DP2015-10

Capital Controls, Monetary Policy,
and Balance Sheets
in a Small Open Economy
Shigeto KITANO
Kenya TAKAKU
Revised October 24, 2017

Capital Controls, Monetary Policy, and Balance Sheets in a
Small Open Economy∗
Shigeto Kitano†

Kenya Takaku‡

Abstract

We develop a small open economy, New Keynesian model that incorporates a financial accelerator in combination with liability dollarization.
Applying a Ramsey-type analysis, we compare the welfare implicationsof an optimal monetary policy under flexible exchange rates and an optimal capital control policy under fixed exchange rates. In an economy
without the financial accelerator, an optimal monetary policy under
flexible exchange rates is superior to an optimal capital control policy
under fixed exchange rates. In contrast, in an economy with the financial accelerator, an optimal capital control under fixed exchange rates
yields higher welfare than an optimal monetary policy under flexible
exchange rates.
Keywords: capital control; monetary policy; balance sheets; Ramsey
policy; exchange rate regimes; small open economy; nominal rigidities;
New Keynesian; DSGE; welfare comparison; incomplete markets; financial accelerator; financial frictions.
JEL Classification: E44, E52, F32, F38, F41.
∗

Earlier versions of the paper were presented at the 9th Annual MIFN Conference, the SWET2015 at Otaru University, the JEA annual meeting at Niigata University, and the 11th Annual
APEA Conference at National Taiwan University. We are grateful to the referee and the co-editor
William Branch for their helpful comments that have improved the paper. We are especiallygrateful to Mark Spiegel, Tomohiro Hirano, Kosuke Aoki, Yongseung Jung, Ippei Fujiwara, andShin-ichi Fukuda for their valuable comments. All remaining errors are ours. This work was
supported by KAKENHI (15H05729, 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

Although capital controls are not a new policy instrument, it is not until the recent
global financial crisis that the potential eﬀects of capital control policies have been
rigorously examined from the theoretical perspective as one of the most important
topics in international finance.1 Given the recent financial crisis, volatile international capital movements in emerging market economies have been the subject ofrigorous discussion among concerned policymakers and economists. Volatile capital flows amplify boom-bust cycles and destabilize emerging market economies.
The recent global financial crisis led to a reconsideration of the merits of capital
account restrictions. An increasing number of policymakers believe that capital
controls can eﬀectively stabilize economies against volatile capital flows. In fact,some emerging market countries have recently responded to instability by imposing
capital controls.2 As well known, even the IMF, a former critic of capital controls,
has been forced to reconsider such measures as an important policy response tovolatile capital flows under certain circumstances.3
Against this background, there has emerged a rapidly growing body of literature related to capital controls.4 Jeanne and Korinek (2010) and Bianchi (2011)
show that there are pecuniary externalities associated with financial crises andprovide a rationale for prudential capital controls. Using a two-country model,
1

An exception is Kitano (2004). Kitano (2004) shows that capital controls not only stem thecapital inflow but also reverse the associated macroeconomic eﬀects, and are eﬀective measuresagainst the capital inflow problem.
2
For details, see, for example, Jongwanich and Kohpaiboon (2012), Ahmed and Zlate (2014),
Forbes et al. (2016), and Ghosh et al. (2017).
3
For details on the IMF position, see Ostry et al. (2010) and Ostry et al. (2012).
4
For details, see, for example, Korinek (2011) or Jeanne et al. (2012). For the earlier literature
on capital controls, see the introduction in Kitano (2011). Kitano (2011) shows that there exists
an optimal degree of capital-account restriction that achieves a higher level of welfare than that
under perfect capital mobility, if the economy has costly financial intermediaries.

2

Brunnermeier and Sannikov (2014) show that pecuniary externalities can lead toconstrained ineﬃcient outcomes and capital controls can be welfare improving.5
In recent years, an increasing number of studies examine the eﬀects of capital
controls as a regular instrument of economic policy from a broader perspective(e.g., Schmitt-Grohé and Uribe (2016), Farhi and Werning (2012), De Paoli and
Lipinska (2013), and Kitano and Takaku (2017c)).6 7 For example, Kitano and
Takaku (2017a) show that as the degree of financial frictions between banks andforeign creditors increases, more aggressive capital controls are appropriate.
Another strand of the literature focuses the relationship between capital controls and various types of monetary policies (Davis and Presno (2014), Liu andSpiegel (2015), Chang et al. (2015), and Agénor and Jia (2015)). For example,
Kitano and Takaku (2017b) show that capital controls can play an alternative roleto the direct credit policy in mitigating the contraction after a crisis.
Our paper is most closely related to De Paoli and Lipinska (2013), Davis andPresno (2014), and Liu and Spiegel (2015) in that we too apply a Ramsey-type
analysis for capital controls. However, we examine optimal capital controls inmodels that highlight balance sheet eﬀects in the presence of liability dollarization.8 Therefore, our paper is also rather closely related to Céspedes et al. (2004),
5

Benigno et al. (2013) consider both ex-ante and ex-post policies in a model with pecuniary
externalities. They show that the design of ex-ante policies depends on that of ex-post policies.
6
Ostry et al. (2010) argue that the use of capital controls is justified under limited circumstances. Jeanne et al. (2012) go further, arguing that “[p]roperly designed capital controls may
even be eﬀective as a regular instrument of economic policy”(p.110).
7
Kitano and Takaku (2017c) incorporate a banking sector with balance sheet frictions into amodel of a small open economy and compare the eﬀectiveness of capital controls and macroprudential regulation.
8
Emerging economies have diﬃculty in borrowing abroad in their own currencies, and face amismatch in the currency denomination of their liabilities and assets. Eichengreen and Hausmann (1999) refer to this incompleteness in financial markets as “original sin.” Eichengreen and
Hausmann (2005) also argue that “[w]hile the quality of institutions and policies varies enormously among developing countries, the extent of original sin does not”(page 6) and that “the3

Devereux et al. (2006), and Elekdağ and Tchakarov (2007). Building upon theframework developed by Bernanke et al. (1999), Céspedes et al. (2004), Devereux
et al. (2006), and Elekdağ and Tchakarov (2007) incorporate a financial accelerator coupled with liability dollarization, in which foreign debt is denominated inforeign currency (not domestic currency). In these models, the financial accelerator works through an endogenous risk premium that is linked to the balance
sheets of entrepreneurs. These balance sheets are also vulnerable to exchange rate
fluctuations owing to the problem of liability dollarization.
Céspedes et al. (2004) and Devereux et al. (2006) find that the conventional
wisdom, that the flexible exchange rate is preferable to the fixed exchange rate,holds in spite of the financial accelerator eﬀects. Elekdağ and Tchakarov (2007)
also confirm that the flexible exchange rate regime has better welfare properties
than the fixed exchange rate regime when the country has perfect access to international capital markets. However, when their model incorporates a financial
accelerator and the leverage ratio exceeds a threshold, they find that the fixedexchange rate regime could become welfare superior.
We develop a small open economy, New Keynesian model with and without afinancial accelerator mechanism, the model structure of which is basically similar toCéspedes et al. (2004), Devereux et al. (2006), and Elekdağ and Tchakarov (2007).
We then apply a Ramsey-type analysis and examine the welfare implications ofcapital control policies.
In the case without the financial accelerator, we compare three cases: optimalmonetary policy under flexible exchange rates, optimal capital control policy (ondiﬃculty emerging markets experience in attempting to borrow abroad in their own currencies
has something to do with the structure of the international system”(page 6).

4households) under fixed exchange rates, and fixed exchange rates (without capital
controls). Our Ramsey-type analysis results indicate that although the optimal
capital control policy significantly improves welfare under fixed exchange rates, theoptimal monetary policy is the most welfare-maximizing in an economy without
the financial accelerator.
In the case with the financial accelerator, we compare the following five cases:
an optimal monetary policy under flexible exchange rates, fixed exchange rates(without capital controls), an optimal capital control policy on entrepreneurs, an
optimal capital control policy on households, and an optimal capital control policy
on both entrepreneurs and households under fixed exchange rates. Our analysis
results indicate that the optimal monetary policy still outperforms the optimal
capital control policy on households. However, the optimal capital control policyon entrepreneurs outperforms the optimal monetary policy. The most welfaremaximizing is the optimal capital control policy on both entrepreneurs and households.
The intuition underlying our analysis results is straightforward. Entrepreneurs
finance investment partly with foreign borrowing, which is subject to financial
frictions in the presence of balance sheet vulnerabilities. In an economy with afinancial accelerator, the key variable is the foreign interest rate augmented by an
external finance premium. Monetary policy works only through domestic interest
rates. However, capital controls on entrepreneurs have a direct control on the key
variable of interest rates at which entrepreneurs borrow abroad. Therefore, capital
controls can be welfare improving in an economy with financial frictions.
The remainder of the paper is organized as follows. In Section 2, we present a
sticky price, small open economy model with and without a financial accelerator5

in combination with liability dollarization. In Section 3, we perform a comparative
analysis of welfare for alternative policy regimes in this economy. For the economy
without the financial accelerator, we compare (i) the flexible exchange rate regime
accompanied by an optimal monetary policy, (ii) the fixed exchange rate regime
accompanied by optimal capital controls on households, and (iii) the fixed exchange rate regime (without capital controls). For the economy with the financial
accelerator, we compare (i) the fixed exchange rate regime accompanied by optimal capital controls on households and entrepreneurs, (ii) the fixed exchange rate
regime accompanied by optimal capital controls on entrepreneurs, (iii) the flexible
exchange rate regime accompanied by an optimal monetary policy, (iv) the fixedexchange rate regime accompanied by optimal capital controls on households, and(v) the fixed exchange rate regime (without capital controls). In Section 4, we
check the robustness of our results. In the previous section, we show the welfare
rankings for three shocks together: productivity shock, export shock, and foreigninterest rate shock. In this section, we show that our results are robust even when
we consider these shocks individually. Conclusions are presented in Section 5.

2

Model

We employ the small open economy structure developed by Galı́ and Monacelli(2005) and Faia and Monacelli (2008). The small open economy model incorporates a financial accelerator a la Bernanke et al. (1999) in combination with liability
dollarization. Our model is close to those in Céspedes et al. (2004), Devereux et al.
(2006), and Elekdağ and Tchakarov (2007). The small open economy consists ofhouseholds, production firms, entrepreneurs, and the government.
6

2.1

Households

A representative household maximizes its expected lifetime utility:

E0

∞
∑

{
β

t=0

t

}
L1+ϕ
Ct1−σ
t
−
,
1−σ 1+ϕ(1)

where Et denotes the mathematical expectations operator conditional on information available at time t, β ∈ (0, 1) is the discount factor, Ct signifies a composite
consumption index, and Lt represents labor eﬀort. Households consume diﬀerentiated goods (produced by both domestic and foreign firms). The composite
consumption index Ct is given by[
η−1
η−1 ] η11
η−1.
Ct ≡ (1 − γ) η CH,tη + γ η CF,tη(2)

η(> 0) is the elasticity of substitution between domestic and foreign goods, andγ ∈ (0, 1) represents the measure of openness. CH,t and CF,t are, respectively, theindices for consumption of domestic and foreign goods, expressed by[∫ 1
CH,t ≡

CH,t (j)

ε−1
ε

ε
] ε−1

dj

[∫ 1
CF,t ≡;

0

CF,t (j)

ε−1
ε

ε
] ε−1

dj

,

(3)

0

where ε(> 1) is the parameter for the elasticity of substitution among diﬀerentiatedgoods. A household’s optimal expenditure allocation in each goods category yields
the demand functions for domestic and foreign diﬀerentiated goods:(
CH,t (j) =PH,t (j)
PH,t

(

)−ε
CH,t ;

CF,t (j) =7

PF,t (j)PF,t)−ε
CF,t ,(4)

where PH,t (j) and PF,t (j) denote the domestic-currency-denominated prices of differentiated goods j produced by domestic and foreign firms, respectively. PH,t andPF,t are the domestic and import price indices, respectively:[∫ 1
PH,t ≡1−εPH,t (j)

1
] 1−ε

dj

[∫ 1
PF,t ≡;01−εPF,t (j)

1
] 1−ε

dj

.

(5)

0

From Eq. (5), we obtain∫ 1∫ 1
PH,t (j) CH,t (j) dj = PH,t CH,t ;PF,t (j) CF,t (j) dj = PF,t CF,t .

0

(6)

0

The optimal expenditure allocation between domestic and imported goods gives
(
)−η
PH,t
CH,t = (1 − γ)
Ct ;
Pt

(

PF,t
CF,t = γ
Pt

)−η
Ct ,

(7)

where Pt represents the consumer price index (CPI):
Pt ≡

[

1−η
1−η
(1 − γ)PH,t+ γPF,t

1
] 1−η

.

(8)

From Eqs. (7) and (8), we obtain

PH,t CH,t + PF,t CF,t = Pt Ct .

(9)Households have access to domestic and international financial markets. A

8household’s budget constraint in period t is given as
Pt Ct +(1+it−1 )At−1 +(1+τh,t−1 )(1+i∗t−1 )Et Bt−1 +Pt

ψB(Bt −B)2 = At +Et Bt +Wt Lt +Th,t +ΠFt .
2(10)Herein, At is the domestic currency debt position, Bt is the foreign currency debt
position, it is the interest rate of domestic currency assets, i∗t is the interest rateof foreign currency assets, and Et is the nominal exchange rate (in terms of thedomestic currency).9 Wt is the nominal wage, ΠFt is dividends from firms, τh,t is the
tax on the foreign currency debt of households, and Th,t is the lump-sum transfer.
Pt ψB (Bt − B)2 /2 is the portfolio adjustment costs, which induce the stationarityof the equilibrium dynamics in the small open economy.10
The households’ optimality conditions are given by
λht = Ct−σ ,Lϕt,Wt /Pt{ h}λt+1 Pt
1 = β(1 + it )Et,
λht Pt+1
λht =

9

(11)

(12)

(13)

The position of the domestic asset At turns out to be zero in equilibrium in our model.
However, the inclusion of the domestic asset At enables us to introduce the domestic interest
rate it into the model as in Eq.(10). Following Devereux et al. (2006) and Elekdağ and Tchakarov(2007), we therefore include the domestic asset At so that we can analyze the eﬀect of monetary
policy of changing the domestic interest rate it .
10
The small open economy model with incomplete asset markets features equilibrium dynamics
that possess a random walk component (Schmitt-Grohé and Uribe (2003)). To yield stationarityof the equilibrium dynamics in a small open economy, Neumeyer and Perri (2005) use a modelwith convex portfolio adjustment costs. The portfolio adjustment cost is often used for “closing”
a small open economy. Schmitt-Grohé and Uribe (2003) present alternative approaches to induce
stationarity.

9

and
[
1 = β(1 + τh,t )(1 + i∗t )ψB Pt (Bt − B)
1−
Et

]−1

{ h
}
λt+1 Pt Et+1
Et.
λht Pt+1 Et(14)Combining (13) and (14) yields the interest parity condition:[{ h}]−1 { h}λt+1 Pt
λt+1 Pt Et+1
ψB Pt (Bt − B)∗
(1+it )Et
= (1+τh,t )(1+it ) 1−
Et.
Et
λht Pt+1
λht Pt+1 Et(15)
Since we assume that the law of one price holds for individual goods, the termsof trade are given as
St ≡

PF,t
Et Pt∗
=
,
PH,t
PH,t

(16)

where Pt∗ denotes the CPI in the foreign country (in terms of foreign currency).11
It follows from (16) that
St
∆Et
=
,
(17)
St−1
ΠH,t
)
)
(
(
PH,t
Et
denote the depreciation rate of the nomand ΠH,t ≡ PH,t−1
where ∆Et ≡ Et−1
inal exchange rate and the rate of domestic inflation, respectively. It follows from
CPI (8) and (16) that
1Pt
= [(1 − γ) + γSt1−η ] 1−η ≡ g(St ).
PH,t(From (18), CPI inflation Πtt≡ PPt−1)
is expressed as

Πt = ΠH,t

11

(18)

g(St ).
g(St−1 )(19)

Without loss of generality, we assume that Pt∗ is exogenous and constant (= 1) for all t.

10From (16) and (18), we obtain the real exchange rate qt as the function of St :
qt ≡

2.2

Et Pt∗St=≡ q(St ).
Ptg(St )(20)

Production firms

Monopolistically competitive firms produce diﬀerentiated goods by using capitaland labor. Each monopolistic firm j in the home economy produces a diﬀerentiatedgood. The firm’s production function is given by

Yt (j) = Zt Kt (j)α Lt (j)1−α ,(21)where Yt (j), Kt (j), Lt (j), and Zt denote the firm’s output level, its capital andlabor inputs, and a stochastic productivity shock, respectively.
From the first-order conditions associated with the firm’s cost minimization
problem, we obtain
)
(
)
Wt
Rt
Kt (j) = α
Nt (j),(1 − α)
PH,t
PH,t
(

(22)

where Rt is the rental rate of capital. The firm’s cost minimization implies thatthe firm’s real marginal cost is given by

M Ct (j) = M Ct =(Rt /PH,t )α (Wt /PH,t )1−α.
Zt αα (1 − α)1−α

11

(23)

The capital accumulation process in the economy is given as[It
ϕI
Kt+1 =
−
Kt
2

(

It
−δ
Kt

)2 ]
Kt + (1 − δ)Kt ,(24)(
where It is aggregate investment and δ is the depreciation rate of capital. ϕ2I KItt −)2
δ Kt denotes the adjustment costs of capital, and ϕI is its parameter value.12 It
is composed of domestic and imported goods:[
η−1η−1 ] η11
η−1It ≡ (1 − γ) η IH,tη + γ η IF,tη,(25)

where IH,t and IF,t are represented by[∫ 1
IH,t ≡

IH,t (j)

ε−1
ε

ε
] ε−1

dj

[∫ 1
IF,t ≡;

0IF,t (j)

ε−1
ε

ε
] ε−1

dj

.

(26)

0

From the optimal allocation of expenditure in each goods category, we obtain thefollowing demand functions:(
IH,t (j) =PH,t (j)
PH,t

)−ε

(
IH,t ;

IF,t (j) =PF,t (j)PF,t)−ε
IF,t .

(27)

The optimal allocation of expenditures between domestic and imported goods
yields()−η
PH,t
IH,t = (1 − γ)
It ;
Pt

12

(

PF,t
IF,t = γ
Pt

)−η
It .

(28)

The capital (or investment) adjustment cost is widely adopted in dynamic stochastic general equilibrium (DSGE) models, mainly because it generally improves their empirical fit (e.g.,
Christiano et al. (2005)). Without the adjustment cost, investment would respond to shocks toomuch compared to empirical evidence. The capital adjustment cost is also important to obtain
the price of capital and to generate movements of asset prices. Changes in asset prices provide an amplification mechanism in models with financial frictions (Kiyotaki and Moore (1997);
Bernanke et al. (1999)).

12

From the profit-maximization problem of capital producers, we can obtain the(nominal) price of capital Qt :[(Qt = PH,t 1 − ϕI

2.3

It
−δ
Kt

)]−1
.

(29)

Price setting

Following Calvo (1983), we assume that in each period, a fraction 1 − ζ of monopolistically competitive firms change their prices, whereas a fraction ζ do notchange their prices. This implies that we can express the domestic price index as

PH,t ≡[1−ε1−ε
ζPH,t−1+ (1 − ζ)P̄H,t

1
] 1−ε

,

(30)

where P̄H,t denotes the price reset in period t. From (30), we obtain1−ε
1 = ζΠ−1+ε+ (1 − ζ)P̃H,t
,
H,t

(31)

P̄

where P̃H,t ≡ PH,t.
H,tEach firm resets its price to maximize the present discounted value of its profit
stream:
max
P̄H,t

∞
∑

n
ζ k Et {Λt,t+k [Yt+k|t (P̄H,t − M Ct+k|t
)]},

(32)

k=0

subject to(
Yt+k|t =P̄H,tPH,t+k)−εYt+k ,(33)n
where Yt+k|t and M Ct+k|t
represent the output level and the nominal marginal

cost, respectively, in t + k for a firm that last reset its price in period t. Λt,t+k ≡

13

λh

Pt
β k λt+k
is the discount factor. Yt+k is the aggregate output level in period t + k.
h P
t+k
t

From the first-order condition associated with the above problem, we obtain the
optimal price:P̃H,t =

ε
ε−1

)−ε−1
{
}
(
PH,t
k
ζ
E
Y
M
C
Λ
t
t+k
t,t+k
t+k|t
k=0
PH,t+k,()−ε}∑∞ k {
PH,t
Yt+k
k=0 ζ Et Λt,t+k PH,t+k

∑∞

(34)

which can be rewritten as
P̃H,t =
where

and

2.4

ε Xt1
,
ε − 1 Xt2

(35)

{
}
1
Xt1 = Yt M Ct + ζEt Λt,t+1 Πε+1
X
H,t+1 t+1 ,

(36)

}
{
2
.
Xt2 = Yt + ζEt Λt,t+1 ΠεH,t+1 Xt+1

(37)

Entrepreneurs

Entrepreneurs have available net worth Nt denominated in domestic currency.
To finance the diﬀerence between their expenditures on capital goods and their
net worth, entrepreneurs borrow from foreign lenders. That is, the entrepreneur
finances investment partly with foreign currency denominated debt.

The en-trepreneur’s balance sheet is therefore given by

PH,t Nt = Qt Kt+1 − Et Dt ,(38)

where Dt is the entrepreneur’s foreign currency debt position. Note that an unanticipated depreciation reduces net worth in the balance sheet (38), which reflects
14the problem of liability dollarization in emerging market economies.
Following Bernanke et al. (1999), we assume that foreign lenders charge anexternal finance premium to entrepreneurs owing to asymmetric information. Entrepreneurs choose Dt and Kt+1 so that the expected return on capital (RK ) equals
the cost of foreign borrowing:(K
Rt+1= (1 + τe,t )(1 + i∗t )

)
Et+1
Ft ,
Et

(39)

where Ft is the external finance premium and τe,t is a tax on the entrepreneur’sforeign borrowing. Following Céspedes et al. (2004), we assume that the externalfinance premium is an increasing function of the value of capital relative to net
worth:()
Qt Kt+1
Ft = Ψ, Ψ(1) = 1, Ψ′ (.) > 1,
PH,t Nt(40)

where the functional form for Ψ is given by Ψ(g) = g µ (µ > 0).13
At the beginning of each period, entrepreneurs collect returns from capitaland repay their foreign debt. Following Céspedes et al. (2004) and Elekdağ andTchakarov (2007), we assume that entrepreneurs consume a fraction 1 − ω of theremainder on imports. The evolution of net worth is thus given as
PH,t Nt = ω[RtK Qt−1 Kt − (1 + τe,t−1 )(1 + i∗t−1 )Ft−1 Et Dt−1 + Te,t ],

13

(41)

Bernanke et al. (1999) show that given the assumptions related to the agency problem
including the characteristics of the distribution of an idiosyncratic return shock, parameter values
associated with monitoring costs, and constant returns to scale in production and monitoring
costs, the agency problem implies that the external finance premium is an increasing function of
the ratio of capital to net worth as in Eq.(40). Especially, the assumption of constant returns toscale in production and monitoring costs is important for the aggregation so that the value ofcapital relative to net worth and the external premium become equal across all entrepreneurs.

15where Te,t denotes a lump-sum transfer from the government.
K
Finally, the return on capital for entrepreneurs Rt+1
is expressed by the sumof the rental rate of capital Rt+1 and the return from capital investment, divided
by the original price of capital Qt :Rt+1 Qt+1
K
+
Rt+1
=
Qt
Qt

2.5

(

[
(1 − δ) + ϕI

)
)2 ]
(
It+1
It+1
ϕI It+1
−δ
−
−δ
.
Kt+1
Kt+1
2 Kt+1(42)

Government

We assume that the government transfers the collected tax on foreign debt tohouseholds and entrepreneurs in a lump-sum manner. The government’s budget
constraints are thus given by
τh,t−1 (1 + i∗t−1 )Et Bt−1 = Th,t(43)

τe,t−1 (1 + i∗t−1 )Ft−1 Et Dt−1 = Te,t .

(44)

and

2.6

Equilibrium and exogenous shocks

The market clearing for domestic goods requires

PH,t Yt = PH,t CH,t + PH,t IH,t + Et EXt ,

16

(45)

where EXt denotes demand for exports, which is assumed to be an exogenous
stochastic process. Dividing both sides of (45) by PH,t we obtain

Yt = CH,t + IH,t + St EXt= (1 − γ)g(St )η (Ct + It ) + St EXt ,

(46)
(47)

where we derive the second equality by considering the demand functions (7), (18),and (28).
From Eq.(21) and the fact that the production function is homogeneous with
degree 1, we obtain∫ 1
Yt (j)dj = Zt Ktα L1−α
,
t

(48)

0

where Kt =∫1

Kt (j)dj and Lt =0∫10

Lt (j)dj. From the demand function fordiﬀerentiated goods, we obtain∫ 1(
0

We define θt ≡PH,t (j)PH,t∫ 1 ( PH,t (j) )−ε
0

PH,t

)−ε
Yt dj = Zt Ktα L1−α
.
t

(49)

dj, which can be expressed as14−εθt = (1 − ζ)P̃H,t+ ζΠεH,t θt−1 .

(50)Then, we can rewrite (49) as
Yt = θt−1 Zt Ktα Lt1−α ,14For the derivation of (50), see Schmitt-Grohé and Uribe (2006).

17

(51)

where θt measures the resource costs induced by price dispersion in the Calvomodel.
The productivity shock Zt , export shock EXt , and foreign (nominal) interestrate shock i∗t are exogenously evolving according to the following processes:
log Zt = (1 − ρz ) log Z + ρz log Zt−1 + εz,t , εz,t ∼ i.i.d. N (0, σz2 ),(52)

2), (53)log EXt = (1 − ρex ) log EX + ρex log EXt−1 + εex,t , εex,t ∼ i.i.d. N (0, σexandi∗t = (1 − ρi )i∗ + ρi i∗t−1 + εi,t , εi,t ∼ i.i.d. N (0, σi2 ).

(54)

The equilibrium of this economy is a set of stationary stochastic processes { Ct ,ttt
, ΠH,t , qt , Yt , M Ct , Kt , It , PQH,t, P̃H,t , Nt , RtK , Ft , Dt , RPtt , W, Xt1 ,
Lt , Bt , Πt , St , PPH,tPt

Xt2 , θt , it , Et }∞t=0 satisfying Eqs. (10)-(14), (17)-(20), (22)-(24), (29), (35)-(37),(38)-(42), (47), (50), and (51) (combined with the equations for other variables),given initial values for B−1 , K0 , N−1 , and D−1 , and exogenous stochastic processes
Zt , EXt , and i∗t .

2.7

Optimal Ramsey policies

We consider optimal Ramsey monetary and capital control policies. We obtain the
Ramsey optimal policies by setting up a Lagrangian problem in which the social
planner maximizes the conditional lifetime utility of the representative household
subject to the first-order conditions of the private agents and the market-clearing
conditions of the economy. We compute this numerically using the Matlab proce-18

dures developed by Levin et al. (2006).15
We let xt denote the N × 1 vector of endogenous variables. Except for thepolicy instrument, the remaining N − 1 endogenous variables in xt satisfy theN − 1 structural conditions, which is expressed with

Et f (xt , xt+1 , ζt ) = 0,(55)

where the vector ζt denotes the exogenous variables. We derive the optimal Ramsey
policy from the maximization problem:

max
E0
∞

{xt }t=0

s.t.

∞
∑

β t U (xt , ζt )t=0

Et f (xt , xt+1 , ζt ) = 0.

(56)

We set up a Lagrangian problem:

L0 = E0∞∑β t {U (xt , ζt ) + λ′t f (xt , xt+1 , ζt )},

(57)

t=0

where λt denotes the Lagrange multipliers associated with the first-order conditionsof the private agents and the market-clearing conditions of the economy in (55).
Taking derivatives of L0 with respect to the N endogenous variables, we obtainthe N first order conditions which are characterized by the following equation:16

U1 (xt , ζt ) + Et λ′t f1 (xt , xt+1 , ζt ) + β −1 λ′t−1 f2 (xt−1 , xt , ζt−1 ) = 0.
15

(58)

Levin et al. (2006)’s program reads a Dynare model file and generates the first-order conditions of a Ramsey policymaker. See Adjemian et al. (2011) for details on Dynare.
16
The first order necessary condition for optimality at t = 0 is (58) with λ−1 = 0.

19

Taking derivatives of L0 with respect to λt , we obtain the N − 1 equilibrium conditions in the private sector in (55). The Ramsey equilibrium process is therefore
characterized by the N −1 equations, (55), and the N equations (58). We have theN elements of x and the N − 1 multipliers, λ. In total, there are 2N − 1 variables
and 2N − 1 equations.
In Section 3, we will examine the optimal Ramsey monetary and capital control
policies. In the peg case without capital controls (i.e, Et = Ē, and τh,t = τe,t = 0
for all t), we have N endogenous variables and N equilibrium conditions. In thepeg case with the optimal capital control policies, we include τh,t and/or τe,t in theendogenous variables and obtain the Ramsey capital control policies by letting τh,t
and/or τe,t be policy instruments. In this case, we have N −1 (or N −2) equilibrium
conditions for N endogenous variables. Including the N − 1 (or N − 2) multipliers,
in total, we have 2N −1 (or 2N −2) variables and 2N −1 (or 2N −2) equations. In
the flexible exchange rate case in which Et is included in the endogenous variables,
we let it be a policy instrument and obtain the Ramsey monetary policy. In thiscase, we have N − 1 equilibrium conditions for N endogenous variables. Including
the N − 1 multipliers, in total, we have 2N − 1 variables and 2N − 1 equations.

2.8

Parameterization

We choose standard parameter values given in the relevant literature, which aresummarized in Table 1. Following many previous studies, we set the quarterly
discount factor β to 0.99. Following Elekdağ and Tchakarov (2007) and Devereux
et al. (2006), we set the inverse of intertemporal elasticity of substitution σ, elasticity of labor supply ϕ, and capital adjustment cost parameter ψ K to 2, 1, and20

12, respectively. We set capital share in production α to 0.32 as in Schmitt-Grohéand Uribe (2003). Following Kollmann (2002) and Devereux et al. (2006), we set
the quarterly depreciation rate δ to 0.025. Following Galı́ and Monacelli (2005),
we set the elasticity of substitution among diﬀerentiated goods ϵ and fraction offirms that do not reset their prices ζ to 6 and 0.75, respectively. As in Ravenna
and Natalucci (2008), we set the elasticity of substitution between domestic andforeign goods η to 1.5. With respect to the degree of openness γ, we follow Cook
(2004) and set it to 0.28. The parameter for bond adjustment cost ψ B and steadystate debt ratio to GDP B
are set to 0.0007 and 0.4, respectively, as in DevereuxY
et al. (2006). We set the steady state level of leverage ratio PQK
at 2.2, which is
HNhigher than in Bernanke et al. (1999) who use 2, but not as high as in Devereux
et al. (2006) who use 3. Following Cespedes et al. (2000) and Merola (2010), we set
the elasticity of external finance premium to leverage ratio µ to 0.02.17 We use thesame values as in Elekdağ and Tchakarov (2007) for the exogenous shocks. The
persistence and the standard deviation of the productivity shock (ρz and σz ) are
set to 0.8 and 0.02, respectively. The persistence and the standard deviation of theexport shock (ρex and σex ) are set to 0.5 and 0.06, respectively. The persistence
and the standard deviation of the foreign interest shock (ρi and σi ) are set to 0.8
and 0.003, respectively.

2.9

Welfare evaluation

We calculate and compare welfare levels under alternative policy regimes. Since
there exist households and entrepreneurs in our model, the overall welfare mea17

Using a maximum-likelihood procedure and post-1979 US data, Christensen and Dib (2008)
report a higher estimated value of 0.042 for this parameter.

21

Table 1: Parameterization.

Parameters

Value

β
σ
ϕ
ψK
α
δ
ϵ
ζ
η
γ
ψB

0.99
2
1
12
0.32
0.025
6
0.75
1.5
0.28
0.0007
0.4
2.2
0.02
0.8
0.02
0.5
0.06
0.8
0.003

B
Y
QK
PH N

µ
ρZ
σZ
ρex
σex
ρi
σi

Discount factor
Inverse of intertemporal elasticity of substitution
Elasticity of labor supply
Capital adjustment cost parameter
Share of capital in output
Depreciation rate of capital
Elasticity of substitution among diﬀerentiated goods
Fraction of firms that do not reset their prices
Elasticity of substitution between domestic and foreign goods
Degree of openness
Parameter for bond adjustment cost
Steady-state ratio of debt to GDP
Steady-state ratio of capital to net worth
Elasticity of external finance premium
Persistence: productivity shockStandard deviation: productivity shock
Persistence: export shockStandard deviation: export shock
Persistence: foreign interest rate shockStandard deviation: foreign interest rate shock22

sure of the eocnomy is the weighted sum of households’ and entrepreneurs’ welfare. However, as argued by Bernanke et al. (1999), we can reasonably assume
that the fraction of entepreneurs’ consumption is negligible. Following Faia andMonacelli (2005) and Elekdağ and Tchakarov (2007), we therefore assume that theentepreneurs’ share of consumption is negligible and the overall welfare measureof the eocnomy corresponds to the households’ welfare level. We let V0a denote theconditional welfare level associated with case (a) (a=i, ii, iii...):

V0a ≡ E0
= E0

∞
∑
t=0
∞
∑

β t U (Cta , Lat ),β t U ((1 − λa )C, L).

(59)

t=0

Here, λa is the welfare cost of adopting policy (a) on the condition of the calibrated steady state. The conditional welfare measure is obtained using the secondorder perturbation methods as described in Schmitt-Grohé and Uribe (2004) andSchmitt-Grohé and Uribe (2007).18 We let the most welfare-maximizing case be
the reference case (ref ). Therefore, λa − λref is the welfare loss in each case,which is the fraction of consumption that compensates a household to a level thatis considered as well oﬀ under policy (a) as in the reference case (ref ).

3

Results

In this section, we present the main results of our analysis. We evaluate the welfare
implications of alternative policy and exchange rate regimes with and without thefinancial accelerator. In Section 3.1, we consider an economy without the financial
18

Kim and Kim (2003) reveal that second-order solutions are necessary because conventional
linearization may generate spurious welfare reversals.

23

accelerator and compare the welfare consequences of an optimal monetary policy
under flexible exchange rates (policy instrument it ), an optimal capital control
policy on households under fixed exchange rates (policy instrument τh , Et = Ē forall t), and a peg regime without an optimal capital control policy (Et = Ē for all t).
In Section 3.2, we analyze an economy with the financial accelerator and compare
the welfare consequences of an optimal monetary policy under flexible exchange
rates (policy instrument it ), an optimal capital control policy on households under
fixed exchange rates (policy instrument τh , Et = Ē for all t), an optimal capital
control policy on entrepreneurs (policy instrument τe , Et = Ē for all t), optimal
capital control policies on households and entrepreneurs (policy instruments τhand τe , Et = Ē for all t), and a peg regime without optimal capital control policy(Et = Ē for all t).

3.1

No financial accelerator

Following Devereux et al. (2006), we also examine the model without entrepreneursin order to explore the importance of the balance sheet eﬀect. In this case, households accumulate capital without the external finance premium. The Appendix
explains the model without entrepreneurs in detail.
We compare welfare levels in an economy without the financial accelerator in
the following cases: (i) an optimal monetary policy under flexible exchange rates(policy instrument it ), (ii) an optimal capital control policy under fixed exchange
rates (policy instrument τh , Et = Ē for all t), and (iii) a fixed exchange rate regime(without capital controls, Et = Ē for all t). Since the optimal monetary policy caseunder flexible exchange rates (i) turns out to be the most welfare-maximizing, we

24

Table 2: Conditional welfare costs: No financial accelerator

Welfare Cost:(λa − λref ) × 100(i) Mon.

(ii) Cap. Con.

(iii) Fixed ER

0

0.106

0.306

Note) The conditional welfare costs in (ii) and (iii) are measured with the most welfaremaximizing case (i) being the reference case.

let (i) to be the reference case (ref ).
The conditional welfare costs in each case (i, ii, and iii) compared with thereference case (ref ) are shown in Table 2. The welfare cost in the case of an
optimal capital control policy under fixed exchange rates (ii) is 0.106%, whereas
the welfare cost in the fixed exchange rate regime (iii) is 0.306%. Hence, we can saythat the optimal capital control policy more than halves the welfare gap between
the flexible exchange rate case (i) and the fixed exchange rate case (iii). However,
it is obvious that the optimal monetary policy under flexible exchange rates (i)outperforms the optimal capital control policy under fixed exchange rates (ii) inan economy without the financial accelerator.
Tables 3 and 4 show the means and standard deviations of the main variablesin the case without the financial accelerator. Since the capital control policy isadopted only in case (ii), by definition, the means and standard deviations of τhin cases (i) and (iii) are zero in Tables 3 and 4. Since the fixed exchange rateeliminates the volatility of the nominal exchange rate, by definition, the standard
deviation of ∆E in cases (ii) and (iii) is zero in Table 4. Further, note that since theoptimal monetary policy under flexible exchange rates (i) is an “inward looking”
policy, it has the lowest domestic price inflation (ΠH ) volatility among the three
regimes in Table 4. In contrast, since the optimal capital control policy under25

Table 3: Means: No financial accelerator

Y
C
I
L
∆E
S
Π
ΠH
id
τh

(i) Mon.

(ii) Cap. Con.

(iii) Fixed ER

1.8042
1.4571
0.34260.69431.00000.99681.00001.00000.00990.00001.8042
1.45650.3422
0.69441.00000.99671.00001.00000.0099-0.0001

1.79871.45350.34200.69441.00000.99451.00001.00000.01000.0000fixed exchange rates (ii) and the fixed exchange rate regime (iii) are “outward
looking” policies, the terms of trade (S) in (ii) and (iii) are more stabilized (i.e.,the standard deviations of S in (ii) and (iii) are smaller) compared to that in case(i) in Table 4.

3.2

With financial accelerator

We next consider alternative policies in an economy with the financial accelerator.
We compare the welfare levels in the following cases: (i) optimal capital controls on
both households and entrepreneurs under fixed exchange rates (policy instruments
τh and τe , Et = Ē for all t), (ii) optimal capital controls on entrepreneurs under fixedexchange rates (policy instrument τe , Et = Ē for all t), (iii) an optimal monetary
policy under flexible exchange rates (policy instrument it ), (iv) optimal capital
controls on households under fixed exchange rates (policy instrument τh , Et = Ēfor all t), and (v) a fixed exchange rate regime (without capital controls, Et = Ē forall t). Since optimal capital controls on both households and entrepreneurs under26

Table 4: Standard Deviations (%): No financial accelerator

Y
C
I
L
∆E
S
Π
ΠH
id
τh

(i) Mon.

(ii) Cap. Con.

(iii) Peg

3.55
1.67
7.60
0.86
2.75
4.06
0.79
0.05
1.00
0.00

3.21
2.06
10.13
1.93
0.00
2.14
0.19
0.27
0.96
1.05

2.97
1.40
6.17
3.62
0.00
2.63
0.59
0.81
0.50
0.00

fixed exchange rates (i) is the most welfare-maximizing, we let (i) be the referencecase (ref ).
We show the welfare ranking for the alternative regimes in Table 5. It should
be noted that the optimal monetary policy under flexible exchange rates (iii),
which was the most welfare-maximizing in the previous subsection 3.1 for the
economy without the financial accelerator, is now ranked third. As argued above,the most welfare-maximizing is optimal capital controls on both households andentrepreneurs under fixed exchange rates (i). Optimal capital controls on households (iv) improves the welfare level of the economy under fixed exchange rates(v). However, the welfare-improving eﬀect of optimal capital controls on households (iv) is limited. Optimal capital controls on households (iv) is inferior to the
optimal monetary policy under flexible exchange rates (iii). In contrast, optimal
capital controls on entrepreneurs (ii) outperforms the optimal monetary policy(iii). Further, optimal capital controls on entrepreneurs (ii) is second only to themost welfare-maximizing case (i).
27

Table 5: Conditional welfare costs: With financial accelerator

Welfare Cost:(λa − λref ) × 100(i) Cap. Con.
ent. & hous.

(ii) Cap. Con.
ent.

(iii) Mon.

(iv) Cap. Con.
hous.

(v) Peg

0

0.215

1.624

1.900

2.385

Note) The conditional welfare costs in (ii) to (v) are measured with the most welfare-maximizing
case (i) being the reference case.

Tables 6 and 7 show the means and standard deviations of the main variablesin the case with the financial accelerator. Comparing column (v) in Table 7 tocolumn (iii) in Table 4, we can see that the standard deviations of Y , C, I, L,
S, Π, and ΠH in column (v) are larger, which implies that the introduction of afinancial accelerator mechanism into an economy increases the volatilities of theeconomy to the same shocks. Figure 1 represents the impulse responses of Y ,C, I, L, S, Π, and ΠH to a foreign interest rate shock in the peg case with andwithout the financial accelerator. From Figure 1, we can also confirm that thefinancial accelerator makes the economy more volatile. It should be noted that inTable 6, the mean of the external finance premium F is the lowest in case (ii) andsecond-lowest in case (i). We can say that capital controls on entrepreneurs curtailthe external finance premium level more significantly than a monetary policy or
capital controls on households.
The intuition underlying our analysis results is as follows. Entrepreneurs finance investment partly with foreign borrowing, which is subject to financial frictions. Entrepreneurs borrow abroad at an interest rate, which is equal to theforeign interest rate, adjusted for expected exchange rate fluctuations, and aug-

28

Table 6: Means: With financial accelerator

Y
C
I
L
∆E
S
Π
ΠH
id
F
τh
τe

(i) Cap. Con.
ent. & hous.

(ii) Cap. Con.
ent.

(iii) Mon.

(iv) Cap. Con.
hous.

(v) Peg

1.73271.2672
0.23480.78191.00000.99661.00001.00000.00981.0109-0.00020.00311.72951.26470.2341
0.78251.00000.99571.00001.00000.01001.01070.00000.00341.7136
1.25330.22380.78651.00010.99581.00011.00010.00991.01530.00000.00001.70651.24950.22040.78741.00000.99351.00001.00000.00961.0164-0.00020.00001.69481.24090.21630.78941.00000.99151.00001.00000.01001.01730.00000.0000

Table 7: Standard Deviations (%): With financial accelerator

Y
C
I
L
∆E
S
Π
ΠH
id
F
τh
τe

(i) Cap. Con.
ent. & hous.

(ii) Cap. Con.
ent.

(iii) Mon.

(iv) Cap. Con.
hous.

(v) Peg

2.83
2.69
7.12
3.35
0.00
1.75
0.21
0.30
1.31
0.10
1.40
0.83

3.13
1.69
10.23
3.48
0.00
2.81
0.57
0.79
0.50
0.17
0.00
1.31

3.77
2.04
9.17
2.43
4.61
5.13
1.46
0.29
2.05
0.20
0.00
0.00

2.88
3.17
8.73
3.90
0.00
1.91
0.19
0.26
1.68
0.15
1.85
0.00

3.52
2.04
11.02
4.50
0.00
2.85
0.65
0.91
0.50
0.34
0.00
0.00

29

Y

C

0

0

-1

-1

-2

-2
0

10

20

30

40

0

10

I

20

30

40

30

40

30

40

L

0

0
-1

-10

FA
NoFA

-2
-3

-20
0

10

20

30

40

0

10

S

20
Π

0.2
0
-0.2
-0.4
-0.6
-0.8

1.5
1
0.5
0
-0.5
0

10

20
ΠH

30

40

0

10

20

30

40

0

10

20

0
-0.5
-1

Figure 1: Model with (−) and without (−−) the financial accelerator; Peg case:
Impulse responses to a foreign interest rate shock

30

mented by an external finance premium. Although it aﬀects the economy throughdomestic interest rates, a monetary policy does not directly aﬀect the interest
rate at which entrepreneurs borrow from abroad. In contrast, capital controls on
entrepreneurs have a direct control on the interest rate at which entrepreneurs
borrow from foreign lenders, and may yield higher welfare in an economy with thefinancial accelerator.

4

Sensitivity analysis

In this section, we examine the robustness of our analysis results in the previous
section. In the previous section, we showed the welfare rankings in the case inwhich all the shocks are included. In this section, we will show that our results
are robust even when we consider these shocks individually.
First, we considered the welfare rankings in an economy without the financial
accelerator. Table 2 shows the welfare ranking in the case in which all the threeshocks are included. The welfare rankings for the individual shocks, which areproductivity shock, export shock, and foreign interest shock, are shown in Tables
8, 9, and 10, respectively. In Tables 8, 9, and 10, we can see that the optimalmonetary policy under flexible exchange rates (i) outperforms the optimal capital
control policy under fixed exchange rates (ii). The welfare rankings for individual
shocks in Tables 8, 9, and 10 are then identical to that for all the shocks in Table
2. Therefore, we confirm that our results are robust even when we consider theindividual shocks in an economy without the financial accelerator.
However, there are some notable diﬀerences among the three cases. Comparing
Tables 8, 9, and 10, we can see that the welfare benefit of monetary policy (i.e., the31

diﬀerence between (i) and (iii)) is the largest for the productivity shock but thesmallest for the foreign interest shock. Another notable diﬀerence is that although
the capital control policy is not as good as the monetary policy in any case, thecapital control policy is the closest to the monetary policy for the foreign interest
shock (i.e., (ii) in Table 10 is smaller than that in Tables 8 and 9).
Table 8: Conditional welfare costs: No financial accelerator – Productivity shock

Welfare Cost:(λa − λref ) × 100(i) Mon.

(ii) Cap. Con.

(iii) Fixed ER

0

0.056

0.182

Table 9: Conditional welfare costs: No financial accelerator – Export shock

Welfare Cost:(λa − λref ) × 100(i) Mon.

(ii) Cap. Con.

(iii) Fixed ER

0

0.044

0.075

Table 10: Conditional welfare costs: No financial accelerator – Foreign interestshock

Welfare Cost:(λa − λref ) × 100(i) Mon.

(ii) Cap. Con.

(iii) Fixed ER

0

0.007

0.049

Next, we consider the welfare rankings in an economy with the financial accelerator. Table 5 shows the welfare ranking in the case in which all the three shocks
are included. The welfare rankings for the individual shocks, which are productivity shock, export shock, and foreign interest shock, are shown in Tables 11, 12, and32

13, respectively. In Tables 11, 12, and 13, we can see that the welfare rankings forindividual shocks are identical to that for all the shocks in Table 5. Therefore, we
confirm that our results are robust even when we consider the individual shocks
in an economy with the financial accelerator.
However, there are some notable diﬀerences among the three cases. Comparing
Tables 11, 12, and 13, we can see that the welfare benefit of capital controls (i.e.,the diﬀerence between (i) and (v)) is the largest for the foreign interest shock.
Another notable diﬀerence is that the monetary policy is furthest behind capital
controls for the foreign interest shock (i.e., the diﬀerence between (i) and (iii) in
Table 13 is larger than that in Tables 11 and 12).
Table 11: Conditional welfare costs: With financial accelerator – Productivity
shock

Welfare Cost:(λa − λref ) × 100(i) Cap. Con.
ent. & hous.

(ii) Cap. Con.
ent.

(iii) Mon.

(iv) Cap. Con.
hous.

(v) Peg

0

0.123

1.663

1.741

1.922

Table 12: Conditional welfare costs: With financial accelerator – Export shock

Welfare Cost:(λa − λref ) × 100(i) Cap. Con.
ent. & hous.

(ii) Cap. Con.
ent.

(iii) Mon.

(iv) Cap. Con.
hous.

(v) Peg

0

0.049

1.630

1.757

1.871

33

Table 13: Conditional welfare costs: With financial accelerator – Foreign interestshock(i) Cap. Con.
ent. & hous.

(ii) Cap. Con.
ent.

(iii) Mon.

(iv) Cap. Con.
hous.

(v) Peg

0

0.043

1.800

1.870

2.064

Welfare Cost:(λa − λref ) × 100

5Conclusion

We have developed a small open economy, New Keynesian model that highlights
the vulnerability of balance sheets to exchange rate fluctuations. We then apply a
Ramsey-type analysis and examine the welfare implications of optimal monetaryand capital control policies. To our knowledge, our paper is the first that examines
the welfare implications of optimal capital control policies in a small open economy, New Keynesian model that incorporates a financial accelerator coupled withliability dollarization.
In the case without the financial accelerator, we have compared three cases: an
optimal monetary policy under flexible exchange rates, an optimal capital control
policy (on households) under fixed exchange rates, and fixed exchange rates (without capital controls). Our Ramsey-type analysis results have shown that although
the optimal capital control policy significantly improves welfare under fixed exchange rates, the optimal monetary policy is the most welfare-maximizing in an
economy without the financial accelerator.
In the case with the financial accelerator, we compared five cases: an optimal monetary policy under flexible exchange rates, fixed exchange rates (without

34

capital controls), an optimal capital control policy on entrepreneurs, an optimal
capital control policy on households, and an optimal capital control policy on both
entrepreneurs and households under fixed exchange rates. Our results have shownthat the optimal monetary policy still outperforms the optimal capital control policy on households. However, the optimal capital control policy on entrepreneurs
outperforms the optimal monetary policy. The most welfare-maximizing is the
optimal capital control policy on both entrepreneurs and households.
The intuition underlying our analysis results is straightforward. Entrepreneurs
finance investment partly with foreign borrowing, which is subject to financial
frictions. In an economy with a financial accelerator, the key variable is the foreigninterest rate augmented by an external finance premium. Whereas monetary policy
works through domestic interest rates, capital controls on entrepreneurs have a
direct control on the interest rate at which entrepreneurs borrow from abroad.
Hence, capital controls under fixed exchange rates can yield higher welfare in an
economy with a financial accelerator coupled with liability dollarization.
As we mention in the introduction, Liu and Spiegel (2015) show that the welfare
gain of capital controls depends on the presence of sterilization, and that capital
controls and sterilization are complementary policies. Although it is beyond thescope of this study, their findings suggest that if we introduce sterilization into ourmodel, it is highly likely that the welfare gain of capital controls becomes larger.
Another useful extension would be to study the role of pecuniary externalities thatlead borrowers to overborrow in a small open economy, as examined by Jeanne andKorinek (2010) and Bianchi (2011). If we incorporate the externalities associatedwith overborrowing into our model, it would magnify the financial-accelerator
mechanism eﬀect in an economy. It would be an interesting project to examine
35

the role of capital controls in an economy with a larger amplification eﬀect due topecuniary externalities. We leave these extensions for future research.

Appendix
In this appendix, we explain the diﬀerences between the models with and without
entrepreneurs. In the economy without entrepreneurs, households directly makeinvestment and accumulate capital. In this case, the households’ budget constraint
is given by
Pt Ct + Pt It + (1 + it−1 )At−1 + (1 + τh,t−1 )(1 + i∗t−1 )Et Bt−1 + Pt ψ2B (Bt − B)2= At + Et Bt + Wt Lt + RtK Qt−1 Kt + Th,t + ΠFt .

(A1)

Therefore, the optimal conditions associated with households’ problem include thefollowing equation:}{ h
λt+1 K Pt
R,
1 = βEt
λht t+1 Pt+1

(A2)

where RtK now denotes the return on capital for households.
Since there is no entrepreneurs in this economy, we omit the optimal conditions
associated with entrepreneurs’ problem (38)-(41). The equilibrium of the economy
without entrepreneurs is therefore characterized by a set of stationary stochastictt, ΠH,t , qt , Yt , M Ct , Kt , It , PQH,t, P̃H,t , RtK , RPtt ,processes { Ct , Lt , Bt , Πt , St , PPH,tWt, Xt1 , Xt2 , θt , it , Et
Pt}∞
t=0 satisfying Eqs. (11)-(14), (17)-(20), (22)-(24), (29),(35)-(37), (42), (47), (50), (51), (A1), and (A2) (combined with the equations forother variables), given initial values for B−1 , and K0 , and exogenous stochastic
processes Zt , EXt , and i∗t .
36

In the peg case without capital controls (i.e, Et = Ē, and τh = 0 for all t), we
have 21 endogenous variables and the same number of conditions. In the peg casewith the optimal capital control policy, we include τth in the endogenous variables
and obtain the Ramsey capital control policy by letting τth be a policy instrument. In the flexible exchange rate case in which Et is included in the endogenous
variables, we let it be a policy instrument and obtain the Ramsey monetary policy.

37

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