DP2016-34

Ca pital Controls a nd Fina ncial Frictions
in a Sma ll Open Economy
Shigeto KITANO
Kenya TAKAKU
Revised May 22, 2017

Capital Controls and Financial Frictions in a
Small Open Economy∗
Shigeto Kitano†

Kenya Takaku‡

Abstract
We develop a small open economy model with financial frictions between
domestic banks and foreign investors, and examine the welfare-improving
eﬀect of capital controls. We show that capital controls are eﬀective in
addressing the amplification eﬀect due to financial frictions. As the degreeof financial frictions increases, the welfare-improving eﬀect of capital controls
becomes larger and a more aggressive policy rule is appropriate. Comparing
two economies, one with and one without “liability dollarization,” we alsofind that the welfare-improving eﬀect of capital controls is larger in thepresence of “liability dollarization,” and the diﬀerence between the eﬀects
becomes larger as the degree of financial frictions increases.

Keywords: capital control; financial frictions; financial intermediaries; balance sheets; small open economy; liability dollarization; DSGE;
welfare.
JEL Classification: E69, F32, F38, F41.

∗

Earlier versions of the paper were presented at the Macroeconomic Workshop at the University of Tokyo, the Japanese Economic Association annual meeting at Waseda University, theJapan Society of Monetary Economics Chubu Area Study Group at Chukyo University, and the
9th Biennial Conference of Hong Kong Economic Association at the University of Hong Kong.
We are extremely grateful to the referee for the insightful comments that have significantly improved the paper. We are also grateful to Ryuzo Miyao, Kosuke Aoki, Kenichi Ueda, Takayuki
Tsuruga, Eiji Okano, and Hao Jin for their valuable comments. Any remaining errors are ours.
This work was supported by KAKENHI (16K03741).
†
Professor, RIEB, Kobe University, 2-1, Rokkodai, Nada, Kobe, 657-8501 Japan, E-mail:kitano@rieb.kobe-u.ac.jp.
‡
Associate Professor, Faculty of International Studies, Hiroshima City University, 3-41, Ozuka-Higashi, Asa-Minami-Ku, Hiroshima, 731-3194, Japan, E-mail: takaku@hiroshimacu.ac.jp1

1

Introduction

As discussed at the G20 summit in February 2016, possible massive capital outflows
from emerging economies, due to prospective increases in the US policy rate, area growing concern among policymakers. The possibility of capital outflows fromemerging economies is preceded by massive inflows to emerging economies dueto the low interest rate policies in developed countries after the global financial
crisis.1 The vulnerability of emerging economies to foreign interest shocks has
been documented by many previous studies (e.g., Calvo et al. (1993), Dooley
et al. (1996), Fernandez-Arias (1996), and Frankel and Okongwu (1996)). An
increasing number of policymakers and economists, including the IMF, think that
capital controls may be able to mitigate the vulnerability of emerging economies
to external shocks.2 Some emerging economies (Brazil, Taiwan, South Korea, andThailand) have indeed responded to the instability by imposing capital controls.3
Against this background, research on capital control policies has regained focus
and been extended to a variety of new directions.4
Related Literature.—A strand of the literature focuses on pecuniary externalities associated with financial crises, and provides a rationale for prudential capital controls to internalize the externalities and prevent excessive borrowing (e.g.,
Jeanne and Korinek (2010), Bianchi (2011), Jeanne et al. (2012), and Brunnermeier and Sannikov (2015)).5 Another strand studies the eﬀects of capital controls
in the presence of nominal rigidities. Developing a disequilibrium model featuring a downward rigid wage and an exchange rate peg, Schmitt-Grohé and Uribe(2016) show that capital controls reduce unemployment and can be an eﬀective
instrument for macroeconomic stabilization. Farhi and Werning (2012) show that
under the peg, capital controls are eﬀective for addressing some shocks, particularly
country-specific risk-premium shocks. They also show that even if the exchange
rate is not fixed, capital controls may be optimal if wages and prices are sticky.
More eﬀects of capital controls as a policy tool have been rigorously examined1

For literature related to issues and policies associated with capital inflows, see Montiel (2014).
For details, see Ostry et al. (2010) and Ostry et al. (2012).
3
For details, see for example, Jongwanich and Kohpaiboon (2012), Ahmed and Zlate (2014),
and Forbes et al. (2016).
4
Capital controls are not a new policy instrument. Already before the recent global financial
crisis, capital controls have been widely discussed, both theoretically and empirically. Theoreticalanalyses on capital controls have been mainly related to the issue of currency crises. Empiricalanalyses of capital controls have been conducted mainly to test whether the presence of capital
account liberalization (or capital controls) is correlated with higher economic growth. For earlier
literature on capital controls, see Kitano (2011).
5
Harberger (1986) points out that foreign borrowing is accompanied with externalities, which
can be internalized by a corrective tax on foreign borrowing. He identifies the externality as thecountry risk premium.
2

2

from a broader perspective. Among many studies, De Paoli and Lipinska (2013)
examine capital controls as a policy tool to manage an economy’s terms of trade.
They show that although capital controls limit international risk sharing, individual countries may benefit from their terms of trade manipulation. Their findings
suggest a possibility of welfare gains from international policy coordination. Davisand Presno (2014) examine welfare gains from capital controls as an additional
tool under flexible exchange rates. They show that the benefits of capital controls
are present even when an optimal monetary policy is employed. Liu and Spiegel(2015) examine the eﬀectiveness and welfare implications of capital controls andsterilization in a small open economy with imperfect international asset substitutability. They show that capital controls and sterilization are complementarypolicies.6 Agénor and Jia (2015) focus on the relationship between countercyclicalcapital controls and reserve requirement rules in cross-border bank borrowing.7
Our study also belongs to the growing body of literature that examines thepossible eﬀects of capital controls as a policy tool. However, our study diﬀers fromthe existing literature in that we focus specifically on the relationship between the
degree of financial frictions and the eﬀectiveness of capital controls. To the bestof our knowledge, this paper is the first to show how the welfare eﬀects of capital
controls depend on the degree of financial frictions between banks and foreign
investors. We show that when the degree of financial frictions is higher, capital
controls are more welfare improving and tighter capital controls are appropriate.
We also show that the welfare-improving eﬀect of capital controls is larger in thepresence of liability dollarization.
Previous studies on financial frictions emphasized credit constraints faced by
non-financial borrowers (e.g., Bernanke et al. (1999) and Lee and Rhee (2013)).
After the global financial crisis, the researchers focused on balance sheets of financial intermediaries, such as banks (e.g., Gertler and Kiyotaki (2010) and Gertler
and Karadi (2011)). As is well known, the share of financial intermediaries suchas banks is more significant in the financial sector in emerging economies than it
is in developed economies. Therefore, we develop a small open economy modelwith financial frictions à la Gertler and Kiyotaki (2010) and Gertler and Karadi(2011).8 Banks fund capital investments using their net worth, obtaining deposits
6

Chang et al. (2015) show that under capital controls and pegs, optimal Ramsey policy
involves the trade oﬀ between inflation and sterilization costs.
7
Kitano and Takaku (2015) compare the welfare implications of an optimal capital control
policy under fixed exchange rates and an optimal monetary policy under flexible exchange rates.
They show that in an economy with a financial accelerator, an optimal capital control policy
under fixed exchange rates is superior to an optimal monetary policy under flexible exchange
rates, and vice versa in an economy without a financial accelerator.
8
Aoki et al. (2016), Ghilardi and Peiris (2016), and Nuguer and Cuadra (2016) also develop
open economy models with financial frictions à la Gertler and Kiyotaki (2010) and Gertler and3

from local households, and borrowing from foreign investors. In this study, we
focus on financial frictions between banks and foreign investors, and examine how
the eﬀectiveness of capital controls depends on the degree of the financial frictions.
We show that capital controls are eﬀective in addressing the amplification eﬀect
due to financial frictions. As the degree of financial frictions increases, the welfareimproving eﬀect of capital controls becomes larger and a more aggressive policy
rule is appropriate.
In our model, banks are assumed to face the “liability dollarization” problem,
and the banks’ liabilities are denominated in foreign currency.9 When the banks’liabilities are “dollarized,” exchange rate behavior may exacerbate the eﬀect offinancial frictions on a small open economy through their balance sheet. We also
examine the case where the economy does not suﬀer from “liability dollarization.”In the “no liability dollarization” economy, there is no direct negative valuationeﬀect of the exchange rate deterioration on the bank’s balance sheet. By comparing
these two cases, we show that the welfare-improving eﬀect of capital controls islarger in the presence of “liability dollarization,” and the diﬀerence between theeﬀects becomes larger as the degree of financial frictions is higher.
The remainder of the paper is organized as follows. In Section 2, we present asmall open economy model with financial frictions à la Gertler and Kiyotaki (2010)
and Gertler and Karadi (2011), in combination with liability dollarization. In Section 3, we examine the welfare-improving eﬀect of capital controls in a small open
economy under diﬀerent degrees of financial frictions. We also compare the welfareimproving eﬀect of capital controls in the economy with “liability dollarization” tothat without “liability dollarization.” In Section 4, we check the robustness of ourresults for diﬀerent values of the key parameters. Our conclusions are presented
in Section 5.

2

Model

The model framework is a real business cycle model of a small open economy. We
incorporate financial frictions à la Gertler and Karadi (2011) and Gertler and Kiyotaki (2010) into a small open economy model. The small open economy consistsof households, banks, non-financial firms (goods producers and capital producers),
and the government. Banks raise funds using their net worth, obtaining deposits
from local households, and borrowing in international financial markets in order
Karadi (2011), although for diﬀerent purposes. The two former are a New Keynesian small open
economy model and the latter is a two-country model.
9
The diﬃculty that emerging economies face in borrowing abroad in their own currencies
is also referred to as “original sin” (for details, see Eichengreen and Hausmann (1999), andEichengreen and Hausmann (2005)).

4

to finance domestic non-financial firms. The government imposes capital controls
to regulate the banks’ foreign borrowing.

2.1

Households

Following Gertler and Kiyotaki (2010) and Gertler and Karadi (2011), we assume
there are two types of members within a representative household: a fraction 1 − fof workers and a fraction f of bankers. Workers supply labor and return theirwages to the household. Each banker manages a bank and returns dividends tothe household. There is a perfect consumption insurance within the household.
For each period, a banker remains a banker in the next period with probability
σ. While (1 − σ)f bankers exit and become workers, the same number of workers
become bankers. The fraction of each type of members remains constant overtime. Exiting bankers transfer their retained earnings to the household, whereas
new bankers receive start-up funds from the household.
The household maximizes the following expected lifetime utility:
E0∞∑

β t U (Ct , Lt ),

(1)

t=0

where
U (Ct , Lt ) =(Ct − φχ Lφt )1−γ − 1
1−γ

.

(2)

Herein, E0 denotes the mathematical expectations operator conditional on information available at time 0, β ∈ (0, 1) is the discount factor, Ct signifies a composite
consumption index, Lt represents labor eﬀort, γ (> 0) is the inverse of intertemporal elasticity of substitution, χ (> 0) is the labor coeﬃcient, and φ (> 1) is thecurvature parameter on labor. We use the so-called GHH preference introducedby Greenwood et al. (1988), which has been used in many open economy models.10
The composite consumption index Ct is given by
[

1
ι

ι−1
ι

1
ι

ι−1
ι

Ct ≡ (1 − υ) CH,t + υ CF,t

ι
] ι−1

,

(3)

where ι (> 0) is the elasticity of substitution between domestic and imported goods(i.e., trade elasticity), and υ ∈ (0, 1) is the degree of trade openness (i.e., inverse
degree of home bias). Households consume domestic goods (CH,t ) and foreign
goods (CF,t ). The optimal expenditure allocation between domestic and imported
10

For details on the GHH preference, see for example, Mendoza (1991) and Neumeyer andPerri (2005).

5

goods gives the following demand functions of CH,t and CF,t :(PH,tCH,t = (1 − υ)
Pt

)−ι

(

Ct ;

PF,t
CF,t = υ
Pt

)−ι
Ct ,

(4)

where PH,t is the domestic price, PF,t is the import price, and Pt represents theconsumer price index (CPI):
Pt ≡

[

1−ι
1−ι
(1 − υ)PH,t+ υPF,t

1
] 1−ι

.

(5)

From Eqs. (4) and (5), we obtain
PH,t CH,t + PF,t CF,t = Pt Ct .

(6)

A household’s budget constraint in period t is given as
Ct + Th,t + Dt = Rt Dt−1 + wt Lt + Πft b ,(7)where Th,t is lump-sum taxes, Dt is bank deposits, Rt is the gross return on bankdeposits, wt is the real wage, and Πft b denotes dividends from financial and nonfinancial firms.
The optimality conditions associated with the household-maximization problem are given by(χ )−γCt − Lφt= ϱt ,(8)φχLφ−1= wt ,t(9)

1 = Et βΛt,t+1 Rt+1 ,

(10)

and
where Λt,t+1 ≡ β ϱt+1
.
ϱt

2.2

Banks

Banks raise funds using their net worth, obtaining deposits from households, andborrowing from foreign investors, and lend them to goods producers. The balance
sheet of a bank is given by
Qt st = nt + et bt + dt ,(11)

where st is the quantity of financial claims on goods producers, Qt is the price ofclaims, nt is the net worth, bt is foreign debts, et is the real exchange rate, and dt
6

is deposits from domestic households.
The net worth of the bank is the diﬀerence between earnings on assets andinterest payments on foreign debts and deposits. Under capital controls, a tax is
imposed on the bank’s foreign borrowing. The evolution of the bank’s net worth
is then given asnt = Rk,t Qt−1 st−1 − (1 + Tt∗ )Rb,t et−1 bt−1 − Rt dt−1 + ζt ,(12)

where Rkt is the gross return on assets, Tt∗ is the tax rate on the bank’s foreign
currency debt, Rbt is the gross interest rate on foreign debts in terms of domestic
currency, Rt is the gross interest rate on deposits, and ζt is a lump-sum transferfrom the government to a bank.
The bank maximizes the present discounted value of future dividends, taking
into account of the probability of exiting the banking industry. The value of thebank at the end of period t is given by
Vt = Et∞∑(1 − σ)σ i−1 Λt,t+i nt+i .

(13)

i=1

There is a possibility for bankers to divert funds. The bank may transfer somefraction of “divertable” assets to the household. However, if a bank diverts assets,
it is forced into bankruptcy. While a fraction θ of assets financed by deposits (dt )and net worth (nt ) is assumed to be “divertable,” a fraction θ∗ of assets financed
by foreign borrowing (et bt ) is assumed to be “divertable.” We assume that theassets financed by foreign borrowing are easier to divert than those financed bydeposits and net worth (i.e., θ∗ > θ). Thus, the following incentive constraint must
hold for lenders to be willing to supply funds to the banker:
Vt (st , bt , dt ) ≥ θ(dt + nt ) + θ∗ et bt .

(14)

The value of a bank, Vt , must be not less than a bank’s benefit from diverting
funds, θ(dt + nt ) + θ∗ et bt , so that households and foreign investors are willing to
supply funds to a bank. For tractability, we set thatθ∗ = (1 + ω)θ,(15)

where ω > 0. If ω = 0, foreign borrowing has the same degree of frictions as
domestic deposits. A higher value of ω(> 0) indicates a higher degree of financial
frictions in foreign borrowing, because it implies that the asset financed by foreign
borrowing is easier to divert than that financed by domestic deposits. Therefore,
the parameter ω indexes the degree of financial frictions between banks and foreign
investors. From the bank’s balance sheet (11) and Eq.(15), we can rewrite the7right-hand side of Eq.(14) asθ(dt + nt ) + θ∗ et bt = θ(dt + nt ) + θ(1 + ω)et bt = θ(Qt st + ωet bt ).

(16)

Since the “divertable” amount of funds financed by foreign borrowing must not begreater than the total amount of the fund financed by foreign borrowing, it must
be that et bt ≥ θ(1 + ω)et bt , and then the upper limit for ω exists (i.e., 1θ − 1 ≥ ω).
The value of the bank at the end of period t − 1 satisfies the Bellman equation:{}
Vt−1 (st−1 , bt−1 , dt−1 ) = Et−1 Λt−1,t (1 − σ)nt + σ max Vt (st , bt , dt ) .
(17)
st ,bt ,dt

We guess and verify that the value function is linear in st , bt , and dt :Vt (st , bt , dt ) = νs,t st − νb,t bt − νt dt ,(18)

where νs,t is the marginal value of assets, νb,t is the marginal cost of internationalborrowing, and νt is the marginal cost of deposits. Maximizing the value function(18) subject to the incentive constraint (14) (and (16)), we obtain the following
first-order conditions:)(νb,t(1 + λt ) = θωλt ,
(19)
νt −
et
(
)
νs,t νb,t−(1 + λt ) = θ(1 + ω)λt ,
(20)
Qt
et
and

[

(
θ−

νs,t
− νt
Qt

)]

)]
(
νb,t
e t b t = ν t nt ,Qt st + θω − νt −
et
[

(21)

where λt is the Lagrange multiplier for the incentive constraint (14). From theseν
conditions and defining µb,t ≡ νt − eb,tt and µt ≡ νQs,tt − νt , we obtainµb,t = ωµt ,andQt st = ϕt nt −
where

ϕt
e t bt ,
ϕb,t

(22)

(23)

ϕt ≡

νt
,
θ − µt(24)

ϕb,t ≡νt.
θω − µb,t

(25)

and

8

By combining the conjectured value function with with the Bellman equation (17)and using (12), we can verify that the value function is linear in (st , bt , dt ) if νt ,µt , and µb,t satisfy
νt = Et Λt,t+1 Ωt+1 Rt+1 ,
(26)

and

µt = Et Λt,t+1 Ωt+1 (Rk,t+1 − Rt+1 ),(27)∗µb,t = Et Λt,t+1 Ωt+1 [Rt+1 − (1 + Tt+1
)Rb,t+1 ],(28)Ωt ≡ (1 − σ) + σ(ϕt µt + νt ).

(29)

where
Since ϕt and ϕb,t are independent of bank-specific factors, we can aggregate
across banks. It follows from Eq.(23) that
Nt =

1
1
Qt St +
et Bt ,
ϕt
ϕb,t

(30)

where capital letters indicate aggregate variables. By using Eqs.(22), (24), and(25), we can rewrite Eq.(30) as
Qt St + ωet Bt = ϕt Nt .

(31)

Substituting (31) into the aggregate balance sheet (Qt St = Nt + et Bt + Dt ), we
obtain the aggregate deposit:
Dt = −(1 + ω)et Bt + (ϕt − 1)Nt .

(32)

In each period, the fraction σ of banks continue to operate in the next period.
As we will argue in Section 2.5, the government returns the tax revenue on capital
controls to banks as a lump-sum transfer in each period (i.e., ζt = Tt∗ Rb,t et−1 bt−1 ).
Therefore, it follows from Eq.(12) that the existing bank’s net worth Net is given
byNe,t = σ(Rk,t Qt−1 St−1 − Rb,t et−1 Bt−1 − Rt Dt−1 ).
(33)
Following previous related studies, we assume that the household transfers thefraction ξ/(1 − σ) of the total final period assets of exiting bankers to its enteringbankers. Thus, the new bank’s net worth is given by
Nn,t = ξRk,t Qt−1 St−1 .

(34)

The total net worth Nt is the sum of the net worth of existing banks Ne,t and thatof new banks Nn,t :Nt = Ne,t + Nn,t .
(35)
9

Substituting (33) and (34) into (35), we obtain the evolution of Nt as follows:
Nt = (σ + ξ)Rk,t Qt−1 St−1 − σRb,t et−1 Bt−1 − σRt Dt−1 .

2.3

(36)

Goods producers

Competitive goods producers produce domestic goods using capital and labor:,
Yt = Ktα L1−αt(37)where Yt is domestic output and Kt is capital. Goods producers finance theircapital acquisition by obtaining funds from banks:
Qt Kt+1 = Qt St .

(38)

We assume that goods producers do not face financial frictions when they obtainfunds from banks, because we focus on financial frictions on banks. From thefirst-order conditions associated with the firm’s optimization, we have
(1 − α)PH,t Yt= wt .
Pt Lt(39)

Since competitive firms earn zero profits, the expected gross return to holding aunit of capital from t to t + 1 is given by
Rk,t+1 =PH,t Yt+1
α Kt+1 + Qt+1 (1 − δ)
Pt

Qt

,

(40)

where δ is the depreciation rate of capital.

2.4

Capital producers

Similarly to Ct in (3), It is composed of domestic and imported goods:
ι
[
ι−1
ι−1 ]
1
1
ι−1
ι
ι
ι
ι
It ≡ (1 − υ) IH,t + υ IF,t.

(41)

The optimal allocation of expenditures between domestic and imported goods
implies that
(
)−ι
)−ι
(
PF,t
PH,t
It ;
IF,t = υIt .
(42)
IH,t = (1 − υ)
Pt
Pt

10

From Eqs.(5) and (42), we have
PH,t IH,t + PF,t IF,t = Pt It .

(43)

Capital producers make new capital subject to adjustment costs on investment.
Therefore, the capital producer’s optimization problem is given by
max Et
It

∞
∑

[

{

(

Λt,t+i Qt+i It+i − 1 + f

i=0

It+i

}

)]

It+i−1

It+i ,(44)

where f (x) = η2i (x − 1)2 is the function of adjustment costs on investment. From
the first-order condition for It , we have that
(
)
(
)
(
)2 (
)
It
It ′ It
It+1′ It+1
Qt = 1 + f+
f− Et Λt,t+1
f
.
(45)
It−1
It−1
It−1
It
It

2.5

Government

As we argue in Section 2.2, we assume that the government returns the tax revenue
on capital controls to banks as a lump-sum transfer in each period (i.e., ζt =Tt∗ Rb,t et−1 bt−1 ). The government’s budget constraint in period t is given by
Gt + Zt = Tt∗ Rb,t et−1 Bt−1 + Th,t ,(46)

where Gt is government spending and Zt is the aggregate variable for ζt . Here, Gt
consists of domestic and imported goods:
ι
[
ι−1
ι−1 ]
1
1
ι−1
ι
+ υ ι GF,tι
Gt ≡ (1 − υ) ι GH,t.

Similarly to Ct and It , it holds that
(
)−ι
PH,t
Gt ;
GH,t = (1 − υ)
Pt

(

PF,t
GF,t = υ
Pt

(47)

)−ι
Gt .

(48)

From Eqs.(5) and (48), we have
PH,t GH,t + PF,t GF,t = Pt Gt .

(49)

We assume that Gt is fixed at its steady state level G. Furthermore, as argued
above, the government returns the tax revenue on capital controls to banks as a
lump-sum transfer. In the government’s budget constraint (46), this implies that
Th,t is also constant. In other words, the role of the government can be reduced,
11

theoretically, to simple taxation of capital flows and return of the collected revenue
to the banks.
We consider a simple rule for capital controls, as follows:
[ (
)
(
)]
eB
et−1 Bt−1∗
Tt = τ log
− log
,
(50)
Qt−1 St−1
QS
eB
where QS
denotes the steady-state level of QettBStt . The capital control rule implies
that the government raises (reduces) the tax rate on the bank’s foreign borrowing
when the fraction of assets financed by foreign borrowing increases (decreases).
This rule is intended to discourage banks from borrowing abroad when banks rely
excessively on foreign creditors. The low interest rates in developed countries after
the recent financial crisis caused a surge in capital inflows into emerging economies.
An abrupt reversal of capital flows may ensue from a surge in capital inflows into
emerging economies. As argued in the introduction, for this reason, some emerging
countries have recently responded to the capital inflows by imposing capital controls. Therefore, we think that the rule denoted as Eq.(50) is appropriate as capital
account restrictions to prevent massive capital inflows to emerging countries.11

2.6International relative prices

By the definition of the terms of trade, we have
qt ≡

PF,t
P∗
= t ,
PH,t
PH,t

(51)

where Pt∗ denotes the price index in the foreign country (in terms of the domestic
currency).12 From the CPI (5) and Eq.(51), we obtaing(qt ) ≡1Pt= [(1 − υ) + υqt1−ι ] 1−ι .
PH,t

(52)

From (51) and (52), the real exchange rate et is given by a function of the termsof trade qt :P∗
qtet ≡ t =.
(53)
Pt
g(qt )
The assumption of a small open economy (i.e., the home country is small enoughnot to aﬀect the price in the foreign country) implies the asymmetric home bias
11

We[ confirm
that )our main
results hold when we employ a diﬀerent form of rules such as(( )]log et−1 Bt−1 − log eB .
Without loss of generality, we assume that PF,t = Pt∗ because the home country is smallenough not to aﬀect the price in the foreign country.

Tt∗ = τ1212

in preference so that the purchasing power parity does not hold (i.e., et ̸= 1).

2.7

Equilibrium

In each period, the domestic goods market must clear. It follows that
Yt = (1 − υ)g(qt )ι (Ct + It + Γt + Gt ) + qt EXt ,
(54)
(
)
It
where Γt ≡ f It−1
It is the adjustment costs on investment, and EXt is the exogenous demand for exports. Eq.(54) indicates that demand for domestic goods comesfrom consumption, investment, its adjustment cost, government expenditure, andexports.
The capital accumulation process is given by
Kt+1 = (1 − δ)Kt + It .

(55)

The trade balance in terms of the CPI is given by
T Bt ≡Yt− Ct − It − Gt − Γt .
g(qt )(56)

Thus, the evolution of foreign debt Bt is given by∗
Bt = Rb,t
Bt−1 −

T Bt
,
et

(57)

∗
where Rb,t
is the bank’s (gross) foreign borrowing rate in terms of foreign currency.
Then, the current account is given by

CAt = −Bt + Bt−1 .

(58)∗
The bank’s (gross) foreign borrowing rate Rb,t
is assumed to be the sum of∗
the world (gross) interest rate Rt , which is an exogenous shock, and a country
premium that is increasing in the ratio of foreign debt to output, as follows:[ {}]qt Bt qB
∗
∗
−
−1 ,
(59)
Rb,t+1 = Rt+1 + ψ exp
Yt
Y

where qB
is the steady-state level of qtYBt t . As in many previous studies, the countryYpremium that is increasing in foreign debt is implemented to induce the stationarityof foreign debt. The world (gross) interest rate Rt∗ is assumed to follow the AR(1)13process:
∗

∗

∗
R
2
log Rt+1= (1 − ρR∗ ) log R∗ + ρR∗ log Rt∗ + εR
t+1 , εt+1 ∼ i.i.d. N (0, σR∗ ).

(60)∗
Rb,t is in terms of domestic currency, while Rb,t
is in terms of foreign currency.
∗
Therefore, the relationship between Rb,t and Rb,t is as follows:∗
Rb,t+1 = Rb,t+1

2.8

et+1
.
et

(61)

Calibration

We choose the standard parameter values given in the relevant literature for calibration, which are summarized in Table 1. For the parameters for households, we
set the discount factor β and the inverse of intertemporal elasticity of substitution
γ to 0.98 and 2, respectively, as in Aguiar and Gopinath (2007). The curvatureparameter on labor φ is set to 1.455, as in Mendoza (1991). The labor coeﬃcientχ is chosen to generate the steady-state labor hours (L) of 0.2.
Following Gertler and Kiyotaki (2010), Gertler and Karadi (2011), and Gertler
et al. (2012), we set the parameters for banks as follows. The fraction of divertableassets, θ, and the transfer to entering banks, ξ, are set to hit the two targets ofa steady-state interest rate spread of 100 basis points per year and a steady-stateleverage ratio of 4. The survival rate of banks σ is chosen to generate an average
horizon of banks of eight years.
The parameters related to the open economy are chosen as follows. The elasticity of substitution between domestic and imported goods ι is set to 1.5, as inRavenna and Natalucci (2008). Following Cook (2004), we set the degree of openness υ to 0.28. The steady-state ratio of foreign debt to GDP, YB , is set to 0.4
as in Devereux et al. (2006). The parameter for the country-specific interest rate
premium ψ is set to 0.03, which fits between 0.0075 in Unsal (2013) and 0.05 in
Akinci and Queraltó (2014). We set the degree of financial frictions, ω, to 0.5 in
the benchmark case. The persistence and the standard deviation of the foreigninterest rate shock, ρR∗ and σR∗ , are set to 0.98 and 0.0025, respectively.
The other parameters are set as in Gertler and Kiyotaki (2010). The steadystate value of the ratio of government expenditure to GDP, YG , is set to 0.2. For
the parameters for goods producers and capital producers, the eﬀective capitalshare α, the inverse elasticity of net investment to the price of capital ηi , and thedepreciation rate of capital δ are set to 0.33, 1.5, and 0.025, respectively.

14

Table 1: Calibration.

Parameters

Value

β
γ
φ
χ
σ
θ
ξ

0.98
2
1.455
4.060
0.96850.391
5.23 × 10−4
0.4
1.5
0.28
0.5
0.03
0.98
0.0025
0.2
1.5
0.33
0.025

B
Y

ι
υ
ω
ψ
ρR ∗
σR ∗
G
Y

ηi
α
δ

Discount factor
Inverse of intertemporal elasticity of substitution
Curvature parameter on labor
Labor coeﬃcient
Survival rate of banks
Fraction of divertable assets
Transfer to entering bankers
Steady-state ratio of foreign debt to GDP
Elasticity of substitution between domestic and imported goods
Degree of openness
Degree of financial frictions
Parameter for country-specific interest rate premium
Persistence: foreign interest rate shockStandard deviation: foreign interest rate shock
Steady-state ratio of government expenditure to GDP
Elasticity of the price of capital to investment
Eﬀective capital share
Depreciation rate of capital

15

2.9

WelfareWe conduct policy evaluations by computing the welfare benefit of a particular
capital control rule relative to a no-capital control case. The perturbation method
presented by Schmitt-Grohé and Uribe (2004) is used to perform a second-orderapproximation of the model.13 Following Schmitt-Grohé and Uribe (2006), we
consider expected welfare conditional on the initial state being the non-stochastic
steady state. We define the welfare associated with a particular value of τ in thecapital control rule (50) conditional on the non-stochastic steady states as
W0 ≡ E0∞∑

β t U (Ct , Lt ) = E0

t=0

∞
∑

β t U ((1 + ϵ)C, L),

(62)

t=0

where C and L denote their non-stochastic steady states. We evaluate the welfareimproving eﬀect of the capital control rule (50) by comparing ϵ associated witheach value of τ to that in the no-capital control case (i.e., τ = 0).

3

Results

This section presents the main results of our analysis. Before examining thewelfare-improving eﬀect of capital controls, we show how the diﬀerence in the
degrees of financial frictions aﬀects the impulse responses of main variables. As
we argued in Section 1, the eﬀect of prospective increases in the US policy rateon emerging economies is a growing concern among policymakers. Therefore, we
consider an increase in foreign interest rates as the exogenous shock.

3.1

Impulse responses of main variables under diﬀerent
degrees of financial frictions

The impulse responses of the main variables to an exogenous increase in foreigninterest rates under diﬀerent degrees of financial frictions are shown in Figure 1.
The initiating disturbance is a 1% unanticipated annual increase in foreign interest
rates R∗ . The bold curve in Figure 1 represents the benchmark case of ω = 0.5.
The dotted curve and thin curve in Figure 1 represent the case of a higher degreeof financial frictions (ω = 0.99) and that of a lower degree of financial frictions(ω = 0.01), respectively.
13

Kim and Kim (2003) show that second-order solutions are necessary, because conventional
linearization may generate spurious welfare reversals when long-run distortions exist in the model.
The second-order computation is conducted with Dynare. See Adjemian et al. (2011) for details
on Dynare.

16An exogenous rise in foreign interest rates increases the bank’s foreign borrowing rate Rb and leads to a decline in the bank net worth N . Since it tightens
the bank’s borrowing constraint, the decline in the net worth reduces bank assets
S(= K) (or capital). The decline in capital leads to a drop in output Y andinvestment I, which causes a decline in the price of capital Q. The drop in theprice of capital exacerbates a decline in the value of capital QK (or bank assets).
The decline in the value of bank assets QS causes a further decline in the bank
net worth. Therefore, the eﬀects of an exogenous increase in foreign interest rates
on output and the other main variables are amplified through the bank’s balance
sheet.
Comparing the three cases of ω = 0.01, ω = 0.5, and ω = 0.99 in Figure 1,
we can see that the negative eﬀects of an exogenous increase in foreign interest
rates on Y , C, I, K, and L become larger as the degree of financial frictions
increases (i.e., ω increases). The size of an increase in the spread between the
expected return on capital and that in the riskless rate E[Rk ] − R also becomeslarger as the degree of financial frictions increases. A larger drop in investment I
compared to that in output Y causes a shortage in the demand for domestic goods
and a depreciation of the real exchange rate e, which leads to an improvementin the current account (to output ratio) CA/Y . The size of the improvement in
the current account (to output ratio) CA/Y (i.e., capital outflow) becomes larger
as the degree of financial frictions increases. As the degree of financial frictions
increases, the size of the depreciation of the real exchange rate e increases, whichraises the value of foreign debt in terms of domestic currency eB and magnifies thebank’s balance sheet eﬀect. Therefore, we can say that as the degree of financial
frictions increases, the size of the economy’s fluctuation due to the exogenous
foreign shock tends to increase.

17

E[RK]-R

4.5

Y

-0.1

= 0.01= 0.50= 0.99

4
3.5

C

0.2

-0.2

0

from ss

-0.3
-0.2

2

%

1.5

-0.4

from ss

Annualized %

2.5

-0.5

= 0.01= 0.50= 0.99-0.6

1%

from ss

3

-0.4

-0.6

-0.8

-0.7
0.5

-0.5

-0.9
0

5

10

15

2

20

25

30

35

40

= 0.01= 0.50= 0.99

-1

-0.8

0

-1.2
0

5

10

15

20

25

30

35

40

0

5

10

15

20

Quarters

Quarters

Quarters

I

K

L

0

0

= 0.01= 0.50= 0.99

-0.2

0

25

30

35

40

-0.1
-0.2

-0.4
-0.3

%

-8

%

= 0.01= 0.50= 0.99-6-0.6

from ss

-4

-0.8

%

from ss

from ss

-2

-1

-0.4
-0.5
-0.6
-0.7

-1.2
-0.8
-10

-1.4

-1.6

-12
0

5

10

15

1

20

25

30

35

-1
0

40

= 0.01= 0.50= 0.99

-0.9

5

10

15

20

25

30

35

40

0

5

10

15

20

Quarters

Quarters

Quarters

Q

N

e

0

2

25

30

35

40

= 0.01= 0.50= 0.99

0
1.5
-5

-1

= 0.01= 0.50= 0.99-4from ss-10= 0.01= 0.50= 0.99

-15

0.5

%

from ss-3%%

from ss

1

-2

0

-5
-20

-0.5

-6

-7

-1

-25

0

5

10

15

20

25

30

35

40

0

5

10

15

Quarters
CA/Y

1.4

20

25

30

35

5

10

15

= 0.01= 0.50= 0.99= 0.01= 0.50= 0.99-4from ss

from ss-12-8Annualized %

0.4

%

-6

-10

30

35

40

= 0.01= 0.50= 0.99

6

1

0.6

25

R

7

-2

0.8

20

Quarters

B

0

1.2

from ss (%)

040

Quarters

-14

0.2

5

4

3

2

1

-16

0

5

10

15

20

25

30

35

40

Quarters

0

5

10

15

20

Quarters

25

30

35

40

0

5

10

15

20

25

30

35

40

Quarters

Rb

2.5= 0.01= 0.50= 0.992from ss

-1

-20

0

Annualized %

0

-18

-0.2

1.5

1

0.5

0

-0.5

-1

-1.5
0

5

10

15

20

25

30

35

40

Quarters

Figure 1: Impulse responses to an increase in the foreign interest rate: ω =0.01, 0.5, 0.99

18

3.2

Impulse responses of main variables, with and without
capital controls

Next, we show the impulse responses of the main variables to the same shock, withand without a low (not necessarily optimal) degree of capital controls. Figure 2
shows the impulse responses with and without the capital control rule in which
τ is set to 0.01 under the benchmark degree of financial frictions (ω = 0.5). In
Figure 2, the solid curve represents the impulse responses with the capital control
rule of τ = 0.01, and the dotted curve represents those without it.
As is clear from Figure 2, the capital control rule dampens the decline in output
Y by mitigating the increase in the spread E[Rk ] − R. The capital control rule
reduces the size of fluctuations in investment I, capital K, and consumption C,
as well as in output Y . The fluctuations in the real exchange rate e, the ratioof the current account to output CA/Y , and foreign debt B are also reduced
significantly by the capital control rule. The impulse response of the tax rate on
foreign borrowing has a similar trajectory to B because of the definition of thecapital control rule (50).

19E[RK]-R

2

Y

-0.1

C

0

No capital control
Capital control

-0.1
-0.2

1.5

from ss

-0.2

%

-0.4

%

Annualized %0.5

from ss

from ss

-0.3
1

-0.3

No capital control
Capital control

-0.4

-0.5

-0.5

No capital control
Capital control

0

-0.6

-0.6
-0.7

-0.5

-0.7
0

5

10

15

1

20

25

30

35

40

-0.8
0

5

10

15

20

25

30

35

40

0

10

15

20

Quarters

Quarters

I

K

L

0

0

No capital control
Capital control0

No capital control
Capital control

-1

25

30

35

40

-0.1

-0.2

-0.2

-2
-3

from ss-0.4

from ss

from ss

5

Quarters

-0.6

%

%

%

-4
-5

No capital control
Capital control

-0.3

-0.4

-0.8
-0.5

-6
-1

-0.6

-7
-8

-1.2

0

5

10

15

1.5

20

25

30

35

40

-0.7
0

5

10

15

20

25

40

0

5

10

15

20

Quarters

q

N

e

0

1

No capital control
Capital control

%

0

30

35

40

No capital control
Capital control

from ss

0.6

-6

-8

%

from ss

-4

0.5

25

0.8

-2

1

from ss

35

Quarters

No capital control
Capital control%

30

Quarters

0.4

0.2

0

-10

-0.2
-0.5
-12

-1

-0.4

-0.6

-14

0

5

10

15

20

25

30

35

40

0

5

10

15

Quarters
CA/Y

1

20

25

30

35

0

40

10

15

No capital control
Capital control

35

40

from ss

from ss2

Annualized %

1.5

%
0.2

30

No capital control
Capital control

2.5

-5

0.4

25

R

3

No capital control
Capital control

0.6

20

Quarters

B

0

0.8

from ss (%)

5

Quarters

-10

0

1

0.5

0

-0.2

-0.5

-15

0

5

10

15

20

25

30

35

40

0

5

10

15

Quarters

25

30

35

40

5

10

15

20

25

30

35

40

tax rate

0.04

No capital control
Capital control

0

Quarters

Quarters

Rb

2

20

No capital control
Capital control

0.02

from ss

1.5

from ss (%)

0

Annualized (%)

1

0.5

-0.02

-0.04

-0.06
0

-0.08

-0.1

-0.5
0

5

10

15

20

Quarters

25

30

35

40

0

5

10

15

20

25

30

35

40

Quarters

Figure 2: Impulse responses to an increase in the foreign interest rate, with andwithout capital controls: ω = 0.5

20

3.3

Welfare analysis

We now examine the welfare-improving eﬀect of capital controls under diﬀerent
degrees of financial frictions. Figure 3 shows the welfare curves associated with
diﬀerent values of τ . In Figure 3, the horizontal axis is τ , and the welfare curves
corresponding to three degrees of financial frictions ω are shown. The bold curve,
the bold dotted curve, and the thin dotted curve represent the benchmark case ofω = 0.5, a higher degree of frictions case of ω = 0.75, and a lower degree of frictions
case of ω = 0.25, respectively. The asterisk “∗” denotes the maximum welfare point
achieved by choosing the optimal level of τ for each of the three degrees of thefinancial frictions. In Figure 3, zero in the vertical axis indicates that the capital
control rule does not improve welfare at all and the welfare-improving eﬀect of
capital controls is zero.
0.5
0.45
0.4
0.35

=0.25
=0.50
=0.75

(%)

0.3
0.25
0.2
0.15
0.1
0.05
0
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Figure 3: Welfare curves with varying τ : diﬀerent degrees of financial frictions

As is clear from Figure 3, there is some range of τ that improves welfare levels
compared to the no-policy case. By comparing the three welfare curves corresponding to the three degrees of financial frictions, we can see that as the degreeof financial frictions increases, the welfare-improving eﬀect of capital controls increases. By comparing the three cases, we can also see that as the degree of21

financial frictions increases, the optimal value of τ becomes larger (i.e., the optimal values of τ corresponding to ω = 0.25, 0.5, and 0.75 are 0.027, 0.034, and 0.043,
respectively.) This result implies that a more aggressive policy rule is appropriate
if the degree of financial frictions is higher.
Figure 4 shows the conditional welfare levels under diﬀerent degrees of financial
frictions ω. In Figure 4, the solid curve represents the maximum level of conditional
welfare, which is achieved by choosing the optimal level of τ under diﬀerent degrees
of financial frictions ω. The dotted curve represents the case where no capital
control is imposed, under diﬀerent degrees of financial frictions ω. As we canguess immediately, the welfare level in the no-capital control case decreases as thedegree of financial frictions increases (i.e., ω increases). The no capital control
welfare curve is downward sloping because of the amplified uncertainty due tofinancial frictions. In contrast, the maximized welfare level achieved by the optimal
capital control rule increases as the degree of financial frictions becomes larger. By
comparing the no capital control welfare curve and the maximum welfare curve,
we can say that the increase in the economy’s conditional welfare level caused by
the optimal capital control rule becomes larger as the degree of financial frictions
increases.
-730
-735

conditional welfare level

-740
-745
-750
no capital control
optimal

-755
-760
-765
-770
-775
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 4: Optimal and no capital control welfare levels

221Figure 5 plots the maximum welfare gain of capital controls measured in termsof the non-stochastic steady state level of consumption C under diﬀerent degrees
of financial frictions ω. As argued in Section 2.9, we evaluate the welfare benefitof the capital control rule corresponding to diﬀerent values of ω by comparing ϵ
in (62) associated with each value of τ to that in the no-capital control case (i.e.,τ = 0), and calculate the maximum welfare gain of capital controls by choosing
the optimal level of τ . Figure 5 shows that as the degree of financial frictions
increases, the maximum welfare gain of the optimal capital control rule increases.
1.2

1

(%)

0.8

0.6

0.4

0.2

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5: Maximum welfare gains of capital controls under diﬀerent degrees offinancial frictions (ω)

23

3.4

Liability dollarization

As we argue in the Introduction, we consider an economy where banks face the“liability dollarization” problem and their foreign borrowing is denominated in foreign currency. When the banks’ liabilities are “dollarized,” exchange rate behavior
exacerbates the eﬀect of financial frictions through their balance sheet.
In this section, we examine how the welfare-improving eﬀect of capital controls
would diﬀer between a “liability dollarization” economy and a “no liability dollarization” economy. In Appendix A2, we formally explain how the two economies
diﬀer. In the “liability dollarization” economy, an unanticipated depreciation in
the domestic currency has a direct negative impact on the bank’s balance sheet.
In contrast, in the “no liability dollarization” economy, the exchange rate change
has no direct valuation eﬀect on the bank’s balance sheet.
1.2

Liability dollarization
No liability dollarization
1

(%)

0.8

0.6

0.4

0.2

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 6: Maximum welfare gains of capital controls under diﬀerent degrees offinancial frictions (ω): Liability dollarization vs. no liability dollarization

Figure 6 represents the welfare gain curve of capital controls in the “no liability dollarization” economy and that in the “liability dollarization” economy. The
welfare gain curve in the “liability dollarization” economy is identical to that in
Figure 5. As is clear from Figure 6, in both cases, the welfare-improving eﬀect of24

capital controls increases as the degree of financial frictions increases. However,
the welfare-improving eﬀect of capital controls in the “liability dollarization” caseis higher than that in the “no liability dollarization” case, and the diﬀerence between the eﬀects becomes larger as ω increases. In the “liability dollarization”
economy, the exchange rate amplifies the eﬀect of a foreign interest rate shock on
the economy through the bank’s balance sheet channel. Therefore, capital controls
have a larger eﬀect in terms of improving welfare in the “liability dollarization”
case with the amplification eﬀect of the exchange rate on the bank’s balance sheet.
The diﬀerence in the welfare levels between the two cases in Figure 6 may notseem very large. However, in the “no liability dollarization” economy, we only
eliminate the direct valuation eﬀect of the exchange rate change on the bank’sbalance sheet, while the eﬀect of exchange rates on the interest payments on foreign
debts (in terms of domestic currency) still exists. That is, the diﬀerence in thewelfare levels between the two cases in Figure 6 is derived only from whether the
direct valuation eﬀect of the exchange rate change on the bank’s balance sheet
exists or not.

25

4

Sensitivity analysis

In this section, we examine the robustness of our analysis results in the previous
section. We conduct robustness checks for varying degrees of country premium(ψ), trade openness (i.e., inverse degree of home bias) (υ), and trade elasticity(ι), which are key parameters in replicating the small open economy’s behavior.
Garcia-Cicco et al. (2010) show that the country-specific interest-rate premium
parameter (ψ) plays an important role in replicating the business cycle in emerging
market economies. The country premium parameter is especially important for the
autocorrelation function of the trade-balance-to-output ratio to be close to data.
Faia and Monacelli (2008) analyze the optimal monetary policy in a small open
economy characterized by home bias in consumption. They examine how thedegree of trade openness υ (i.e., inverse degree of home bias) aﬀects a small open
economy, and show that υ is especially important for inflation and exchange rate
volatilities. The parameter of trade elasticity (or elasticity between domestic andforeign goods) (ι) is also a key parameter in the dynamics of a small open economy.
As shown in Faia and Monacelli (2008) and Thoenissen (2011), the parameter of
trade elasticity is critical to the behavior of a real exchange rate in a small open
economy.

4.1

Robustness check for varying degrees of the country
premium parameter ψ

We examine how the welfare-improving eﬀect of capital controls changes as thecountry premium parameter (ψ) varies. Figure 7 shows the welfare benefit curves
for diﬀerent degrees of financial frictions (ω) in the three cases of ψ = 0.02, 0.03,
and 0.04. In Figure 7, we find that the welfare benefit in the case of ψ = 0.02 ishigher than that in the benchmark case of ψ = 0.03, and the welfare benefit in
the case of ψ = 0.04 is lower than that in the benchmark case, for any value of ω.
Thus, we can say that as the country premium parameter (ψ) becomes smaller, themaximum welfare gain of capital controls becomes larger. However, in all cases,
similarly to the previous section, we confirm that as the degree of financial frictions
increases, the maximum welfare gain of capital controls becomes larger.
Figure 8 shows the welfare curves associated with diﬀerent values of τ in thecase of ψ = 0.02 or 0.04, whereas Figure 3 shows those in the benchmark case ofψ = 0.03. Similarly to the benchmark case of ψ = 0.03, we can see that as thedegree of financial frictions increases, the optimal value of τ becomes larger, which
implies that a more aggressive policy rule is appropriate if the degree of financial
frictions is higher. Comparing the two cases of ψ = 0.02 and 0.04 in Figure 8, we
can see that the optimal value of τ in the case of ψ = 0.04 is higher than that in
the case of ψ = 0.02 for any value of ω. This implies that a higher value of the
26

2.5

=0.02
=0.03
=0.04

2

(%)

1.5

1

0.5

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 7: Maximum welfare gain of capital controls under diﬀerent degrees offinancial frictions (ω): varying country premium parameter (ψ)

27country risk premium parameter ψ requires tighter capital controls.
Figure 9 shows the welfare gain curve of capital controls in the “no liability
dollarization” economy and that in the “liability dollarization” economy in thecase of ψ = 0.02 or 0.04, whereas Figure 6 shows those in the benchmark caseof ψ = 0.03. Similarly to the benchmark case of ψ = 0.03, we can see that thediﬀerence between the eﬀects becomes larger as the degree of financial frictions ishigher.

28

= 0.020.8= 0.04

0.35

0.7

0.3

0.6

0.4

=0.25
=0.50
=0.75

0.2

(%)

(%)

0.25

=0.25
=0.50
=0.75

0.5

0.15
0.3
0.1
0.2
0.05

0.1

0

0
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Figure 8: Welfare curves with varying τ : diﬀerent degrees of financial frictions(ψ = 0.02, 0.04)= 0.022.5= 0.040.8

Liability dollarization
No liability dollarization

Liability dollarization
No liability dollarization

0.7

2
0.6

0.5

(%)

(%)

1.5

1

0.4

0.3

0.2
0.5
0.1

0

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 9: Maximum welfare gains of capital controls under diﬀerent degrees offinancial frictions (ω): Liability dollarization vs. no liability dollarization (ψ =0.02, 0.04)

29

4.2

Robustness check for varying degrees of the trade openness (i.e., inverse degree of home bias) parameter υ

We next examine how the welfare-improving eﬀect of capital controls changes if
the trade openness (or inverse degree of home bias) parameter (υ) varies. Figure
10 shows the welfare gain curves for diﬀerent degrees of financial frictions (ω) in
the three cases of υ = 0.10, 0.28, and 0.50. In Figure 10, we see that, unlike ψ,
the relationship between the welfare gain and the parameter value of υ is not necessarily monotonic, although when ω is high, the maximum welfare gain of capital
controls becomes larger as the degree of trade openness (υ) increases. However,
we find that in all cases, it holds that as the degree of financial frictions increases,
the maximum welfare gain of the capital controls becomes larger.
1.8

=0.10
=0.28
=0.50

1.6
1.4

(%)

1.2
1
0.8
0.6
0.4
0.2
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 10: Maximum welfare gain of capital controls under diﬀerent degrees offinancial frictions (ω): varying trade openness (υ)

Figure 11 shows the welfare curves associated with diﬀerent values of τ in thecase of υ = 0.10 or 0.50, whereas Figure 3 shows those in the benchmark case ofυ = 0.28. Similarly to the benchmark case of υ = 0.28, we can see that as thedegree of financial frictions increases, the optimal value of τ becomes larger, which30implies that a more aggressive policy rule is appropriate if the degree of financial
frictions is higher.
Figure 12 shows the welfare gain curve of capital controls in the “no liability
dollarization” economy and that in the “liability dollarization” economy in thecase of υ = 0.10 or 0.50, whereas Figure 6 shows those in the benchmark caseof υ = 0.28. Similarly to the benchmark case of υ = 0.28, we can see that thediﬀerence between the eﬀects becomes larger as the degree of financial frictions ishigher.

31

= 0.100.25= 0.50

0.6

0.5
0.2

=0.25
=0.50
=0.75

=0.25
=0.50
=0.75

0.4

(%)

(%)

0.15

0.3

0.1
0.2

0.05
0.1

0

0
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Figure 11: Welfare curves with varying τ : diﬀerent degrees of financial frictions(υ = 0.10, 0.50)= 0.100.4

0.35= 0.501.8

Liability dollarization
No liability dollarization

Liability dollarization
No liability dollarization

1.6
1.4

0.3

1.2

(%)

(%)

0.25

0.2

1
0.8

0.15
0.6
0.1

0.4

0.05

0.2

0

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 12: Maximum welfare gains of capital controls under diﬀerent degrees offinancial frictions (ω): Liability dollarization vs. no liability dollarization (υ =0.10, 0.50)

32

4.3

Robustness check for varying degrees of trade elasticity
parameter ιFigure 13 shows the welfare benefit curves of capital controls under diﬀerent degrees of financial frictions (ω) in the three cases of ι = 0.5, 1.5, and 2.5. In Figure
13, similarly to the case of ψ, we find the monotonic relationship between thewelfare gain and the parameter value of ι, although the welfare gain in the case ofι = 2.5 is close to that in the benchmark case of ι = 1.5. However, in all cases, itagain holds that as the degree of financial frictions increases, the maximum welfare
gain of capital controls becomes larger.
1.4

=0.5
=1.5
=2.5

1.2

(%)

1

0.8

0.6

0.4

0.2

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 13: Maximum welfare gain of capital controls under diﬀerent degrees offinancial frictions (ω): varying trade elasticity (ι)

Figure 14 shows the welfare curves associated with diﬀerent values of τ in thecase of ι = 0.5 or 2.5, whereas Figure 3 shows those in the benchmark case ofι = 1.5. Similarly to the benchmark case of ι = 1.5, we can see that as the degreeof financial frictions increases, the optimal value of τ becomes larger, which implies
that a more aggressive policy rule is appropriate if the degree of financial frictions
is higher.

33

Figure 15 shows the welfare gain curve of capital controls in the “no liability
dollarization” economy and that in the “liability dollarization” economy in thecase of ι = 0.5 or 2.5, whereas Figure 6 shows those in the benchmark case ofι = 1.5. Similarly to the benchmark case of ι = 1.5, we can see that the diﬀerence
between the eﬀects becomes larger as the degree of financial frictions is higher.

34

= 0.5

0.5
0.45

0.45

0.4

0.4

0.35

0.35

=0.25
=0.50
=0.75

=0.25
=0.50
=0.75

0.3

(%)

0.3

(%)

= 2.5

0.5

0.25

0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05

0

0
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Figure 14: Welfare curves with varying τ : diﬀerent degrees of financial frictions(ι = 0.5, 2.5)

= 0.5

1.2

= 2.5

1.4

Liability dollarization
No liability dollarization

Liability dollarization
No liability dollarization

1.2

1

1

(%)

(%)

0.8

0.6

0.8

0.6
0.4
0.4
0.2

0.2

0

0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 15: Maximum welfare gains of capital controls under diﬀerent degrees offinancial frictions (ω): Liability dollarization vs. no liability dollarization (ι =0.5, 2.5)35

5Conclusion

This study falls within a strand of studies that examine the possible eﬀects ofusing capital controls as a policy tool for open economies. However, our study
diﬀers from the existing literature in that we examine the welfare-improving eﬀectof capital controls under diﬀerent degrees of financial frictions between banks andforeign investors. To this end, we develop a small open economy model withfinancial frictions à la Gertler and Kiyotaki (2010) and Gertler and Karadi (2011).
Banks face financial frictions in the form of time-varying endogenous balance sheet
constraints due to the agency problem with foreign investors.
We show that capital controls can be an eﬀective instrument for addressing
the amplification eﬀect due to financial frictions. When the degree of financial
frictions between banks and foreign investors is higher, capital controls are more
welfare improving. We also show that as the degree of financial frictions increases,
a more aggressive policy rule is appropriate. In our model, banks also face the“liability dollarization” problem, which we compare with an economy that does
not face the same problem. Here, we find that the welfare-improving eﬀect of
capital controls in the “liability dollarization” case is larger than that in the “noliability dollarization” case, and the diﬀerence between the eﬀects becomes larger
as the degree of financial frictions increases. This result reflects the fact thatthe amplification eﬀect of exchange rates through the balance sheet channel issignificant in the “liability dollarization” economy. We confirm the robustness of
our main finding for the varying degrees of the three key parameters on country
premium, home bias, and trade elasticity.
The intuitive explanation for why capital controls are eﬀective in addressing theamplification eﬀect of financial frictions follows immediately from the argument ofGertler et al. (2012) that “there exists a pecuniary externality which banks do notproperly internalize when deciding their balance sheet structure” (page 530). In
other words, capital controls can play a role of internalizing the above-mentioned
externality due to the financial frictions.
Reflecting the recent policy reactions of emerging countries to their capital
inflow problems, we examine “cyclical policies” by which the government increases
taxes on capital inflows when a surge in capital inflows occurs. Although it isbeyond the scope of this study, it is also important to examine “permanent policies”
such as those aﬀecting the steady state fraction of bank lending financed by foreign
borrowing. We can also extend our model to include credit constraints faced by
non-financial borrowers, which is emphasized by Bernanke et al. (1999). Although
this extension is beyond the scope of this study, it seems interesting to explore
how the welfare consequences of capital controls would change under this type offinancial frictions. We leave these for future research.

36

Appendices
A1

Steady state

In the steady state, we have
Λ = β,

(A1)

1
,
β

(A2)

Q = 1,(A3)

q = 1,(A4)

g(q) = 1,(A5)

e = 1,(A6)

CA = 0,(A7)

Γ = 0,
( )
Rk
Rk =
R,
R

(A8)

R=

Y
Q(Rk − 1 + δ)
,
=
PH
K
α
P
I
= δ,
K
( )−1
I
I Y
=
,
Y
K K
Rb = R − ω(Rk − R),
TB
B= (Rb − 1) ,
Y
Y
C
1
I
G
Γ
TB
=
− − − −,
Yg(q) YYYY
1( )− 1−α
Y
K
,
=
L
K
1
{
(
)( )α } φ−1(1 − α) PH
K
L=
,
χ
P
L
( )
K
K=
L,
L
37

(A9)
(A10)
(A11)
(A12)
(A13)
(A14)
(A15)
(A16)
(A17)
(A18)

EX =

S = K,(A19)

Y = K α L1−α ,
( )
I
I=
Y,
Y
( )
B
B=
Y,
Y
( )
G
Y,
G=
Y
( )
C
C=
Y,
Y

(A20)

]
1[
Y − (1 − υ)g(q)ι (C + I + G + Γ) ,
q
(
)−γ
χ φ
ρ= C− L
,
φ
( )−1
K
N =K
,
N

(A22)
(A23)
(A24)
(A25)
(A26)
(A27)

Rb∗ = Rb ,(A28)

R∗ = Rb ,

(A29)

eB
S
+ω ,
N
N
D = QS − eB − N,
ϕ=Q

ξ=

(A21)

1
(N + σRb eB + σRD − σRk QS),
Rk QS
ϕ
,
ω
1−σ
Ω=
,
1 − σ{ϕΛ(Rk − R) + ΛR}
ϕb =

(A30)
(A31)
(A32)
(A33)
(A34)

ν = ΛΩR,(A35)µ = ΛΩ(Rk − R),(A36)µb = ΛΩ(R − Rb ),νθ =µ+ ,
ϕ

(A37)

38

(A38)

and

T ∗ = 0.

(A39)

In Figure A1, the solid curve represents the non-stochastic steady-state levels of
welfare corresponding to diﬀerent degrees of financial frictions. The dotted curvein Figure A1 is the conditional welfare level corresponding to diﬀerent degrees offinancial frictions, which is identical to the dotted curve in Figure 4. The curveof the non-stochastic steady-state level of welfare is upward sloping, because ahigher value of ω decreases the steady-state levels of foreign interest rates (A13)and the trade balance (A14), which leads to higher levels of consumption (A15)and welfare. However, note that although the curve of the non-stochastic steadystate level of welfare is upward sloping, the curve of the conditional welfare level is
downward sloping because of the amplified uncertainty due to financial frictions.
-730
-735
-740

welfare level

-745
-750
conditional welfare level
non-stochasitc steady-state level of welfare

-755
-760
-765
-770
-775
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure A1: Conditional welfare level and non-stochastic steady-state level of welfare

39

A2

The economy without “liability dollarization”

In this appendix, we formally show how an economy without “liability dollarization” diﬀers from an economy with “liability dollarization” considered in the maintext. In an economy without “liability dollarization,” the bank’s foreign debt bt(and Bt ) is denominated in domestic currency. The bank’s balance sheet (11) andthe evolution of the bank’s net worth (12) change as follows:

andQt st = nt + bt + dt ,(A40)

nt = Rk,t Qt−1 st−1 − (1 + Tt∗ )Rb,t bt−1 − Rt dt−1 + ζt .

(A41)

Accordingly, the bank’s incentive constraint (14) changes toVt (st , bt , dt ) ≥ θ(dt + nt ) + θ∗ bt .

(A42)

The bank’s first-order conditions (19), (20), and (21) change to:()νt − νb,t (1 + λt ) = θωλt ,
(

and

[

(
θ−

)
νs,t
− νb,t (1 + λt ) = θ(1 + ω)λt ,
Qt

νs,t
− νt
Qt

(A43)

(A44)

)]
Qt st + [θω − (νt − νb,t )]bt = νt nt .

(A45)

Eqs.(31) and (32) change to:Qt St + ωBt = ϕt Nt ,(A46)

Dt = −(1 + ω)Bt + (ϕt − 1)Nt .

(A47)

and
The equations of the foreign debt (57) and the country specific interest rate premium (59) change to:
Bt = Rb,t Bt−1 − T Bt ,
(A48)
[

and
∗
Rb,t
= Rt∗ + ψ{g(qt )Bt g(q)B
−
exp
Yt
Y

40

}

]
−1 .

(A49)

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45