0.87044
0.63827
0.87044
0.63827
1.1457
-0.27528
0.91355
-0.27528
1.1457
-0.27528
0.91355
-0.27528
Welfare gain
(|xw):(5)/(4)-l
(5) Surplus
(liberalization)
(4) Surplus
(autarky)
Entrepreneurs
(liberalisation)
(3) Log rates of return
(autarky)
(2)-(3)
Workers
0.51370
0.48125
0.31793
2-2. theta = 0.6, r* = 1.04 : Capitalinflow (fig. 4.4)
Productive-
Productive-
productive
unproductive
Unproductiveproductive
Unproductiveunproductive
Welfare gain (ji/)
0.6761
0.7024
-0.13239
-0.11877
Decomposition
(1) Log wealth change
(2) Log rates of return
0.75067
0.75067
0.092208
0.092208
1.013
0.54983
1.013
0.54983
1.2472
-0.23422
0.76847
-0.21864
1.2472
-0.23422
0.76847
-0.21864
Welfare gain
(ilw):(5)/(4)-l
(5) Surplus
(liberalization)
(4) Surplus
(autarky)
Entrepreneurs
(liberalisation)
(3) Log rates of return
(autarky)
(2)-(3)
Workers
0.37307
0.57294
0.41727
(continued)
Table4.2
(continued)
2-3. theta = 0.6, r* = 1.07: Capitaloutflow (fig. 4.5)
Entrepreneurs
Welfaregain (n/)
Decomposition
(1) Log wealth change
(2) Log ratesof return
(liberalisation)
(3) Log ratesof return
(autarky)
(2)-(3)
Workers
Productiveproductive
Productive- Unproductive- Unproductiveunproductive
unproductive
productive
-0.18723
-0.18723
0.0717
0.0717
-0.29909
-0.29909
-0.022579
-0.022579
1.339
0.86026
1.339
0.86026
1.2472
0.091784
0.76847
0.091786
1.2472
0.091784
0.76847
0.091786
Welfaregain
(jiw):(5)/(4)-l
(5) Surplus
(liberalization)
(4) Surplus
(autarky)
-0.12289
0.36599
0.41727
2-4. theta increasesfrom 0.2 to 0.6 following liberalization,r* = 2.04 (fig. 4.6)
Entrepreneurs
Welfaregain (m-1)
Decomposition
(1) Log wealth change
(2) Log ratesof return
(liberalisation)
(3) Log ratesof return
(autarky)
(2H3)
Productiveproductive
0.77164
0.38446
0.38768
0.084408
0.6435
0.6435
0.39922
0.39922
1.0741
0.59536
1.0741
0.59536
1.1457
-0.071591
0.91355
-0.31819
1.1457
-0.071591
0.91355
-0.31819
(5) Surplus
(liberalization)
(4) Surplus
(autarky)
0.5391
0.31793
Welfaregain
(jiw):(5)/(4)-l
Workers
Productive- Unproductive- Unproductiveproductive
unproductive
unproductive
0.69566
2-5. theta increasesfrom 0.6 to 0.76 following liberalization,r* = 1.07 (fig. 4.7)
Entrepreneurs
Welfaregain (p,1)
Decomposition
(1) Log wealth change
(2) Log ratesof return
(liberalisation)
(3) Log ratesof return
(autarky)
(2)-(3)
Productiveproductive
Productive- Unproductive- Unproductiveunproductive
productive
unproductive
0.12446
0.2717
-0.027941
0.099349
0.16057
0.16057
0.014931
0.014931
1.204
0.84826
1.204
0.84826
1.2472
-0.04327
0.76847
0.079787
1.2472
-0.04327
0.76847
0.079787
CapitalFlows and Asset Prices
199
Table 4.2
(continued)
Workers
Welfaregain
(jt"):(5)/(4)-l
0.30302
(5) Surplus
(liberalization)
(4) Surplus
(autarky)
0.54371
0.41727
Notes:Welfaregain of an entrepreneur(muAi)representsthe permanentincreaseor decreasein consumptionthatmakesthe agentindifferentbetween liberalisationand autarky.Forexample,welfare
gain of 0.2931in table2-1 meansthatthe welfarebenefitof moving to liberalizationfromautarkyis
equivalentto thepermanentincreasein consumptionof 29.31percent.Seeequation(29).Typesof entrepreneurs:productive-productiverepresentsan agentwho is productivejustbeforeliberalization
(thus he is a borrower) and remains productive at the time of liberalization.Unproductiveproductiverepresentsan agent who is unproductivejust beforeliberalization(thus he is a lender)
and switches to productiveat the time of liberalization.The other two types are similarlydefined.
Log wealth change refersto the firsttermof the right-handside of equation(30) in the paper.Log
ratesof return(liberalization)refersto the second termof equation(30),and log ratesof return(autarky)refersto the thirdterm.Workers:surplus(autarky)refersto the second termof the right-hand
side of equation(31),and surplus(liberalization)refersto the firstterm.Welfaregain of the workers
is definedas the percentagechangein the presentvalue of surplusbeforeand afterthe liberalization.
leverage.Theeffectsof the changein the expectedratesof returnsis negative, as in row (2) and (3), but it is dominated by the positive wealth
revaluationeffect. The workersbenefit from the liberalizationbecause,
due to the initial expansion accompaniedby capital inflows, wages are
=
higher than autarkyduring the transition.For figure 4.4 case (6 0.6
=
are
and r* 1.04),productiveentrepreneurspriorto liberalization more
leveraged and own the majorityof land: therefore,they are the main
beneficiariesof the wealth revaluationeffect. Thus, the entrepreneurs
who were unproductiveprior to liberalizationlose, because the negative effect coming from the lower rateof returnsdominatesthe positive
but smallerwealth revaluationeffect.
When the financialsuppressionis severe relativeto the foreign economy with the medium degree of financialdevelopment as in figure 4.5
(0 = 0.6 and r* = 1.07),the economy experiencesan initial recessionbefore becoming productive-efficientin the long run. The welfare effects
of capital account liberalizationare mixed. The workers lose since the
loss from the lower wages during the initial recession is too large compared to the possible long-rungains in the distant future.Forthe entrepreneurs that are productive before the liberalization, the negative
wealth revaluationeffect caused by lower asset prices dominates the
positive effect of the higher foreign interestrate.On the otherhand, the
entrepreneursthat are unproductivebefore the liberalizationwill gain
since the negative wealth effect is smaller for the entrepreneurswho
200
Aoki, Benigno,and Kiyotaki
were lendersthanthe positive effectof higherratesof returnsin the subsequent periods.
Fromthese analysis,we learnthat the welfare of the workersand the
entrepreneurswith leverage (who areproductivepriorto the liberalization) tend to be more influencedby the short-runmovement of the aggregate economy immediately after the liberalization.In contrast,the
unproductiveentrepreneurs(who are lenders) tend to care more about
the subsequent rates of returns on saving, which depends upon the
long-run performanceof the economy. These welfare effects may explain why the capitalaccountliberalizationtends to be unpopularto the
workers and the credit constrainedentrepreneursin the countryof the
medium degree of the domestic financialdevelopment.
4.4.3 IndirectEffectsof Capital Account Liberalization
Prasadet al. (2006)arguethat,farmoreimportantthanthe directgrowth
effects of access to internationalcapital markets is how capital flows
generate a number of what they label as potential collateralbenefits of
financialintegration.Indeed, a growing literatureshows that financial
openness can, among otherthings, promotedevelopment of the domestic financialsector and generateefficiencygains among domestic firms
by better corporategovernance. In particularKlein and Olivei (2006)
find that, in financiallyintegratedeconomies, the degree of domestic financialsectordevelopment is higher than in countriesthat maintainrestrictionson capitalaccounttransactions.15
In orderto capturethe idea that,by capitalaccountliberalization,the
countrycan increasethe efficiencyof the domestic financialsystem, we
will examine the effect of capital account liberalizationthat improves
domestic financialsystem throughan increasein 6.
Figure 4.6 shows the response of the economy following capital account liberalizationthatsimultaneouslyincreases6 from0.2 to 0.6,starting fromthe autarkysteady stateas in figure4.3.Theautarkyinterestrate
is above the foreign one due to the cost suppressionwith low initial 6.
Following capitalaccountliberalizationand the increasein 6, the economy enters into sustainable boom with improved domestic financial
market.Theasset priceincreasessubstantiallyand permanentlybecause
agents anticipatehigher user costs in the long run. As the domestic financial market shifts more purchasing power from the unproductive
entrepreneursto the productive entrepreneurs,TFPrises permanently.
Froma welfare perspective,the improvementof the domestic collateral
Figure 4.6
Dynamicsafterliberalization:Capitalinflow 0 increasesfrom0.2 to 0.6:A. Interestrate;
B.Efficientand inefficientinvestment
202
Aoki, Benigno,and Kiyotaki
factor,along with capitalaccountliberalization,generatesgains forboth
entrepreneursand workers.Once again,the positive wealth effectof the
increasein asset prices dominatesthe negativebut smallereffectof a reduction in the ratesof returnfor both productiveand unproductiveentrepreneurs.
Figure4.7 considers the same experimentas before but for the economy with significantfinancialsuppression relativeto the foreign economy under autarky as in figure 4.5: the autarky interest rate is lower
than the foreign one. Now most of the costs of capital account liberalization associatedwith the capitaloutflow is mitigatedby the improved
domestic financial system. The asset price, output, wage, and TFPall
rise quicklyand permanently.Thewelfarelevel of the workersand most
of the entrepreneursincreasessubstantially(except that a group of the
entrepreneurswho switched from unproductive to productive at the
time of liberalizationsufferin a small amountbecause the expectedrate
of returnsis lower due to the higher cost of production).
4.5 Vulnerability to Shocks
4.5.1 Shockto Domestic Credit
There are series of episodes in which problems in domestic financial
marketand those in internationalfinancialmarketsinteractwith each
other.For example, Kaminskyand Reinhart(1999)reportthat banking
crisisand currencycrisisareclosely related.16
Calvo and Reinhart(2000),
in describingthe sudden stop of capitalinflows in LatinAmericanand
Asian countriesin the 1990s,point out that the bankingsectorproblems
often begin before the sudden stop and that, in their sample, banking
crises are often associatedwith a reversalof capitalflow from inflow to
outflow.17
In order to examine how a domestic financeproblem (e.g., domestic
banking problem) may propagate to internationalborrowing and aggregate productionin the economy aftercapital accountliberalization,
we conduct the following crude exercise:Suppose thatthereis an unanticipated permanent fall in the fractionof future output that becomes
collateralfor domesticborrowing(domesticcollateralfactor0), starting
from the steady state equilibrium under liberalized capital accounts
with foreign debt outstanding.
In figure 4.8, we consider an unanticipateddrop in the domestic collateralfactor8 from0.6 to 0.2 at date 0, startingfromthe new steady state
after liberalizationin figure 4.4. Following the drop in 0, the domestic
Figure 4.7
Dynamicsafterliberalization:Capitaloutflow 0 increasesfrom0.6 to 0.76:A. Interest
rate;B.Efficientand inefficientinvestment
Note:When0 = 0.76,interestrateunderautarkyis 1.07.
Figure 4.8
Dynamicsaftershockto 0:A. Interestrate;B. Efficientand inefficientinvestment
CapitalFlowsandAssetPrices
205
credit to the productive entrepreneursshrinks together with their investment.Theassetpricefalls,which furtherdecreasesthe investmentof
the productiveentrepreneurswith the leverage.The drop in asset prices
also tightensthe internationalborrowingconstraint,which causes an increasein the domesticinterestrate.The increasein the domesticinterest
rate furthercontractsthe production.Therefore,the domestic collateral
constraint and internationalcollateral constraint reinforce with each
otherthroughasset prices,which bringsa severe recession.On the other
hand, the unproductiveagents will benefit from lower productioncost
and the higher interest rate (as net lenders). Therefore,TFP endogenously decreases,and the economyfailsto recoverfromrecessionas long
as the problemof domesticfinancecontinues(6 continuesto be low).
4.5.2 Vulnerabilityto ForeignInterestRate Shock
Externalfactorsare often referredto as a cause of financialcrisis.Forexample, Russia'sdefault in 1998caused a large increasein interestrates
for many emerging market economies. Calvo and Talvi (2005) report
that interest rate spreads for the majorLatin Americancountries rose
from 450 basis points prior to the crises to 1600basis points in the immediateaftermath.Moreover,the increasein the spreadswas persistent:
it took almostfive yearsfor the spreadsto be backat the level priorto the
crisis.In all the majorLatinAmericancountries,the increasein the cost
of externalfinancewas accompaniedby a decline in asset prices and a
reductionin private capital flows.18A similar shock contributedto the
depression of Finlandin the early 1990s,as interestrates in Europeincreasedfollowing Germanreunification.(See Honkapohjaand Koskela
1999).
Here,we examinequalitativelyhow an exogenous increasein the foreign interestaffectsour economy.Figure4.9 shows the responses of the
economy when the foreign interestrate unexpectedlyincreasespermanently from 4 percentto 5 percentat time 0, startingfrom the postliberalizationsteady state with foreign debt position in figure4.4.
Following the increase in the foreign interest rate, the asset price
drops because the discount factorof future user costs is higher and because the future user costs are expected to be lower anticipatingrecession. The decrease in asset prices decreases the internationalcollateral
and increasesthe domesticinterestrate,leading to drop in output. In response to a 1 percentincreasein the foreign interestrate, the domestic
interestrateinitiallyincreasesmore than 1 percent.19
Figure 4.9
Dynamicsaftershockto world interestrate:A. Interestrate;B. Efficientand inefficient
investment
CapitalFlowsandAssetPrices
207
The drop in asset prices has a contractionaryeffect on productive
agents with leverage,more so than the unproductiveagents. Thus TFP
deteriorates,contributingto furtherdecreasein output.In the transition,
productive entrepreneursgradually recover their scale of production,
since their domestic borrowing capacityhas not changed (0 is still the
same) and productioncosts are lower following the initialrecession.As
long as the domestic financialsystem is intact,eventually TFPand output recoverto the preshocklevel.
4.6 Conclusions
In this chapterwe propose a frameworkto analyze how the economy
adjuststo the liberalizationof internationalfinancialtransactions,and
how the economy after the liberalizationreacts to shocks to domestic
and external finance. Differently from Aoki, Benigno, and Kiyotaki
(2006),centralto our analysisis the behaviorof asset prices,since the domestic and internationalcredit limits depend endogenously on the
value of the fixed asset.
Our model predictsthat the adjustmentof the economy to capitalaccount liberalizationdepends upon the depth of the domestic financial
system. When the domestic financialsystem is very underdeveloped,
the economy has low TFPand factorpricesbeforethe liberalization,and
experiencesa short-runboom with capitalinflow and asset price hikes
afterthe liberalization.This boom is not sustainablein the long run,because TFPfails to improve with the underdevelopeddomestic financial
system.
For the intermediatelevel of domestic financialdevelopment, since
the interest rate is lower than the foreign one under financialautarky,
capitalaccountliberalizationcauses capital outflow, falling asset price,
and a short-runrecession. In the long run, the economy will recover
with improvementof TFP.
The welfare of workers and productive entrepreneurswith the outstandingdebt aremoreinfluencedby the short-runfluctuationsthanthe
long-runperformanceof the economy. The welfare of the lenders (unproductive entrepreneurs)depends more on the rate of returnsin the
long run than the short-runeffects. These differencesin the welfare effects acrossdifferentgroups of people may partlycontributeto the controversy on capital account liberalization.If the economy succeeds in
improvingthe domestic financialsystem simultaneouslywith the capital account liberalization,then the economy will prosper persistently
with the improvementof welfare widely distributed.
208
Aoki, Benigno,and Kiyotaki
Our model also sheds lights on why the problems of domestic finance
and external finance may exacerbate each other through the asset price,
causing a twin-crisis style recession after capital account liberalization if
the domestic financial system is underdeveloped.
Our conclusions here need to acknowledge that the scope of our analysis is limited to international transaction of private financial assets
debts
and
so
that
we
have
omitted
other
private
equities
important
components of capital flows (such as foreign direct investment and sovereign debt flows) that are also relevant in many countries' experiences.
Those topics are left for future research.
Acknowledgments
We thank Francesco Giavazzi, Andy Haldane, Sebnem Kalemci-Ozcan,
and participants at the LSE seminar, ISOM-Istanbul conference, and the
Far Eastern Meeting of the Econometric Society for useful comments.
Notes
1. PeterHenry(2005)arguesthatcapitalaccountliberalizationshould have beneficialeffects to the level of aggregateoutput, not to the long-rungrowth rate,and presentsevidence for this prediction.
2. For more recent literatureon the directionof capital flow under credit frictions,see
Sakuragawaand Hamada (2001);Caballero,Farhi,and Gounrinchas(2006);and Mendoza, Quadrini,and Rios-Rull(2007).In this chapter,we focus our attentionon the direction of net privatefinancialflows.
3. Bernardet al. (2003)use the U. S. Census of Manufacturesto show that the laborproductivitydiffersacrossplans in the rangeof 1/4 to 4 times the mean productivity,(with
the standarddeviationof log productivityequal to 0.66),even in the same 4-digit industry.The differenceis not due to the differencein capital-laborratios.
This transitionimplies that the fractionof productiveentrepreneursis stationaryand
equal to n/(\ + n), given that the economy startswith such populationdistribution.We
assume thatthe probabilityof the productivityshiftsis not too large:
8 + m8<1.
Thisassumptionis equivalentto a positiveserialcorrelationof theproductivityof eachentrepreneur.Weintroducethis turnoverof individualproductivityin orderto separatethe
distributionof productivityfrom the distributionof wealth, so that there are significant
needs for externalfinanceeven in the steady state.
4. In equilibrium,typicallythe unproductiveagentswill becomecreditorsin the domestic financialmarkets.
5. If the producer-borrower
threatensto walk away fromproductionin orderto renegotiatewith the creditorsbeforecompletingthe production,it is efficientforthe producerto
pay some to creditorsin orderto completethe production.We assume the outside credi-
CapitalFlows and Asset Prices
209
torsareweak againstthe producerand the leadcreditorin the renegotiation.Thenthe lead
creditorpays the outside creditorsthe value of collateralland in orderto acquirethe outside creditors'rightto the land as seniorcreditors.(Itis efficientto makethe outside creditors seniorcreditorsin order to maximizethe borrowingfrom them.) After the outside
creditorsleave, the lead creditorand the producer-debtornegotiate.We assume the producerhas all the bargainingpower.Then,afterthe producerpays 0 fractionof maximum
outputand the value of collateralland to the lead creditor,the produceris allowed to complete the productionto obtain1-0 fractionof maximumoutput.The resourceallocation
is efficientex post. But the ex ante resourceallocationmay not be efficientbecauseof the
creditconstraintthatarisesfromthe possibilityof the defaultand negotiation.Weassume
thereis no reputationto enforcedebts becausethereis no record-keepingof the past defaults. Here, we apply Hart and Moore (1994)and Aghion, Hart, and Moore (1992)on
defaultand renegotiationbetween privateparties.
6. We assume there is no rentalmarketfor land becauseof a potentialhold-up problem
betweenlandlordsand tenants,and thatthe producerhas to buy land.
7. Wewill laterverify this inequalityholds in equilibrium.
8. Noting (13)has fourequations,we have fifteenequationsto determinefifteenendogenous variables.
9. Wehave eleven equations,as (25)containsfourequations,in additionto the definition
ofX.
10. This propertyholds alsoin Aoki, Benigno,and Kiyotaki(2006).Here, on the other
hand, the thresholdvalues (6 and 8*) depends upon the share of land out of gross output, K.
11. Thus,we verify r, < l/£ in the neighborhoodof the autarkysteady state as we claim
beforeequation(17).We can show this inequalitycontinuesto hold aftercapitalliberalizationfor 0 e (0, 0). When6 were higherthan6, TFP(definedby equation[23])would be
alreadyits maximumvalue, a beforeliberalization.
12. As we derived in section4.2, the dynamicsof the economyare given by the sequence
of (qt,ut, wt, rt,Kt,K't,Lt,h\, M,, M\, Z,, sf, xt, Zt+l,st+1)that satisfies (7), (8), (11), (13),
(14),(15),(16),(18),(19),(20),(21),and (22)fora given the initialland and debtsof the productive entrepreneursand foreign debt of the unproductiveentrepreneurs(Kt_lfBt, Bf,
andB*')
13. When 6 = 0.2, the steady state gross interestrate under autarkyis 1.079and higher
than r*. Therefore,when r* = 1.07, the directionof capital flow depends on the value
of e- capitalinflow with low 0 and capitaloutflow with high 0 (but not too high)- as in
figure4.1.
14. Herewe do not addresswhetherthe welfareeffectsof those who gain fromcapitalaccount liberalizationoffset the negative consequencesof those who lose, because it is not
easy to enforcethe redistributionin our economy of limited collateral.Also, even if possible, the redistributionwould changethe allocationsystematically.
15. Kleinand Olivei (1999)use indicatorsof financialintermediarydevelopmentas measuresof financialdevelopment.Theyfind thatthe deepeningof financialmarketsgoes beyond the level of financialconvergence.Theyalso show thattheirresultsaredrivenby the
inclusionin the cross-countrysampleby OrganizationforEconomicCooperationand Development(OECD)countries:indeed, when they restricttheiranalysisto non-OECDdevelopingcountriesthe linkbetweencapitalaccountliberalizationand financialdeepening
is weakened.
210
Aoki, Benigno, and Kiyotaki
16. See, also, Honkapohja et al. (2006) for the case of Finland, and Englund (1999) for the
case of Sweden. Ozatay and Sak (2002) point out the fragility of the banking sector as one
of the reasons behind the 2000-2001 crisis in Turkey.
17. Calvo and Reinhart (2000) classify banking crises using events-based criterion. Their
approach is motivated by the lack of high frequency data that capture when a banking crisis is underway. Using this approach, they identify several episodes of banking crisis.
18. For the Chilean experience, interest rate spreads more than tripled and the stock market declined by 37 percent between the second quarter of 1998 and the fourth quarter of
2002. Following the tightening in credit conditions, Chile also experienced a sudden stop
in external financial flows (see again Calvo and Talvi 2005).
19. The more than proportional increase in the domestic interest rate depends on the share
of land in production. The larger the share, the larger the increase in the domestic interest
rate.
20. See, for example, Sargent (1987), chapter 1.7
References
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of open economies. Journalof Monetary Economics51:1077-1106.
Aghion, P., O. Hart, and J. Moore. 1992. The economics of bankruptcy reform. Journalof
Law,Economics,and Organization8 (3): 523-46.
Aoki, K., G. Benigno, and N. Kiyotaki. 2006. Adjusting to Capital Account Liberalization.
London School of Economics and Princeton University. Unpublished Manuscript.
Bernard, A., J. Eaton, J. B. Jensen, and S. S. Kortum. 2003. Plants and productivity in international trade. AmericanEconomicReview 93 (4): 1268-90.
Caballero, R., E. Farhi, and P. O. Gourinchas. 2006. An equilibrium model of "global imbalances" and low interest rates. NBER Working Paper no. 11996. Cambridge, MA: National Bureau of Economic Research, February.
Caballero, R., and A. Krishnamurthy. 2001. International and domestic collateral constraints in a model of emerging market crises. Journalof Monetary Economics48:513-41.
Calvo, G., and C. Reinhart. 2000. When capital inflows come to a sudden stop: Consequences and policy options. In Key issues in reformof the internationalmonetaryandfinancial
system, P. Kenen and A. Swoboda, 175-201. Washington, D. G: International Monetary
Fund.
Calvo, G., and E. Talvi. 2005. Sudden stop, financial factors, and economic collapse in Latin
America: Learning from Argentina and Chile. NBER Working Paper no. 11153. Cambridge, MA: National Bureau of Economic Research, February.
Englund, P. 1999. The Swedish banking crisis: roots and consequences. Oxford Review of
EconomicPolicy 15 (3): 80-97.
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Henry, P. 2005. Capital account liberalization: Theory, evidence, and speculation. Stanford University Graduate School of Business Research Paper no. 1974.
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Appendix A
Section4.2
In this appendix,we describethe details of the entrepreneurs'optimization problemand derive equations (15),(20),and (21).
Consider the productive entrepreneurs.From the production function (2) and the minimized cost function (12), we observe that a/wfw*
Aoki, Benigno,and Kiyotaki
212
representsthe rate of returnof productionwithout borrowingfrom the
domesticlenders.Theproductiveentrepreneursborrowup to the limits
when rt < ol/w^w). By substitutingthe binding borrowing constraints
(4), (5), and the minimized cost (12)into the flow of funds constraint(6),
we can express the flow of funds constraintof the productiveentrepreneurs as
-
ct + e#[ 1
)
= zt,
(Al)
where
et = utkt+ wtlt + mt
representsthe minimized cost of productionand
- 2#= y#+ 9#*f-i b# fcf
representsthe net worth at the beginning of time t. Also, notice that the
binding borrowingconstraints(4) and (5) imply that zt+1can be rewritten as
(1-9)^
=
z-
=
f^<-
(A2)
(Herewe use (12)to obtainthe last expression).By using (Al) and (A2),
the flow of funds constraintis written as
z-
=
^7^Wz'~Cl)-
(A3)
Here the term (l-Q)/(u*w*/a-Q/rt) representsthe rate of returnof the
productive agents when they borrow up to the borrowinglimits. They
maximize (1) subjectto (A3).The firstordercondition is given by
1 _~
(1-6)
7t P^/a-e/r,EV
1
(A4)
Whenthe entrepreneurs^utility is logarithmic,it is well-known thatthe
consumptionfunctionof this type of optimizationproblemis given by.20
"
(A5)
ct = (1 p)zr
Then,(Al) and (A5)imply thatwhen they borrowup to the limits the investment of the productiveentrepreneursis given by
CapitalFlows and Asset Prices
et - utkt+ wtlt + mt =
^-.
213
(A6)
rt ufuti
As stated previously,this equationholds if a/u*w) > rr On the contrary,if the borrowing constraintsare not binding (i.e., the right-hand
side of equation(A6)is largerthanthe left hand side), a/uKtw)= rtholds.
Aggregationof (A6) over the productiveentrepreneursleads to equation
(15).Notice thatstZtin equation(15)representsthe aggregatenet worth
of the productiveentrepreneurs.Finally,(A3) shows that the excess returnof the productiveentrepreneursis given by equation(20).
Now turnto the unproductiveentrepreneurs.They specializein lending if (16) holds with strictinequality.On the contrary,(16) holds with
equalitywhen they produce.Similarlyto the case of the productiveentrepreneurs,we can express the flow of funds constraintof the unproductive entrepreneursas
z'M= rt{z\-c't),
(AT)
where z' and c', respectively,representthe net worth and consumption
of the unproductive agent. They maximize utility (1) subject to (A7).
Thereforethe consumptionequationis again given by
c; = (1-P)z;.
(A8)
Equations(A5)and (A8)implythatthe aggregateconsumptionis givenby
C, = (l-p)Z,,
(A9)
and the aggregatesaving is thereforegiven by ($Zr
Finally,by aggregating(A3), (AT),and using (20),the evolution of the
aggregatenet worth is given by equation(21).
Appendix B
Section4.3
This section derives the two thresholdvalues 0 and 0* discussed in section 4.3. (When 0 < 0, the unproductiveentrepreneursproduce under
the autarkysteady state. When 0 > 0*, then the productive entrepreneurs become unconstrained.)
214
Aoki, Benigno, and Kiyotaki
Derivation of Q
Forsimplicityof notation,express the aggregateinvestmentexpenditure as
uK + w1+*L + M + M' = E + Ef,
where E and E', respectively,denote the aggregateinvestmentexpenditureof the productiveand unproductiveentrepreneurs.Fromequations
(24)and (26),we obtain
E + E' = (5Z- Ik.
(Bl)
Under the production function (2), cost minimizationimplies that the
expenditureon land uKis given by a fractionk of the total expenditure
(see equation [25]).This implies that
K = -(E + E').
(B2)
Substituting(B2)into the right-handside of (Bl) and solving for E + E',
one obtains
Q7
E + E' =
!-
JT"-
(B3)
Here we used equation (24) in order to simplify the right-handside of
(B3).Fromthis equation,we observethatwhen the unproductiveentrepreneursproduce (E' > 0),
E<
?5_.
(B4)
Notice that r = y/(uKwx)when E' > 0 (see equation [16]).In this case,
from equation (15),E is given by
psZ
Substituting(B5)into (B4),we obtain
7
r-1
215
CapitalFlowsandAssetPrices
Notice thats is given by X/x. From(16)and (20)evaluated at the steady
state,x is given by
a- y
(B7)
x-T^'
and r is given by (27)as
By using (B7)and (B8),we can express (B6)in terms of X as
G(X)- 0(k - 1)X2
+ 1 + P(k - 1) + -^^p
X - ^-
^-(1- P) < 0.
(B9)
In addition to this, for q to be finite in the steady state, we need r > 1.
From(B8),this requires
X < P"1- 1.
(BIO)
Since function G(X) satisfies G(p"1- 1) >_0 and G(0) < 0, there exists
unique X such that 0 < X < p"1- 1 and G(X)= 0.
What we have shown so far is that E' > 0 implies G(X) < 0 in the
autarky steady state. Finally, from equation (28), we observe that if
F[X,(a - 7)/(7 - 0a)] > 0, we have G(X)< 0. It is shown thatF[X,(a - y)/
(7 - 0a)] >0 holds if
(l-8)X + n8
a-7
_7
/ x
Equation(Bll) defines the threshold value 6 discussed in section 4.3.
Equation (B9) implies that dX/dn < 0, and (Bll) implies dQ/dX > 0,
therefored0/dK<O.
Derivation of Q
In the steady state where the productive entrepreneurs are unconstrained,r = a/(uKwx).Then,fromequation(20),the excess returnx = 0
in this steady state.Then, (27)and (28)imply that r = P"1.Togetherwith
these facts,the transitionequationof stimplies thats = n/(l + n), which
is equal to the fractionof the number of the productive entrepreneurs
(see note 3). The productiveentrepreneursare unconstrainedwhen
216
Aoki, Benigno,and Kiyotaki
n
psZ
=
E<^T^r uKwk
Pl + nZ
~^r-
(B12)
Since E' = 0 in this steady state, equation (B3)becomes
pz
pz
r-1
(1-P)
where we used r = P"1.By substituting(B13)into (B12)and solving for
6, we obtain
e>e-1-TT7(1
+
T^?4
This defines 0* in section 4.3.
<B14»