DP2013-36

External Debt and T aylor Rules
in a Sm all Open Economy
Shigeto KITANO
Kenya TAKAKU
Revised January 13, 2016

External debt and Taylor rules in a small open economy∗
Shigeto Kitano†

Kenya Takaku‡

Abstract
We develop a dynamic stochastic general equilibrium model of a small
open economy in which both price rigidity and financial friction exist.
We compare two cases featuring diﬀerent interest rate rules. Bothcases use the standard Taylor-type interest rate rules, but the secondcase also considers external debt levels. We find that when friction inforeign borrowing is large, adding an external debt level to Taylor rules
improves welfare. The welfare curve, however, exhibits a hump shapesince excessive reactions to changes in external debt reduce welfare.

Keywords: External debt; Taylor rules; small open economy;
DSGE; welfare; emerging market economies.
JEL Classification: E5, F4.
∗

Earlier versions of the paper were presented at the tenth annual conference, AsiaPacific Economic Association in Bangkok, the Japan Society of Monetary Economics,
and Kobe University. The authors thank the seminar participants for helpful comments.
The authors are especially grateful to two anonymous referees, Takashi Kamihigashi, Ryo
Kato, Masahiko Shibamoto, Eiji Okano, and Chikafumi Nakamura for valuable comments.
Any remaining errors are ours. This work was supported by Grants-in-Aid for Scientific
Research.
†
RIEB, Kobe University, 2-1, Rokkodai, Nada, Kobe, 657-8501 Japan, E-mail:kitano@rieb.kobe-u.ac.jp.
‡
Faculty of Business, Aichi Shukutoku University, 23, Sakuragaoka, Chikusa, Nagoya,464-8671, Japan, E-mail: ktakaku@asu.aasa.ac.jp.

11Introduction

Taylor rules are simple monetary policy rules that govern how a central bankshould systematically adjust the nominal interest rate in response to changes
in inflation and other macroeconomic variables. Since Taylor (1993), a large
body of literature has shown that these rules provide a reasonable empiricaldescription of the policy behavior exhibited by many central banks (e.g.,
Clarida et al. (1998)).
In addition, further studies have examined whether welfare can be improved if other macro-variables such as foreign exchange rates and asset prices
are added to the standard Taylor rules. Taylor (2001) surveyed literature examining the policy eﬀect when exchange rates are added to Taylor rules(e.g., Ball (1999) and Svensson (2000)). Taylor (2001) concluded that theeconomic improvement would be small or might even decline if exchange rates
were added when controlling inflation rate and output gap volatility. Senay(2008) performed a welfare analysis based on a small open dynamic stochastic
general equilibrium (DSGE) model with price rigidity and micro-foundations.
The results suggested that including exchange rates would reduce welfare.1
Bernanke and Gertler (1999) incorporated a bubble crisis into the financial
accelerator model of Bernanke et al. (1999) and examined whether to add
asset prices to Taylor-type interest rate rules. They concluded that monetary
authorities should not consider asset prices in their monetary policy. However, Cecchetti et al. (2000) considered a generalized version of the model
1

The theoretical models in the literature presented by Taylor (2001) lacked microfoundations. Whereas Svensson (2000) developed a model based on micro-foundations,
the welfare loss function is set in an ad hoc way.

2

used by Bernanke and Gertler (1999) and advised that interest rates respondto stock prices.
The recent financial crisis has revived the long-standing debate concerningwhether monetary authorities should consider variables other than inflationand output gaps. More recent studies have suggested that the central bankmay improve welfare by including such additional variables in monetary policy rules. Studies such as those by Christiano et al. (2007), Christiano et al.
(2008), Cúrdia and Woodford (2010), Gray et al. (2011), and Kannan et al.
(2012) have shown that gains can result from including additional variables
such as credit growth, credit spreads, or financial stability indicators.
This paper focuses on emerging market economies. Business cycles insuch economies are amplified by recurrent capital flow booms and busts.
Increasing interest in this phenomenon has resulted in a fast-growing bodyof literature investigating prudential policies concerning capital inflows (e.g.,
Jeanne and Korinek (2010); Korinek (2011); Jeanne et al. (2012)).2 Buildingon this background, we developed a model that includes external debt in thestandard Taylor rules. We considered whether it is welfare improving to use
monetary policy to increase interest rates when capital inflows are booming
and external debt is accumulating. To examine if including external debt in
the standard Taylor rules may improve an economy’s welfare, we developed astandard DSGE model of a small open economy calibrated to reflect emerging
market economies, incorporating both price rigidity and a reduced form offinancial friction à la Garcia-Cicco et al. (2010).
2

For details on the new literature on capital controls, see Korinek (2011) or Jeanne
et al. (2012). For the earlier literature, see the introduction in Kitano (2011).

3

Our argument is closely related to the argument made by Garcia-Cicco
et al. (2010) on a country-specific interest-rate premium. Garcia-Cicco et al.
(2010) showed that the country-specific interest-rate premium parameter canplay an important role in replicating the business cycle seen in emerging market economies. Moreover, they argued that ”the role of the debt elasticityof the country premium is no longer limited to simply inducing stationarity, but to potentially act as the reduced form of a financial friction shaping
the model’s response to aggregate disturbances.” The country premiums ofemerging market economies are significantly higher than those of developed
countries. In addition, the country premium rises as a country accumulates
external debt. Our analysis showed that as the debt elasticity of the country
premium rises, it becomes increasingly important for policy makers in emerging market economies to incorporate external debt levels into their monetary
policy decisions.
The remainder of the paper is organized as follows. In Section 2, we
present a DSGE model of a small open economy including both price rigidityand financial friction. In Section 3, we calibrate our model to match key
characteristics of emerging economies. In Section 4, we perform a comparative analysis of welfare in two interest rate rule scenarios. Both cases use thestandard Taylor-type interest rate rules, but the second case also considers
external debt levels. Conclusions are presented in Section 5.

4

2

The Model

We employ a simple small open sticky price DSGE model.3 The model’s
world economy consists of two separate economies, a small open economy(home country) and the rest of the world’s economy (foreign country). Eacheconomy includes a continuum of infinitely-lived agents (households andfirms).
Households have access to domestic and foreign asset markets. We assume
that households face a country-specific interest rate premium in their foreign
borrowing. Firms produce diﬀerentiated goods by using capital and labor ina monopolistic competitive market.

2.1

Households

A representative household will seek to maximize

E0

∞
∑
t=0

(
βt

Ct − χNtϕ

)1−σ

−1

1−σ

, χ > 0, ϕ > 1, σ > 0,(1)

where Et denotes the mathematical expectations operator conditional on information available at time t, β ∈ (0, 1) is the discount factor, Ct signifies acomposite consumption index, and Nt represents labor eﬀort. The intertemporal elasticity of substitution is given by σ1 , and the elasticity of labor supply
1
is given by ϕ−1. Households consume diﬀerentiated goods (produced by both

domestic and foreign firms). The composite consumption index Ct is given

3

The model here is based on the small open economy structure developed by Galı́ andMonacelli (2005) and Faia and Monacelli (2008).

5

by

[

η−1
η

1
η

1
η

η−1
η

Ct ≡ (1 − γ) CH,t + γ CF,t

η
] η−1

.

(2)

The parameter η(> 0) is the elasticity of substitution between domestic andforeign goods, and the parameter γ ∈ (0, 1) represents the measure of openness. CH,t and CF,t are the indices of consumption of domestic and foreign
goods, expressed by[∫ 1
CH,t ≡

CH,t (j)

ε−1
ε

ε
] ε−1

[∫ 1
CF,t ≡;

dj

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 diﬀerentiated goods. A household’s optimal expenditure allocation in each goods
category yields the demand functions for domestic and foreign diﬀerentiatedgoods:4(
CH,t (j) =PH,t (j)
PH,t

)−ε

(
CH,t ;

CF,t (j) =PF,t (j)PF,t)−ε
CF,t ,(4)

where PH,t (j) and PF,t (j) denote the domestic-currency-denominated pricesof diﬀerentiated goods j produced by domestic and foreign firms, respectively.
PH,t and PF,t are the domestic and import price index, respectively:[∫ 1
PH,t ≡

PH,t (j)

1−ε

1
] 1−ε

dj

[∫ 1
PF,t ≡;

0

PF,t (j)

1−ε

1
] 1−ε

dj

.

(5)

0

4

More specifically, the optimal expenditure allocation is given by minimizing
ε
] ε−1
[
∫1
ε−1
for i = H or F .
Pi,t (j) Ci,t (j) dj, subject to Ci,t ≡ 0 Ci,t (j) ε dj
0

∫1

6

From Eq. (5), it follows that
∫ 1

∫ 1
PH,t (j) CH,t (j) dj = PH,t CH,t ;PF,t (j) CF,t (j) dj = PF,t CF,t .

(6)

0

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):] 1[
1−η 1−η1−η
+ γPF,tPt ≡ (1 − γ)PH,t.

(8)

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

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

(9)

A household’s budget constraint in period t is given as

Pt Ct +Pt It +Tt +(1+it−1 )At−1 +(1+ift−1 )Et Bt−1 = At +Et Bt +Wt Nt +Rt Kt +ΠFt ,(10)
where It is aggregate investment, Tt is lump-sum tax, it is the interest rate at
which households can borrow in the domestic asset market (i.e., the nominalinterest rate), At is the domestic debt position, ift is the interest rate at whichhouseholds can borrow in the foreign asset market, Et represents the nominal
exchange rate (in terms of the domestic currency), Bt is the country’s foreign
debt position, Wt is the nominal wage, Rt is the rental rate of capital, Kt

7

stands for capital, and ΠFt denotes dividends from firms. It is composed ofdomestic and imported goods:[
η−1η−1 ] η
1
1
η−1
η
η
η
It ≡ (1 − γ) IH,t + γ IF,tη.

(11)

IH,t and IF,t are the indices of investment of domestic and foreign goods,
represented by[∫ 1
IH,t ≡

IH,t (j)

ε−1
ε

ε
] ε−1

dj

[∫ 1
;

IF,t ≡

0IF,t (j)

ε
] ε−1

ε−1
ε

dj

.

(12)

0

The optimal allocation of expenditure in each goods category yields the following demand functions:(
IH,t (j) =PH,t (j)
PH,t

)−ε

(
IH,t ;

IF,t (j) =PF,t (j)PF,t)−ε
IF,t .

(13)

The optimal allocation of expenditures between domestic and imported goods
gives

(
)−η
PH,t
IH,t = (1 − γ)
It ;
Pt

(

PF,t
IF,t = γ
Pt

)−η
It .

(14)

From Eqs. (8) and (14), we obtain

PH,t IH,t + PF,t IF,t = Pt It .

(15)

The capital accumulation process is given as
ψK(Kt+1 − Kt )2 ,Kt+1 = (1 − δ)Kt + It −
2

8

(16)

where ψ K is the capital adjustment cost parameter and δ is the depreciation
rate of physical capital.
The interest rate at which households can borrow in the foreign asset
market ift is given by
˜ t } − 1).
ift = i∗t + ψ B (exp{By(17)i∗t is the foreign nominal interest rate (henceforth, we use asterisks to denoteforeign variables). ψ B (> 0) is the parameter for the country-specific interest)(
˜ t ≡ Et Bt − E B denotes foreign debt to output ratio’s
rate premium. By
Pt Y tP Y
deviation from its steady-state value. This implies that as the foreign debt
position deviates from its steady-state level, the cost of foreign borrowing
increases.
The optimality conditions associated with households’ maximization problem are given by(

Ct − χ Ntϕ)−σ

χ ϕ Ntϕ−1 ={1 = β(1 + ift )Et

(18)

Wt
,
Pt

(19)

}
λt+1 Pt,
λt Pt+1(20)}
λt+1 Pt Et+1,
λt Pt+1 Et(21){
1 = β(1 + it )Et= λt ,

and{1 + ψ (Kt+1 − Kt ) = βEt
K

[
]}
Rt+1
λt+1
K
1 − δ + ψ (Kt+2 − Kt+1 ) +. (22)λt
Pt+1

9Combining (20) and (21), we obtain the interest parity condition:{(1 + it )Et

λt+1 Pt
λt Pt+1}{= (1 + ift )Et}
λt+1 Pt Et+1.
λt Pt+1 Et(23)

We assume that the law of one price holds for individual goods. The
terms of trade are therefore given as

St ≡

PF,t
Et Pt∗
=
,
PH,t
PH,t

(24)

where Pt∗ denotes the CPI in the foreign country (in terms of foreign currency).5 It follows from Eq. (24) that
∆Et
St
=
,
St−1
ΠH,t
(
where ΠH,tPH,t≡ PH,t−1)(

Etand ∆Et ≡ Et−1

(25))
represent the rate of domestic in-flation and the depreciation rate of the nominal exchange rate, respectively.
From the CPI (8) and Eq.(24), we have
1Pt
= [(1 − γ) + γSt1−η ] 1−η ≡ g(St ).
PH,t

(26)

It follows from Eq. (26) thatΠt = ΠH,tg(St ),g(St−1 )

(27)

)
(
t
denotes the rate of CPI inflation. From Eqs. (24) andwhere Πt ≡ PPt−1
5

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

10

(26), we can express the real exchange rate Qt as the function of St :
Qt ≡

2.2

Et Pt∗St=≡ q(St ).
Ptg(St )

(28)

Firms

Each monopolistic firm j in the home economy produces a diﬀerentiated goodwith the following production function:

Yt (j) = Zt Kt (j)α Nt (j)1−α ,(29)where Yt (j), Kt (j), Nt (j), and Zt denote the firm’s output level, its capitaland labor inputs, and a stochastic productivity shock, respectively.
From the first-order conditions associated with the firm’s cost minimization, we have

(
)
( K)
Wt
Rt
Kt (j) = α
Nt (j).
(1 − α)
PH,t
PH,t

(30)

Considering (30), we obtain the firm’s real marginal cost:

M Ct (j) = M Ct =(Rt /PH,t )α (Wt /PH,t )1−α.
Zt αα (1 − α)1−α(31)

Following Calvo (1983), we assume that in each period, a fraction 1 − ζ offirms reset their prices, while a fraction ζ keep their prices unchanged. Thisimplies that the domestic price index can be expressed as
[
] 1
1−ε
1−ε 1−εPH,t ≡ ζPH,t−1+ (1 − ζ)P̄H,t
,

11

(32)

where P̄H,t represents the price reset in period t. Transforming (32) yields
1−ε
1 = ζΠ−1+ε+ (1 − ζ)P̃H,t
,
H,t

(33)

P̄

H,t
denotes the relative price of a good, the price of which iswhere P̃H,t ≡ PH,tadjusted in period t in terms of the composite good.
Each firm chooses 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
)]},

(34)

k=0

subject to(
Yt+k|t =P̄H,tPH,t+k)−εYt+k ,(35)n
where Yt+k|t and M Ct+k|t
denote the output level and the nominal marginal

cost, respectively, in t + k for a firm that last reset its price in period t.
Pt
is the discount factor. Yt+k is the aggregate output levelΛt,t+k ≡ β k λλt+kt Pt+kin period t + k. From the first-order condition associated with the above
problem, the optimal price is determined as

P̃H,t =

ε
ε−1

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

∑∞

k

12

(36)

2.3

Government

We assume that the government collects a lump-sum tax to finance government spending. The government’s budget constraint is given by

where

Tt = Pt Gt ,

(37)

[
η−1
η−1 ] η11
η−1
η+ γ η GF,tη.
Gt ≡ (1 − γ) η GH,t

(38)

Similar to Ct and It , it holds that(

PH,t
GH,t = (1 − γ)
Pt

)−η

(

Gt ;

PF,t
GF,t = γ
Pt

)−η
Gt .

(39)

From Eqs. (8) and (39), we obtain

PH,t GH,t + PF,t GF,t = Pt Gt .

(40)

Since the government’s budget is balanced in each period, there is no public
debt in our model. We do not include public debt in our model because
our study focuses on examining how monetary policy can be conducted to
manage the private sector’s capital inflow and outflow and stabilize the boom
and bust cycle of emerging market economies.

13

2.4

Equilibrium and exogenous shocks

Market clearing for domestic goods must satisfy

PH,t Yt = PH,t CH,t + PH,t IH,t + PH,t GH,t + Et EXt ,(41)

where the domestic good is also exported to the foreign country, demand forwhich is assumed to be an exogenous stochastic process, EXt . Dividing bothsides of (41) by PH,t yields

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

(42)
(43)

where the second equality is derived by considering the demand functions(7), (14), (26), and (39).
Eq. (29) and the homogeneous of degree 1 production function imply
that

∫ 1
Yt (j)dj = Zt Ktα Nt1−α ,

(44)

0

where Kt =∫1

Kt (j)dj, and Nt =0∫10

Nt (j)dj. From the demand function fordiﬀerentiated goods, it follows that
∫ 1(
0

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

PH,t

)−ε
Yt dj = Zt Ktα Nt1−α .

(45)

dj, which indicates a measure of price dispersion

14

across firms. Here, θt can also be expressed as6−εθt = (1 − ζ)P̃H,t+ ζΠεH,t θt−1 .

(46)

Using θt , we also can rewrite (45) as
Yt = θt−1 Zt Ktα Nt1−α .

(47)

Eq. (47) shows that a larger value of θt means the larger resource cost, owing
to the price dispersion.
It follows from (9), (15), and (40) that

{PH,t Yt −PH,t (CH,t +IH,t +GH,t )}−{PF,t (CF,t +IF,t +GF,t )} = PH,t Yt −Pt (Ct +It +Gt ).
(48)
Dividing (48) by PH,t and from (26), we define the trade balance as
T Bt ≡ Yt − g(St )(Ct + It + Gt ).

(49)

From the budget constraints of both households (10) and the government(37), we define the current account as

CAt ≡ St (−Bt + Bt−1 ) = T Bt − ift−1 St Bt−1 .

(50)

The productivity shock Zt , the export shock EXt , the foreign (nominal)
interest-rate shock i∗t , and the government spending shock Gt are exogenously
6

For the derivation of (46), see Schmitt-Grohé and Uribe (2006).

15

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 )(51)

2log EXt = (1 − ρex ) log EX + ρex log EXt−1 + εex,t , εex,t ∼ i.i.d. N (0, σex)(52)i∗t = (1 − ρi )i∗ + ρi i∗t−1 + εi,t , εi,t ∼ i.i.d. N (0, σi2 )

(53)

and

log Gt = (1 − ρg ) log G + ρg log Gt−1 + εg,t . εg,t ∼ i.i.d. N (0, σg2 )

2.5

(54)

Monetary policy rule

We posit the following simple monetary policy rule:˜ t,ĩt = ΓΠ Π̃H,t + ΓY Ỹt + ΓB By

(55)

)
(
(
)
Π −Π
where ĩt (≡ it − i) , Π̃H,t ≡ H,tΠH H , and Ỹt ≡ YtY−Y denote the nominalinterest rate, domestic inflation, and output deviations from their steadystate values, respectively. ΓΠ , ΓY , and ΓB are the parameter values that
represent the monetary authority’s policy stance. In the case of ΓB = 0, themonetary policy rule can be reduced to a standard Taylor-type interest raterule. On the other hand, in the case of ΓB > 0, the monetary authority raises
the nominal interest rate against a rise of the foreign debt to output ratio.

16

3

Calibration

This subsection presents calibration of the model parameters and stochastic
shocks, which are summarized in Table 1. Following Elekdağ and Tchakarov(2007), we use the U.S. 3-month certificate of deposit (CD) rate from 1990Q1
to 2013Q1 to calibrate the foreign interest rate shock.7 We seasonally adjusted the data using the Census Bureau’s X-12-ARIMA program and applied
the Hodrick–Prescott filter with a smoothing parameter of 1600 to obtainthe following parameter estimates: ρi = 0.93 and σi = 0.004. We also follow
Elekdağ and Tchakarov (2007) to calibrate the export shock and use the export volume series for available emerging countries.8 We fit Eq. (52) to eachcountry’s detrended data. We averaged the estimates to obtain ρex = 0.43
and σex = 0.056. To calibrate the government’s spending shock for relevant
emerging countries, we used government consumption expenditures from theInternational Financial Statistics database.9 We averaged the estimates todetermine that ρg = 0.50 and σg = 0.043. It is generally diﬃcult to obtainreliable productivity series for emerging countries owing to the limited availability of data. Following previous studies (e.g., Neumeyer and Perri (2005)),
we assumed that the productivity series had the same persistence as the pro7

The source for the 3-month certificate of deposit:
secondary market
rate (CD3M) is the Federal Reserve Bank of St.
Louis FRED Database:
http://research.stlouisfed.org/fred2/series/CD3M/downloaddata.
8
Export volume data for Brazil, Korea, Thailand, and Turkey are available from theInternational Monetary Fund’s International Financial Statistics (IFS) database. Data
are collected from 1990Q1 to 2012Q4 (except for Brazil, which is collected up to 2013Q1).
The raw series were seasonally adjusted, logged, and detrended using the Hodrick–Prescottfilter.
9
Data are collected from 1990Q1 to 2012Q4 (except for Korea and Turkey, for whichdata are collected up to 2012Q3). We used GDP deflators to determine government
consumption expenditure in real terms. The raw series were seasonally adjusted, logged,
and filtered using the Hodrick–Prescott filter.

17

cess estimated for developed countries and accordingly set the productivity
shock volatility to render the model close to the data.10
Standard values for the other parameters followed those used in the relevant literature. We set the quarterly discount factor (β) to 0.99 (e.g., Galı́
and Monacelli (2005)). The inverse of intertemporal elasticity of substitution(σ) was set to 2. Following Neumeyer and Perri (2005), we set the curvature1of labor ϕ to 1.6, which implies the elasticity of labor supply given by ϕ−1

is about 1.7. χ was chosen to generate steady-state labor hours (h) of onethird. The capital share in production (α) was set to 0.32. Following Galı́
and Monacelli (2005), we set the elasticity of substitution among diﬀerentiated goods ϵ to 6. Following Galı́ and Monacelli (2005), we set the fractionof firms that do not reset their prices ζ to 0.75. Following Kollmann (2002),
we set physical capital’s quarterly depreciation rate δ to 0.025. Following
Ravenna and Natalucci (2008), we set the elasticity of substitution between
domestic and foreign goods (η) to 1.5. Following Cook (2004), we set thedegree of openness γ to 0.28. The capital adjustment cost parameter ψ K
and the country-specific interest rate premium parameter ψ B govern investment and the trade balance to output ratio volatilities. We set ψ K and ψ B tomatch the standard deviation of investment as well as of the trade balance tooutput ratio with their data as closely as possible (ψ K = 9 and ψ B = 0.08).
Following Aguiar and Gopinath (2007), we set the steady-state level of foreign debt to GDP ( yb ) to 0.1. In calibrating interest rate rules, we followed
Taylor (1993)’s estimates and set ΓΠ and ΓY to 1.5 and 0.5, respectively.
10

We set ρz to 0.73, which fits between Galı́ and Monacelli (2005)’s estimation of 0.66
for Canada and DeJong and Dave (2011)’s estimation of 0.78 for the United States.

18

Table 1: Calibration.
Parameters Value
ρi
σi
ρex
σex
ρg
σg
ρz
σz
β
σ
ϕ
χ
h
α
ϵ
ζ
δ
η
γ
ψK
ψB
b
y

ΓΠ
ΓY

0.93
0.004
0.43
0.056
0.50
0.043
0.73
0.045
0.99
2
1.6
1.8
0.33
0.32
6
0.75
0.025
1.5
0.28
9
0.08
0.1
1.5
0.5

Persistence: foreign interest rate shockStandard deviation: foreign interest rate shock
Persistence: export shockStandard deviation: export shock
Persistence: government spending shockStandard deviation: government spending shock
Persistence: productivity shockStandard deviation: productivity shock
Discount factor
Inverse of intertemporal elasticity of substitution
Curvature parameter in labor
Labor coeﬃcient
Steady-state value of labor
Share of capital in output
Elasticity of substitution among diﬀerentiated goods
Fraction of firms that do not reset their prices
Depreciation rate of capital
Elasticity of substitution between domestic and foreign goods
Degree of openness
Capital adjustment cost parameter
Parameter for country-specific interest rate premium
Steady state level of foreign debt to GDP
Domestic inflation coeﬃcient of interest rate rules
Output coeﬃcient of interest rate rules

19Following Elekdağ and Tchakarov (2007), we chose Argentina, Brazil,
Indonesia, Korea, Malaysia, the Philippines, Thailand, and Turkey as our
subject emerging market economies and reported their key business cycle
statistics.11

12

The model competently replicates key variable dynamics.

Although it predicts slightly lower volatility of T B/Y ratio than the data
average, all simulated moments range between the sample countries’ minimum and maximum values, and most simulated moments are close to thedata moments averages.

11

The raw series were seasonally adjusted and transformed to both real and per capita
terms. We took logs (except for the T B/Y ratio) and applied the Hodrick–Prescott filter
with a smoothing parameter of 1600.
12
Neumeyer and Perri (2005) and Unsal (2013) chose Argentina, Brazil, Korea, Mexico,and the Philippines as emerging economies. Similarly, as in Unsal (2013), we compare thesimulated moments with the data, including the average values.

20Table 2: Business cycles in emerging economies: Data vs. model

OutputStandard deviations (in %)Consumption
Investment

TB/Y ratio

Argentina
BrazilIndonesia
Korea
Malaysia
Philippines
ThailandTurkey

4.70
1.94
2.88
2.52
2.65
1.41
3.68
3.82

5.80
2.16
4.32
4.06
4.11
1.12
3.47
4.32

12.51
4.88
6.93
5.37
11.43
5.57
11.91
11.40

2.53
0.83
2.23
2.76
4.20
2.56
4.09
2.43

average
model

2.95
3.25

3.67
3.99

8.75
8.12

2.71
2.04

Autocorrelation

Standard deviations relative to output

Argentina
BrazilIndonesia
Korea
Malaysia
Philippines
ThailandTurkey

0.82
0.33
0.79
0.79
0.81
0.78
0.74
0.72

1.23
1.12
1.50
1.61
1.55
0.80
0.94
1.13

2.66
2.52
2.41
2.13
4.31
3.96
3.24
2.99

0.54
0.43
0.78
1.09
1.59
1.82
1.11
0.64

average
model

0.72
0.77

1.24
1.23

3.03
2.50

1.00
0.63

Note) The samples are as follows: Argentina, 1993Q1–2012Q4; Brazil, 1995Q1–2011Q4; Indonesia, 1997Q1–2012Q4; Korea, 1990Q1–2012Q3; Malaysia, 1991Q1–2012Q4; The Philippines, 1990Q1–2012Q4; Thailand, 1993Q1–2012Q4; Turkey, 1990Q1–2012Q3. Source:
IFS.

21

4

WelfareWe perform a comparative welfare analysis in two cases featuring diﬀerent
interest rate rules. Both cases use the standard Taylor-type interest raterules, but the second case also considers external debt levels.
We use the perturbation methods presented by Schmitt-Grohé and Uribe(2004) for computing second-order accurate solutions to measure lifetime
utility levels.13 We conduct policy evaluations by comparing measured welfare levels under diﬀerent values of ΓB to the welfare level under standard
Taylor-type interest rate rules (i.e., ΓB = 0).
We define lifetime utility in the case of the standard Taylor-type interest
rate rules (i.e., ΓB = 0) as the benchmark case (i.e., “policy regime b”):∞∑

V0b ≡ E0

β t U (Ctb , Ntb ).

t=0

We next define lifetime utility having diﬀerent ΓB values as alternative policy
regimes (i.e., “policy regime a”):

V0a ≡ E0∞∑

β t U (Cta , Nta ).

t=0

Then, we define κ as the welfare benefit of adopting policy regime a rather
than adopting policy regime b. Formally, κ can be defined as

V0a = E0∞∑

β t U ((1 + κ)Ctb , Ntb ).

t=0

13

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

22In other words, κ is the fraction of regime b’s consumption process thatcompensates a household to a level considered as well oﬀ under regime b as
under regime a.14
The solid curve in Figure 1 depicts the welfare benefits (κ) of adopting
diﬀerent ΓB values instead of the benchmark case of ΓB = 0. In Figure 1,
the economy’s welfare curve forms a hump shape. Clearly, some range ofΓB (0 < ΓB < 0.47) improves welfare levels compared to the benchmark caseof ΓB = 0. The optimal value of ΓB , 0.22, achieves the maximum value ofthe welfare benefit of 3.9%. To provide the rationale behind our results, we
present the standard deviations of debt to output ratio By t , output Yt , andinterest rate it that correspond to diﬀerent ΓB values in Figure 2. Figure
2 (a) shows that higher ΓB decreases the volatility of debt to output ratio
By t . Eq. (55) shows that a higher ΓB indicates that the monetary authority
will react to a change in debt more strongly, leading to reduced volatility in
By t . Decreased debt volatility lowers volatility of the country-specific interest
rate premium in Eq. (17). This implies that, starting from 0, a higher ΓBvalue leads to reduced volatility of interest rate it as shown in Figure 2 (c).
However, a higher ΓB in Eq. (55) implies a lower relative weight of output
deviations compared with that of debt deviations in monetary policy. As
shown in Figure 2 (b), therefore, the higher ΓB results in higher output Yt
volatility. Since output volatility increases monotonically (as ΓB increases),
we can determine from Eq. (55) that interest rate volatility finally begins
14

Specifically, we obtained κ as follows. We first measured the percentage change fromthe deterministic steady-state consumption level that would in each case give households
the same expected utility in the stochastic economy. Using the measured percentagechange in each case, we calculated the welfare benefits of adopting diﬀerent ΓB values
instead of the benchmark case of ΓB = 0.

23increasing. Due to the trade-oﬀ between debt and output volatility, we have a
U-shaped curve in the interest rate volatility (in Figure 2 (c)), which implies
the hump-shaped welfare curve seen in Figure 1. We can also confirm thatthe volatility of domestic inflation ΠH has the U-shaped curve as shown in
Figure 2 (d), consistent with the hump-shaped welfare curve in Figure 1.
Figure 3 plots the impulse responses of By , Y , i, and ΠH to one standard
deviation of the productivity shock εz . In Figure 3, the solid line, “—,”indicates the impulse response of each variable in the benchmark case ofΓB = 0, while the dashed line, “- - -,” indicates the impulse response of eachvariable in the optimal case of ΓB = 0.22. From Figure 3 (a), we find that the
optimal value of ΓB leads to reduced volatility of By (i.e., the dashed line ofthe optimal case, “- - -,” is closer to zero than the solid line of the benchmark
case, “—”). However, Figure 3 (b) indicates that the optimal value of ΓB
leads to increased volatility of Y (i.e., the dashed line of the optimal case, “- -,” is farther from zero than the solid line of the benchmark case, “—”). This
contrast between By and Y is consistent with the trade-oﬀ between debt andoutput volatility shown in Figure 2. A higher ΓB results in a higher volatilityof Y (as shown in Figure 2 (b)), but results in a lower volatility of By (asshown in Figure 2 (a)). With regard to the interest rate i and domestic
inflation ΠH , Figures 3 (c) and (d) indicate that the optimal value of ΓB
leads to reduced volatility of i and ΠH , respectively (i.e., the dashed line ofthe optimal case, “- - -,” is closer to zero than the solid line of the benchmark
case, “—”). These results on i and ΠH are consistent with the finding that
we have a U-shaped curve in the volatility of interest rate i (Figure 2 (c))
and that of domestic inflation ΠH (Figure 2 (d)).
24

To clarify the results of our analysis, we compare the economy’s welfare
benefit curve in this case with those cases in which the country-specific interest rate premium parameter ψB is set to higher values. The dash-dottedcurve (−·) and dashed curve (−−) in Figure 1 depict the welfare benefits
corresponding to the various values of ΓB for the cases in which ψB increases
by half and double the calibrated value (i.e., 0.12 and 0.16, respectively).
A comparison of these three cases (i.e., the solid, dash-dotted, and dashedcurves) shows that as the country-specific interest rate premium increases,
the maximum welfare benefit achieved by the optimal value of ΓB increases.
This implies that the positive eﬀect from adding the external debt level tothe standard Taylor rule becomes increasingly important, as the friction inforeign borrowing becomes greater.

25

6

ψB =0.08
ψB =0.12

5

ψB =0.16
4

κ (%)

3

2

1

0

-1
0

0.05

0.1

0.15

0.2

0.25

ΓB

Figure 1: Welfare

26

0.3

0.35

0.4

0.45

0.5

(a)

s.d. of By (%)

12.5
12
11.5
11
0

0.1

0.2

0.4

0.5

0.3

0.4

0.5

0.3

0.4

0.5

0.3

0.4

0.5

(b)

8

s.d. of Y (%)

0.3

6
4
2
0

0.1

0.2

(c)

s.d. of i (%)

7

6

5
0

0.1

0.2

(d)

H

s.d. of Π (%)

6

5

4
0

0.1

0.2
ΓB

Figure 2: Standard deviations of debt to output ratio, output, interest rate,and domestic inflation27

(a) B Y
-1
-2
-3
0

5

10

15

20

15

20

(b) Y

2
1
0
0

5

10

(c) i

0
-2
-4
0

5

10
(d) ΠH

15

20

0

5

10

15

20

0
-2
-4

Figure 3: Impulse responses (in percent)28

5Conclusion

In this paper, we developed a standard DSGE model of a small open economy
calibrated specifically to emerging market economies incorporating both pricerigidity and a reduced form of financial friction à la Garcia-Cicco et al. (2010).
Comparing a case featuring the standard Taylor-type interest rate rule with
one using an augmented rule with an external debt level, we found that when
the debt elasticity of the country premium is large, adding an external debt
level to the Taylor rule can improve welfare. Country premiums of emerging
market economies are significantly higher than those of developed countries,
and they tend to rise as the countries accumulate external debt. Our result
implies that, given the greater friction in foreign borrowing, policy makers inemerging market economies should consider external debt levels when making
monetary policy decisions.
In this study, following Garcia-Cicco et al. (2010) and Aguiar and Gopinath(2007), we adopt the simple setting that the country’s risk premium increases
as the private foreign-debt level increases (and vice versa). This is because
our study focuses on private capital flows and related policies in emerging
economies. However, as Corsetti et al. (2013) argue, other factors, such as
sovereign risk, can also aﬀect a country’s risk premium, in addition to its
external debt position. A more general argument related to a country’s risk
premium might be important. We leave this as a subject for future research.

29

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34