Foreign Reserve Accumulation, Foreign Direct
Investment, and Economic Growth
Hidehiko Matsumoto
Bank of Japan
February 18, 2019

Abstract
This paper develops a quantitative small-open-economy model to assess the optimal pace of foreign reserve accumulation by emerging and developing countries. In the model, reserve accumulation depreciates the real exchange rate andattracts foreign direct investment (FDI) in‡ows, which promotes productivity
growth through endogenous …rm dynamics. The economy is also subject to sudden stops in the form of an occasionally binding constraint on foreign borrowing,
and accumulated reserves are used to prevent severe economic downturns. The
model shows that two factors are the key determinants of the optimal pace ofreserve accumulation: the elasticity of the foreign borrowing spread with respect
to foreign debt, and the entry cost for FDI entry. The model suggests that these
two factors can explain a substantial amount of the cross-country variation in theobserved pace of reserve accumulation.

Keywords: Foreign reserve accumulation, foreign direct investment, sudden stop, endogenous growth, real exchange rate, gross capital ‡ows
JEL code: F23, F31, F32, F41, F43

I am grateful to Felipe Sa¢ e for his advice and guidance on this project. I would like to thank Kosuke Aoki, Boragan Aruoba, Rasmus Fatum, Tomohiro Hirano, Sebnem Kalemli-Ozcan, Ryo Kato, Nuno
Limao, John Shea, Ina Simonovska, Luminita Stevens, Nao Sudo, and seminar participants at the Economic
Graduate Students Conference at Washington University in St. Louis, 2017 Fall Midwest Macroeconomics
Meetings, 2018 SED Annual Meetings, Bank of Japan, Bank of Korea, and the University of Maryland for
useful comments and discussions. All errors are my own. The views expressed in this paper are my own anddo not necessarily re‡ect the o¢ cial views of the Bank of Japan. Email: hidehiko.matsumoto@boj.or.jp.

1

Introduction

The active accumulation of foreign reserves by emerging economies, especially those in Eastand Southeast Asia, is one of the most prominent developments in the international …nancial
system over the past 25 years. The left panel in Figure 1 shows that the average reserve-toGDP ratio across 67 emerging and developing countries has increased from lower than 10%
before 1990 to almost 25% by 2010. A large volume of literature investigates the motives forthis active reserve accumulation, and identi…es two main motives: a precautionary motive toprevent severe economic downturns caused by sudden stops in capital in‡ows, and a growthstrategy through exchange rate depreciation and export promotion.1
Although these bene…ts of reserve accumulation are well understood, there is a wide crosscountry variation in how actively each country pursues these bene…ts. The right panel in
Figure 1 shows the average annual change in reserve holdings in terms of the ratio to GDP
for 19 selected emerging and developing countries in 1991-2010. It illustrates that Asian
countries such as China, Malaysia, and Thailand have been accumulating reserves equivalent
to 3:55% of GDP on average, while many Latin American countries are accumulating

reserves less than 1% of GDP. In spite of active research on the optimal reserve policy
throughout the past decade, the literature still tells little about what the optimal pace ofreserve accumulation for each country is, and why di¤erent countries accumulate reserves atdi¤erent paces.
To answer the above questions, this paper develops a quantitative small-open-economy
model of reserve accumulation. The main novelty of this paper is twofold. First, the model
incorporates the key bene…ts and costs of reserve accumulation into a uni…ed quantitative
framework. On the bene…t side, reserve accumulation promotes productivity growth in
the tradable sector through real exchange rate depreciation. When a sudden stop in capitalin‡ows occurs, accumulated reserves are used to mitigate the negative e¤ects on the economy.
Most existing theoretical papers studying optimal reserve policy incorporate only one of these
two e¤ects. On the cost side, reserve accumulation takes away resources that could otherwise
1

Ghosh, Ostry, and Tsangarides (2017) provide empirical evidence to show that the motives of reserve
accumulation have been shifting over time. They show that the precautionary motive for current accountshocks was important in the 1980s, but since the 1990s, the precautionary motive for capital account shocks
and the currency-depreciation motive have become more important.

1

Figure 1: Reserve accumulation by emerging and developing countries

Annual increase in reserves, ratio to GDP

0.05

Reserve-to-GDP

0.25
0.2
0.15
0.1
0.05
0
1980 1985 1990 1995 2000 2005 2010 2015

Pace of reserve accumulation in 1991-2010

0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0

Ecuador
Domi. Rep.
South Africa
Venezuela
MexicoArgentina
Colombia
TurkeyChile
BrazilUruguay
Tunisia
Indonesia
Philippines
Egypt
Peru
Thailand
Malaysia
China

Reserve-to-GDP ratio, 67 developing countries
0.3

have been used by domestic agents, and reduces consumption in the short run and crowds
out investment.2 The optimal pace of reserve accumulation in the model is determined by
the trade-o¤ between these bene…ts and costs.
The second novel contribution is that instead of trying to identify the unique optimalpace of reserve accumulation for a representative emerging economy, this paper asks whydi¤erent countries accumulate reserves at di¤erent paces.3 As shown in the main analysis,
it is crucially important to take into account country-speci…c characteristics in considering
the optimal reserve policy. One of the key messages of this paper is that it is not optimalfor Latin American countries to accumulate reserves at a pace similar to Asian countries.
The model describes a small open economy with tradable and non-tradable sectors. Corresponding to the two bene…ts of reserve accumulation mentioned above, two features are
introduced into the model: endogenous growth with foreign direct investment (FDI) entry,
2

Crowding-out of investment resulting from reserve accumulation is documented by Reinhart, Reinhart,
and Tashiro (2016) at the macro level, and shown empirically by Cook and Yetman (2012) at the micro level.
3
Benigno and Fornaro (2012) and Korinek and Servén (2016) are two examples of the papers that study
the optimal pace of reserve accumulation for a representative emerging country.

2

Figure 2: Reserve accumulation, GDP per capita growth, FDI in‡ow
Reserve accumulation and GDP per capita growth, 1991-2010
10

9

Reserve accumulation and FDI inflow, 1991-2010= 0.56 (0.21)

8

Average FDI inflow, % of GDP

Average GDP per capita growth rate

= 0.52 (0.13)
8

6

4

2

7

6

5

4

3

2

0
1

-2
-2

-1

0

1

2

3

4

5

0
-2

6

Average change in reserves, % of GDP

-1

0

1

2

3

4

5

6

Average change in reserves, % of GDP

and sudden stops in capital in‡ows. Endogenous growth is modeled as a version of theSchumpeterian growth model in which intermediate goods-producing …rms in the tradable
sector invest in innovation and increase productivity. FDI is introduced in order to capture
the idea that reserve accumulation promotes growth in part by attracting FDI from developed countries as well.4 Sudden stops are modeled as an occasionally binding borrowing
constraint on private foreign debt and working capital …nancing.
The government reserve policy consists of two interventions. First, in normal times when
the borrowing constraint is not binding, the government collects taxes on tradable goods
to accumulate reserves. Since tradable goods become relatively scarce compared with nontradable goods, the relative price of non-tradable goods falls, which is real exchange rate
depreciation. Real depreciation increases the relative pro…tability of the tradable sector,
and induces a labor shift to the tradable sector. This labor shift brings higher pro…ts
for intermediate …rms, which induces more investment and attracts FDI, and promotes
productivity growth. Figure 2 presents some empirical evidence that is in line with thismechanism. The left panel shows that countries with a faster pace of reserve accumulation
4

Dooley, Folkerts-Landau, and Garber (2007) and Dooley, Folkerts-Landau, and Garber (2014) argue
that Asian countries’growth strategy is to repress real wages by foreign exchange rate intervention and to
attract FDI.

3

are likely to have faster growth in GDP per capita. The right panel indicates a signi…cantpositive correlation between the pace of reserve accumulation and the FDI in‡ow-to-GDP
ratio.5
Second, when the borrowing constraint becomes binding, the government provides accumulated reserves to bail out private agents. Government bailouts relax the binding borrowing
constraint and prevent severe economic downturns. In addition to the contemporaneous effects, bailouts induce …rms’ investment and attract FDI ex ante in normal times, because
investment and FDI entry are forward-looking decisions, and anticipation of future bailouts
increases the expected future pro…ts for …rms.
Fast and stable growth by reserve accumulation comes at a cost. As the government
collects tax revenue to accumulate reserves, private agents borrow more from abroad tocompensate for the loss of resources. In the model, the interest rate on foreign borrowing
is debt-elastic, and the higher debt-to-GDP ratio leads to a higher interest rate spread.
This higher interest rate spread causes two costs of reserve accumulation. First, it prevents
private agents from fully o¤setting reserve accumulation by increasing foreign borrowing,
thus lowering consumption in the short run. The optimal reserve policy therefore balances
the costs of short-run austerity with the bene…ts of higher long-run consumption. Second,
the higher spread discourages investment in capital and innovation, a form of crowding-out,
which reduces the growth-promoting e¤ect of reserve accumulation.
In the quantitative analysis, the model is calibrated to the average of the 19 emerging
and developing countries in the right panel of Figure 1.6 Since the bene…t of receiving FDI
is the crucial part of the quantitative analysis, parameters related to FDI are set to matchseveral targets taken from empirical papers on FDI.
The …rst important result using this model is that the optimal pace of reserve accumulation and its welfare impact depend crucially on two characteristics of each country: thedebt-elasticity of the foreign borrowing spread, and the FDI entry cost. In countries where
5

There are also several empirical papers that document the correlations between reserve accumulation
and real depreciation, and real depreciation and GDP per capita growth. See the literature review for details.
6
These countries are chosen for two reasons. First, the development levels of these countries are similarin the sense that most of them were lower middle-income countries in 1991 and became upper middle-income
countries by 2010. The second reason is the data availability for the foreign borrowing spread and FDI in‡ow
by sectors.

4the spread has a higher debt-elasticity, even small increase in private debt increases the spread
substantially, which increases the costs of short-run lower consumption and crowding-out ofinvestment. In countries with a higher FDI entry cost, reserve accumulation is not as e¤ective in attracting FDI and the growth-promoting e¤ect is therefore limited. In this case, theoptimal pace of reserve accumulation is slower, and the welfare gain is limited.
Given these results, this paper takes these two factors into account when evaluating thepace of reserve accumulation for each of the 19 countries. The debt-elasticity of the foreign borrowing spread is estimated using panel regression for the sample countries. Because
the debt-elasticity of the spread is signi…cantly associated with the default history of eachcountry, the sample 19 countries are divided into 5 groups according to the number of pastdefaults, and the elasticity is estimated for each group. The FDI entry cost parameter isadjusted to match the FDI in‡ow-to-GDP ratio for each country in the data.7 Then the
optimal pace of reserve accumulation is derived for each country and compared with the actual pace of reserve accumulation in the data. The second important result is that many of
the sample countries are roughly in line with the optimal pace in the model, suggesting thatthese two factors can explain a substantial amount of the observed cross-country variation in
the pace of reserve accumulation. The average optimal pace in the model across the 19 countries is 1:43% of GDP while it is 1:71% in the data, and the correlation coe¢ cient between
the optimal and actual pace across the countries is 0:73. A few countries including China,
however, have been accumulating reserves much faster than the optimal pace suggested by
the model.
The remainder of the paper is organized as follows. Section 2 reviews the related literature. Section 3 introduces the model. Section 4 discusses the mechanisms of how thereserve policy works in the model. Section 5 presents the calibration of the model and thequantitative analysis. Section 6 studies the key determinants of the optimal pace of reserve
accumulation. Section 7 evaluates the actual pace of reserve accumulation by developing
countries. Section 8 concludes.
7

As an alternative approach, the appendix of this paper explicitly estimates the FDI entry cost using theStarting a Business Index from the World Bank’s Doing Business Surveys.

5

2

Related Literature

Foreign reserve accumulation by developing countries has been an active research area in thelast decade. One strand of literature focuses on the growth-promoting e¤ect. As an empiricalmotivation, Aguiar and Amador (2011) …nd that there is a positive correlation between
government net foreign asset growth and GDP growth across developing countries, which isin stark contrast to the predictions of neo-classical growth models. Gourinchas and Jeanne(2013) and Alfaro, Kalemli-Ozcan, and Volosovych (2014) show that this correlation is driven
mainly by reserve accumulation by the public sector. Regarding the mechanism throughwhich reserve accumulation promotes growth, Levy-Yeyati, Sturzenegger, and Gluzmann(2013) shows that reserve accumulation causes real exchange rate depreciation and that
real depreciation in turn promotes economic growth. Rodrik (2008) also shows that realdepreciation promotes economic growth and further presents suggestive evidence that a labor
shift to the industry sector is the channel through which real depreciation promotes growth.
In line with these empirical studies, Aizenman and Lee (2010) and Korinek and Servén (2016)
develop models with a learning-by-doing externality in the tradable sector and study the
optimal reserve policy to promote growth. The present model shares with these papers thepremise that reserve accumulation causes real depreciation and a labor shift to the tradable
sector, but di¤ers in that productivity increases through …rms’endogenous investment and
FDI entry. Attracting FDI is another proposed channel through which reserve accumulation
promotes productivity growth. Dooley, Folkerts-Landau, and Garber (2007) and Dooley,
Folkerts-Landau, and Garber (2014) argue that Asian countries’growth strategy has been
to repress real wages through foreign exchange rate intervention in order to attract FDI fromdeveloped countries.
Another strand of literature studies the precautionary bene…ts of reserve accumulation.
Jeanne and Rancière (2011) model reserve accumulation as an insurance contract that payso¤ in a sudden stop and quantify the optimal amount of reserve holdings. Bianchi, Hatchondo, and Martinez (2016) and Hernández (2017) build a sovereign default model in which
the government holds reserve assets to insure against future defaults and loss of access tointernational …nancial markets. Hur and Kondo (2016) develop a model of bank-run style6

sudden stops and show that a small increase in rollover risk can explain the outburst of
sudden stop episodes in the late 1990s and the following active reserve accumulation by
developing countries in the 2000s.
All of these theoretical papers focus on either the growth-promoting e¤ect or the precautionary e¤ect of reserve accumulation, but not both. The model in this paper incorporates both e¤ects into a uni…ed framework and studies the interaction between the growthpromoting e¤ect and the precautionary e¤ect. In this sense, the present model is similar
to the model in Benigno and Fornaro (2012). Benigno and Fornaro (2012) develop a stylized model in which reserve accumulation in normal times and bailouts during crisis induce
private agents to use more imported inputs, which improves productivity through a learningby-doing type assumption. In the present model, in contrast, productivity increases throughfull-‡edged endogenous …rm dynamics. This framework captures two important e¤ects ofreserve policy that are absent in Benigno and Fornaro (2012). First, anticipation of future bailouts during crises induces …rms to invest more in normal times ex ante, because
bailouts stabilize the economy, and …rms’ investment is forward-looking. Second, reserve
accumulation takes away some domestic resources from private agents, causing crowding-out
of domestic investment. The analyses in this paper show that these two e¤ects constitutean important part of the growth-promoting e¤ect and the welfare impact of reserve policy.
Studies focused on the cross-country di¤erences in reserve accumulation are scarce. Obstfeld, Shambaugh, and Taylor (2010) consider the risk of simultaneous domestic capital ‡ight
and sudden stops of foreign capital in‡ows, and show that the size of the banking sector has astrong explanatory power for cross-country di¤erences in the size of reserve holdings. Aguiarand Amador (2011) develop a neo-classical growth model with political frictions and showthat the degree of political friction matters for the speed of net public debt reduction by thegovernment. The present paper focuses on two other factors that can explain cross-country
variation in the pace of reserve accumulation, the debt-elasticity of the spread on foreign
borrowing and the FDI entry cost.
The structure of the model rests on two strands of literature. First, the endogenous
growth framework is based on a version of the Schumpeterian growth model developed byAtes and Sa¢ e (2016). They incorporate the growth model developed by Klette and Kortum7

(2004) into a DSGE framework and introduce heterogeneous innovations. The present model
extends the framework in Ates and Sa¢ e (2016) by introducing FDI and innovation byforeign …rms. Second, sudden stops are modeled as an occasionally binding constraint on
foreign borrowing, following Mendoza (2010). The di¤erence from Mendoza (2010) is thatthe fraction of capital used as collateral is stochastic and the collateral value of capital isset at book value rather than market value, similarly to Bianchi (2016). The present modeldi¤ers from this literature in combining endogenous growth and non-linear crisis dynamics
caused by an occasionally binding constraint.
Lastly, this paper shares with several recent papers the feature that crises have a permanent negative impact on productivity. Queralto (2015) builds a model based on the Cominand Gertler (2006) version of the product-variety expansion model and shows that the model
can explain the persistent negative e¤ect of the 1998 sudden stop on productivity in Korea.
Gornemann (2015) also adopts the product-variety expansion model and develops a modelthat captures a very persistent negative e¤ect of sovereign default on productivity. Ates andSa¢ e (2016) introduce heterogeneous …rms and …nancial selection into the Schumpeterian
growth model and show that …rm heterogeneity has a persistent e¤ect on productivity growth
after sudden stops.

3

Model

The model framework is based on an in…nite-horizon small open economy with tradable andnon-tradable sectors. Figure 3 presents a diagram for the model economy. There are six
agents in the model: tradable goods producers, non-tradable goods producers, domestic andforeign intermediate …rms, foreign investors, households, and the government. There are
two driving forces of economic growth: capital accumulation by households, and endogenous
productivity growth in the intermediate sector. Unlike standard business cycle models, theeconomy starts with scarce capital, accumulates capital and grows fast toward the balanced
growth path. The focus of the model is how the reserve policy should be conducted during
the transition period.

8

Figure 3: Model overview

3.1

Tradable Goods Producers

Tradable goods are the numeraire of this model economy, and their price is normalized
at one. The representative tradable goods producer uses capital KtD , unit-mass variety ofintermediate goods fyt (i)g1i=0 , and imported inputs Mt to produce output YtT following the
Cobb-Douglas production function:
YtT = (KtD ) (ItM ) (Mt )1;(1)

where ItM is the composite of intermediate goods:
ItM = exp

Z 1

ln yt (i)di :(2)

0

Before production materializes, a …xed fractionof the cost of intermediate goods andimported inputs needs to be paid. This payment is …nanced by within-period borrowing
from abroad with no interest cost. In addition, the tradable goods producer borrows fromabroad using one-period non-contingent debt Bt on behalf of households.8 Foreign borrowing
8This assumption is just to simplify the algebra. It would be an equivalent model even if households
borrow directly from abroad.

9

is subject to an occasionally binding borrowing constraint. Speci…cally, the borrowing limit
is given byt Kt 1 ,wheret

is a collateral shock and takes either of two values,

L , following a two-state Markov process.

beginning of period t.

H

H

or

Kt 1 is the capital stock of this country at theis the value in normal times, and it is large enough that theborrowing constraint never binds. With exogenous probability,

t switches from

H to

L,

which is small enough that the borrowing constraint may bind depending on the state of
the economy. In particular, in the transition when capital is scarce, the borrowing limit is
low but there is a large incentive to borrow from abroad to accumulate capital. In this case,a collateral shock

L is likely to cause a binding borrowing constraint.

As shown below,

the binding borrowing constraint endogenously generates drops in output, consumption,
investment in capital and innovation, FDI in‡ows, and intermediate …rms’ pro…ts. In thelong run when capital has reached a steady state condition, the borrowing limit is large
enough that the borrowing constraint never binds even withL.

Given these settings, the maximization problem by the representative tradable goods
producer is as follows:
max
1

fKtD ;fyt (i)gi=0 ;Mt ;Bt g1
t=0

E0

X1

t=0

t

t

T
t ;

subject to the production function (1) andTTt = Ytrt KtDZ 1

P M Mtpt (i)yt (i)di

Bt + Rt 1 Bt 1

Tt + Vt ;

(3)

0

Bt +

Z 1

pt (i)yt (i)di + P M Mt

Vt

t Kt 1 ;

(4)

0

where

t is the marginal utility of tradable goods consumption by households, pt (i) is theprice of intermediate goods i, P M is the price of imported inputs, and Rt 1 is the grossinterest rate on foreign debt repaid at period t. Tt is a lump-sum tax that the government
collects to accumulate reserves, and Vt is a bailout by the government, which are explained
in detail in a later section. For each period, the tradable goods producer chooses capitaldemand KtD , intermediate goods demand fyt (i)g1i=0 , imported inputs Mt , and foreign debt
Bt to maximize the expected pro…t discounted by household’s discount rate adjusted by themarginal utility

t.

Let

t denote the Lagrange multiplier on the borrowing constraint (4).

10The …rst-order conditions with respect to the choice variables are as follows:
KtD : rt =

YtT
;
KtD
t

yt (i) : pt (i) 1 +t

Mt : P M

1+

t

=

(5)
YtT
;
yt (i)
YT
) t ;
Mt

= (1

t

Bt :
t :

t

Z 1

Bt +

t

t =

(6)
(7)
(8)

Rt Et ( t+1 );pt (i)yt (i)di + P M Mt

Vt

t Kt 1

= 0,

t

(9)

0:

0

The …rst three equations are the demand functions for capital, intermediate goods, andimported inputs. When the borrowing constraint is slack,t = 0 and the demand functions

for intermediate goods (6) and imported inputs (7) are the standard ones equating the priceand the marginal products. When the borrowing constraint binds, strictly positivet appears

as the external …nancing premium on working capital payments, which increases the e¤ective
cost of inputs. Equation (8) is the Euler equation with respect to foreign debt. Given thatt is the marginal utility of tradable goods consumption by households, it is the standard

Euler equation except when the Lagrange multiplier on the borrowing constraint

t appears.

This term captures the external …nancing premium on foreign debt when the borrowing
constraint binds, which increases the e¤ective real interest rate on foreign debt, as explainedin Mendoza (2010). The last equation (9) is the complementary slackness condition for the
borrowing constraint.
The gross interest rate on foreign borrowing Rt is endogenously determined. Following
Schmitt-Grohé and Uribe (2003), Rt is a function of the aggregate debt-to-GDP ratio:
Rt = R +where GDP is given by YtT

b

exp

Bt
GDPt

b

1 ;

(10)

P M Mt + PtN YtN M , with PtN YtN being the non-tradable goods

11price times output.9 As shown in Schmitt-Grohé and Uribe (2003), this formulation guarantees that the debt-to-GDP ratio will converge to the given value b, and Rt will be R in
the long run, so that the balanced growth path is uniquely pinned down. In this model,
however, the debt-elastic spread plays an important role in determining the cost of reserve
accumulation, namely, lower consumption in the short run and crowding-out of investment.
Section 4.2 discusses these key mechanisms and their implications for the optimal policy.

3.2

Intermediate Goods Producing Firms

There is a unit-mass variety of di¤erentiated intermediate goods in the tradable sector,
indexed by i. Following the version of the Schumpeterian growth model developed by Kletteand Kortum (2004), a …rm is de…ned as a collection of one or more product line(s) among
these di¤erentiated goods. Each …rm produces the product line(s) using labor, and innovatesover other product lines. The production technology is given by:
yt (i) = at (i)`t (i);(11)

where at (i) is the labor productivity and `t (i) is labor input. Labor productivity at (i) is
heterogeneous across i, and improves over time by entry and innovations by domestic andforeign …rms. The dynamics of the intermediate sector such as entry and innovation are laidout in the next subsection. This subsection focuses on the static part of the sector and showsthat only the productivity leader produces goods for each product line, and that pro…t isdetermined by the size of the productivity lead by the productivity leader over rival …rms.
As shown in equation (6), demand for each product line from the tradable goods producer
is a unit-elastic demand function. This implies that the solution to the pro…t-maximization
problem for a monopolist is to set the price in…nitely high. In the Schumpeterian growthmodel, however, there are rival …rms that can produce the same type of good with lower
productivity, who could steal the market by setting a price slightly below the monopoly
price. Therefore, through Bertrand competition, the pro…t-maximizing behavior by the9

Following Schmitt-Grohé and Uribe (2003), it is assumed that tradable goods producers do not internalize
the e¤ect of debt on the interest rate.

12

productivity leader is to set the price equal to the marginal cost of the closest rival …rm andmonopolize the demand.
Let 1 +

t (i) denote the productivity lead by the leader for product line i over the closest

rival. The productivity level of the closest rival is then given by at (i)= (1 +t (i)), and the

optimal price for the leader pt (i) is:pt (i) =Wtat (i)= (1 +t (i))(12);

where Wt is a real wage. The corresponding pro…t for the leadert (i) can be written as

follows:t (i) =

YtT
1+

t= t

Wt `t (i) =

t (i)

1+

t (i) 1 +

YtT
t= t

(13)

:

The …rst expression implies that larger demand from the tradable goods producer and acheaper real wage bring higher pro…ts. The second expression indicates that pro…t for eachproduct line depends on the productivity lead by the leader over the closest rivalt (i). Notealso that the borrowing constraint on the tradable goods producer a¤ects pro…t through the
Lagrange multipliert . When the borrowing constraint binds, the tradable goods producer

faces a higher e¤ective cost of buying intermediate goods, demand for them thereby being
reduced. Equation (13) shows that the smaller demand directly translates into lower pro…tfor the intermediate goods producing …rms.
The next subsection on …rm dynamics shows that there are only two cases for the productivity lead by the leader, depending on whether the leader is a domestic …rm or a foreign…rm. The productivity lead by a domestic leader is denoted byDt , and it isF
t for a foreign

leader. Therefore, there are only two types of pro…ts:

t (i) =

8
<
:

D
t

1+ D
t 1+
F
t

1+

F 1+
t

YtT
t= t

if leader is a domestic …rm

YtT
t= t

if leader is a foreign …rm:

It follows from the …rst expression in (13) that labor hired by each product line `t (i) also
depends only on the leader type. More explicitly, labor hired by each product line is given13

as follows:`t (i) =Hereafter let

D
t and

F
t

t (i)
t (i)Wt(14):

denote a pro…t for each domestic and foreign product line, and `Dtand `Ft denote labor hired by each domestic and foreign product line respectively.

3.3

Innovation and Firm Dynamics

The …rm dynamics in this economy are characterized by four di¤erent types of innovations:domestic entry, FDI entry, domestic incumbent innovation, and foreign incumbent innovation. Figure 4 illustrates an example of the evolution of …rms from one period to the next.
The upper panel shows six product lines with productivity a1 to a6 . The …rst three lines
are owned and produced by domestic …rm 1, and the latter three lines by foreign …rm 1. In
the next period, depicted in the lower panel, three things are happening: First, for productline 1, foreign investors acquire the line from domestic …rm 1 via FDI entry. It is assumed
that FDI entry takes place only on domestic product lines. FDI entry improves productivityof the recipient product line by the factor of (1 +Ft )=(1 +Dt ).

Second, for product line

3, foreign …rm 1 succeeds in innovation and replaces domestic …rm 1 as the productivity
leader. Incumbent …rms always innovate over product lines owned by other …rms because
innovating on its own product line would give a lower bene…t with the same cost. Domestic
incumbent innovation improves the productivity by a factor of (1 +Dt ), and by (1 +Ft ) forforeign incumbent innovation. Third, for product line 6, domestic entry occurs and a newdomestic …rm replaces foreign …rm 1 as the productivity leader. Domestic entry may occur
for any product line. Through such entry and innovation, …rms compete with each otherand endogenously expand, shrink, enter and exit, and increase the overall productivity of
the intermediate sector.
This framework captures the several features of FDI entry and foreign …rms documented
by empirical studies: (1) Most FDI entry is through the acquisition of domestic …rms rather
than green…eld investment.10 (2) Some domestic …rms are forced to exit through competition
with foreign …rms.11 Later sections will also show: (3) Foreign …rms innovate more often
1011Barba-Navaretti and Venables (2004) show that 90% of FDI is in the form of acquisitions.
See Aitken and Harrison (1999).

14

Figure 4: Firm dynamics

15

than domestic …rms.12 (4) In a crisis, foreign …rms invest more in innovation than domestic…rms and survive better.13
The productivity improvement process explained above can be summarized as follows:8>>(1 + Dt )at 1 (i) if domestic entry or innovation>>>>< (1 + F )=(1 + D )a (i) if FDI entry
t 1
t
t
:
at (i) =
>
F
>
(1
+
)a
(i)
if
foreigninnovation
t 1
>
t
>
>
>
: a (i) if nothing happenst 1

Under this process, the productivity lead over the closest rival is determined by whether the
productivity leader is a domestic …rm or a foreign …rm. In the former case the productivity
lead is by a factor of (1 +Dt ), and in the latter case it is by a factor of (1 +Ft ). Combinedwith the discussion in the previous subsection, this implies that there are only two types ofpro…t for each product line,

D
t or

F
t , depending on whether the productivity leader is adomestic …rm or a foreign …rm.
It is assumed that the productivity step size

D
t and

F
t

decline as capital accumulates.

Speci…cally, the following functional forms are assumed:
D
t =

D

F
t =

F

kss
kt 1

;

(15)

kss
kt 1

;

(16)

where kss = Kt 1 =At is the capital stock normalized by the aggregate productivity along
the balanced growth path, which is constant, and kt 1 = Kt 1 =At is the same variable in
the transition, which trends upward over time.

> 0 andF>D

are parameters. In thetransition in which capital is scarce, kss =kt 1 > 1 and the step sizes are large. As capital
accumulates and kt 1 gets close to kss , kss =kt 1 declines toward 1 and the step sizes converge
to

D

and

F

along the balanced growth path.14 The idea behind this assumption is that

12

See Arnold and Javorcik (2009) and Guadalupe, Kuzmina, and Thomas (2012).
See Alfaro and Chen (2012).
14
This assumption implies that the growth-promoting e¤ect of reserve accumulation declines over time.
Without this assumption, it would be optimal for the government to keep accumulating reserves permanently
to promote productivity growth, which is unrealistic.
13

16

capital scarcity indicates the technological distance from the world frontier, and when there
is a large distance, the economy can grow faster through the catching-up e¤ect. The following
subsections explain each type of entry and innovation in turn.
3.3.1

Innovation by Foreign Incumbent Firms

Consider a foreign …rm that owns n product lines. As seen before, operating pro…t depends
only on the owner type and is independent of the individual …rms’s productivity. Therefore
the total operating pro…t of this …rm is n Ft . It is assumed that a …rm with n product lines
has n opportunities for innovation. The idea behind this assumption is that an incumbent…rm’s innovation is based on and spins o¤ from the existing technology in practice. For
each innovation opportunity, …rms invest …nal tradable goods to create the innovation. The
success probability of innovation iFt for each innovation opportunity is a concave function of
tradable goods ZtF that a …rm invests:
iFt =
where

F

F

ZtF
At

1

> 0 is the productivity coe¢ cient and 0 <

(17)

;

< 1 is the parameter that governs theconcavity. As is common in Schumpeterian growth models, innovation is undirected in thesense that innovation is equally likely to apply to any product line. This feature is preservedin this model by the structure that the operating pro…t is independent of productivity. Undirected innovations by many …rms imply that each product line faces the same replacement
probability. Let dt denote this probability, and de…ne as P (i; n; p) the probability of having
i successes in n trials for a binomial process with success probability p. Namely,
P (i; n; p) =

n i
p (1
i

p)1 i :The value of a foreign …rm with n product lines can be written in a recursive form as follows:(

VtF (n) = max n Ft
ZtF

" n
n
X
X
1
F
(n + inZtF + F
P (i; n; iFt )P (j; n; dt )Et Vt+1
R
i=0
j=0

17

j)

!#)

:

The …rst two terms are the operating pro…t minus the innovation investment cost. RF is
the world interest rate, and foreign investors who own foreign …rms discount future pro…tsby this rate. The bracketed term is the expected value of this …rm in the next period. The…rst summation adds up the expected value over the n + 1 cases for the number of successful
innovations, from 0 to n. The second summation adds up over the n + 1 cases for the numberof replacements, again from 0 to n. Thus for a foreign …rm with n product lines, there are (n+1)2 di¤erent possible combinations of the number of successful innovations and replacements.
F
Note, however, that the expected value of the …rm in each case, Et Vt+1
(n + ionly on the number of the product lines, n + ij) , depends

j, and not on the speci…c combination of thenumber of innovations and replacements. For example, 3 innovations and 2 replacements willFgive the same expected value as 4 innovations and 3 replacements, namely Et (Vt+1(n + 1)).

Following Ates and Sa¢ e (2016), it can be shown by using a guess-and-verify methodthat the value of a foreign …rm with n product lines is equal to n times the value of a foreign…rm with a single product line:
VtF (n) = nVtF (1):The formal proof is left to the Appendix. This linear relation enables aggregation of the …rm
dynamics in a tractable way without keeping track of the …rm size distribution. The valueof a foreign …rm with a single product line is given by:
VtF (1) = max
ZtF

F
t

ZtF +

1
(1 + iFt
RFFdt )Et (Vt+1(1)) :(18)

Taking into account equation (17), the …rst-order condition with respect to ZtF gives the
optimal investment condition:
F

Since 0 <

(1

)

ZtF
At

1 1
F
Et (Vt+1(1)) = 1:
At R F(19)< 1, investment ZtF and the probability of successful innovation iFt are increasingin the expected value of a product line next period.

18

3.3.2FDI Entry

FDI entry takes the form of the acquisition of a domestic-owned product line by foreign
investors. There are in…nitely many foreign investors who can consider acquiring a productline and entering this country via FDI. There are three types of cost for FDI entry. First,
foreign investors need to pay a …xed fraction 0 << 1 of the discounted expected value ofFa product line (1=RF )Et (Vt+1(1)) to the domestic …rm that owns the product line.

can beinterpreted as the negotiation power of the domestic owner …rm against foreign investors.15
Second, there is a …xed entry cost At C F . This is in line with Helpman, Melitz, and Yeaple(2004) in that FDI entry is characterized by a large …xed entry cost. Third, there is acongestion cost of entry, which is linearly increasing in the aggregate number of productlines acquired by FDI in each period. Since there is an in…nite number of potential foreign
investors, FDI entry continues until the congestion cost pushes down the net expected pro…tof entry to zero. Therefore FDI entry in each period, denoted by eFt , is determined by thefollowing zero-pro…t condition:
At F
where

F

eFt
1

= (1

)

t 1

1
F
Et (Vt+1(1))
RF

At C F ;is a coe¢ cient on the congestion cost. The denominator 1(20)
t 1 is the fraction ofdomestic-owned product lines at the beginning of period t. This is introduced to capture theidea that it is more costly to …nd a good product line to acquire as the number of domesticowned product lines falls. Both the congestion cost and the …xed entry cost increase overtime along with the aggregate productivity of the economy At , so that FDI entry eFt will be
constant in the long run. Similarly to innovation by foreign incumbent …rms, FDI entry eFt
is an increasing function of the expected value of a product line.
15
For the domestic owner …rm to be willing to sell a product line to foreign investors, the incentive comFD
patibility condition must be satis…ed. This condition is given by (1=RF )Et (Vt+1(1)) Et ( t;t+1 Vt+1
(1))
where the right-hand side is the expected value of a domestic-owned product line discounted by the households’stochastic discount factor. Because this condition is always satis…ed under the calibrated parametervalues, it is not considered explicitly here.

193.3.3Innovation by Domestic Incumbent Firms

Characterization of domestic incumbent …rms is similar to foreign incumbent …rms, butdi¤erent in one key aspect: there is the possibility that product lines are acquired by foreign
investors via FDI. Consider a domestic …rm with n product lines. This …rm has n innovation
opportunities, as assumed in the case of foreign …rms. For each opportunity, the …rm invests
ZtD units of tradable goods, and the probability of successful innovation iD
t is given by thefollowing equation:iDt =with 0 <

D

ZtD
At

1

(21)

;

< 1. Let Qt denote the price that foreign investors pay to the domestic owner…rm to acquire a product line via FDI. From the last subsection this is given by:
Qt =

1
F
Et (Vt+1
(1)):
RF

(22)

Using Qt , the replacement probability dt , and the probability for a binomial process P (i; n; p),
the value of a domestic …rm with n product lines can be recursively written as follows:

VtD (n)=

max n D
nZtD
t
ZtD
8
2
n
n
n
<X
X
Xj
eF
t
+4
P (i; n; iD
P (j; n; dt )P k; n j;
t )
:
1
t 1
i=0
j=0
k=0
2
39
!
n
n
=
X
Xj
eF
t
4
+
P (j; n; dt )P k; n j;
kQt 5 :
;
1
t 1
j=0

Et

D
t;t+1 Vt+1 (n + i

j

!93
=
5
k)
;

k=0

Compared with the value of a foreign …rm, the additional terms are the third summationin the second line and the third line. The third summation in the second line adds up the
expected value over the nj + 1 cases for the number of product lines acquired via FDI byforeign investors, from 0 to n

j, given that j product lines are replaced. eFt =(1t 1 ) isthe probability that each product line is acquired via FDI by foreign investors. Note thatthe expected value of the …rm in the next period is discounted by the households’stochastic
discount factort;t+1 . Note also that the number of product lines the …rm owns in the next

period is given by n + ijk. The third line adds up the acquisition price of FDI entry

20

over the same n

j + 1 cases given j replacements. Using the same guess-and-verify method,

it can be shown that a linear relation holds for the value of a domestic …rm:
VtD (n) = nVtD (1);and the value of a domestic …rm with a single product line is given by:
VtD (1) = max
ZtD

D
t

ZtD + iDt + (1dt ) 1eFt
1D
Et ( t;t+1 Vt+1(1)) + (1

t 1

dt )

eF
t
1

Qt :
t 1

(23)

The …rst-order condition with respect to ZtD gives the optimal condition for domestic innovation investment:
D

3.3.4

(1

)

ZtD
At

1
D
Et ( t;t+1 Vt+1(1)) = 1:At(24)

Domestic Entry

Finally, entry of new domestic …rms comes from innovation by households and poaches a
product line from incumbent …rms. Households invest ZtE units of tradable goods to create
new …rms. The number of …rms created from ZtE units of investment is given by:
eD
t =

E

ZtE
At

1

:

(25)

The optimal investment ZtE satis…es that the marginal bene…t of investment is equal to themarginal cost, therefore:
E

3.4

(1

)

ZtE
At

1
D
Et ( t;t+1 Vt+1(1)) = 1:At(26)

Aggregation and Productivity GrowthThis subsection characterizes how …rm dynamics translate into macroeconomic dynamics,
speci…cally the transition of the share of product lines owned by foreign …rms, and productivity growth.
First, replacement of a product line happens for three di¤erent reasons: domestic incumbent innovations, foreign incumbent innovations, and domestic entry. Thus the replacement
21

rate dt is the sum of these three probabilities:
dt = (1Dt 1 )it +DF
t 1 it + et

(27)

FNote that the successful innovation probabilities by incumbents, iDt and it , are multiplied by

the share of domestic-owned and foreign-owned product lines respectively. Next, the shareof product lines owned by foreign …rms,

t , increases for two reasons:innovation over domestic-owned product lines, and FDI entry.

foreign incumbent

t decreases for two reasons:domestic incumbent innovation and domestic entry over foreign-owned product lines. The
transition oft is thus given by the following law of motion:

t

=

t 1+

=

F
t 1 + etFFt 1 )it + et

t 1 (1DFt 1 et + (itt 1 (1iDt ) t 1 (1Dt 1 )itt 1 ):

Dt 1 et(28)

Next, the expressions for aggregate productivity and its growth can be obtained in thefollowing way: First, combine (13) and (14) to obtain the ratio between labor input byFdomestic-owned product lines `Dt and foreign-owned product lines `t :

`D
1+
t
=
F
`t
1+

F
t
:
D
t

Combining this with total labor hired by the intermediate …rms in the tradable sector LTt =(1Dt 1 )`t +F
t 1 `t ,the following expressions for labor input by domestic-owned andforeign-owned product lines are obtained:
`D
t =

`Ft =

(1

1 + FtFt 1) t +

D
t 1 t

(1

1+ D
t
F
t 1) t +

D
t 1 t

LTt ;

LTt :

Plugging these equations and the production function for intermediate goods (11) into (2),22the composite of intermediate goods ItM can be written as follows:
ItM = At LTt

D t 1(1 + Ft )1 t 1t )Dt 1 )(1 +t ) + (1(1 +
t 1 (1 +

F
t )

(29)

;

where aggregate productivity At is given by:
At = exp

Z 1

ln at (i)di :0

As is clear from this expression, aggregate productivity At grows as productivity of eachproduct line at (i) improves. Using the four di¤erent innovation rates and the innovation
step sizes, the growth rate of At is characterized as follows:
At+1= 1 + gt =
At

1+
1+

F
t
D
t

eF
t

(1 +

D eD
t
t ) (1 +

D (1
t )

D
t 1 )it

(1 +

F t
t )

F
1 it

:

(30)

The four terms in the right-hand side correspond respectively to FDI entry, domestic entry, domestic incumbent innovation, and foreign incumbent innovation. This completes thecharacterization of …rm dynamics and its e¤ect on aggregate productivity growth.

3.5

Non-Tradable Goods Producers

The non-tradable goods producer hires labor from households and produces non-tradable
goods. The production function is given as follows:
1
YtN = At (LNt )where 0 < 1

N

N

;

(31)

< 1 is the labor share in non-tradable goods production. It is assumed

that total factor productivity in non-tradable goods production increases at the same rate
as aggregate productivity in the tradable sector. This assumption comes from the empiricalfact that productivity spillovers from multinational …rms to domestic …rms happens throughworker mobility.16 Since this spillover to non-tradable goods production is not internalized
by innovation investment decisions, it works as an externality that may cause too little
16

Dasgupta (2012) reviews the relevant empirical literature.

23

innovation. This spillover guarantees that production of tradable goods and non-tradable
goods will grow at the same rate in the long run. Let PtN denote the non-tradable goods
price. Since the law of one price holds for tradable goods between this country and therest of the world, the non-tradable goods price PtN determines the real exchange rate of thiscountry. Thus PtN can be considered the real exchange rate of this economy, and an increasein PtN is real appreciation. The …rst-order condition of the non-tradable goods producer isgiven by:
Wt = PtN At (1

N

)(LN
t )

N

(32)

:

Labor is assumed to be mobile between the tradable and non-tradable sectors. Therefore,
the real wage Wt is common in both sectors. Using PtN and Wt the pro…t for non-tradable
goods producer is given by:N
N N
t = P t Yt

W t LNt ;(33)which is paid to households.

3.6

Households

The representative household consumes tradable goods CtT and non-tradable goods CtN ,supplies labor Lt elastically, accumulates and rents capital Kt to the tradable goods producer,
and invests ZtE units of tradable goods in domestic entry. They receive the wage income
Wt Lt , capital income rt Kt 1 , and pro…ts from tradable goods producers
goods producers

Nt , and domestic intermediate goods producing …rms (1Tt , non-tradable
Dt 1 )( tZtD ).

They also receive FDI in‡ow eFt QFt , which is revenue from the sales of domestic-owned
product lines to foreign investors. The representative household’s optimization problem isthen given as follows:
max

fCtT ;CtN ;Lt ;Kt g1
t=0

E0

X1

t=0

h
" 1
Ct = ( )1=" (CtT ) " + (124

[ln Ct(Lt )! ] ;" 1)1=" (CtN ) "

i""1

;

(34)

subject to
CtT + PtN CtN + It + ZtE = Wt Lt + rt Kt 1 +It = Kt
where(1)Kt 1 +

T
t +

k

2

2

Kt
Kt 1

Kt 1

ZtD ) + eFt QFt ; (35)D
t 1 )( tNt + (1(1 + g)(36);

is a parameter to determine the weight of tradable goods in composite consumption

Ct , " is the constant elasticity of substitution between tradable and non-tradable consumption, andis the depreciation rate of capital. Capital accumulation is subject to a capitaladjustment cost that slows down the transition process, andk is the parameter that gov-

erns the size of this cost. The functional form of the capital adjustment cost is taken from
Neumeyer and Perri (2005) to be consistent with long-run growth of the economy.
Optimal investment in domestic entry ZtE is determined by equation (25). The …rst-orderconditions for the rest of the choice variables can be summarized as follows:
CtT
=
1
CtN
! 1

!(Lt )

t

1+

k

Kt
Kt 1

(1 + g)= Et"(PtN )" ;

Wt
=
Ct
(

t+1

(37)
1="

Ct
CtT

(38)

;
k

rt+1 + 1

2

2(1 + g)

Kt+1
Kt

2

!)#

;

(39)
where

t is the marginal utility of tradable consumption given by:

1
t =
Ct
The stochastic discount factor

Ct
CtT

t;t+1 is then given by1=":
t;t+1 =

(40)
t+1 = t . Equation (37) relates

the optimal ratio of tradable and non-tradable goods consumption to the real exchange rate.
Equation (38) gives the optimal labor supply Lt , and equation (39) is the Euler equation
with respect to capital.17
17

It is assumed that households do not internalize the fact that capital accumulation will relax the borrowing limit on foreign debt and working capital …nancing.

25

3.7

Government

The government in this model engages in a reserve policy to improve household’s welfare.
The reserve policy consists of two types of interventions: reserve accumulation in normal
times and bailouts during crisis.
When

t =

H

and the borrowing constraint is loose, the government collects Tt unitsof tradable goods through a lump-sum tax and accumulates reserves. In general Tt canbe any function of the state of the economy, but in this paper only a simple tax rule isconsidered in which the government collects a …xed fractionof tradable goods output YtTeach period. The government keeps accumulating YtT units of reserves each period until
it becomes suboptimal to do so. There are two reasons why accumulating reserves becomessuboptimal at some point in the transition. First, the bene…t from attracting FDI becomes
smaller as capital accumulates and the step sizeFt (kt 1 ) becomes smaller. Second, as capital

accumulates, the collateral value becomes large enough at some point that the borrowing
constraint never binds and there is no need for bailouts. For these reasons it is optimal forthe government to stop accumulating reserves once capital is su¢ ciently accumulated.18
Bailouts in sudden stops are modeled as follows. The borrowing constraint being binding
implies that the tradable goods producer cannot borrow as much as they would if the borrowing constraint was loose. Let YtT;loose denote tradable goods output when the constraint
is loose. The shortage of foreign borrowing, denoted by St , can be written as follows:
St = maxn) YtT;loose

Bt + (1o

L Kt 1 ; 0:

The …rst two terms are the borrowing amount when the constraint is loose, and

L Kt 1is the borrowing limit, so that the gap is the shortage of foreign borrowing. A negative
gap implies that the borrowing limit

L Kt 1 is large enough to cover the necessary amountof borrowing, and in this case a max operator sets St = 0. When St is positive, i.e. theborrowing constraint binds without a bailout, the government gives reserves to cover the18

It is also optimal for the government not to rebate reserves after reserve accumulation stops, because
rebating reserves would reduce the growth rate. The redundant reserves are lost from the economy, but thewelfare loss is limited because the value of goods received after 30 periods or further in the future is heavily
discounted.

26

shortage up to the amount of reserves at hand. The size of a bailout, denoted by Vt , is givenas:Vt = min St ; RF Ft 1 ;where RF Ft 1 is the amount of reserves at the beginning of period t.
Given the tax rule in normal times and bailouts in sudden stops, the amount of reserves
Ft follows the transition equation given as follows:

Ft =

3.8

8
< RF F

when

t =

H

Vt whent =L

t 1 + Tt

: RF F

t 1

:

(41)

Market Clearing Conditions

To close the model, this subsection lists the market clearing conditions. The capital market,
labor market, and non-tradable goods market clearing conditions are given as follows:
Kt 1 = KtD ;(42)

Lt = LTt + LN
t ;

(43)

YtN = CtN ;(44)

and labor in the tradable sector satis…es:
LTt = (1Dt 1 )`t +F
t 1 `t :(45)

This completes the exposition of the model economy. The appendix formally de…nes theequilibrium of the model economy and the stationarized equilibrium conditions that areused to solve the model numerically.

4

Discussion on Reserve Policy

This section elaborates on the key mechanism of the model, namely how the reserve policy
attracts FDI, promotes growth, and improves welfare. The section starts by describing the27main bene…t of the reserve policy and explains how the reserve policy may improve welfare.
The section then discusses the cost of the reserve policy, and explains the key trade-o¤ thatthe reserve policy faces, i.e. lower consumption in the short run and higher consumption in
the long run.

4.1

Bene…ts of Reserve Policy

The bene…ts of a reserve policy are that it promotes productivity growth by inducing moredomestic entry and incumbent …rms’ investment, and it also attracts FDI. Both reserve
accumulation in normal times and bailouts during crises induce these …rm dynamics.
In normal times when the borrowing constraint is loose, the government collects taxes
from private agents to accumulate reserves. As some resources are taken away by the government, households reduce tradable goods consumption.19 This reduction in tradable goods
consumption leads to a fall in non-tradable goods price through equation (37), which is realexchange rate depreciation. Real depreciation in turn a¤ects the relative pro…tability between the tradable and non-tradable sectors, and causes a labor shift across sectors. To see
this, combine equations (1), (7), (13), (29) and (32) to obtain the wage equality condition
across sectors:

Wt = At F (Kt 1 ; t 1 ) LTt+= PtN At (1

N

)(Lt

LTt )

N

;

(46)

where F (Kt 1 ; t 1 ) is a function of the state variables. Note that production is concave
in labor in both sectors, and thus the marginal product of labor is decreasing in labor inboth sectors. This implies that a reduction in PtN causes a labor shift from the non-tradable
sector to the tradable sector through (46). As more labor becomes available in the tradable
sector, pro…t for each …rm in the intermediate sector increases, which induces more entry andinvestment by …rms, and attracts FDI entry. This mechanism is in line with the empirical19

Private agents have an incentive to borrow more from abroad to compensate for the loss of resources. As
shown in Jeanne (2012), if reserve accumulation is completely o¤set by private foreign borrowing, there would
be no e¤ect on the consumption path, and thus reserve accumulation would not cause real depreciation. In
this model, the debt-elastic foreign spread prevents full o¤set. As private agents borrow more from abroad,the interest spread rises through equation (10) and makes foreign borrowing more costly. Therefore the o¤set
is only partial.

28

…ndings by Rodrik (2008) that real depreciation promotes productivity growth by shifting
more production resources to the tradable sector.
When the borrowing constraint binds, bailouts by the government help the tradable
goods producer …nance working capital payments, and prevent sharp drops in pro…ts forintermediate …rms, as shown in (13). As explained in the previous sections, …rms’investment
and FDI entry decisions are forward-looking, and anticipation of future bailouts increases
the expected value of …rms ex ante and induces more investment and FDI entry.
The reason why these government interventions may improve households’welfare is because private agents do not internalize the fact that their actions a¤ect FDI entry decisions
by foreign investors, thus there is an externality in the model. The reserve policy corrects
this externality through the two channels explained above, namely reserve accumulationin normal times and bailouts during crisis. However, whether the reserve policy actually
improves welfare depends on its cost. The next subsection discusses this point.

4.2

Costs of Reserve Policy

There are two types of costs associated with the reserve policy in the model. First, as
explained above, reserve accumulation takes away some tradable goods from private agents,
so that consumption of tradable goods becomes lower in the short run. Consumption of nontradable goods also becomes lower because reserve accumulation shifts labor to the tradable
sector. As is clear from the discussion in the previous subsection, lower consumption anda labor shift to the tradable sector are the essential parts of the mechanism of how reserve
policy works. In this sense these are the unavoidable costs of the reserve policy. At thecost of short-run lower consumption, the reserve policy promotes productivity growth andhouseholds enjoy higher consumption in the long run. Therefore, for the reserve policy toimprove welfare, the long-run gain of higher consumption must exceed the short-run loss oflower consumption. This is the key trade-o¤ that the reserve policy faces.
The second cost is a crowding-out e¤ect of reserve accumulation. Reinhart, Reinhart,
and Tashiro (2016) show that there is a strong negative correlation between the reserve-toGDP ratio and the investment-to-GDP ratio in Asian countries after 2000, suggesting that
active reserve accumulation crowds out investment. Cook and Yetman (2012) use micro-level29

data to show empirically that reserve accumulation reduces bank lending in emerging Asian
countries. In the current model, the crowding-out e¤ect results from the debt-elastic spreadon foreign borrowing. As the government accumulates reserves by collecting taxes, private
agents borrow more from abroad to compensate for the loss of resources, at least partially.
Higher borrowing then increases the interest rate on foreign debt through equation (10).
A higher interest rate causes crowding-out of investment in both capital and innovationin the intermediate sector. On the one hand, a higher interest rate requires a higher capital
return through the arbitrage condition, thereby discouraging capital investment. On theother hand, a higher interest rate reduces the stochastic discount factor by households,
which in turn reduces the expected value of product lines in the intermediate sector. To
see this point, arrange the Euler equation with respect to foreign debt (8) to obtain theexpression for the stochastic discount factor as follows:
Et ( t;t+1 ) =Et ( t+1 )
t

=

1

t
t

1
:
Rt

(47)

This equation indicates that a higher interest rate on foreign debt Rt reduces the stochastic
discount factor, implying that households evaluate future tradable consumption less highly
compared with tradable consumption today. Since investment in domestic …rm entry andinnovation are forward-looking, the lower stochastic discount factor leads to lower investment.
In summary, the reserve policy brings higher consumption in the long run at the costof lower consumption in the short run. The optimal reserve policy is one that achieves abalance between the marginal gain and the marginal loss. The policy analysis section showsthat the debt-elasticity of the spreadb and the FDI entry cost a¤ect the optimal reserve

policy and its welfare gain.

5

Quantitative Analysis

This section calibrates the model parameters, demonstrates the baseline simulation, anddiscusses the model features. The model is solved numerically by two steps: First, theequilibrium conditions are divided by productivity level At to stationarize the equations.

30

In the second step, the stationarized model is solved globally using a version of the policy
function iteration algorithm to deal with the occasionally binding borrowing constraint. The
stationarized equilibrium conditions and the details of the solution procedure are left to theappendix.

5.1

Calibration

One period in the model is meant to be annual. There are 30 parameters to be determinedin the model, except the debt-elasticity of spreadbwhich is estimated from the data

below. Conventional parameters are set to the conventional values in the literature, and theother parameters are calibrated to target the data for a sample of 19 developing countries
from 1991-2010.20 Table 1 presents 17 externally-determined parameter values. Parameters
regarding preferences are set to the conventional values in the literature. The discount factor= 0:96 and gross return on the safe asset RF = 1:02 are standard values for annual models.
The weight on tradable goods in consumption= 0:34 is set following Mendoza (2005) andDurdu, Mendoza, and Terrones (2009). The elasticity of substitution between tradable andnon-tradable goods in consumption, " = 0:6, is in the middle of the range discussed in
Mendoza (2005). The coe¢ cient on labor disutility= 0:525 is set so that labor supply inthe long run is equal to 1. The parameter for the labor supply elasticity ! = 1:455 is set
following Mendoza (1991).
Regarding the production parameters, capital’s share in tradable production
the capital depreciation rate

= 0:3 and= 0:1 are set to the conventional values. The imported input

price P M is set to be 1, and labor’s share in non-tradable production 1
from Schmitt-Grohé and Uribe (2016). The share of intermediate goodsN= 0:75 is taken= 0:54 is set sothat the imported inputs-to-GDP ratio matches the data at 10%. The fraction of the input
cost subject to the working capital requirement

is determined by the method adopted in

Mendoza (2010), in which the ratio of domestic credit to private …rms to GDP is used as aproxy for working capital. This ratio is 47% on average for the sample countries, and this20

The countries are the 19 countries in the right panel of Figure 1. These counties are chosen based on
the data availability and due to similar development levels. See footnote 6.

31

Table 1: Externally-determined parameters
Variable
Discount factor
Return on reserve asset
Tradable share in consumption
CES between T and NTLabor disutility
Frisch elasticity 1=(! 1)Capital share
Intermediate input share
Imported input price
Labor share in non-tradable
Capital depreciation rate
Share of input subject to WKLong-run debt/GDP
Long-run interest rate
Transition matrix of t
Concavity of innovation investment

RF
"
!

PM
1

N

b
R
PHL ; P LH

results in

Value

Source and Target

0.96
1.02
0.34
0.6
0.525
1.455
0.3
0.54
1
0.75
0.1
1.05
-0.36
1.06350.080, 0.851
0.5Standard
Standard
Mendoza (2005)
Middle value in literature
Unit labor supply
Mendoza (1991)
Standard
Imported input/GDP 10%
Normalized value
Schmitt-Grohe Uribe (2016)
Standard
Private credit/GDP 47%
Data
Consistent with BGP growthFrequency and duration of SS
Akcigit and Kerr (2015)= 1:05.21 The long-run debt-to-GDP ratio b is set to the average of the sample

countries in recent years at 36%. The long-run interest rate on foreign borrowing R is set
to be consistent with the long-run growth rate satisfying R = 1 + g, where the long-run
growth rate g is determined below.
The only uncertainty in the model is a stochastic borrowing limit coe¢ cient
follows a two-state Markov process with a 2t.

t

2 transition matrix. Following Jeanne andRancière (2011), the average frequency and duration of sudden stop episodes are derived in
the following way: a given country in a given year is in a sudden stop if the capital in‡owto-GDP ratio drops more than 5% from the previous year. Using the same sample of 33
countries as in Jeanne and Rancière (2011) over the period of 1980-2009, the unconditional
probability of sudden stops is 8.6%, and each sudden stop episode continues for two years
with probability 14.9%. Accordingly, the transition matrix is set so that PHL = 0:080 and
PLH = 0:851.
For the parameters related to innovation and FDI entry, the concavity parameter governing investment, , is set to 0:5 following Akcigit and Kerr (2015) and their literature review.
21

This value is higher than 0:26 in Mendoza (2010), but close to 1 in Neumeyer and Perri (2005) and 1:25
in Uribe and Yue (2006).

32

Table 2: Jointly-determined parameters
Variable
D
E
F
F

CF
D
F

Value

Domestic innovation coe¤.
Domestic entry coe¤.
Foreign innovation coe¤.
Coe¤. of FDI congestion cost
Share of FDI …rm value paid
Fixed entry cost
Domestic innovation size
Foreign innovation size

The eight parameters regarding growth,

0.20
0.72
0.17
0.60
0.71
0.16
0.24
0.36
D

TargetModel

Manu. R&D/GDP 2.4%
2.4%
Domestic entry rate 8.11%
8.11%
Relative innovation rate 1.387
1.387
FDI value-added in manu. 32.25% 32.25%
Manu. FDI in‡ow/GDP 1.57%
1.57%
Value of a line/…xed cost 1.1
1.1
Long-run growth rate 2.1%
2.1%
11% productivity gain upon FDI entry; E; F ;F, ; CF ;D;F, are jointly determined

to match eight moments in the data to those in the model in the long run, as summarized inTable 2. Each of the following moments is tightly related to the above eight parameters inthe same order. (1) The ratio of R&D expenditure in the manufacturing sector to GDP isclosely related toD, which governs the scale of domestic innovation. This ratio is in general

small in developing countries and high in developed countries. The long-run ratio in themodel is set to match the average of developed countries in the recent data, which is 2:4%.
(2) The domestic entry rate is closely related to

E. The data is taken from The World

Development Indicators. The average of the sample countries is 8:11%. (3) The innovation
rate of foreign …rms relative to domestic …rms identi…esF, which governs foreign incum-

bents’innovation. Guadalupe, Kuzmina, and Thomas (2012) document that foreign …rms in
Spain conduct product innovations 1:387 times more often than domestic …rms, which is set
as the calibration target. (4) The value added share of foreign …rms in the manufacturingsector identi…esF, the congestion cost of FDI entry. This target is meant to pin down theeconomic presence of foreign …rms in the tradable sector in the model. Ramstetter (2009)
reports this value for Malaysia, Thailand, and Vietnam, and Ramondo (2009) reports this for
Chile. The average of these four countries is 32:25%, which is set as the target. (5) The ratioof FDI in‡ows to the manufacturing sector to GDP helps to pin down the cost of acquisition
for FDI. Because the data for FDI in‡ows by sector are limited, the sample is extended to
twelve countries including six out-of-sample developing countries.22 The average of the ratio
22

The in-sample countries are Colombia, Ecuador, Malaysia, Mexico, Turkey, and Uruguay, and the outof-sample countries are Costa Rica, Hungary, Pakistan, Poland, Romania, and Vietnam. The data can befound at the International Trade Centre’s website.

33

Table 3: Parameters related to transitional dynamics
Variable
L
k

Value

Target

0.85
15
0.25

SS dynamics
Drop in investment in SS
Avg. growth 3% in transition

Borrowing limit coe¢ cient
Capital adjustment cost
Exponent on catch-up termof FDI in‡ows to the manufacturing sector to GDP for these countries is 1:57%, which is set
as the target. (6) There is no data or reliable estimation for the …xed cost of FDI entry C F .
The ratio of the expected value of a foreign product line to the …xed entry cost determines
the elasticity of FDI in‡ows to the expected value of a line, as suggested in equation (20).
This ratio is set to target 1:1, so that the dynamics of FDI in‡ows during sudden stops matchthe data as shown in the next subsection. (7) The long-run growth rate helps to pin downD, the productivity gain of domestic innovation. The long-run growth rate is set to 2:1%,

which is the average growth rate of developed countries in recent years. (8) The productivity
gain from FDI entry identi…esF. Arnold and Javorcik (2009) and Guadalupe, Kuzmina,

and Thomas (2012) estimate the productivity gain from FDI entry in Indonesia and Spainusing the propensity score matching method to mitigate the cherry-picking e¤ect of FDI
entry choice. These papers show that in the year of entry, …rm productivity increases by
11%. HenceF

is set so that (1 +FD)=(1 +) = 1:11. When each country’s reserve policyFis evaluated below, the FDI congestion cost

and the …xed entry cost C F are adjusted

across countries to match variation in the relevant moments.
Finally, the borrowing limit coe¢ cient

L , the capital adjustment cost parameterk,and the exponent on the catch-up term are determined to target the model behavior in thetransition, because these parameters are irrelevant along the balanced growth path.

L andk are set to match the sudden stop dynamics of the model with the data shown in the next

subsection.

governs the growth rate of the economy in the transition, and thus is set tomatch the average growth rate of the model economy in the …rst 30 periods with the average
growth rate of the sample countries from 1980 to 2010. The average GDP growth rate in
the data is about 3%. With = 0:25, along with the initial capital holdings k 1 = 0:45kss ,the average growth rate of the …rst 30 periods is 3%. In determining these parameter values,
the pace of capital accumulation is not targeted. According to the Penn World Table, the34

capital holdings of the sample countries in 1980 is 28% of that in 2010. In the model, theinitial capital K 1 is about 28% of the capital holdings at period 30.

5.2

Quantitative Performance of the Model

This subsection documents the quantitative performance of the model and demonstrates therole of the reserve policy. It starts by showing a sample dynamic simulation path to give an
idea of what the transition dynamics look like. Figure 5 presents a sample dynamic path ofthe model. The debt-elasticity of spread is set at

b = 0:0561, which is a middle value of the

19 sample countries estimated below. Initial capital is 45% of its long-run level as measured
by the productivity-adjusted value, initial debt is 33% of GDP to match with the data in
1980, and the initial share of foreign-owned product lines is 0. The solid lines are the paths
with reserve policy, and the dashed lines are the paths without reserve policy. The tax rate
, which is the pace of reserve accumulation, is set to 3%.
As the …rst panel shows, there is a borrowing constraint shock at period 11. The second
panel shows that reserve is accumulated in normal times, and used for a bailout when the
borrowing constraint shock hits the economy. Responding to reserve accumulation by thegovernment, private agents borrow more from abroad to compensate for the loss of resources,
as displayed in panel 3. As discussed in the previous section, reserve accumulation causes
real depreciation and a labor shift to the tradable sector in panel 4 and 5. Panel 4 also
shows that a bailout by the government prevents a sharp drop in real exchange rate in acrisis. Panel 6 shows that as private agents borrow more from abroad, the interest spreadon foreign borrowing rises.
Panels 7, 8, and 9 show the log gaps in GDP, capital investment, and consumption
compared with the path without shocks or reserve policy. When the borrowing constraint
shock hits the economy, all three variables drop sharply without policy intervention. But asshown in panels 7 and 8, reserve policy induces faster growth of GDP and capital investment,
and a bailout in crisis cancels the negative e¤ect of the shock on these variables. Panel 9shows that consumption becomes lower in the short run but higher in the long run withreserve policy, which is the key trade-o¤ that reserve policy faces, as discussed in the previous
section.
35

Figure 5: Model simulation ( b =0.0561)
1

1. Borrowing constraint shock

2. Reserv e/GDP

0.2

3. Debt/GDP ratio=0.03
No reserve

-0.3
0.15
-0.4
0.1
-0.5
0.05
-0.6
0

0

5

10

15

20

4. Real exchange rate

0.38

0

0.46

0.34

0.44

0.32

0.42

0.3

0.4
0

5

10

15

20

7. Log gap in GDP

0.05

0.38

5

10

15

20

5. Labor in Tradable

0.48

0.36

0.28

0

0

5

10

15

20

6. Interest Spread

0.02

0.01

0

0

5

10

15

20

8. Log gap in capital inv estment

0.05

-0.01

0

5

10

15

20

9. Log gap in consumption

0.01
0

0

0

-0.05

-0.05

-0.01
-0.02
-0.03

-0.1

0

5

10

15

20

10. FDI entry

-0.1

0

5

10

15

20

11. Foreign innov ation rate

0.0092

-0.04

0

5

10

15

20

12. Share of f oreign product lines

0.25

0.03
0.2

0.009
0.025

0.15
0.00880.1

0.02

0.0086

0.015
0

5

10

15

20

13. Domestic entry

0.085

0.0085

0.007

0.08

0.0065

0.075

0.006

0.07

0.0055

0.065

0.005

0.05
0

5

10

15

20

14. Domestic innov ation rate

0

0

5

10

15

20

15. Productiv ity growth rate

0.024
0.023
0.022
0.021

0

5

10

15

20

0.02
0

5

10

16. Log productiv ity gap

0.02

0.01

0.00
0

5

10

15

20

36

15

20

0.019

0

5

10

15

20

Turning to …rm dynamics and innovation, panels 10, 11, 13, and 14 show that FDI
entry, foreign innovations, domestic entry, and domestic innovations all drop in a crisis
without policy intervention. These panels also indicate that the size of the drop is muchlarger for domestic innovations compared with foreign innovations. This di¤erence comesfrom the fact that the stochastic discount factor by domestic households drops due to thebinding borrowing constraint as shown in equation (47), and thus domestic …rms reduce
their investment substantially, while foreign …rms discount future pro…ts by the …xed rate
1=RF . These di¤erent responses by domestic and foreign …rms are consistent with theempirical facts documented by Alfaro and Chen (2012). Reserve policy induces more entry
and innovations in normal times and mitigates the shocks from crisis by a bailout. As aresult, productivity grows faster and more stably with reserve policy as shown in panel 15.
The last panel shows that the reserve policy in this simulation increases the productivity
level by 1:8% in 20 periods. It also shows that a sudden stop has a permanent negative e¤ect
on productivity without policy intervention. This is in line with empirical evidence shownin Cerra and Saxena (2008) that crises in general have a very persistent negative e¤ect on
economic growth.
To evaluate the quantitative performance of the model in capturing sudden stop dynamics, Figure 6 compares the dynamics of the key variables in the data and the model. The
data dynamics show the average percentage deviations of the variables from the HP-…lteredsmooth trends. The sudden stop episodes are taken from the same samples that are used todetermine the Markov transition matrix in calibration.23 The model dynamics are createdas follows: the model is simulated 1,000 times with stochastic shocks, starting from the same
initial state as the above sample simulation, and the …rst sudden stop episode for each simulation is picked up. For each sudden stop episode, the percentage deviation of the variablesfrom the smooth path without shocks is computed, and the average of all the sudden stop
episodes across 1,000 simulations is taken.
Figure 6 shows that there is a small underprediction of a drop in real GDP and a small
overprediction of a drop in real consumption, but drops in capital investment and FDI
23

The data for GDP, consumption, and investment are taken from the World Development Indicators.
The FDI in‡ow-to-GDP ratio is computed using the data from Broner, Didier, Erce, and Schmukler (2013).

37

Figure 6: Sudden stop dynamics; model and data
0.005

Real GDP, % deviation from trend

0.02

Real Consumption, % deviation from trend

model
data

0

0
-0.005-0.02-0.01-0.015

-0.04

-0.02
-0.06
-0.025
-0.03
t-1

0.05

t

t+1

-0.08
t-1

t+2

Investment, % deviation from trend

0

t

t+1

t+2

-3
10 FDI inflow/GDP, % deviation from trend

-0.5

0

-1
-0.05
-1.5
-0.1
-2
-0.15

-0.2
t-1

-2.5

t

t+1

-3
t-1

t+2

t

t+1

t+2

in‡ow-to-GDP ratio are well captured in the model. Overall the model replicates well thequantitative dynamics of the average sudden stop episodes in the data.

6

Determinants of Optimal Accumulation Pace

This section studies how the optimal reserve policy is determined, and shows the …rst main
result of the paper: the debt-elasticity of the interest rate spread and the FDI entry cost
are key determinants of the optimal pace of reserve accumulation. As discussed in themodel section, the analysis considers a simple policy rule that the government collects a…xed fractionof tradable output every period to accumulate reserves. The government

optimally stops accumulating reserves when capital holdings adjusted by the productivity

38

level reach 90% of the balanced growth level.24 This level is reached at around period 35
of simulation, and the economy will follow a smooth balanced growth path in the following
periods.

6.1

Role of Debt-Elasticity of Spread

This subsection shows how the debt-elasticity of spreadb a¤ects the optimal reserve policy.

This elasticity is empirically estimated for the sample 19 developing countries in the next
section. The result indicates that the elasticity varies from 0:0223 to 0:0899 across countries,
which implies that if the debt-to-GDP ratio increases by 10%, the spread increases by 22:3
to 89:9 basis points. The analysis below uses these estimated elasticities.
The optimal pace of reserve accumulation is derived as follows: Given each value ofthe model is solved and simulated with reserve policiesb,= 0:01 to 0:06 for 300 periods

100,000 times, and the expected utility over these simulations is computed. The optimalpace of reserve accumulation is the value ofthat gives the highest expected utility.

The result is presented in Figure 7. The welfare gain by each reserve policy on the verticalaxis is evaluated in terms of the permanent consumption gain in percentage compared withthe economy without reserve policy, as is common in the literature. The …gure clearly
indicates that the optimal pace of reserve accumulationof spreadb , and the associated welfare gain is larger.

To understand the role ofwithb

tax rate

is faster with lower debt-elasticity= 0:0223 andbb , Figure 8 plots the dynamics of key variables in simulations= 0:0899. This …gure is created by simulating the model with

= 0:04 for both economies 100,000 times with stochastic shocks and taking the

average path of each variable. The …rst panel shows that the debt-to-GDP ratio becomesmuch larger with low elasticity of the spreadb . This di¤erence comes from the di¤erence inforeign borrowing spread plotted in the second panel. Under highb , the interest spread goesup quickly, which prevents private agents from increasing foreign borrowing. As a result,consumption becomes lower in the short run under high24

b , while it barely declines under

To be precise, it is assumed that the government reduces the tax rate linearly from to 0 as capital
accumulates from 85% to 90% of the productivity-adjusted long-run level. This assumption avoids a clear
kink in the decision rule and makes numerical solution easier and more accurate.

39

Figure 7: Welfare impact with di¤erentb

0.5=0.0223bpermanent consumption gain in %0.45

=0.0561b=0.0899

0.4

b

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

0

0.01

0.02

0.03

0.04

0.05

0.06

value oflow

b . This implies that the short-run cost of reserve accumulation becomes higher as thedebt-elasticity of the spreadb becomes higher.

Another implication of di¤erent
becomes lower under highb is its e¤ect on productivity growth. As consumptionb , the real exchange rate depreciates more and a larger amountof labor shifts to the tradable sector, as the …rst and second panels in the second row show.
This brings higher pro…ts for intermediate …rms and induces more entry and innovation,
which leads to faster productivity growth as shown in the last panel. However, there isa counteracting e¤ect on productivity growth, which is crowding-out by the high interest
spread. A high interest spread implies high costs for domestic investment, thus it discourages
domestic investment in both capital and innovation.
To quantify the crowding-out e¤ect of a high interest spread on productivity growth,
consider the following three economies: the …rst one is without reserve policy, the second
one is with reserve policy, and the last one is with reserve policy and innovation rates
manipulated as follows: when the borrowing constraint is not binding, the expected value ofa domestic product line is taken from the economy with reserve policy, but it is multiplied by40

Figure 8: E¤ects of

Debt-to-GDP ratio

0.010

b on transitional dynamics

Interest spreadGap from no policy

0.04

Consumption
Log gap from no policy=0.0223b=0.0899

b

-0.4

0.008

0.03

0.006

0.02

0.004

0.01

0.002

0

-0.5
-0.6
-0.7

0

0.02

10

20

30

40

Real exchange rate
% gap from no policy

0.000
0

0.1

10

20

30

40

Labor in tradable sector% gap from no policy

-0.01

0

0.03

10

20

30

40

Productivity
Log gap from no policy

0.01
0.02

0.05

0
-0.01

0.01
0

-0.02
-0.03

0

10

20

30

40

0

10

20

30

40

0

0

10

20

30

40

the interest rate with policy and then divided by the interest rate without policy. Namely,
Et (D
t;t+1 Vt+1 (1)) manipulated = Et (D
t;t+1 Vt+1 (1)) policy

Rtpolicy
Rtnopolicy

Since the stochastic discount factor Et ( t;t+1 ) is the inverse of the interest rate when the
borrowing constraint is not binding, this manipulation gives approximately the expectedvalue of a domestic product line with policy discounted by the low interest rate without
policy. Domestic investment in entry and innovation are then computed by the …rst orderconditions (24) and (26) using this manipulated value of a product line, and consumption isadjusted according to changes in investment. This manipulation is intended to remove thecrowding-out e¤ect of a high interest rate on domestic investment on entry and innovation,
preserving the e¤ect of a labor shift to the tradable sector by reserve accumulation.
41

Figure 9: Productivity loss by crowding-out
0.000=0.0223b=0.0899b-0.001-0.002-0.0030b n
0:0223
0:0561
0:0899

10

20

30

40

Table 4: Welfare loss by crowding-out
0:01
0:02
0:03
0:04
0:05
0:040
0:070
0:097
0:123
0:140
0:053
0:092
0:121
0:145
0:164
0:060
0:102
0:131
0:152
0:177

0:06
0:155
0:181
0:193

Figure 9 plots the log gaps in productivity in the economy with normal reserve policy
compared with the economy with a manipulated …rm value (no crowding-out), computedfrom the average of 100,000 stochastic simulations. It suggests that the productivity loss bycrowding-out is 0.26% under low

b and 0.30% under highb at period 40. These numbers

may look small, but the welfare impact is not. Table 4 presents the welfare losses causedby these productivity losses, which are the gaps in the expected utility in the economy withnormal reserve policy compared with the economy without crowding-out. It shows thatthe welfare loss by crowding-out in terms of permanent consumption is not small, and canbe larger than 0:1% asbecomes higher than 0:03. It also indicates that the welfare loss

becomes larger as the debt-elasticity of the spread becomes higher.
In short, high debt-elasticity of the spread

42b

prevents private agents from o¤setting

reserve accumulation by borrowing from abroad, increasing the short-run cost of lower consumption. This short-run lower consumption causes larger real depreciation and labor shift
to the tradable sector, but the positive e¤ect of this labor shift on productivity growthis counteracted by a higher interest spread, reducing the long-run bene…t of higher consumption. This implies that the high debt-elasticity of the spread worsens the trade-o¤ that
reserve policy faces. In this case, the optimal pace of reserve accumulation becomes slower toreduce the short-run cost and achieve a balance between the short-run cost and the long-run
bene…t.

6.2

Role of the FDI Entry Cost

Another key determinant of the optimal reserve policy in the model is the FDI entry cost.
There is a vast literature on the determinants of FDI in‡ows, and many factors have been
identi…ed as signi…cant determinants, such as the host country’s institutions, relative laborendowments, and so on.25 FDI entry costs in the model can be interpreted as these implicit
factors that a¤ect and govern the size of FDI in‡ows to the country.26
Comparison of two countries with di¤erent FDI entry costF

helps to show how the FDI

entry cost a¤ects the optimal pace of reserve accumulation. One country’s FDI entry cost is
set to target the FDI in‡ow-to-GDP ratio of 1:09%, which is the average of the 19 sample
countries.27 The other country’s FDI entry cost is lower, and set to target 1:5 times the FDI
in‡ow-to-GDP ratio, at 1:63%. The …xed entry cost C F is also adjusted to keep the ratio of
the expected value of a product line to the …xed entry cost at 1:1, and the innovation step
sizes

D

and

F

relative size (1 +are adjusted to have the same long-run growth rate at 2:1%, keeping theF)=(1 +

D) = 1:11 unchanged. The other parameters are left unchanged.

Figure 10 presents the welfare impact of reserve policy in these two countries. It is clearthat the optimal pace of reserve accumulation is faster for a country with low FDI entry
cost, and the welfare gain is substantially larger. This result suggests that attracting FDI is
25

Blonigen (2005) and Blonigen and Piger (2011) review the literature on the determinants of FDI.
As an alternative approach, the appendix explicitly estimates the FDI entry cost using the Starting a
Business Index from the World Bank’s Doing Business Surveys.
27
Since the data for the manifacturing sector’s share of FDI in‡ow is not available for every country inthe sample, it is assumed that each country has the same share 40:7%, which is the average of the twelve
countries used in calibration.
26

43

Figure 10: Welfare impact with di¤erent FDI entry costs

permanent consumption gain in %

0.3

0.2

0.1

0

-0.1

-0.2

low entry costhigh entry cost
0

0.01

0.02

0.03

0.04

0.05

0.06

value ofan important channel through which the reserve policy improves welfare. If some factors of
the country impede FDI in‡ow and the reserve policy is not e¤ective in attracting FDI, theoptimal pace of reserve accumulation is slower, and the welfare impact is likely to be limited.
The appendix of this paper conducts a decomposition analysis of the e¤ect of reserve
policy on growth and welfare. To summarize: (1) about 68% of the productivity gain byreserve policy comes from reserve accumulation in normal times, and 32% from bailouts incrisis; (2) about 60% of the productivity gain by reserve policy comes from higher domestic
entry and innovation, and 40% comes from higher FDI entry and foreign innovation; (3) 64%
of welfare gain by bailouts comes from …nancing working capital payment, and 36% from
rebating accumulated reserves to private agents.

7

Evaluation of Reserve Policy

This section conducts the second main analysis of the paper: evaluation of the actual reserve
policies of developing countries. The …rst subsection estimates the debt-elasticity of the44

spread for developing countries from the data. Then the second subsection derives the
optimal pace of reserve accumulation for each country and compares it with the actual paceobserved in the data.

7.1

Estimation of Debt-Elasticity of Spread

There is a large amount of literature on the determinants of the foreign borrowing spreadin developing countries, but there are not many studies that estimate the debt-elasticity ofthe spread for each country.28 Reinhart and Rogo¤ (2009) argue that the history of defaulta¤ects how foreign investors see each developing country when they consider lending, anda history of serial default implies lower thresholds for safe lending. According to the datain the Chartbook for their book, Reinhart (2010), the number of defaults for the 19 sample
countries before 1994 varies from 0 to 9. Accordingly, the 19 sample countries are divided
into …ve groups depending the number of past defaults, 0 or 1, 2 or 3, 4 or 5, 6 or 7, and 8 or
9, and each group is assigned a number from 0 to 4. Then consider the following regression:
Si;t =

0+

1 debtGDPi;t +2 (debtGDPi;tDefaulti ) +i+t + "i;t ;where Si;t is the interest rate spread on external borrowing in percent, Defaulti is the indicator
for the default history from 0 to 4,

i is a country-speci…c …xed e¤ect,

t is a time-speci…c…xed e¤ect, and "i;t is an error term. The data for the spread is taken from JP Morgan’s
EMBI Global, as is common in the literature.29 Since the time period of the available data
is di¤erent across countries, this is an unbalanced panel regression with 19 countries withmaximum time period 1994-2015. The debt-to-GDP ratio is computed using the data from
Lane and Milesi-Ferretti (2017). The data is annual and the total number of observations is
323.
The result is presented in Table 5. This result implies that the debt-elasticity of the
spread for countries with 0 or 1 default is 0:0223, and the elasticity increases by 0:0169 as
28

One of the main questions in the literature is whether a developing country’s spread is determinedby global factors or the country’s fundamentals. See for example Kennedy and Palerm (2014) and theirliterature review.
29
It would be better to use the data for private foreign debt spreads, but this is not available for many
developing countries. As many papers show, private and public spreads have very high correlations.

45

Table 5: Estimation of debt-elasticity of spread
Explanatory Variables
1 : Debt-GDP ratio
2 : Debt-GDP ratio

Default

Coe¢ cient (S.E.)

t-value

0.0223(0.0161)
0.0169*** (0.0049)

1.39
3.45

the number of defaults increases: 0:0392 for 2 or 3 defaults, 0:0561 for 4 or 5 defaults, 0:0730
for 6 or 7 defaults, and 0:0899 for 8 or 9 defaults.30 This result is similar to the resultsof other papers that include more controls, such as 0:0447 in Dell’Erba, Hausmann, andPanizza (2013) and 0:0567 in Kennedy and Palerm (2014).

7.2

Evaluation of Each Country’s Reserve Policy

Given the estimated debt-elasticity of the spread, this subsection evaluates each country’s
reserve policy. The analysis proceeds as follows: (1) For each country, the FDI entry cost
parameters and innovation step sizes are adjusted to match the FDI in‡ow–to-GDP ratio
in the model to the data.31 (2) Given the new parameters and the estimatedb , the modelis numerically solved and simulated, and the optimal reserve accumulation pacethatmaximizes household’s expected utility is derived. (3) The optimal pace in the model is thencompared with the reserve accumulation pace in the data.32 The reserve accumulation pacein the data is obtained by computing reserve increase-to-GDP ratio every year from 1991
to 2010 and taking the average across the years. The data is from the World Development
Indicators. The results are presented in Figure 11 and Table 6.
Figure 11 plots each country in the 45-degree line diagram, in which the observed paceof reserve accumulation is on the horizontal axis and the optimal pace in the model is on
the vertical axis. Most countries are located close to the 45 degree line, implying that theobserved pace is close to the optimal pace. The average optimal pace across the 19 countries
is 1:43% of GDP while it is 1:71% in the data, and the correlation coe¢ cient between the
optimal and actual paces across the countries is 0:73. On the other hand, it is also observed
30

Although the constant term is not signi…cant, it would become at least 10% signi…cant with a larger
number of countries.
31
As in the previous section, it is assumed that 40.7% of FDI in‡ow goes to the manufacturing sector foreach country. Accordingly, the target is 40.7% of the FDI–to-GDP ratio for each country.
32
In the model, a 1% tax on tradable output corresponds to 0.63% of GDP on average in the …rst 30
periods.

46

Optimal pace of reserve accumulation, % of GDP

Figure 11: Pace of reserve accumulation, model and data5

correlation coefficient = 0.73
4.5
4

MYS

model > data
CHL

3.5
3

THL

CHN

2.5
2

DOM

1.5

PER
EGY

TUN

COL
1

ARG
MEX

0.5

ECU
0

0

0.5

data > model

PHL
URY

BRA

VEN
ZAF
TUR IDN
1

1.5

2

2.5

3

3.5

4

4.5

5

Actual pace of reserve accumulation, % of GDP

that two countries have large deviations. Chile seems to be accumulating reserves much lessactively compared with the optimal pace, while China seems to be accumulating reserves
too actively.
Table 6 presents more detailed results including the welfare gain/loss by the actual andoptimal pace of reserve accumulation. It can be observed that the welfare gain from the actual
policy is close to the optimal level for most countries. Looking at each country in detail, Chileand China have much room for welfare improvement. Indonesia and Turkey may be losing
welfare by accumulating reserve too actively compared with the optimal pace. Regarding
the debt-elasticity of the spread, most Latin American countries have high elasticity becauseof their default history. This reduces the optimal pace of reserve accumulation, but most
Latin American countries are actually in line with the optimal pace.
This overall result suggests that the debt-elasticity of the foreign borrowing spread andthe FDI entry cost can explain a substantial amount of the cross-country variation in thepace of reserve accumulation. The appendix shows that if the debt-elasticity of the spread is…xed at 0:0561 for every country and only the FDI entry cost is adjusted across countries, the47Table 6: Comparison of Reserve Accumulation Pace and Welfare
Country
Argentina
BrazilChile
China
Colombia
Dominican Rep.
Ecuador
Egypt
Indonesia
Malaysia
MexicoPeru
Philippines
South Africa
ThailandTunisia
TurkeyUruguay
Venezuela

Accum. Pace (% of GDP)
ActualOptimal
0.88
1.24
1.23
4.99
0.96
0.67
0.11
2.31
1.44
4.26
0.84
2.50
2.26
0.76
3.42
1.43
1.03
1.42
0.80

0.88
0.64
3.52
2.88
1.28
1.60
0.32
1.60
0.16
4.00
0.80
1.76
1.28
0.40
2.88
1.60
0.16
0.96
0.48

Welfare (%)
Actual Optimal
0.06
0.02
0.34
0.22
0.10
0.10
0.01
0.11
-0.11
0.54
0.05
0.15
0.00
0.01
0.25
0.15
-0.06
0.04
0.02

0.06
0.04
0.55
0.36
0.10
0.14
0.01
0.13
0.00
0.54
0.05
0.18
0.05
0.02
0.26
0.15
0.00
0.06
0.03

Elasticity of
SpreadFDI In‡ow/ GDP (%)

0.07300.08990.08990.03920.07300.07300.08990.03920.03920.02230.08990.08990.02230.03920.02230.0561
0.05610.08990.0899

2.44
2.34
5.85
3.96
2.86
3.19
1.71
2.58
0.86
4.35
2.42
3.63
1.55
1.33
3.00
3.02
1.08
2.56
2.12

correlation coe¢ cient between the optimal and actual paces reduces from 0:73 to 0:43. Thisimplies that FDI entry cost may be slightly more important in explaining the cross-country
variation, but the debt-elasticity of the spread also makes a substantial contribution.

8

Conclusion

Active accumulation of foreign reserves by developing countries has been both an active research area and a central area of policy debate in the past decade. However, the literature
still tells little about the optimal reserve policy for individual countries and the reason for
the wide variation in the amount and pace of reserve accumulation across countries. This
paper contributes to the literature by developing a quantitative model of reserve accumulation and studying the determinants of the optimal pace of reserve accumulation. The model
incorporates the key bene…ts and costs of reserve accumulation. On the bene…t side, endogenous growth and sudden stops are introduced to incorporate the growth-promoting e¤ect
48

and the precautionary e¤ect of reserve accumulation. FDI in‡ow is also introduced into
the endogenous growth framework, which constitutes an important channel through which
reserve accumulation promotes growth and welfare. On the cost side, reserve accumulationin the model causes crowding-out of investment.
Using the model, this paper identi…ed two factors that are important determinants of the
optimal pace of reserve accumulation: the debt-elasticity of the foreign borrowing interest
rate spread, and the FDI entry cost. In countries where debt-elasticity of the spread is high,active reserve accumulation causes a large drop in consumption in the short run, and also
severely crowds out investment, which reduces the growth-promoting e¤ect. In countries
with high FDI entry costs, reserve policies are not e¤ective in attracting FDI, and thegrowth-promoting e¤ect is limited. In these cases, the optimal pace of reserve accumulationis slower, and the welfare gain is limited.
Taking into account di¤erences in the debt-elasticity of the spread and the FDI entry
cost across countries, most developing countries are roughly in line with the optimal pace ofreserve accumulation suggested by the model. This result implies that these two factors can
explain a substantial amount of the cross-country variation in the observed pace of reserve
accumulation.

49

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54

Appendix
A

Equilibrium and Stationarized Equilibrium

This section de…nes the equilibrium of the model economy and the stationarized equilibrium.

A.1

Equilibrium

De…nition: The equilibrium of the model economy is de…ned by the initial states A0 , R 1 B 1 ,K 1,

1, F 1,

1
1
1 ; the stochastic process f t gt=0 , the government policy rules fTt ; Vt gt=0

and the following:
1. Tradable goods producers: Given prices frt ; Wt ; Rt g1
t=0 and the government policy rules
DMT
fTt ; Vt g1
t=0 , fKt ; Mt ; Bt ; It ; Yt ;

T
t ;

1
t gt=0 satisfy (1), (3), (5), (7), (8). (9), (29).

2. Foreign intermediate goods producing …rms: Given prices fWt g1
t=0 and tradable goods
FF
output fYtT g1
t=0 , f`t ; Zt ;F F
Ft ; it ; Vt ;F 1
t gt=0 satisfy (13), (14), (16), (17), (18), (19).

3. Domestic intermediate goods producing …rms: Given prices fWt g1
t=0 and tradable goods
DD
output fYtT g1
t=0 , f`t ; Zt ;D
D D
t ; it ; Vt ;D 1
t gt=0 satisfy (13), (14), (15), (21), (23), (24).

4. Foreign investors: feFt ; QFt g1
t=0 satisfy (20) (22).
NN
5. Non-tradable goods producers: Given prices fWt ; PtN g1
t=0 , fYt ; Lt ;N 1
t gt=0satisfy(31), (32), (33).
T
N
E
E
6. Households: Given prices frt ; Wt ; PtN g1
t=0 , fCt ; Ct ; Ct ; Lt ; Kt ; Zt ; It ; et ;1
t gt=0 satisfy(25), (26), (34), (35), (36), (37), (38), (39), (40).
7. Foreign reserves: fFt g1
t=0 follows the transition equation given by (41).
8. Aggregate variables fAt ; t ; dt g1
t=0 satisfy (27), (28), (30).
T 1
9. Prices frt ; Wt ; PtN ; Rt g1
t=0 and labor in tradable sector fLt gt=0 satisfy (10), (42), (43),(44), (45).
55

A.2

Stationarized Equilibrium

To stationarize the model, the equilibrium conditions are divided by aggregate productivity
At . Let the lower-case letters denote stationarized variables, and use gt to denote the productivity growth rate At+1 =At . After some arrangements to reduce the number of equations,the following is the complete list of equations to characterize the stationarized equilibriumof the model:
Tradable goods producers
ytT =

wt =

kt 1
1 + gt 1

TiM
t = Lt(1 +
t 1 (1 +t 1 (1 +D ) + (1

(1 +

1
(iM
t ) (mt )(1 + F )1 t 1
D ) + (1t 1 )(1 +D)

t 1

t 1 )(1 +D )(1 +F)yT
) t = PM
mt

1

t

t

bt +

t

t (1 + gt )

t

bt
gdpt

exp

b

)ytT
t= t

(1
1+

t

1+
t+1

= Rt Et

Rt = R +ytT
1
TLt 1 + t = t

ytT
kt 1 =(1 + gt 1 )

rtk =
(1

F)

F)

b

1

t

=0

Foreign intermediate goods producing …rms
F
t =

F
t =

vtF =

F
t

F
t

1+

kss
kt 1

F

ytT

F
t

ztF + iFt + (1

56

1
1+

t= t

dt ) (1 + gt )1F)
Et (vt+1
FR

iFt =FF(ztF )1)(ztF ) (1 + gt )(11
D
Et (vt+1)=1
RF

Domestic intermediate goods producing …rms
D
t =

D
t =

vtD =

D
t

ztD + iDt + (1dt ) 1

D
t

ytT

D
t

1+
eFt
1

1
1+

t= t

D
(1 + gt )Et ( t;t+1 vt+1
) + (1

t 1

iD
t =
D

kss
kt 1

D

D

dt )

(ztD )1D)(ztD ) (1 + gt )Et ( t;t+1 vt+1)=1

(1

FDI entry
eFt
1

=

F

(1

)(1 + gt )t 1

qtF = (1 + gt )1F
Et (vt+1
)
RF

cF

1
F
Et (vt+1)
RF

Aggregate variables
dt = eDt + (1t =1 + gt =F
t 1 + et

1+
1+

F
t
D
t

D
t 1 )it +DFt 1 et + (it

eF
t

(1 +

D eD
t
t ) (1 +Ft 1 itiDt ) t 1 (1
F (1
t )

D
t 1 )it

Non-tradable goods producers
LTt )1

N

)(Lt

LTt )

ytN = (Lt
wt = PtN (1

N

57

N

t 1)

(1 +

F t
t )

F
1 it

eFt
1

t 1

qtF

Households
cTt + bt + kt + ztE = ytT

P M mtFt 1 t

Dt 1 )zt + (1

(1

cTt
=
1
ytN

1+

k

kt (1 + gt 1 )kt 1!(Lt )"((1 + g)= Et

t+1
t (1 + gt )kt 1
R t 1 bt 1
F
+
+ eF
t qt
1 + gt 1
1 + gt 1

Ktt(PtN )"

wt
=
ct

! 1

)

ct
cTt

1
"

k

rt+1 + 1

1
t =
ct

ct
cTt

2

2

(1 + g)kt+1 (1 + gt )
kt

2

!)#

1="

Domestic …rm entry
eD
t =
E

E

(ztE )1D)(ztE ) (1 + gt )Et ( t;t+1 vt+1)=1

(1Foreign reserves transition
ft = RFft 1+
1 + gt 1tvt

TThe stationarized equilibrium is characterized by 33 variables fytT , kt , gt , iMt , m t , Lt ,

wt ,

t,

k
t , rt ,

F
t ,

F
F
F
F
t , vt , zt , it ,

D
t ,

t,

E
T
N
N
F
F
D D
D
D
t , vt , zt , it , et , qt , dt , Rt , yt , Lt , Pt , ct , bt , zt ,1eD
t , ft gt=0 and the above 33 equations, given the initial state R 1 b 1 =(1+g 1 ), k 1 =(1+g 1 ),1 , f 1 =(1+g 1 ),B

1
1
1 , the government policy f t ; vt gt=0 , and the stochastic process f t gt=0 .

Numerical Solution

This section sketches the numerical solution method and presents the accuracy of the solution.

58

B.1

Solution Method

The solution method is a version of the policy function iteration, modi…ed to deal with theoccasionally binding constraint. Below is the procedure to obtain the numerical solution.
1. Set the equally-spaced grid points for the endogenous state variables, foreign debt
Rt 1 bt 1 =(1 + gt 1 ), capital kt 1 =(1 + gt 1 ), share of product lines owned by foreign…rms

t 1 , and foreign reserve holdings ft 1 =(1 + gt 1 ).

The number of grid points is

set to 31 for debt, capital, and reserves, and 5 for the share of foreign product lines.
There are also 2 states for the borrowing limitt.

2. For each grid point, set the initial guess for 5 variables: bt , ztD , ztF , LTt , and theright-hand side of the Euler equation with respect to capital (RHSEE).
3. For each grid point, do the following:(a) Leave the 5 variables for which the guess was made as unknown variables, andexpress all the other endogenous variables in terms of the state variables and5 unknowns. In this process, …rst assume that the borrowing constraint is notbinding and proceed. Later check if the constraint is satis…ed. If it is not satis…ed,
recalculate all the variables using the binding borrowing constraint. The otherendogenous variables, which include next-period state variables, are now functionsof the 5 variables.
(b) Using multi-dimensional linear interpolation over the next-period state variables
and the guess for the 5 variables (bt , ztD , ztF , LTt , RHSEE), compute all theendogenous variables next period. Then calculate all the forward-looking expectation terms, such as the right-hand side of the Euler equations and the valuefunctions.
(c) All the equilibrium conditions are now the functions of the initial 5 unknowns.
There are 4 equations that are not used in step (a), and the explicit expression
for RHSEE, thus 5 equations in total. Solve for the 5 unknowns using non-linear
solver.
59

4. Check the gap between the guess and the newly-obtained values for the 5 variables.
If they are close enough, stop. If not, update the guess by the newly-obtained values,
and go back to step 3. Repeat this process until the gap becomes su¢ ciently small.

B.2

Accuracy of the Solution

This subsection presents the accuracy of the numerical solution obtained by the above
method. Following Aruoba, Fernández-Villaverde, and Rubio-Ramírez (2006), the Euler
equation error of the solution is computed. Here the Euler equation with respect to foreign
borrowing is used, because it is subject to the occasionally binding borrowing constraint,
and thus likely to cause a larger error. For each value ofb and, the model is simulated

for 50 periods with the initial states used in the main analysis and stochastic shocks to theborrowing constraint. The reason for stopping simulation at period 50 is because the economy after period 50 follows a smooth path with no borrowing constraint binding, and thus
errors are very small. This simulation is repeated 10,000 times. For each period t in eachsimulation i, the Euler equation error de…ned as follows is computed:"

errort;i = log10 1

#
cT;EE
t;i
;
cTt;i

is
where cTt;i is tradable consumption computed directly from the decision rules, and cT;EE
t;icomputed by using the Euler equation with respect to foreign borrowing. Figure 12 plots
the distribution of the Euler equation errors obtained by this method. As a reference, thedistributions of the Euler equation errors for the models with three di¤erent
corresponding optimalb with theare plotted. For each case, the average error is smaller than -4 andthe maximum error is smaller than -2, which is reasonably small when compared with theliterature. With di¤erent values ofb and, the distributions of errors are similar.

60Figure 12: Euler Equation Error

61

C

Proof of Linearity in Value Functions

This section shows the detailed procedure of the guess-and-verify method to prove the linear
relation in value functions for intermediate producing …rms.

C.1

Foreign Firms

The value of a foreign …rm with a single product line is given as follows:
VtF (1) = max
ZtF

(

F
t

" 1
1
X
X
1
F
F
F
P (i; 1; it )P (j; 1; dt )Et Vt+1
(1 + iZt + F
R
i=0
j=0

j)

!#)

:

There are four cases next period, depending on whether innovation is successful or not, andF(0) = 0,replacement happens or not. Writing out all four cases and noting Vt+1

VtF (1)

F
t

= max
ZtF

ZtF +

1
F
P (0; 1; iFt )P (0; 1; dt )Et Vt+1 (1)RFF+P (1; 1; iFt )P (1; 1; dt )Et Vt+1 (1)F+P (1; 1; iFt )P (0; 1; dt )Et Vt+1 (2)

=

F
t

max
ZtF

ZtF +

1
(1
RF

iF
t )(1

F
dt )Et Vt+1
(1)

F
F
+ iF
t dt Et Vt+1 (1) + it (1Fdt )Et Vt+1
(2)

F
F
(1),
(2) = 2Vt+1
Guess the linear relation VtF (n) = nVtF (1). Using the linear relation Vt+1

VtF (1)

= max

F
t

ZtF +

1
(1
RF

max

F
t

ZtF +

1
(1 + iF
t
RF

ZtF

ZtF

iF
t )(1

F
dt )Et Vt+1
(1)Fdt )Et Vt+1
(1)

F
F
+ iF
t dt Et Vt+1 (1) + 2it (1Fdt )Et Vt+1
(1);

which is equation (18) in the main text. Next, the value of a foreign …rm with n productlines is given as:
VtF (n) = max
ZtF

(

n

F
t

nZtF +

" n
n
X
1 X
F
F
P (i; n; it )P (j; n; dt )Et Vt+1
(n + i
F
R
i=0
j=0

62

j)

!#)

:

:

F
Using the linear relation Vt+1
(n + i(VtF (n) = max n Ft
ZtF(

= max n Ft
ZtFj) = (n + i

Fj)Vt+1
(1),

" n
!#)
n
X
X
1
F
(1)
P (i; n; iFt )P (j; n; dt )(n + i j)Et Vt+1
nZtF + F
R
i=0
j=0
" n
#)
n
X
X
1
F
nZtF + F Et Vt+1
(1)
P (i; n; iFt )P (j; n; dt )(n + i j)
:
R
i=0
j=0

Inside the brackets can be written as follows:nX

P (i; n; iFt )

i=0

n
X

P (j; n; dt )(n+i j) = n+

j=0

n
X
i=0

P (i; n; iFt )inX

P (j; n; dt )j = n+niFt

ndt :

j=0

Note that the last two terms are just the expected number of successes for each binomial
process. Thus VtF (n) can be written as follows:
VtF (n) = max n Ft
ZtF

= n max
ZtF

F
t

1
F
n(1 + iFt
dt )Et Vt+1
(1)
RF
1
F
ZtF + F (1 + iFtdt )Et Vt+1
(1)
R

nZtF += nVtF (1):This veri…es that the initial guess VtF (n) = nVtF (1) is correct.

C.2

Domestic Firms

Similarly to foreign …rms, the proof starts with the value of a domestic …rm with a single
product line, this time taking into account acquisition by foreign investors:
VtD (1)= max D
ZtD
t
ZtD
8
2
1 j
1
1
<X
X
X
eF
t
D
4
+
P (i; 1; it )P (j; 1; dt )P k; 1 j;
:
1
t 1
i=0
j=0
k=0
2
39
!
1 j
1
=
X
X
eF
t
4
kQt 5 :+
P (j; 1; dt )P k; 1 j;
;
1
t 1
j=0
k=0

63

Et

D
t;t+1 Vt+1 (1 + i

j

!93
=
5
k)
;

There are now six cases next period: Whether innovation is successful or not, and whether
the product line is replaced, acquired, or survives. Writing out the second line,
1X

P (i; 1; iD
t )

i=0

8
1
<X
:

1 j
X

P (j; 1; dt )

j=0

P

k; 1

j;

k=0

= P (0; 1; iDt )P (0; 1; dt )P0; 1;+P (1; 1; iDt )P (0; 1; dt )P

eF
t
1

0; 1;

+P (1; 1; iDt )P (0; 1; dt )P

1; 1;+P (1; 1; iDt )P (1; 1; dt )Et11

Dt;t+1 Vt+1 (2)EtDt;t+1 Vt+1 (1)t 1Dt;t+1 Vt+1 (2)Dt;t+1 Vt+1 (1 + i

Et
t 1

Et

t 1

eF
t

1

j

k)

!9
=

D
t;t+1 Vt+1 (1)

Et

t 1
eF
t

eF
t

;

:

D
D
Guess the linear relation VtD (n) = nVtD (1). Using the linear relation Vt+1
(2) = 2Vt+1(1),=

P (0; 1; iDt )P (0; 1; dt )P

0; 1;

=

1

+ P (1; 1; iDt )P (0; 1; dt )P0; 1;+ P (1; 1; iDt )P (0; 1; dt )P

1; 1;+ P (1; 1; iDt )P (1; 1; dt )Et
=

eF
t

(1

iD
t )(1

+2iD
t (1

dt ) 1

+iD
t (1

dt )

1
1

D
t;t+1 Vt+1 (1)Dt;t+1 Vt+1 (1)

Et
Et

t 1

eF
t

D
t;t+1 Vt+1 (1)Dt;t+1 Vt+1 (1)

1

1

Et
t 1

t 1

eF
t

Et
t 1
D
+iD
t;t+1 Vt+1 (1)t d t Et
eF
t
iD
+
(1
d
)
1
t
t

D
t;t+1 Vt+1 (1)2EtDt;t+1 Vt+1 (1)11Dt;t+1 Vt+1 (1)

t 1

eF
t

eF
t

dt ) 1

Et

t 1
eF
t

Et
t 1

D
t;t+1 Vt+1 (1):Next, writing out the third line,
1X
j=0

P (j; 1; dt )

1 j
X

P

k; 1

j;

k=0

eF
t
1

kQt
t 1

!

= (1

dt )

eF
t
1

Qt :
t 1

Therefore VtD (1) can be written as follows:
VtD (1) = max
ZtD

D
t

ZtD + iDt + (1dt ) 1

eF
t
1

t 1

64

D
Et ( t;t+1 Vt+1(1)) + (1

dt )

eF
t
1

Qt ;
t 1

which is equation (23) in the main text. Next, the value of a domestic …rm with n productlines is given as:
VtD (n)=

max n D
nZtD
t
ZtD
8
2
n
n
n
<X
X
Xj
eF
t
+4
P (i; n; iD
)
P
k;
n
j;
P
(j;
n;
d
)
t
t
:
1
t 1
i=0
j=0
k=0
9
3
2
!
n
n
=
Xj
X
eF
t
4
kQt 5 :+
P k; n j;
P (j; n; dt )
;
1
t 1
j=0

D
t;t+1 Vt+1 (n + i

Et

j

!93
=
5
k)
;

k=0

D
(n + iUsing the linear relation Vt+1

VtD (n)=jk) = (n + i

D(1),k)Vt+1jmax n D
nZtD
t
ZtD
8
2
n
n
n
<X
X
Xj
eF
t
+4
P (i; n; iD
)
P
(j;
n;
d
)
P k; n j;
t
t
:
1
t 1
i=0
j=0
k=0
9
3
2
!
n
n
=
F
X
Xj
e
t
kQt 5
+4
P (j; n; dt )P k; n j;
;
1
t 1
j=0

(n + i

j

j;

eF
t

k)Et

!93
=
D
5
t;t+1 Vt+1 (1)
;

k=0

=

max n

D
t

+ Et

2
n
n
n
X
Xj
X
D
4
P (j; n; dt )P
P (i; n; iD
t;t+1 Vt+1 (1)
t )

ZtD

nZtD

j=0

i=0

2
n
n
X
Xj
+ Qt 4
P (j; n; dt )
P
j=0

k; n

j;

k=0

P (i; n; iD
t )

i=0

=

n + niDt= n + niDtnX

P (j; n; dt )

j=0

eF
t

t 1

ndt
ndt

n
Xj

P

k; n

j=0
n
X

P (j; n; dt )

n
Xj

P

k; n

P (j; n; dt ) (n

j)

= n

iD
t + (1

ndt

n

eF
t

1

dt ) 1

+ ndt
t 1
eF
t

1

:
t 1

65

1

(n + i

j

t 1

eF
t
1

eF
t
1

eF
t
1

eF
t

j;

k=0

j=0

= n + niD
t

j;

k=0

n
X

t 1

k=0

1

(n + i

1

39
=
k5 :
;

The bracketed term in the second line is:
n
X

k; n

t 1

t 1

k
t 1

k)

j

3

k)5

The bracketed term in the last line is:nX

P (j; n; dt )

j=0

n
Xj

P

k; n

j;

k=0

eF
t
1

k = n (1
t 1

dt )

eF
t
1

:
t 1

Therefore VtD (n) can be written as follows:
VtD (n)=

max n D
t
ZtD

nZtD

+ n iDt + (1dt ) 1+ n (1

eF
t

dt )

1

eF
t
1

Et
t 1

D
t;t+1 Vt+1 (1)Qt
t 1= nVtD (1):This veri…es that the initial guess VtD (n) = nVtD (1) is correct.

D

Alternative Policy and Decomposition

The analysis in the main text considers a reserve policy which consists of reserve accumulationin normal times and bailouts during crisis. This section studies two other di¤erent typesof reserve policy schemes and decomposes the policy e¤ect on productivity and welfare intodi¤erent channels.
The …rst policy scheme considered in this section is a "no-bailout" scheme, in which thegovernment accumulates reserves but never uses them for bailouts. The second one is a"lending" scheme, in which the government provides accumulated reserves to private agentsto help …nance working capital payments, but private agents need to repay these reserves to
the government after production. In the analysis below, the FDI entry cost parameters are
set to target 40:7% of the average FDI-to-GDP ratio for the 19 sample countries, which is
1:09%, and the debt-elasticity of the spread is set at the middle value

D.1

b = 0:0561.

Policy E¤ect on Productivity

Figure 13 shows the log gaps in productivity with each policy scheme compared with thecase without reserve policy, computed by taking the average of 100,000 stochastic simula-

66

Figure 13: E¤ect of three policy schemes on productivity
0.02

Baseline policy

No bailout

0.02

full effectonly domestic

0.015

0.015

0.015

0.01

0.01

0.01

0.005

0.005

0.005

0

0

10

20

30

40

50

0

0

10

20

30

Lending

0.02

40

50

0

0

10

20

30

40

50

tions. The reserve accumulation paceis set at the average of the optimal accumulation

paces across the 19 countries, which is= 0:022. There are three observations. First, theno-bailout scheme promotes productivity growth only through the channel of reserve accumulation causing real depreciation. Therefore, the gap between the impact of the baseline
policy and the no-bailout scheme is the e¤ect of policy on growth through bailouts, including anticipation of bailouts. This implies that 68% of the growth-promoting e¤ect of reserve
policy comes from the real depreciation channel, and 32% comes from the bailout channel.
Second, productivity gain by the lending scheme is slightly higher than the baseline
policy. This implies two things. First, note that the lending scheme helps …nance working
capital payment, but does not rebate accumulated reserves. This means that the growthpromoting e¤ect through bailouts mainly comes from helping working capital payment andnot from rebate of reserves. Second, slightly higher productivity gain by the lending schemesuggests the existence of moral-hazard borrowing by private agents. In the baseline policy,
private agents anticipate that they will receive a bailout from the government when the
borrowing constraint binds. This induces private agents to borrow more in normal times,
which mitigates the e¤ect of reserve accumulation on real exchange rate and a labor shift,
reducing the e¤ect on productivity growth slightly compared with the lending scheme.
Third, the red dotted lines in Figure 13 are created by …xing FDI entry and foreign
innovation rates at the rates without policy. Thus, these lines show the productivity gain67

permanent consumption gain in %Figure 14: E¤ect of three policy schemes on welfare
full policy
lendingno bailout

0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5

0

0.01

0.02

0.03

0.04

0.05

0.06

value ofby each policy scheme only through higher domestic entry and innovation rates. The ratio
of productivity gain by only domestic factors to the total gain is 60:2%, 49:5%, and 58:1%
respectively from the left in Figure 13.

D.2

Policy E¤ect on Welfare

Figure 14 plots the welfare gain/loss by the above three policy schemes with accumulation
paces

from 0:01 to 0:06. The welfare gain/loss is again measured in terms of the permanent

consumption gain/loss in percentage. The …rst observation is that the no-bailout scheme
never improves welfare, and the gap in welfare between the baseline policy and the nobailout scheme is substantial. This gap in welfare comes from whether the government uses
accumulated reserves for bailout or not.
The second observation is that the welfare impact by the lending scheme is substantiallybetter than the no-bailout scheme, although it is still negative. The di¤erence between thelending scheme and the no-bailout scheme is whether the government helps …nance working
capital payment using reserves or not.
These observations imply that the welfare impact of bailouts by the government can bedivided into two channels: one works through rebating reserves, which is the gap between the68Optimal pace of reserve accumulation, % of GDP

Figure 15: Pace of reserve accumulation,b = 0:0561

5

correlation coef ficient = 0.428
4.5

CHL

4
3.5

model > data

3

MYS

2.5

CHN

PER
2

DOM

1.5
1

ECU

0.5
0

TUN
MEX
ARG URY
COL
BRA
VEN
ZAF
TUR

0

0.5

1

THL
EGY

data > model

PHL
IDN

1.5

2

2.5

3

3.5

4

4.5

5

Actual pace of reserve accum ulation, % of GDP

baseline policy and the lending scheme, and the other works through helping working capital
payment, which is the gap between the lending scheme and the no-bailout scheme. Figure
14 shows that for any , about 64% of the welfare impact of bailouts comes from helping
working capital …nance (the gap between lending and no-bailout), and the remaining 36%
comes from rebating (the gap between baseline and lending.)

E

Relative Importance of Two Determinants

This section studies the relative importance of the two determinants of the optimal pace ofreserve accumulation by conducting the following analysis: For each country, the FDI entry
cost is adjusted in the same way as the main analysis, but the debt-elasticity of the spreadis constant at

b = 0:0561 across countries. Then the optimal pace of reserve accumulation

is derived for each country and compared with the observed pace.
Figure 15 plots the result. The correlation coe¢ cient between the optimal and actual
paces is 0:43 compared with 0:73 when both are adjusted. This result may suggest thatthe variation in the FDI entry cost is relatively more important, but the variation in the69

elasticity of the spread also makes a substantial contribution. Another observation is that
actively reserve-accumulating countries such as Malaysia and Thailand have a much lower
optimal pace compared with the main analysis and also the data. This implies that Asian
countries are bene…tting substantially from the low elasticity of the spread.

F

Policy Evaluation with Estimated FDI Entry Cost

This section presents an alternative analysis of reserve policy evaluation. In the main text,
the FDI entry cost parameters are adjusted to target the FDI in‡ow-to-GDP ratio for eachcountry, and the reserve policy is evaluated. This section estimates the FDI entry cost foreach country using the Starting a Business Index from the World Bank’s Doing Business
Surveys, and evaluates each country’s pace of reserve accumulation.

F.1

Estimation of FDI Entry Cost

The Starting a Business Index measures the e¤ective cost of starting a new business in eachcountry by taking into account the minimum capital requirement, number of procedures,and time and cost to start up a new business. The Index takes a value between 0 and 100,with a higher value implying lower cost to start a new business. The Index is created withthe focus on domestically-owned …rms, but the analysis below uses this Index as a proxy forthe cost for foreign investors to start a new business.
To con…rm that this Index can be used as a proxy for FDI entry cost, Figure 16 plots eachcountry’s Index on the horizontal axis and the FDI in‡ow-to-GDP ratio on the vertical axis.
The FDI in‡ow-to-GDP ratio is the average for 1991-2010, and the Starting a Business Index
is the average over the maximum available period for each country, which is 2004-2017 formost countries. The red line is the simple regression line whose slope is 0:046 with almost
7% signi…cant. This slope would become more signi…cantly positive as more developing
countries are included.
Given this result, the FDI entry cost parameters are estimated using the Starting a
Business Index in the following way. First, assume that the congestion cost coe¢ cient for

70

Figure 16: Starting a Business Index and FDI-to-GDP ratio
6

CHL= 0.046

FDI inflows, % of GDP

5

MYS
4

CHN
PER
DOM TUN
THL
COL
URY
EGY
ARG
MEX

3

BRA
2

VEN
ECU
PHL
ZAF
TUR

1

0
40

IDN

45

50

55

60

65

70

75

80

85

90

Starting a Business Index

FDI entry is a function of the Index:
1= Fi =
where0+

1 (Indexi )2;

F
i is the congestion cost coe¢ cient for country i, and Indexi is the Starting a BusinessFiIndex for the same country. The reason for taking the inverse of
implies lower cost. Then three parameters

0,

1,

2

is that a higher Index

are chosen to minimize the sumof squared gaps in the FDI in‡ow-to-GDP ratios between the model and the data acrosscountries. Namely,min0; 1; 2

19
X
i=1

"

FDI
GDP

data
i

FDI
GDP

#
model 2:i

Following the analysis in the main text, the …xed entry cost C F is adjusted to keep the …rmvalue-to-…xed entry cost ratio at 1:1, and the step sizes

D

and

F

same long-run growth rate as in the baseline model. The result is
2 = 10:61.

cost

are adjusted to have the0 = 0:61,

1 = 9:38, andFigure 17 plots the FDI in‡ow-to-GDP ratios using the estimated FDI entry

Fi , along with the ratios in the data.

Each country has two points, a blue circle that71

Figure 17: FDI-to-GDP ratios based on estimated entry cost
6

CHL

model
data

FDI inflows, % of GDP

5
MYS
4

CHN
PER
DOM

3
EGY
URY
ARG

BRA
2

TUN
THL
COL
MEX

VEN
ECU
PHL
ZAF
TUR

1

0
45

IDN

50

55

60

65

70

75

80

85

Starting a Business Index

indicates the data FDI-to-GDP ratio, and a red diamond that is the FDI-to-GDP ratio basedon the estimated FDI entry cost, both of which have the same Index value on the horizontal
axis. Large gaps between the data points and the model points in the vertical distance imply
that those countries have a high FDI-to-GDP ratio and a low Index, or the opposite.

F.2

Evaluation of Each Country’s Reserve Policy

This subsection evaluates each country’s reserve policy using the estimated FDI entry cost.
The optimal pace of reserve accumulation and the welfare gain/loss for each country arecomputed in the same way as in the main text. The results are presented in Figure 18 andTable 7. Figure 18 shows that there are more gaps between the actual pace and the optimalpace compared with the analysis in the main text. But the correlation between them is still
0:45. The average of the optimal pace is 1:78% of GDP compared with 1:71% in the data.
Table 7 shows that welfare gains for most countries are close to the optimal level, suggesting that most countries are still not very far from the optimal pace. But China has aneven larger gap between the optimal and actual pace, compared with the main analysis. Due
72

Optimal pace of reserve accumulation, % of GDP

Figure 18: Pace of reserve accumulation based on estimated FDI entry cost5

correlation coefficient = 0.45
4.5
4

THL

model > data

MYS

3.5

TUR

3
2.5

MEX
CHL
ZAF

2

CHN

COL
DOM

1.5
1

ECU
0.5
0

TUN

PHL
EGY

IDN
ARG URY

data > model

PER

VEN BRA
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Actual pace of reserve accum ulation, % of GDP

to this large gap, China has a large welfare loss by the actual pace of reserve accumulation.
This is because the Starting a Business Index is relatively low in China, and the estimated
FDI entry cost is relatively high. Another clear di¤erence from the main analysis is Turkey,
which has now a large welfare gain and the optimal pace is much faster than that in themain analysis. Figure 17 shows that Turkey has a very high Starting a Business Index, which
implies a low FDI entry cost.

73

Table 7: Comparison of Reserve Accumulation Pace and Welfare
Country
Argentina
BrazilChile
China
Colombia
Dominican Rep.
Ecuador
Egypt
Indonesia
Malaysia
MexicoPeru
Philippines
South Africa
ThailandTunisia
TurkeyUruguay
Venezuela

Accum. Pace (%)
Actual Optimal

Welfare (%)
Actual Optimal

0.88
1.24
1.23
4.99
0.96
0.67
0.11
2.31
1.44
4.26
0.84
2.50
2.26
0.76
3.42
1.43
1.03
1.42
0.80

0.06
-0.04
0.22
-0.16
0.15
0.10
0.01
0.12
0.03
0.41
0.18
-0.06
0.09
0.13
0.43
0.27
0.24
0.04
-0.01

0.88
0.32
2.24
1.92
1.76
1.60
0.75
1.60
0.96
3.68
2.24
0.96
1.60
2.24
3.84
2.88
3.04
0.96
0.40

74

0.06
0.02
0.25
0.18
0.19
0.14
0.02
0.14
0.05
0.42
0.28
0.07
0.10
0.23
0.43
0.33
0.42
0.06
0.01

Elasticity of
SpreadEstimated
FDI/GDP0.07300.08990.08990.03920.07300.07300.08990.03920.03920.02230.08990.08990.02230.03920.02230.0561
0.05610.08990.0899

2.45
1.83
4.12
2.94
3.53
3.10
1.93
2.67
1.85
3.77
4.29
2.67
2.00
3.27
3.80
4.15
4.63
2.56
1.80