DP2023-12

Capital Controls or
Macroprudential Policies:
Which is Better for Land Booms
and Busts?
Ya n g Z H O U
S h i g e t o K I TA N O

Revised April 24, 2024

Capital controls or macroprudential policies:
Which is better for land booms and busts?∗
Yang Zhou†‡

Shigeto Kitano§

Abstract
Emerging markets have experienced land booms and busts along with international capital inﬂows and outﬂows repeatedly. This study quantitatively
examines the eﬀectiveness of (i) macroprudential policies targeting land markets and (ii) capital controls targeting capital inﬂows and outﬂows. We analyze
which policy better manages the coincidence between land booms (busts) andcapital inﬂows (outﬂows). We build a small open economy NK-DSGE modelin which banks choose their asset portfolio between physical capital and land
subject to ﬁnancial constraints. The quantitative results show that the superiority of the two policies depends on the type of shock impacting a small
open economy. In the case of domestic land market shocks, macroprudential
policies enhance welfare, whereas capital controls reduce welfare. Conversely,in the case of foreign interest rate shocks, the superiority of the two policies
is reversed: capital controls enhance welfare, while macroprudential policies
deteriorate welfare.
Keywords: Capital control, Macroprudential policy, Financial frictions,
Balance sheets channel, DSGE
JEL classiﬁcation: E69, F32, F38, F41∗

This work was supported by JSPS KAKENHI Grant Numbers JP23K18796, JP20K01744,
JP20H05633. An earlier version of the paper was presented at the JSME annual meeting in fall
2023. We are grateful to Eiji Okano, Shin-Ichi Nishiyama, and two anonymous referees for theirhelpful comments.
†
Institute of Developing Economies, JETRO, 3-2-2, Wakaba, Mihama-ku, Chiba, 261-8545
Japan. Email: Yang_Zhou@ide.go.jp.
‡
RIEB, Kobe University, 2-1, Rokkodai, Nada, Kobe, 657-8501 Japan.
§
RIEB, Kobe University, 2-1, Rokkodai, Nada, Kobe, 657-8501 Japan, E-mail:kitano@rieb.kobe-u.ac.jp.

1

Introduction

There is a long historical association between international capital inﬂows, real estatebooms, and ensuing ﬁnancial crises (Reinhart and Rogoﬀ, 2009). After 2000, many
countries suﬀered from real estate booms (busts) and capital inﬂows (outﬂows) during the same period. The coincidence between real estate booms (busts) and capitalinﬂows (outﬂows) is a robust global phenomenon in advanced and emerging countries (Ferrero, 2015). Large capital inﬂows and real estate booms in the UnitedStates before the global ﬁnancial crisis of 2008–9 have elicited considerable discussion (e.g., Bernanke, 2010). Against this background, the coincidence between realestate booms (busts) and international capital inﬂows (outﬂows) since the 2000s has
been rigorously examined in many studies (e.g., Obstfeld and Rogoﬀ, 2009; Aizenman and Jinjarak, 2009; Favilukis et al., 2013; Ferrero, 2015; Cesa-Bianchi et al.,2015).
Emerging countries have long been suﬀering from this issue. For example, thecoincidence between real estate booms and capital inﬂows in emerging countries occurred before the Asian crisis of the 1990s (Obstfeld and Rogoﬀ, 2009). Anotherwell-known episode is the unprecedented capital inﬂows and asset price bubbles inemerging countries before and after the global ﬁnancial crisis (Ahmed and Zlate,2014). Real estate boom-bust cycles and capital inﬂow-outﬂow cycles are important
issues for policymakers, especially in emerging countries. Policymakers have twomain policy alternatives: macroprudential policies targeting real estate markets andcapital controls targeting capital ﬂows. A reasonable question arises: which of thesetwo policies should be adopted when dealing with the problematic coincidence? This
study investigates the comparative advantages of macroprudential policies targeting
real estate markets and capital controls limiting capital ﬂows to address the problematic coincidence between real estate booms (busts) and capital inﬂows (outﬂows)
in emerging countries. To examine which policy is more suitable, we incorporate
land assets into a small open economy New Keynesian Dynamic Stochastic General1

Equilibrium (NK-DSGE) model with banks borrowing from abroad à la Aoki et al.
(2016).1 2 In our model, banks provide capital and land funds to ﬁrms for production. We consider two exogenous shocks: external (international) and internal(domestic). In our model, both types of exogenous shock replicate the coincidence
between real estate booms (busts) and capital inﬂows (outﬂows). The two exogenous
shocks are ampliﬁed through banks’ balance sheets owing to the ﬁnancial accelerator
mechanism.
We ﬁnd that the superiority between the two policies depends on the types of exogenous shocks striking a small open economy. When a small open economy suﬀers
from foreign interest rate shocks, capital controls are welfare-enhancing, mitigate
capital inﬂow-outﬂow cycles, and stabilize the ﬂuctuation of the other macroeconomic variables. Conversely, macroprudential policies deteriorate welfare. Althoughmacroprudential policies mitigate real estate boom-bust cycles, they cannot stabilize
other macroeconomic variables such as output and consumption.
However, when a small open economy suﬀers from domestic land market shocks,
the superiority between the two policies is reversed: macroprudential policies are
better than capital controls. Capital controls deteriorate welfare in this case; although capital controls mitigate capital inﬂow-outﬂow cycles, they cannot stabilize
other macroeconomic variables such as output and consumption. Contrarily, macroprudential policies are welfare-enhancing; they mitigate real estate boom-bust cycles
and stabilize the ﬂuctuation of other macroeconomic variables.
The remainder of this paper is organized as follows. In Section 2, we present a
1

The seminal works modeling ﬁnancial frictions in real estate markets are Iacoviello (2005,2015), Iacoviello and Neri (2010), and Liu et al. (2013). They show that a collateral constraint that
restricts household borrowing to a fraction of real estate ampliﬁes business cycle ﬂuctuations. Thereis extensive literature based on this mechanism (e.g., Kannan et al., 2012; Rubio and CarrascoGallego, 2015; Alpanda and Zubairy, 2017; Chen et al., 2020; Ferrero et al., 2022; Forster and Sun,2022).
2
The seminal works modeling ﬁnancial intermediaries are Gertler and Kiyotaki (2010), Gertler
and Karadi (2011), and Gertler et al. (2012). A growing body of literature exists on small open
economy models based on the ﬁnancial accelerator mechanism, including Aoki et al. (2016) (e.g.,
Ghilardi and Peiris, 2016; Jin and Xiong, 2018; Agénor et al., 2018; Cuadra and Nuguer, 2018;
Kitano and Takaku, 2017, 2018; Mimir and Sunel, 2019).

2

small open economy NK-DSGE model à la Aoki et al. (2016) augmented with realestates (lands). Section 3 describes our calibration. Section 4 presents numericalexperiments that shed light on the role of capital controls and macroprudential
policies. Finally, Section 5 concludes the paper.
Related Literature.—Korinek and Sandri (2016) are the ﬁrst to diﬀerentiate
between macroprudential policies and capital controls.3 4 By distinguishing between
domestic and foreign lending, they show that both policy measures stabilize theeconomy and reduce the severity of crises. They ﬁnd that it is desirable to employ
both instruments in a calibration based on the East Asian crisis countries. Buildingon Korinek and Sandri (2016)’s framework, Matschke (2022) shows that the analysis is most suitable for countries with less-developed domestic ﬁnancial markets.
Nispi Landi (2017) shows that the desirability between capital controls and macroprudential policies is shock-dependent. Capital controls are preferred over macroprudential policies under foreign interest rate and ﬁnancial shocks. Conversely,
macroprudential policies are more desirable under technology shocks. Kitano and
Takaku (2020) show that the superiority between the two policies depends on the
degree of ﬁnancial friction between domestic banks and foreign investors. Under low
ﬁnancial friction in foreign borrowing, macroprudential policies are more appropriate than capital controls. Conversely, capital controls are more appropriate thanmacroprudential policies under high ﬁnancial friction in foreign borrowing.
It is noteworthy that any of the above studies diﬀerentiating between macroprudential policies and capital controls do not consider real estates. To the bestof our knowledge, this study is the ﬁrst to analyze the superiority between the twopolicies for the problematic coincidence by incorporating real estates into a small
3

Capital controls were ﬁrst discussed as a policy tool for internalizing the externalities associatedwith ﬁnancial crises and preventing excessive borrowing (e.g., Jeanne and Korinek, 2010; Bianchi,
2011; Brunnermeier and Sannikov, 2015). More studies have examined capital controls as a regularpolicy tool from diﬀerent perspectives (e.g., Liu and Spiegel, 2015; Chang et al., 2015; Jin, 2016;
Jung, 2016; Davis and Presno, 2017; Kitano and Takaku, 2018; ?; Johnson, 2021).
4
Macroprudential policy has been examined mainly in terms of its interaction with monetary
policy (e.g., Angeloni and Faia, 2013; Angelini et al., 2014; Levine and Lima, 2015; De Paoli andPaustian, 2017; Gelain and Ilbas, 2017; Van der Ghote, 2018; Palek and Schwanebeck, 2019).

3

open economy model.

2

Model

The model framework is similar to Aoki et al. (2016). However, we incorporate land
assets into a small open economy NK-DSGE model à la Aoki et al. (2016). The
model has seven types of agents: households, ﬁnal goods ﬁrms, intermediate goods
ﬁrms, capital investment ﬁrms, land investment ﬁrms, the government, and banks.
Intermediate goods ﬁrms require land, in addition to capital, as a production input.
Firms obtain funds from banks for land and capital acquisitions. Banks provide
loans to ﬁrms using their net worth, household deposits, and foreign borrowing.
The government uses capital controls to regulate banks’ foreign borrowing. The
government also uses macroprudential policies to regulate bank ﬁnancing of ﬁrms’
land acquisitions.

2.1

Households

Following Gertler and Kiyotaki (2010), we assume that within a representative
household, a fraction, f , are bankers, and a fraction, 1 − f , are workers. Workers supply labor to intermediate goods ﬁrms and obtain wages for the representative
household. Each banker manages a ﬁnancial institution and transfers dividends tothe household. The banker is assumed to stay in the market with probability σ
to limit the banker’s ability to accumulate wealth. The expected survival time ofa banker is 1/ (1 − σ), and (1 − σ) f of bankers exit and transfer their remaining
net worth as dividends to the household. Exited bankers become workers, and thesame number of workers become bankers. The household supplies new bankers withstart-up funds.
We adopt the GHH preference for the representative household’s expected life-4

time utility as follows:

E0

"∞
X



ζ0 1+ζ
β ln Ct −
h
1+ζ t
t=0
t

#
,

(1)

where E0 is the expectation operator conditional on date 0 information.5 Ct andht denote consumption and labor supply, respectively. β ∈ (0, 1), ζ, and ζ0 (> 0)
denote the discount factor, the inverse of Frisch elasticity of labor supply, and therelative utility weight of labor, respectively.
The household’s budget constraint is given by
Ct + Qt Kth + χ Kth + Qlt Lht + χl Lht + Dth= wt ht + Πt + (Zt + λQt ) Kt−1
+ Ztl + λl Qlt ξtl Lht−1 + Rt Dt−1 , (2)where wt is the real wage, and Kth and Lht denote households’ capital and landholdings, respectively. The payoﬀs in period t for holding capital and the land
acquired in period t − 1 are (Zt + λQt ) and Ztl + λl Qlt ξtl , respectively. Zt and Ztl
are the rental rates for capital and land, respectively. Qt and Qlt are capital andland prices, respectively. λ and λl denote one minus depreciation rates of capitaland land, respectively. ξtl represents the land market shock. We assume that there is
the land market shock ξtl to introduce an exogenous source of variation in the returnon landholding in a simple way.6 Dt is the household’s bank deposit. The gross real
return on deposits, Rt , is given byRt =1 + it−1
,
πt

5

(3)

The GHH preference by Greenwood et al. (1988) is commonly used in open economy literature.
It abstracts from the wealth eﬀects on labor supply and captures procyclical employment (Aokiet al., 2016). This is suitable for matching open economies’ second moments (Correia et al., 1995;
Raﬀo, 2008; Luk and Zheng, 2020). For more details, see, for example, Mendoza (1991) andNeumeyer and Perri (2005).
6
The land shock corresponds to the capital shock in Gertler et al. (2012) and Gertler and Karadi(2011), which serves as an exogenous trigger of asset price dynamics.

5

where it denotes the nominal interest rate on the deposit, and πt = Pt /Pt−1 is theinﬂation rate. We assume that although households can directly obtain capital andland, there exist extra management costs for capital and landholdings (Aoki et al.,2016): κ
2
χ Kth =Kth ,2

 κ l h 2
χl Lht =
Lt ,
2

(4)

where the positive values of κ and κ l (> 0) imply a disadvantage for workers inﬁnancing relative to bankers. Πt in (2) denotes the total proﬁts from ﬁrms andbanks (net start-up funds for bankers). We show the details of Πt in Appendix A3.
The representative household chooses labor supply ht , deposit Dt , capital holding
Kth , land holding Lht , and consumption Ct to maximize the expected lifetime utility(1) subject to the budget constraint (2). The household’s ﬁrst-order conditions are
given by
wt = ζ0 hζt ,(5)

1 = Et (Λt,t+1 Rt+1 ) ,
Zt+1 + λQt+1
1 = Et Λt,t+1,
Qt + κKth(6)
1 = Etl
Zt+1+ λl Qlt+1 lξΛt,t+1,
Qlt + κ l Lht t+1

andΛt,t+1 ≡ β

ζ0Ct − 1+ζ
h1+ζ
t
ζ0
h1+ζ
Ct+1 − 1+ζ
t+1

,

(7)

(8)

(9)

where Λt,t+1 denotes the stochastic discount factor.

2.2

Non-ﬁnancial ﬁrms

There are four types of nonﬁnancial ﬁrms: (i) ﬁnal goods ﬁrms, (ii) intermediate
goods ﬁrms, (iii) capital investment ﬁrms, and (iv) land investment ﬁrms.

6

2.2.1

Final goods ﬁrms

The ﬁnal goods are produced under perfect competition using a range of diﬀerentiated intermediate goods yit , i ∈ [0, 1]:
Z 1
Yt =

η−1
η

η
 η−1

yit di(10),0where η(> 1) is the elasticity of substitution across diﬀerentiated goods. Subject tothe production function (10), the representative ﬁnal goods producer chooses yit tomaximize its proﬁt:

Z 1
Pt Yt −

pit yit di,0where pit is the nominal price of good i, and Pt is the aggregate price index:
Z 1
p1−η
it di

Pt =

1
 1−η

.

0

The ﬁrst-order condition for intermediate good i yields7

yit =

2.2.2

pit
Pt

−η
(11)

Yt .

Intermediate goods ﬁrms

There is a continuum of intermediate goods ﬁrms indexed by i ∈ [0, 1] that produce
diﬀerentiated intermediate goods and sell them to ﬁnal goods ﬁrms. Monopolisticallycompetitive ﬁrms produce diﬀerentiated intermediate goods using capital kit , land
lit , imported goods mit , and labor hit :
yit = At

7

kit
αK

α K 

lit
αL

αL 

mit
αM

α M 

hit
1 − αK − αL − αM

1−αK −αL −αM

Substituting Eq.(11) into Eq.(10) provides the aggregate price index Pt .

7

,

(12)

where αK , αL , αM > 0, αK + αL + αM ∈ (0, 1), and At denotes aggregate total factor
productivity. Subject to the demand function of intermediate goods (11) and theintermediate goods production function (12), the intermediate goods ﬁrms choose
kit , lit , mit , and hit to minimize the cost Zt kit + Ztl lit + ϵt mit + wt hit . Here, ϵt denotes
the price of the imported goods, which equals the real exchange rate. The minimized
unit cost is given bymCt =1 αK l αL αM 1−αK −αL −αM
ϵt w t
.
Z
Zt
At t

(13)

We deﬁne aggregate capital Kt , land Lt , imported goods Mt , and labor ht as
Z 1
Kt =

Z 1
kit di,

Lt =

0

Z 1
lit di,

Mt =

0

Z 1
mit di,ht =0

hit di.
0

In symmetric equilibrium, the aggregated production function is given by
Yt = At

Kt−1
αK

α K 

Lt−1
αL

α L 

Mt
αM

α M 

ht
1 − αK − αL − αM

1−αK −αL −αM. (14)

The ﬁrst-order conditions for cost minimization are given by
Ztl Lt−1
αL=,
Zt Kt−1αK
ϵ t MtαM=,
Zt Kt−1
αK

(15)
(16)

and
w t ht1 − αK − αL − αM=.
Zt Kt−1
αK(17)

We assume that each intermediate goods ﬁrm produces a single variety and faces
nominal rigidity in the form of quadratic price adjustment costs à la Rotemberg(1982) to introduce price stickiness. The intermediate goods ﬁrm pays capital andland expenditure before production by borrowing funds from banks and households.
8

The intermediate goods ﬁrm i chooses price pit to maximize the discounted value of
its proﬁts,

E0

(∞
X

"
Λ0,t

t=0



2 #)
κ
pit
pit
C
− mt yit −− 1 Yt,Pt
2 pit−1(18)

subject to Eq.(11). κ is the adjustment cost parameter that determines the degreeof nominal price rigidity. Imposing symmetry on ﬁrms (i.e., pit = Pt and yit = Yt ),we obtain the ﬁrst-order condition with respect to pit :8



1
Yt+1
C
(πt − 1) πt =1 − η + ηmt + Et Λt,t+1
πt+1 (πt+1 − 1) .
κ
Yt
2.2.3

(19)

Capital and land investment ﬁrms

Capital and land investments, It and Itl , are accompanied by adjustment costs.
2
 

It
κI It
− 1 It ,Ψ· It =
I
2 I

2
 l

It
κlI ItllΨl− 1 Itl ,· It =
l
l
I
2 I

(20)

where I and I l denote steady-state levels. Ψ (·) and Ψl (·) satisfy Ψ (1) = Ψl (1) =′′Ψ′ (1) = Ψ′l (1) = 0; Ψ′′ (·) > 0, and Ψl (·) > 0. Maximizing the discounted proﬁts,

E0

∞
X
t=0

"

"

Λ0,t Qt It − 1 +

κI
2



2 # #
It
−1
It ,
I

E0

∞
X
t=0

"
Λ0,t

"

 l
2 # #It
Qlt Itl − 1 +
−1
Itl ,
l
2 I
κlI

with respect to It and Itl , we obtain the ﬁrst-order conditions for capital and land:κI
Qt = 1 +
2

8



It
−1
I

2

  

It
It
+
κI
−1 ,
I
I

(21)

Following Aoki et al. (2016), we setκ=(η − 1) ω,(1 − ω) (1 − βω)

where ω denotes the probability of maintaining price. Setting κ in this manner, we obtain thesame New Keynesian Phillip as in Calvo (1983).

9

and
 l
2  l   l

It
It
It
l
−1 +
κI
−1 ,
2 Il
Il
Il

κl
Qlt = 1 + I(22)respectively.

2.3

Banks

Banks raise funds from households by issuing one-period riskless deposits dt at thegross real interest rate Rt+1 . They also raise funds from foreigners by issuing foreign debt d∗t at the exogenous gross real foreign interest rate Rt∗ . They lend funds
on capital and land (ktb and ltb ) to intermediate goods ﬁrms at prices Qt and Qlt ,respectively. As we explain in Section 2.4, the government imposes capital controls
and macroprudential policies. We characterize capital controls and macroprudential
policies as tax rates on banks’ foreign debt and land holdings, respectively.
A bank’s balance sheet is given byQt ktb + 1 + τtl Qlt ltb = (1 + τtn ) nt + dt + (1 − τt∗ ) ϵt d∗t ,(23)

where τt∗ , τtl , nt , and τtn denote tax rates on banks’ foreign debt and land holdings,
banks’ net worth, and subsidy rates on banks’ net worth, respectively. The bank’sbalance sheet (23) includes the real exchange rate ϵt , which implies that the bankfaces a liability dollarization problem.9
The bank’s net worth evolves as the diﬀerence between the gross return on assets
and the cost of borrowing, as follows: b∗bd∗t−1 .
− Rt dt−1 − ϵt Rt−1
+ Ztl + λl Qlt ξtl lt−1
nt = (Zt + λQt ) kt−1

(24)

As argued in section 2.1, Zt and Ztl denote the rental prices of capital and land,
9

See Eichengreen and Hausmann (1999) and Eichengreen and Hausmann (2005) for the liability
dollarization problem (or “original sin”).

10
respectively. (Zt + λQt ) and Ztl + λl Qlt ξtl are the gross returns on capital andland, respectively. ξtl denotes the land market shock mentioned in Section 2.1.
As we argue in Section 2.1, the banker exits the market with probability σ ineach period. The banker’s objective is to maximize the expected present value of
future wealth given by

Vt = max Et"∞
X#Λt,t+j σ j−1 (1 − σ) nt+j ,

(25)

j=1

where nt+j denotes the net worth of the bank that survives until period t + j − 1 but
exits the market in period t + j. As the bank belongs to a representative household,
we use the household’s stochastic discount factor Λt,t+j to discount the stream ofthe bank’s net worth.
We assume that ﬁnancial frictions exist when banks obtain funds from both
depositors and foreign creditors. When banks raise funds, they can divert a fractionof the funds and transfer it to the representative household or hold their assets until
payoﬀs are realized and repay their liabilities to creditors. When creditors supply
funds, they require the banks’ expected present value of future wealth, Vt , to be
not less than the amount that banks can divert. This introduces the incentivecompatibility constraint for banks as follows:
Vt ≥ Θ (xt ) Qt ktb + Qlt ltb ,(26)

where Θ (xt ) is the proportion of assets that banks can divert. Following Aoki et al.
(2016), we assume as follows:γ 
Θ (xt ) = θ 1 + x2t ,2where xt ≡ϵt d∗t,Qt ktb + Qlt ltb(27)

which implies that, as the ratio of a bank’s foreign debt to assets increases, banks
can divert a larger fraction of assets.

11

The bank’s optimization problem is to choose its asset and liability positions tomaximize its expected present value of future wealth:Vt = max Et {Λt,t+1 [(1 − σ) nt+1 + σVt+1 ]} ,(28)

subject to the balance sheet constraint (23), law of motion of net worth (24), andincentive compatibility constraint (26).
Following Aoki et al. (2016), we express Eq.(28) as


Vt
nt+1
ψt ≡
= max Et Λt,t+1 (1 − σ + σψt+1 )
.
nt
nt

(29)

We also express Eq.(23) as Qlt ltb
Qt ktbdt
ϵt d∗tQt ktb + Qlt ltb+ 1 + τtl
= (1 + τtn ) ++ (1 − τt∗ )
,
nt
nt
nt
nt
Qt ktb + Qlt ltb| {z }
|{z}
|
{z
}
ϕt

ϕlt

(30)

xt

where ϕt ≡ Qt ktb /nt , ϕlt ≡ Qlt ltb /nt , and xt ≡ ϵt d∗t /(Qt ktb + Qlt ltb ). By using ϕt , ϕlt , andψt ( and Eq.(27)), we rewrite the incentive-compatibility constraint (26) as




γ 
ψt ≥ Θ (xt ) ϕt + ϕlt = θ 1 + x2t ϕt + ϕlt .
2(31)

By using ϕt , ϕlt , xt and Eq.(30), we rewrite the law motion of net worth (24) as10
#
"
 l


l

Zt+1
+ λl Qlt+1 ξt+1
nt+1
(Zt+1 + λQt+1 )=− Rt+1 ϕt +− 1 + τtl Rt+1 ϕlt
l
nt
Qt
Qt



ϵt+1 ∗+ (1 − τt∗ ) Rt+1 −Rt xt ϕt + ϕlt + (1 + τtn ) Rt+1 .
(32)
ϵt
Substituting Eq.(32) into (29), we can rewrite (29) as

ψt = max

ϕt ,ϕlt ,xt

10




µt ϕt + µlt ϕlt + µ∗t ϕt + ϕlt xt + νt ,For the detail on the derivation of Eq.(32), see Appendix A4.

12

(33)

where









 (Z + λQ )


 t+1

t+1
µt = Et Ωt+1 −Rt+1  ,

Qt






|
{z
}




Rkt+1








 l

l
l
l


Z
+
λ
Q
ξ
t+1
t+1
t+1
l
l

−R
,
−
τ
R
µt = Et Ωt+1 
t+1 
t t+1



Qlt






|
{z
}













(35)

Rlt+1






 



ϵ
t+1
∗
∗
∗
µt = Et Ωt+1 
R + τt Rt+1 Rt+1 −
 ,

ϵt t




|
{z
} 




∗







(34)



(36)

RD
t+1

and νt = Et {Ωt+1 (1 + τtn ) Rt+1 } .

(37)Here, we deﬁne Ωt+1 ≡ Λt,t+1 (1 − σ + σψt+1 ) as banks’ augmented stochastic dist+1 ),count factor. In Eqs.(34), (35), and (36), we deﬁne that Rkt+1 ≡ (Zt+1 +λQ
Qt
l
l
l
l
∗
(Z +λ Q )ξϵt+1 ∗∗
Rlt+1 ≡ t+1 Ql t+1 t+1 − τtl Rt+1 , and RD
t+1 ≡ ϵt Rt + τt Rt+1 , which denote thetreturns on capital and land holdings and the cost on foreign debt holding, respectively. µt is the net return on capital holdings, µlt is the net return on land holdings,
and µ∗t is the cost advantage of foreign borrowing.
Banks choose ϕt , ϕlt , and xt to maximize Eq.(33), subject to the incentive compatibility constraint (31). The ﬁrst-order conditions for ϕt , ϕlt , and xt areυtΘ (xt ) ,1 + υtυtµlt + µ∗t xt =Θ (xt ) ,1 + υtυt
Θ′ (xt ) ,and µ∗t =1 + υtµt + µ∗t xt =

(38)
(39)
(40)

where υt denotes the Lagrangian multiplier on Eq.(31).11 When the incentive com


l
l l
∗
l
The Lagrangian
is
L
=
ψ
+
υ
(ψ
−
Θ
(x
)
ϕ
+
ϕ
)
=
(1
+
υ
)(µ
ϕ
+
µ
ϕ
+
µ
ϕ
+
ϕ
xt +
t
t
t
t
t
t
t
t
t
t
t
t
t
t


l
νt ) − υt Θ (xt ) ϕt + ϕt ).
1113

patibility constraint is not binding (i.e.,υt = 0), we have µt = µht = µ∗t = 0, whichindicates that the interest rate spreads (µt , µht , and µ∗t ) are zero. When the incentive
compatibility constraint is binding (i.e., υt > 0), the interest rate spreads (µt , µht ,and µ∗t ) become positive.
From Eqs.(38) and (39), we obtainµt = µlt ,(41)

which indicates that, in equilibrium, banks earn the same rate of return from capitaland land holdings (i.e., Rkt = Rlt in Eqs.(34) and (35)).
We deﬁne the bank’s leverage ratio as Φt ≡ (Qt ktb +Qlt ltb )/nt . With ϕt (≡ Qt ktb /nt )and ϕlt (≡ Qlt ltb /nt ), the bank’s leverage ratio can be expressed as
Φt = ϕt + ϕlt .

(42)

Combining Eq.(31) with (33) and (41), we can transform the expression Φt (= ϕt +ϕlt )
into

Φt =

θ

1 + γ2 x2t

νt,− µt − µ∗t xt(43)

which indicates that the bank’s leverage ratio Φt is decreasing in the parameter ofthe banks’ diversion θ, and increasing in the net return on capital and land holdingsµt (= µlt ) and the cost advantage of foreign debt µ∗t .
Combining Eq.(39) with (40) (and using (31)), we obtain xt as12r
12 ˜∗ 2xt = ∗ −1 + 1 +
µ
,
γ t
µ˜t

µ˜∗

µ˜∗

(44)

From (39) and (40) (and using (31)), we have that 2t x2t +xt − γt = 0. By solving this problem,
we obtain Eq.(44).
1214whereµ˜∗t ≡ µ∗t /µlt .

(45)

As ϕt , ϕlt , and xt are independent of bank-speciﬁc factors, we have
Qt Ktb,Nt
Q l Lbϕlt = t t ,Nt
ϵt Dt∗and xt =,Qt Ktb + Qlt Lbt
ϕt =

(46)
(47)
(48)

where the capital letters indicate aggregate variables.
Following related studies, we assume that new bankers receive a fraction of ξ/(1−σ) of exiting bankers’ total ﬁnal period assets.13 As the aggregate net worth Nt is
the sum of the net worth of existing and new bankers, we obtain the evolution ofNt from Eq.(24) as follows:




b
∗
∗
Nt = (σ + ξ) (Zt + λQt ) Kt−1
+ Ztl + λl Qlt ξtl Lbt−1 −σ Rt Dt−1 + ϵt Rt−1
Dt−1
.
(49)
As we argue in Section 2.4, the government returns tax revenues from capital
controls and macroprudential policies to banks as a subsidy for banks’ net worth.
Thus, the aggregate balance sheet is given byQt Ktb + Qlt Lbt = Nt + Dt + ϵt Dt∗ .

2.4

(50)

Government

As argued in Section 2.3, the government imposes capital controls and macroprudential policies. We characterize capital controls and macroprudential policies astaxes on foreign debt and landholdings, respectively. τt∗ and τtl in the bank’s bal13

For example, see Gertler and Kiyotaki (2010) and Gertler and Karadi (2011).

15

ance sheets (23) are the tax rates on foreign debt and landholdings, respectively.
We assume that τt∗ and τtl follow the following simple rules:τt∗ = ω ∗ ln Dt∗ − ln D̄∗ ,(51)

τtl = ω l ln Qlt − ln Q̄l ,

(52)

and

where D̄∗ and Q̄l denote the steady-state values of Dt∗ and Qlt , respectively. Eqs.(51)
and (52) imply that the government adjusts the tax rates on foreign debt τt∗ responding to the aggregate foreign debt of the entire banking sector Dt∗ and adjusts the tax
rates on land holdings τtl responding to the land price Qlt . Following Gertler et al.
(2012) and Aoki et al. (2016), we assume that collected taxes are returned to banks
as subsidies for their net worth Nt :
τtn Nt = τt∗ ϵt Dt∗ + τtl Qlt Lbt .

(53)

We posit the following simple monetary policy rule:it − ī = (1 − ρi ) ωπ (πt − 1) + ρi (it−1 − ī) ,(54)

where ī denotes the steady-state level of it .

2.5

Equilibrium

Demand for ﬁnal goods comprises consumption (Ct ), capital and land investment(It and Itl ), the accompanied adjustment costs (Ψ (·) It and Ψl (·) Itl ), the household’s extra management costs on capital and land investment (χ (·) and χl (·)), the16

adjustment cost of changing prices in Eq.(18), and foreign demand EXt , as follows:


 

 l 
 κItI
Yt = C t + 1 + Ψ
It + 1 + Ψl tl
Itl +χ Kth +χl Lht + (πt − 1)2 Yt +EXt .
I
I
2
(55)
Following Aoki et al. (2016), we assume that foreign demand decreases with relative
price and increases with foreign income:

EXt =

Pt
et Pt∗

−φYt∗ = ϵφt Yt∗ ,(56)

where ϵt is the real exchange rate, and Yt∗ is the exogenous foreign income.
Foreign debt Dt∗ is evolved according to∗∗
Dt∗ = Rt−1
Dt−1
+ Mt −

1
EXt ,
ϵt

(57)

and the current account CAt is given by∗
CAt = Dt∗ − Dt−1.

(58)

The laws of motion for aggregate capital Kt and land Lt are given by

Kt = It + λKt−1 ,(59)

and Lt = ξtl Itl + λl Lt−1 ,

(60)

where

Kt ≡ Ktb + Kth ,(61)

and Lt ≡ Lbt + Lht .

(62)

Here, ξtl denotes the land market shock mentioned in Sections 2.1 and 2.3.
We consider two exogenous stochastic processes. The foreign (gross) interest rate17

Rt∗ and land market shock ξtl are given by∗ln Rt∗ − ln R∗ = ρR∗ ln Rt−1
− ln R∗ + ϵRt∗ ,
ϵRt∗ ∼ N 0, σR2 ∗ ,ϵξt ∼ N 0, σξ2 ,lln ξtl = ρξ ln ξt−1
+ ϵξt ,

(63)
(64)

where the innovation of these shocks is assumed to be i.i.d and uncorrelated.
The recursive competitive equilibrium is given by 11 price variables { Rt , it , πt ,∞lwt , Zt , Ztl , Qt , Qlt , ϵt , mC
t , Λt,t+1 }t=0 , 17 quantity variables { Ct , ht , Dt , It , It , Yt ,

Mt , EXt , Kt , Kth , Ktb , Lt , Lht , Lbt , Nt , Dt∗ , CAt }∞t=0 , 10 bank related variables { xt ,∗l ∞ψt , ϕt , ϕlt , Φt , νt , µt , µlt , µ∗t , µ˜∗t }∞t=0 , 2 exogenous shocks { Rt , ξt }t=0 , which satisfy

39 equations (3), (5)-(9), (13)-(17), (19), (21), (22), (33)-(37), (41)-(50), (54)-(64).
Appendices A1 and A2 summarize the equilibrium conditions and the steady state,
respectively.

3

Calibration

Table 1 lists the baseline parameter values in our model. The model is calibrated atquarterly frequency. We basically follow Aoki et al. (2016) and choose the conventional parameter values used in related literature. For some parameters, we choose
their values to match the conventional steady-state levels used in related literature.
We set the parameters related to households as follows. The discount factor β
is set to 0.985 (R = 1/β = 1.015), implying a steady-state domestic deposit rateof 1.5% (6% annually). The inverse of Frisch elasticity of labor supply ζ and therelative utility weight of labor ζ0 are set at 0.2 and 5.89, respectively. The cost
parameter for households’ direct ﬁnancing of capital κ is set at 9.85 × 10−4 . We set
the same value for the cost parameter of households’ direct land ﬁnancing κ l .
Following Iacoviello and Neri (2010), we set the land share in production αL andone minus depreciation rate on land λl at 0.1 and 0.99, respectively. Following Aoki
et al. (2016), we set the other parameters related to producers. The capital share18

in production αK , imported share in production αM , and one minus the depreciation rate of capital λ are set at 0.3, 0.15, and 0.98, respectively. The elasticity of
substitution among diﬀerentiated goods η, the probability of keeping prices ω, andthe price elasticity of export demand φ are set to 9, 0.66, and 1, respectively. The
adjustment cost parameter for capital investment, κI , is set to 1. We set the samevalue for the adjustment cost parameter for land investment, κlI .
We target the steady-state levels of the aggregate banks’ leverage ratio Φ, spread(i.e., return rate on capital (or land) minus deposit rate) Rl − R, and banks’ foreign
debt-to-assets ratio x at 6, 0.02, and 0.25, respectively. To match the steady-statelevel targets, we choose the divertable fraction of assets θ, home bias in funding γ,
and fraction of transfers to entering banks ξ at 0.6, 5, and 4 × 10−4 , respectively.
We set the banks’ survival probability σ to 0.93, which is slightly lower than 0.94 in
Aoki et al. (2016).
We choose the persistence and standard deviation of foreign interest shocks (ρR∗and σR∗ ) as 0.95 and 0.00075, respectively. The steady-state foreign interest rate R̄∗is set at 1.005% (1.02% annually). The coeﬃcient and persistence for the monetary
policy rule (ωπ and ρi ) are set at 1.5 and 0.85, respectively. For the land shock, we
set the values of ρξ and σξ to 0.66 and 0.05, respectively. These are the same values
for the capital quality shock in Gertler and Kiyotaki (2010).

19

Variable
β
ζ
ζ0
κ
κl
αK
αL
αM
λ
λl
η
ω
κI
κlI
φ
σ
θ
γ
ξ
ωπ
ρi
ρR ∗
σR ∗
ρξ
σξ
R∗

Description
Parameters related to households
discount factor
inverse of Frisch elasticity of labor supply
relative utility weight of labor
cost parameter of direct ﬁnance: capital
cost parameter of direct ﬁnance: landParameters related to ﬁrms
capital shareland shareimported goods share
one minus depreciation rate: capital
one minus depreciation rate: landelasticity of substitution
probability of retaining prices
adjustment cost on capital investment
adjustment cost on land investment
price elasticity of export demand
Parameters related to banks
survival probability
divertable fraction of assets
home bias in fundingtransfer to entering banks
Other parameters
coeﬃcient for monetary policy rulepersistence: monetary policy rulepersistence: foreign interest rate shock
standard deviation: foreign interest rate shock
persistence: land shock
standard deviation: land shocksteady state foreign interest rate (in annual)

Value
0.985
0.2
5.89
9.85 × 10−4
9.85 × 10−4
0.3
0.1
0.15
0.98
0.99
9
0.66
1
1
1
0.93
0.6
5.0
4 × 10−4
1.5
0.85
0.95
0.00075
0.66
0.05
1.02

Table 1: Parameters

4

Numerical Experiments

Next, we present numerical experiments to shed light on the roles of capital controls
and macroprudential policies. We consider two exogenous shocks: foreign interest
rate and land market shocks.

20

4.1

Impulse responses to foreign interest rate shocks

First, we show how capital controls and macroprudential policies aﬀect the impulse
responses of the main variables to foreign interest rate shocks.

4.1.1

Capital controls to foreign interest rate shocks

In this section, we analyze the impulse responses of the main variables, with andwithout capital controls, to foreign interest rate shocks. We consider a 0.075%
unanticipated decrease in foreign interest rates Rt∗ (with a persistence coeﬃcient of0.95) as an initiating disturbance. In Figure 1, the solid (red) lines show impulse
responses without capital controls. The dashed (blue) lines show impulse responses
with capital controls. In the latter case, we select the optimal value of ω ∗ (= 6) inEq.(51), which we will explain in detail in Section 4.3.
From Eq.(36), we can infer that without capital controls, a fall in foreign interest
rates Rt∗ would reduce the cost of raising funds through foreign borrowing and causet
is in deﬁcit,
capital inﬂows. This implies that the current account (to GDP ratio) CA
Ytforeign debt Dt∗ increases, and the real exchange rate ϵt appreciates, as shown by
the solid (red) lines in Figure 1. From Eq.(49), it is evident that the cost reduction
in raising funds due to the fall in foreign interest rates Rt∗ raises the banks’ net
worth Nt . The increase in net worth Nt reduces the banks’ borrowing constraints
and raises capital and land investments (It and Itl ). Capital and land prices (Qt and
Qlt ) also increase with increases in It and Itl . With this loosening, the credit spread
Rkt+1 − Rt+1 (which equals Rlt+1 − Rt+1 in the equilibrium) decreases. A fall in thecredit spread reduces borrowers’ costs and increases capital and land investments(It and Itl ). Capital and land prices (Qt and Qlt ) increase further with increases in It
and Itl . In other words, the ﬁnancial accelerator mechanism ampliﬁes the volatilityof the main variables due to a foreign interest rate shock through the banks’ balance
sheets. As the appreciation of the real exchange rate ϵt reduces foreign demand, theoutput Yt falls ﬁrst. However, the output gradually increases owing to a decrease in
21

5

10-3

10-3

output10-3 real interest rate

consumption

04

real exchange rate

5
-0.01
2
0

-0.02

0
0

-5

-5
5

10

15

20

capital price

0.03

-0.03

-2
5

10

15

land price

0.03

-0.04

20

5

10

15

capital investment

0.03

5

20
0.03

0.02

0.02

0.02

0.02

0.01

0.01

0.01

0.01

0

0
5

10

15

20

credit spread

0

0
5

10

15

10

-3

10

15

20

20

10

15

20

current account / Y
0
-0.2

1

0.05

5

foreign debt

1.5

0.1
-1

5

2

0.15

-0.5

15

0

20

net worth0.2

10land investment

-0.4

0.5
-0.6

0

-1.5
5
10

10

15

20

-3 foreign debt tax

-2

4
3

0
5

10

15

20

5

10

15

20

5

10

15

-4

no capital control

2(optimal) capital control * = 6

-6
1
0

-8
5

10

15

20

20

-4
interest shock
10foreign

5

10

15

20

Figure 1: Impulse responses to foreign interest rate shocks with and without capital
controls

22foreign interest rates Rt∗ through the ﬁnancial accelerator mechanism. Consumption(Ct ) follows the output path (Yt ), and the real interest rate (ln Rt ) moves in the
opposite direction to consumption (Ct ).
However, if we use capital controls, with the tax rate reacting to the banks’
percentage deviation of foreign debt from its steady-state level in Eq.(51), the results
are diﬀerent. Capital controls with an optimal value of ω ∗ (= 6) (dashed blue lines)
achieve smaller ﬂuctuations in the main variables. Capital controls also mitigate
the appreciation of the real exchange rate (ϵt ), the rise in foreign debt (Dt∗ ), andt
the current account deﬁcit ( CA). Capital controls dampen the ampliﬁcation eﬀect
Yt

in the banking sector through the ﬁnancial accelerator mechanism. Capital controls
mitigate the increases in banks’ net worth (Nt ), capital and land investments (It andItl ), and capital and land prices (Qt and Qlt ). The decrease in the credit spread isalso mitigated, restraining the ampliﬁcation eﬀect through the ﬁnancial accelerator
mechanism. By dampening the ampliﬁcation eﬀect through the ﬁnancial accelerator
mechanism, capital controls stabilize output (Yt ), consumption (Ct ), and the realinterest rate (ln Rt ).
4.1.2

Macroprudential policies to foreign interest rate shocks

Next, we analyze the impulse responses of the main variables with and without
macroprudential policies on banks’ land funding in response to foreign interest rate
shocks. We consider the same initiating disturbance as in the capital controls case,which is a 0.075% unanticipated fall in foreign interest rates, Rt∗ with a persistencecoeﬃcient of 0.95. In Figure 2, the impulse responses without macroprudential
policies are shown by the solid (red) lines, which are the same as those in Figure 1.
The dashed (blue) lines show impulse responses with macroprudential policies. In
the latter case, we set an arbitrary value of ω l (= 0.6) in Eq.(52). We do so because,
as we show in Section 4.3, macroprudential policies responding to foreign interest
rate shocks do not improve welfare, and there is no optimal value of ω l .

23

5

10-3

outputconsumption

0.01

0
-5

6

0.005

4

0

2

-0.005

0

-0.01

-10
5

10

15

20

capital price

0.04

10

15

land price

-0.04

-0.06
5

10

15

20

capital investment

0.04

5
0.03

0.03

0.02

real exchange rate

-0.02

20

0.02

10

15

20

land investment

0.02

0.02
0.01

0.01
0

10

-3

10

15

20

0.01

0.01

0
5

0

0

-2
5

0.03

0.03

10-3 real interest rate

05credit spread

10

15

0

20

net worth

5
3

10

-3

10

15

20

5

foreign debt

10

15

20

current account / Y
0

0.2
-5

2.5

0.15

-10

0.1

2

-15

0.05

1.5

0

-20
5

10

15

20

land tax

0.01

1
5

-2

-0.5

10

15

20

-1
5

10

15

20

5

10

15

20

-4
interest shock
10foreign-4

no Macroprudential

0.005

Macroprudential policy

l

= 0.6

-6

0

-8
5

10

15

20

5

10

15

20

Figure 2: Impulse responses to foreign interest rate shocks with and without macroprudential policies

24When the macroprudential policy on the banks’ land funding is in place, as thepolicy intends, it restrains land investment (Itl ) and land price (Qlt ) from rising compared with the no-policy case. However, simultaneously, the macroprudential policy
on banks’ land funding boosts capital investment (It ) and capital prices (Qt ). The
rise in capital investment and price leads to a greater decline in the credit spread(Rkt+1 − Rt+1 ) than in the no-policy case. Therefore, contrary to the policy’s intention, the macroprudential policy on banks’ land funding ampliﬁes the eﬀect throughthe ﬁnancial accelerator mechanism. This causes further capital inﬂows, implying atlarger deﬁcit in the current account (to GDP ratio) CA, a larger increase in foreignYt

debt Dt∗ , and a higher degree of the real exchange rate ϵt appreciation. Enforcing theampliﬁcation eﬀect through the ﬁnancial accelerator mechanism, the macroprudential policy on the banks’ land funding destabilizes output (Yt ), consumption (Ct ),and the real interest rate (ln Rt ).
In summary, the macroprudential policy on banks’ land funding mitigates theboom in land investment and prices. However, it boosts the rise in capital investment
and price. It ampliﬁes the eﬀect of foreign interest rate shocks on aggregate variables
through the ﬁnancial accelerator mechanism. In other words, the macroprudential
policy on the banks’ land funding has the distortion eﬀect of directing capital inﬂows
from land investment to capital investment and, therefore, results in exacerbating
the ampliﬁcation eﬀect through the ﬁnancial accelerator mechanism.

4.2

Impulse responses to land market shocks

The last section considers the impulse responses to external foreign interest rate
shocks with and without capital controls and macroprudential policies. This section
analyzes the impulse responses to internal land market shocks. As we argue insections 2.1 and 2.3, land market shocks capture exogenous variations in the valueof land holding in a simple manner. The land shock is equivalent to the capital shock,which is an exogenous trigger for asset price dynamics in Gertler and Kiyotaki (2010)25

and Gertler et al. (2012).

4.2.1

Capital Controls to land market shocks

In this section, we show the impulse responses of the main variables, with andwithout capital controls, to land market shocks. We consider a 5% unanticipatedincrease in land value with a persistence coeﬃcient of 0.66 as a land market shockξtl . In Figure 3, the solid (red) lines indicate impulse responses without capital
controls.14 The dashed (blue) lines indicate impulse responses to capital controls.
In the latter case, we set an arbitrary value of ωτ∗ (= 1.17) in Eq.(51). We do so
because, as shown in section 4.3, capital controls responding to land market shocks
prove not to be welfare-improving. Therefore, there is no optimal value of ωτ∗ in thiscase.
From Eq.(49), we know that the exogenous increase in the land value raises
the banks’ net worth Nt . The rise in net worth Nt reduces the banks’ borrowing
constraints and raises capital and land investments (It and Itl ). Capital and land
prices (Qt and Qlt ) increase with increases in It and Itl . With this loosening, the credit
spread Rkt+1 −Rt+1 (which equals Rlt+1 −Rt+1 in the equilibrium) decreases. As a fallin the credit spread reduces the cost for borrowers, capital and land investments (Itand Itl ) increase further through the ﬁnancial accelerator mechanism, which raises
output (Yt ) and consumption (Ct ). An expansion in the banks’ balance sheets alsotraises foreign borrowing and capital inﬂows, which implies the current account ( CA)Yt

deﬁcit, foreign debt (Dt∗ ) expansion, and real exchange rate (ϵt ) appreciation.
When capital controls are in place, as the policy intends, they mitigate thet) deﬁcit, foreign debt (Dt∗ ) expansion, and real exchange ratecurrent account ( CAYt(ϵt ) appreciation. Mitigating the change in credit spread Rkt+1 − Rt+1 (or Rlt+1 −Rt+1 ), capital controls also dampen volatile changes in capital and land investments(It and Itl ) and capital and land prices (Qt and Qlt ). Nevertheless, by changing the
14

In Figures 3 and 4, we follow Gertler and Kiyotaki (2010) and Gertler et al. (2012) and simulate
the impulse responses for 40 quarters, which are longer than in Figures 1 and 2.

26

output

0.04

0.03

0.035

0.025

0.03

0.02

0.025

consumption

510-3 real interest rate

0.05

0

0

-5
-0.05

0.02

0.015

real exchange rate

-10
10

20

30

40

capital price

0.08

10

20

30

40

land price

0.1

10
0.08

20

30

40

capital investment

10
0.1

0.06

0.05

0.06

0.05

0.04

0

0.04

0

0.02

-0.05

0.02

-0.05

0

-0.1
10

20

30

40

credit spread

0

0
10

30

40

30

40

land investment

-0.1
10

net worth

0.6

-0.01

20

20

20

30

40

10

foreign debt

20

30

40

current account / Y

0.01

0

0.4

-1
0.005

-0.02

0.2

-0.03

0
10

6

-2

10

20

30

40

-3 foreign debt tax

0.06

4

0.04

2

0.02

-3

0
10

20

30

40

10

20

30

40

no capital control

0

10

20

30

capital control

*

0
10

20

30

40

40

land market shock

10

20

30

40

Figure 3: Impulse responses to land shocks with and without capital controls

27= 1.17foreign debt tax, τt∗ in Eq.(36), capital controls distort the real interest rate (ln Rt )and result in destabilizing output (Yt ) and consumption (Ct ) compared with the nopolicy case.
4.2.2

Macroprudential policies to land market shocks

Next, we analyze the impulse responses of the main variables with and without
macroprudential policies in response to land market shocks. In Figure 4, the impulse
responses without macroprudential policies are indicated by the solid (red) lines.
The dashed (blue) lines indicate the impulse responses to macroprudential policies.
In the latter case, we select the optimal value of ω l (= 0.04) in Eq.(52), which wewill explain in detail in Section 4.3.
When the macroprudential policy is in place, as the policy intends, it mitigatesthe credit spread Rkt+1 − Rt+1 (or Rlt+1 − Rt+1 ) and dampens volatile changes in capital and land prices (Qt and Qlt ) as well as capital and land investments (It and Itl ).
t
The macroprudential policy also dampens the current account ( CA
) deﬁcit, foreignYt

debt (Dt∗ ) expansion, and real exchange rate (ϵt ) appreciation. Simultaneously, themacroprudential policy to change τtl in Eq.(35) has the distortion eﬀect on the realinterest rate (ln Rt ). However, the magnitude of the policy distortion in this case issmaller than that in the previous capital control case. Overall, the macroprudential
policy mitigates the ﬂuctuations of capital and land investments and their prices. It
also stabilizes the other main variables, such as output and consumption, in response
to land market shocks.

4.3

Welfare analysis

Thus far, we have analyzed the impact of unexpected shocks on the economy using
a ﬁrst-order approximation. However, the ﬁrst-order approximation is unsuitablefor comparing welfare levels under diﬀerent policies.15 This section uses a second15

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.

28

consumption

output
0.022

0.026

0.02

0.024

0.018

0.022

2

10-3 real interest rate

0.05

real exchange rate

1
0

0

0.016

-1
-0.05

0.02
10

20

30

0.08

10

40

capital price

-2
20

30

40

land price

0.1

10
0.08

20

30

40

10

capital investment

0.1

0.06

0.05

0.06

0.05

0.04

0

0.04

0

0.02

-0.05

0.02

-0.05

0

-0.1

0

10

20

30

40

credit spread

10

30

40

30

40

-0.1
10

net worth

0.6

0

20

20

land investment

20

30

40

10

foreign debt

20

30

40

current account / Y

0.01
0
0.005

0.4

-0.01

-1

0
-0.02

0.2

-0.03

0
10

4

10

-3

20

30

40

land tax

2

0.04

0

0.02

-2

-3

-0.01
10

0.06

-2

-0.005

20

30

40

-4
10

20

30

40

10

20

30

40

land market shockno Macroprudential(optimal) Macroprudential policyl= 0.04

0
10

20

30

40

10

20

30

40

Figure 4: Impulse responses to land shocks with and without macroprudential policies

29order approximation to examine the welfare implications of capital controls andmacroprudential policies. For policy evaluation, we compute welfare levels for arange of policy rules and compare them with the no-policy case.
The welfare criterion is deﬁned using a recursive household lifetime utility function:
Wt = u (Ct , ht ) + βEt Wt+1 ,where Wt denotes the welfare level, and u (Ct , ht ) is the utility function in Eq.(1).
We compare the diﬀerent policies using Schmitt-Grohé and Uribe (2007)’s deﬁnitionof the consumption equivalent. Speciﬁcally, we deﬁne the proportion ιw of thehousehold’s steady-state consumption level as
∞
X



1+ξ
ξ0
E0
β ln (1 + ιw ) C̄ −
h̄
1+ξ
t=0



t

= E0

∞
X
t=0


β

t


ξ0
1+ξ
(ht )
, (65)
Ct −1+ξ

where C̄ and h̄ denote consumption and labor levels in their non-stochastic steadystates, respectively.16 We examine the welfare implications of capital controls andmacroprudential policies by comparing the values of ιw in the range of ω ∗ in (51)and ω l in (52) to those in the no-policy regime (ω ∗ = ωl = 0).
From the welfare gain perspective, we compare the two policies in response to
the foreign interest rate shock in section 4.3.1 and the land market shock in section
4.3.2. We show a stark contrast between the two cases. In the former case, capital
controls improve welfare, whereas macroprudential policies are welfare worsening.
In the latter case, the opposite is true; capital controls worsen welfare, whereas
macroprudential policies improve welfare.

We conducted second-order computations using Dynare. See Adjemian et al. (2011) for further
details. We also used the method developed by Kim et al. (2008) to eliminate explosive paths bypruning the terms of the high-order eﬀects.
16
The steady-state levels of consumption and labor are identical in the policy and no-policy
regimes because the steady state levels of tax rates on banks’ foreign debt and land holdings (τt∗and τtl ) are zero.

30

4.3.1

Welfare comparison between capital controls and macroprudential
policies to foreign interest rate shocks

Figures 5a and 5b show the welfare gains from capital controls and macroprudential
policies, respectively, in response to foreign interest rate shocks.

0.045

0

0.04
-0.02
0.035
-0.04

0.03
0.025

-0.06
0.02
-0.08

0.015
0.01

-0.1
0.005
0

-0.12
0

5

10

15

20

25

30

0

(a) Capital controls

5

10

15

20

25

30

(b) Macroprudential policies

Figure 5: Welfare gains of capital controls and macroprudential policies in response
to foreign interest rate shocks
Figure 5a presents the corresponding welfare gains of diﬀerent degrees of capital
controls (i.e., adopting diﬀerent values of ω ∗ instead of the no-policy case (ω ∗ = 0)).
The horizontal axis represents ω ∗ . The vertical axis represents the welfare gain,
which is the diﬀerence between the value of ιw associated with each value of ω ∗ andthat in the no-policy case. We ﬁnd that there exists a range of ω ∗ that improves
welfare levels compared with the no-policy case. The optimal value of ω ∗ is 6.0,
which maximizes the welfare gain from capital controls. The maximum welfare gainis 0.04.
Figure 5b presents the corresponding welfare gains of diﬀerent degrees of macroprudential policies (i.e., adopting diﬀerent values of ω l instead of the no-policy case(ω l = 0)). Figure 5b shows that, as macroprudential policies are more responsive(i.e., a higher value of ω l ), the welfare deteriorates more, which implies that macroprudential policy responding to foreign interest rate shocks causes a distortion.17
17

We have conducted the sensitivity analysis on key parameters related to the banking sector

31

Our welfare analysis is consistent with the impulse-response analysis in section
4.1. The impulse responses of the main variables to foreign interest rate shocks in
Section 4.1 suggest that capital controls are superior to macroprudential policies instabilizing economies aﬀected by foreign interest rate shocks. Our results conﬁrm
that capital controls are appropriate for responding to foreign interest rate shocks;
however, macroprudential policies are not.18

4.3.2

Welfare comparison between capital controls and macroprudential
policies to land market shocks

Thus far, we have analyzed the welfare implications of capital controls and macroprudential policies in response to foreign interest rate shocks. Next, we examine thewelfare-improving eﬀects of these two policies in response to land market shocks.
Figures 6a and 6b show the welfare gains from capital controls and macroprudential
policies, respectively, in response to land market shocks.

0

0.05

-0.005

0.04

-0.01

0.03

-0.015

0.02

-0.02

0.01

-0.025

0

-0.03

-0.01

-0.035

-0.02
0

0.05

0.1

0.15

0.2

0.25

0.3

0

(a) Capital controls

0.05

0.1

0.15

0.2

0.25

0.3

(b) Macroprudential policies

Figure 6: Welfare gains of capital controls and macroprudential policies in response
to land market shocks
Figure 6a presents the corresponding welfare gains of diﬀerent degrees of capitaland land markets (γ, κlI , θ, and κ l ). Obtaining welfare curves similar to Figure 5a and 5b, we
conﬁrm that the main result remains robust for the diﬀerent values of the parameters.
18
We also conﬁrm that even when two shocks occur simultaneously (Kwon, 1998), our main
policy implications remain unchanged if the foreign interest rate shock is dominant.

32

controls in response to land market shocks (i.e., adopting diﬀerent values of ω ∗instead of the no-policy case (ω ∗ = 0)). Figure 6a shows that as capital controls are
more responsive (i.e., a higher value of ω ∗ ), the welfare deteriorates more, implyingthat capital controls responding to land market shocks cause a distortion.
Figure 6b presents the corresponding welfare gains of diﬀerent degrees of macroprudential policies (i.e., adopting diﬀerent values of ω l instead of the no-policy case(ω l = 0)). We ﬁnd that there exists a range of ω l that improves welfare levels compared with the no-policy case.19 The optimal value of ω l that maximizes the welfare
gain from capital controls is 0.04. The maximum welfare gain is 0.045.20

5Conclusion

Faced with the problem of coincidence between real estate booms (busts) and capitalinﬂows (outﬂows), policymakers can implement macroprudential policies targeting
domestic real estate markets and capital controls targeting international capital
ﬂows. Building a small open economy NK-DSGE model, in which banks choose
their asset portfolio between physical capital and land, we quantitatively examinedthe eﬀectiveness of the two policies and analyzed which policy is more appropriate for managing the coincidence between land booms (busts) and capital inﬂows(outﬂows). As foreign and domestic exogenous shocks are ampliﬁed through theﬁnancial accelerator mechanism due to the banks’ balance sheets, both capital controls on capital ﬂows and macroprudential policies on the banks’ land funding seemto be potentially welfare-enhancing. However, the quantitative results show that thesuperiority of the two policies depends on the type of shock impacting a small open
economy. In the case of foreign interest rate shocks, capital controls improve welfare,
whereas macroprudential policies reduce welfare. Conversely, the superiority of the19

We have conducted the sensitivity analysis on key parameters related to the banking sector
and land markets (γ, κlI , θ, and κ l ). Obtaining welfare curves similar to Figure 6a and 6b, we
conﬁrm that the main result remains robust for the diﬀerent values of the parameters.
20
We also conﬁrm that even when two shocks occur simultaneously (Kwon, 1998), our main
policy implications remain unchanged if the land market shock is dominant.

33

two policies is reversed in the case of domestic land market shocks. In this case,macroprudential policies improve welfare, whereas capital controls reduce welfare.
In other words, our results imply that employing policies directly related to shocks(i.e., foreign policies to foreign shocks and domestic policies to domestic shocks) arelikely to be appropriate, but employing policies indirectly related to shocks are not.
The policy implications of this study are as follows. Identifying the source ofthe shock generating the coincidence between real estate booms (busts) and capitalinﬂows (outﬂows) is important. If the exogenous shock is domestic, macroprudential
policies are likely to be more eﬀective than capital controls. Conversely, if it is foreign, capital controls are likely to be more eﬀective than macroprudential policies.
The empirical literature starting from Calvo et al. (1993) has a long tradition of
examining which of the domestic (or ‘pull’) factors or the external (or ‘push’) factors are more important in determining capital ﬂows in emerging countries. Many
empirical studies (e.g., Dooley et al., 1996; Frankel and Okongwu, 1996; FernandezArias, 1996) suggest that the external (or “push”) factors are more important thanthe domestic (or “pull”) factors. If this is the case, our results imply that capital
controls would be more suitable for managing the coincidence of real estate booms(busts) and capital inﬂows (outﬂows) compared with macroprudential policies.
This study also has the implications for policy responses of emerging economies
to the Federal Reserve’s recent interest hikes. After the large-scale inﬂows of capital into emerging economies, their sharp reversals have been repeatedly witnessed
once interest rates in developed countries rise. For example, in 2013, when Fed
Chair Bernanke hinted that the Federal Reserve would reduce the pace of asset purchases under its quantitative easing (QE) program, many emerging economies suchas Argentina, Turkey, and Indonesia experienced problems with capital outﬂow andcurrency depreciation, which is referred to “taper tantrum.” The recent normalization of U.S. monetary policy may cause another episode revealing the vulnerabilityof emerging economies to foreign interest shocks. The eﬄux of capital from emerging

34

countries is likely to be accompanied with credit crunch and real estate bust. Our
paper’s results suggest that policy makers in emerging economies need to be carefulin making policy decisions when facing the boom and bust of real estate markets.

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42

Appendices
A1

Equilibrium conditions
Rt =Λt,t+1 = β

Yt = Atα K 

ζ0h1+ζ
Ct − 1+ζtζ0
Ct+1 − 1+ζ
h1+ζ
t+1

(A3)

1 = Et (Λt,t+1 Rt+1 ) ,(A4)

1 = Et





Lt−1
αL

(A2)

,

Zt+1 + λQt+1
Λt,t+1
Qt + κKth

1 = Et

Kt−1
αK

(A1)

wt = ζ0 hζt ,

1 + it−1,πtZ l + λl Qlt+1
Λt,t+1 t+1l
Qt + κ l Lht

α L 

Mt
αM

α M 

,

(A5)

l
ξt+1
,

(A6)

ht
1 − αK − αL − αM

1−αK −αL −αM
,
(A7)

mC
t =

1 αK l αL αM 1−αK −αL −αMZZtϵt w t.
At t
Ztl Lt−1
αL=,
Zt Kt−1
αK

43

(A8)

(A9)

ϵ t Mt
αM=,
Zt Kt−1
αK(A10)w t ht1 − αK − αL − αM=.
Zt Kt−1
αK

(A11)




Yt+1
1
C
(πt − 1) πt =1 − η + ηmt + Et Λt,t+1
πt+1 (πt+1 − 1) .
κ
Yt
  

It
It
+
κI
−1 ,
I
I

(A13)

 l
2  l   l

It
It
It
l
−1 +
κI
−1 .
2 Il
Il
Il

(A14)

κI
Qt = 1 +
2



It
−1
I

2

κl
Qlt = 1 + I

ψt = max

ϕt ,ϕlt ,xtµt ϕt + µlt ϕlt + µ∗t ϕt + ϕlt xt + νt(Zt+1 + λQt+1 )µt = Et Λt,t+1 (1 − σ + σψt+1 )− Rt+1 ,
Qt








(A12)

(A15)

(A16)





 l
 l


l
l


Z
+
λ
Q
ξ
t+1
t+1
t+1
l
l


µt = Et Λt,t+1 (1 − σ + σψt+1 ) − τt Rt+1 −Rt+1  , (A17)

Qlt


|



{z
}






Rlt+1

44













 




ϵ
t+1
∗
∗
∗


µt = Et Λt,t+1 (1 − σ + σψt+1 ) Rt+1 −R + τt Rt+1  ,


ϵt t




|
{z
} 




∗
D
R


(A18)

t+1

νt = Et {Λt,t+1 (1 − σ + σψt+1 ) (1 + τtn ) Rt+1 } ,(A19)µt = µlt ,(A20)

Φt = ϕt + ϕtl .

(A21)

ν
t
,
− µt − µ∗t xt

(A22)

r


1
2 ˜∗ 2xt = ∗ −1 + 1 +
µ
,
γ t
µ˜t

(A23)

µ˜∗t = µ∗t /µlt .

(A24)

Φt =

θ

1 + γ2 x2t

45

Qt Ktb,Nt
Q l Lbϕlt = t t ,Nt
ϵt Dt∗,xt =Qt Ktb + Qlt Lbt

ϕt =

(A25)
(A26)
(A27)





∗
∗
b
Dt−1
.
+ Ztl + λl Qlt ξtl Lbt−1 −σ Rt Dt−1 + ϵt Rt−1
Nt = (σ + ξ) (Zt + λQt ) Kt−1
(A28)

Qt Ktb + Qlt Lbt = Nt + Dt + ϵt Dt∗ .

(A29)it − ī = (1 − ρi ) ωπ (πt − 1) + ρi (it−1 − ī) .

(A30)



 

 l 
 κItI
Yt = C t + 1 + Ψ
It + 1 + Ψ tl
Itl +χ Kth +χl Lht + (πt − 1)2 Yt +EXt .
I
I
2
(A31)

EXt =

Pt
et Pt∗

−φYt∗ = ϵφt Yt∗ ,

(A32)

1
EXt .
ϵt

(A33)

∗
∗
+ Mt −
Dt−1
Dt∗ = Rt−1

Kt = It + λKt−1 ,

(A34)


Lt = ξtl Itl + λl Lt−1 ,

(A35)

46

Kt ≡ Ktb + Kth ,(A36)

Lt ≡ Ltb + Lht .

(A37)


ϵRt∗ ∼ N 0, σR2 ∗ ,ϵξt ∼ N 0, σξ2 ,∗ln Rt∗ − ln R̄∗ = ρR∗ ln Rt−1
− ln R̄∗ + ϵRt∗ ,l+ ϵξt ,
ln ξtl = ρξ ln ξt−1

A2

Steady state

In the steady state, we set the following:R∗ = 1.005,
A = 1,τ ∗ = 0,τ l = 0,
τ n = 0,π = 1,
ϵ = 1.

47

(A38)
(A39)

In the steady state, we obtain

Q = 1,

from (A13)

Ql = 1,from (A14)

R=

1
,
β

Λ = β,

from (A2) and (A4)from (A4)1− 1, from (A1)β1mC = 1 − . from eq. (A12)
η
i=

(A40)

We deﬁne s, sl , and s∗ as follows:s ≡ β (Z + λ) − 1, from (A16)sl ≡ β Z l + λl − 1, from (A17)

(A41)
(A42)

s∗ ≡ 1 − βR∗ . from (A44)
Note that while s∗ is determined exogenously, s and sl remain endogenous.
From (A20), we obtain thats = sl .

(A43)

From (A16), (A17), (A24), and (A43), we obtainµ∗µ˜∗ = l
µ



s∗
= l
s


=

s∗
.
s

(A44)

Subsequently, we can express x as

x=

s 
−1 +
s∗


 ∗ 22 s
 . from eq. (A23)
1+
γ s

s

48

(A45)

Using Eqs.(A25), (A26), and (A27) and the deﬁnitions of s, sl , s∗ , we can rewrite
Eq.(A28) in the steady state, as follows:
"

#
"

 #
Z l + λl Ql Lb RD + ϵR∗ D∗
Z l + λl Q l L b(Z + λQ) K b(Z + λQ) K b
β = σβ
+
−
+
+ ξβ
N
N
N
N
N
h




i
= σβ (Z + λ − R) ϕ + Z l + λl − R ϕl + (R − R∗ ) ϕ + ϕl x + R
h

 i
l
l l
+ ξβ (Z + λQ) ϕ + Z + λ Q ϕl
h


i
h
i
= σ (s + s∗ x) ϕ + sl + s∗ x ϕl + 1 + ξ (1 + s)ϕ + (1 + sl )ϕl ,= σ + [σ (s + s∗ x) + ξ (1 + s)] ϕ + ϕl . using s = sl

From last equation, we can express Φ as

Φ ≡ ϕ + ϕl =β−σ.
σ (s + s∗ x) + ξ (1 + s)

(A46)

Substituting (A16), (A17), and (A44) into (A15) and using the deﬁnitions of s, sl ,s∗ , we obtain the following:ψ = µϕ + µl ϕl + µ∗ ϕ + ϕl x + ν,
= (1 − σ + σψ) (s + s∗ x) ϕ + sl + s∗ x ϕl + 1 .
Thus, using s = sl , we can express ψ as

(1 − σ) (s + s∗ x) ϕ + ϕl + 1.
ψ=
1 − σ − σ (s + s∗ x) (ϕ + ϕl )(A47)

From incentive-compatibility constraint (31), we obtainψ = Θ (xt ) Φ.

49

(A48)

Combining Eqs.(A47) with (A48), we obtain(1 − σ) [(s + s∗ x) Φ + 1]
= Θ (xt ) Φ.
1 − σ − σ (s + s∗ x) Φ(A49)

Substituting (A46) into (A49) yields:
H (s, s∗ ) ≡ (1 − σ) [β (s + s∗ x) + ξ (1 + s)] [σ (s + s∗ x) + ξ (1 + s)]− Θ (x) (β − σ) [(1 − β) σ (s + s∗ x) + ξ (1 + s) (1 − σ)] = 0.

(A50)

From (A45), we obtain thatr2s x = s2 + (s∗ )2 − s,γ∗

which shows that “s∗ x” in (A50) is the function of endogenous “s” and exogenous“s∗ .” Thus, we can obtain the steady state value of “s” by solving (A50).
Once we obtain the steady-state value of s, we obtain sl in (A43), x in (A45),and Φ in (A46) as well. Using the steady state value of “s,” we obtain the otherendogenous variables as follows:1+s− λ, from (A41)β
1 + slZl =− λl , from (A42)βsK h = , from (A5) κ lss
Lh = l = l . from (A6)κκZ=

Using Eqs.(A7), (A8), and (A40), we have

 

K
mC α K
1 αK
=
= 1−
,
Y
Z
η Z


1 αL
L
= 1−
.
Y
η Zl
50

(A51)
(A52)

Using Eqs.(A3), (A7), (A8), (A9), (A10), (A11), (A51), and (A52), we obtain

Y =h

(

1
(1 − αK − αL − αM ) ζ0
ζ

i ζ1

1
1−
η

(αK +αL +αM )ζ+1 

A
αL αM αKl
(Z ) ϵ Z

With Y , we obtain
1 αK
K =Y 1−, from (A51)
η Z


1 αL
L=Y 1−. from (A52)η Zl

Using K and L, we obtain
αM ZK, from (A10)
αK ϵ

 1
1 − αK − αH − αM ZK 1+ζ
h=
,
αK
ζ0

M=

w = ζ 0 Lζ ,from (A3) and (A11)from (A3)

Kb = K − Kh = K −Lb = L − Lh = L −

s
,
κ

sl
,
κl

from (A36)from (A37)

I = (1 − λ) K, from (A34)
I l = 1 − λl L. from (A35)∗

From (A33) (using x ≡ QK bϵD), we obtain EYX :+Ql Lb
EX
= αM
Y



1
1−
η




x QKtb + Qh H b+ (R − 1),Y∗which yields EX = EYX Y .
From (A31), we obtain C:

C = Y − I − I l − EX −51

κ h 2 κl h 2(K ) − (L ) .
2
2

1
1+ζ ) ζ (1−αK −α
L −αM ).

From (A21), (A25), and (A26), we obtain that
ΦQK b,
QK b + Ql Lb
ΦQl Lbϕl =,QK b + Ql Lb
QK b
N=
.
ϕ
ϕ=

From the deﬁnition of x (A27), we obtain

b
l b
x
QK
+
Q
L
.
D∗ =
ϵ
From the balance sheets (A29), we obtain
D = QK b + Ql Lb − N − ϵD∗ .

From (A48), we obtainγ 
ψ = θ 1 + x2 Φ.
2Using ψ, we obtain(Z + λQ)
µ=Ω
−R ,
Q
"
#
 l
l
l l
Z
+
λ
Q
ξ
µl = Ω−R ,Qlµ∗ = Ω [R − R∗ ] ,ν = ΩR,
where Ω ≡ Λ (1 − σ + σψ) .

52

A3

The household’s proﬁts from ﬁrms and banks

In Eq.(2), Πt denotes the total proﬁts of ﬁrms and banks (net start-up funds forbankers). Πt is given by:


2 #
κ
p
pit
it
− mC
yit −
− 1 Yt diΠt =tP
2 pit−1t
0|{z}
proﬁt from intermediate goods ﬁrms  l ItIl+ Qt − 1 − ΨItl
It + Qt − 1 − Ψl tl
I
I
|
{z
}
proﬁt from capital and land investment ﬁrms



∗
∗
b
Dt−1
+ (1 − σ) (Zt + λQt ) Kt−1
+ Ztl + λl Qlt ξtl Lbt−1 − Rt Dt−1 − ϵt Rt−1|{z}dividend from bankers− ξ (Zt + λQt ) Kt−1 + Ztl + λl Qlt ξtl Lt−1 .
{z}|start-up fund for bankers
Z 1 "

The household’s proﬁt from the ﬁnal goods ﬁrms is zero due to perfect competition.

A4

Derivation of Eq.(32)

It follows from Eq.(24):
 l
l
∗
Zt+1
+ λl Qlt+1 ξt+1
Ql ltbnt+1(Zt+1 + λQt+1 ) Qt ktb
dt∗ ϵt+1 ϵt dt
=
+
−
R
−
R
.
t+1
t
nt
Qt
nt
nt
nt
ϵt n t
Qlt
Using ϕt ≡ Qt ktb /nt , ϕlt ≡ Qlt ltb /nt , xt ≡ϵt d∗t, and Eq.(30), we have
(Qt ktb +Qlt ltb ) ll
+ λl Qlt+1 ξt+1
Zt+1
nt+1
(Zt+1 + λQt+1 )ll∗ ϵt+1
=
ϕt +
x
ϕ
+
ϕ
ϕ
−
R
t
t
t
t
t
nt
Qt
ϵt
Qlt



− Rt+1 ϕt + 1 + τtl ϕlt − (1 + τtn ) − xt (1 − τt∗ ) ϕt + ϕlt .

53

Transforming this equation, we obtain Eq.(32).
#
"
 h


l

Zt+1
+ λl Qlt+1 ξt+1
nt+1
(Zt+1 + λQt+1 )=− Rt+1 ϕt +− 1 + τtl Rt+1 ϕlt
nt
Qt
Qlt



ϵt+1 ∗∗+ (1 − τt ) Rt+1 −Rt xt ϕt + ϕlt + (1 + τtn ) Rt+1 .
ϵt54