Discussion Papers In Economics
And Business
The Resilience of FDI to Natural Disasters throughIndustrial Linkages

Hayato KatoToshihiro Okubo

Discussion Paper 21-06

June 2021

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Resilience of FDI to Natural Disasters throughIndustrial Linkages∗
Hayato Kato† and Toshihiro Okubo‡
June 2, 2021

Abstract
When do multinationals show resilience during natural disasters? To answer this, wedevelop a simple model in which multinationals and local firms in the host country areinteracted through input-output linkages. When natural disasters seriously hit local
firms and thus increase the cost of sourcing local intermediates, most multinationals
may leave the host country. However, they are likely to stay if they are tightly linked
with local suppliers and face low trade costs of importing foreign intermediates. We
further provide two extensions of the basic model to allow for multinationals withheterogeneous productivity and disaster reconstruction.

JEL codes: F12; F23; Q54; R11.
Keywords: Foreign direct investment (FDI); Multinational enterprises (MNEs); Input–
output linkages; Supply chain disruptions; Multiple equilibria.
∗

This is a substantially revised version of our earlier working paper entitled “The Impact of a Natural
Disaster on Foreign Direct Investment and Vertical Linkages” (Kato and Okubo, 2017). It is conducted as apart of the Project “Economic Policy Issues in the Global Economy” undertaken at the Research Instituteof Economy, Trade and Industry (RIETI). We wish to thank Akira Sasahara for extensive discussions andseminar participants at RIETI, Hosei U and Osaka U for useful comments. Financial support from the theJapan Society for the Promotion of Science (Grant Numbers: JP19K13693; JP99K13693; JP20K22122) aregratefully acknowledged. All remaining errors are our sole responsibility.
†
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka, 560-0043,
Japan. E-mail address: hayato.kato@econ.osaka-u.ac.jp‡
Faculty of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan. E-mail address:
okubo@econ.keio.ac.jp1

1

Introduction

Multinational enterprises (MNEs) play a vital role in helping developing countries grow bycontributing to local employment and productivity improvement in normal times. However,
MNEs may play a more crucial role during crisis times, especially in natural disasters. Thailand’s experience of large-scale floods in 2011 is a notable example of the destructive effects
of a natural disaster on multinationals. The estimated economic damage is 46.5 billion USD
across all sectors, and manufacturing alone suffered 32 billion USD of damage (Abe and Ye,
2013; Haraguchi and Lall, 2015). Seven industrial parks and 904 factories were inundated,
more than half of which were Japanese MNEs. Thus, the business operation of many factories completely ceased for one to two months. Even non-inundated multinational plants
were forced to reduce production due to the lack of parts from damaged suppliers. The
disaster-hit economy hopes multinationals to show resilience so that they continue to source
local intermediates and help local industry recover. The Bank of Thailand cautioned against
this optimistic idea by stating that, unless the government took appropriate measures, theflood would relocate more multinationals to other Asian countries in the long run (BOT,2012). The exit of footloose multinationals would weaken their input-output linkages withlocal suppliers, damaging the economy further. Indeed, using country-level data, Escaleras
and Register (2011) and Doytch (2019) find that natural disasters have negative effects on
aggregate foreign direct investment (FDI) inflows.1
Only a limited attention in the literature has been paid to how MNEs respond to natural
disasters and little is known about underlying mechanisms, despite its importance in the realworld. This paper theoretically investigates under what conditions multinationals leave their
host country once it is hit by negative supply shocks such as natural disasters and which
factor helps them stay there. To address these, our model takes into account two noticeablecharacteristics of multinationals: (i) input-output (or vertical) industrial linkages and (ii)footloose-ness. Vertical linkages imply that multinationals have important complementarities with local industry (Markusen and Venables, 1999). Sourcing by multinationals helps
the local supply industry grow, leading to a lower price of inputs and thus benefiting themselves. The footloose-ness arises because the location choice of foreign capital is based on thecomparison of profits made in different countries. Multinationals are sensitive to negative
1

Using aggregate data on FDI inflows into Thailand, Anuchitworawong and Thampanishvong (2015)
construct a severity index of natural disasters consisting of their frequencies and damages and find that thisnegatively affects aggregate FDI inflows into Thailand in 1971–2012.

2

shocks in their location; thus, compared with local firms, they are likely to enter and exit ahost country (Görg and Strobl, 2003; Bernard and Jensen, 2007).
Our main findings are threefold. First, multiple equilibria, one in which multinationals
enter and the other in which they do not, may exist. Second, a substantial negative supply shock, even if it damages local suppliers only, results in a switch from one equilibriumwith multinationals to the other without them. The negative shock reduces the number of
local suppliers and hence raises the cost of sourcing inputs. Multinationals may find thedamaged country unprofitable and leave, shrinking local industry further. This mechanism
helps understand the (sometimes long-lasting) negative disaster impact on FDI found in
empirical studies (Escaleras and Register, 2011; Doytch, 2019; Toner-Rodgers and Friedt,
2020). Finally, conditions that prevent multinational relocation are identified. Specifically,
they are more likely to stay in the disaster-hit country, if local inputs are more important in
multinational production or trade costs of importing foreign inputs are lower. Contrary to
the warning by the Bank of Thailand, the 2011 Thailand floods did not cause long-lasting
relocation and restructuring by manufacturing MNEs, perhaps because of strong industrial
linkages between local and multinational firms and progressive trade liberalization (Milner
et al., 2006; Feliciano and Doytch, 2020).2
We further extend the basic model to allow for heterogeneous productivity and gradual
recovery from disasters, giving similar results and yielding additional implications. Amongothers, we find that the least efficient multinationals are the first to leave the host country
once a disaster hits. Put differently, multinationals staying in the host are likely to be themost efficient ones. This result may help us understand the observation that in the aftermathof the 2011 floods, larger Japanese MNEs in Thailand did not change their local procurement
share as much as smaller ones (Hayakawa et al., 2015).

1.1

Relation to the literature

We aim to contribute primarily to the literature investigating the impact of multinationals
on industrial development (Alfaro, 2015 for a survey). For example, using Irish micro-level
data, Görg and Strobl (2002) find that the presence of multinationals promotes the entry2

Using the information on Japanese-Thailand bilateral input-output table, Milner et al. (2006) find asizable and robust association between the number of Japanese affiliates in Thailand and their linkages withThailand’s industries. Feliciano and Doytch (2020) document the recent development of Thailand’s Free
Trade Agreements. Using Thailand’s firm-level data, they find that reductions in import tariffs improve theperformance of both local and foreign-owned firms.

3

of local manufacturing firms.3 Among many channels through which multinationals benefit
host economies, an important one is vertical industrial linkages (e.g., Javorcik, 2004; AlfaroUreña et al., 2020). Alfaro-Ureña et al. (2020) use firm-to-firm transaction data in Costa
Rica and find that local firms increase their size and productivity after becoming a supplier
to multinationals.
Although many theoretical attempts seek to understand the role of multinationals in vertically linked industries, only a limited number of studies have described (de)industrialization
as switches between multiple equilibria in the model economy (Rodrı́guez-Clare, 1996; Markusen
and Venables, 1999; Carluccio and Fally, 2013).4 Markusen and Venables (1999) numericallyillustrate the situation where the entry of downstream MNEs fosters local upstream industry. These studies, however, have analyzed each equilibrium only separately and not exploredwhich shocks trigger a shift from one equilibrium to another or how the transition proceeds.
We rely on their framework and take one step further to analytically characterize the conditions under which an exogenous supply shock leads to an equilibrium switch and which factor
promotes or prevents it. In doing so, our theoretical results can be related to disaster impacts
on multinationals. In contrast to Carluccio and Fally (2013), who model a “technologicalincompatibility” of local intermediates with multinational production, we deliberately keep
the technology side as simple as possible to highlight the impact of negative supply shocks.
Some studies examine the impact of various types of risk on multinational behavior (Aizenman, 2003; Aizenman and Marion, 2004; Russ, 2007; Fillat and Garetto, 2015). Aizenman
and Marion (2004) investigate how the volatility of demand and supply shocks affect differently market-seeking FDI and efficiency-seeking FDI. For instance, Fillat and Garetto (2015)
model multinational entry as a real-option problem, where multinationals show resilienceagainst negative shocks because of the sunk cost they have paid to enter. Unlike thesestudies focusing on risk under uncertainty, our model highlights actual physical damages,
given the context of developing countries that are vulnerable to severe disasters (ADB, 2013;
Sivapuram and Shaw, 2020).
3

By contrast, studies reporting negative impacts include Aitken and Harrison (1999) for Venezuela; Görg
and Strobl (2002) for Ireland; and Lu et al. (2017) for China.
4
We differ from more recent theoretical studies on MNEs such as Alfaro et al. (2010), Garetto (2013),
Ramondo and Rodrı́guez-Clare (2013), Arkolakis et al., 2018, Adachi and Saito (2020), and Gumpert et al.
(2020) in that exogenous shocks always lead to smooth changes in equilibrium in these models unlike in ourmodels. Economic geography models deal with multiple equilibria but typically assume away distinction
between local and multinational firms and/or input-output linkages (e.g., Redding and Turner, 2015, Section
20.3.7; Akamatsu et al., 2020; Gaspar, 2020). A few exceptions include Fujita and Thisse (2006), Hsu et al.
(2020), and Kato and Okoshi (2020), although disaster impact is outside the scope of these studies.

4Simulation studies investigating disaster impact in an economy with industrial linkages
are complementary to ours (Okuyama and Chang, 2004; Henriet et al., 2012; Inoue and Todo,
2019; Galbusera and Giannopoulos, 2018 for a survey).5 In an economy where buyer-supplier
relationship constitutes a complex network, Henriet et al. (2012) show how network features
such as concentration, clustering and connectedness between subregions either dampen or
magnify the effects of a natural disaster. We differ from these studies in terms of bothin focus and modelling strategies. They describe regional economies by fixing the locationof production, whereas we emphasize the footloose-ness of internationally mobile MNEs indeveloping countries. Although input-output linkages in our model are admittedly far simpler
than theirs, we hope it serves as the first step toward a more comprehensive analysis on
disasters and multinationals.
This paper is also related to the vast body of empirical literature assessing disaster impact
on firm performance.6 Recent studies using micro-level data have found that natural disasters
destroy enormous amounts of physical capital, which may be a good chance of updating
capital (Leiter et al., 2009; Vu and Noy, 2018; Okazaki et al., 2019) or a bad one of decreasing
productivity and the survival rates of firms (Tanaka, 2015; Cainelli et al., 2018; Cole et al.,2019).7
Only a limited number of empirical studies examined the nexus between natural disasters
and multinationals. They find mixed results on whether the disaster effect is positive or
negative and short- or long term (Escaleras and Register, 2011; Oh and Oetzel, 2011; Anuchitworawong and Thampanishvong, 2015; Doytch, 2019; Toner-Rodgers and Friedt, 2020).
Doytch (2019) examines sectoral FDI inflows in 69 countries from 1980 to 2011. Her dynamic
panel regression results show negative effects in general, but also suggest that the effects varydepending on the type of disasters, industries, and regions. Using data from foreign affiliates of 71 European MNEs, Oh and Oetzel (2011) find that major natural disasters haveno significant impact on the number of affiliates, whereas terrorist attacks and technologicaldisasters have negative impacts. Closely examining disaster events in India in 2006–2019,5

For empirical studies on the impact of negative shocks including natural disasters in supply chains, seeTodo et al. (2015), Barrot and Sauvagnat (2016), Carvalho et al. (2020), Dhyne et al. (2021), and Kashiwagi
et al. (2021).
6
Empirical studies on the disaster impact on economic growth are also extensive. For a summary offinding, see Tables 1 and 2 in Cavallo and Noy (2011); and Table 1 in Felbermayr and Gröschl (2013).
Theoretical contributions in this line include Hallegatte and Dumas (2009), Ikefuji and Horii (2012), Akao
and Sakamoto (2018), and Schubert and Smulders (2019).
7
Some studies have reported negative impacts on export and import performance of affected firms at leastin the short run (Ando and Kimura, 2012; Boehm et al., 2019; Elliott et al., 2019).

5

Toner-Rodgers and Friedt (2020) report persistent intra-national shifts in multinationals’
investment patterns from disaster-affected regions to non-affected regions. Our theory may
help sort out these empirical findings by uncovering why and when natural disasters may
have a long-term negative impact on multinationals and local industry.

1.2

Disaster impact on FDI: an empirical example

To motivate theoretical analysis, this subsection provides suggestive evidence on natural disasters and FDI. We first check the negative impact of natural disasters on FDI inflows todeveloping countries. We then confirm that the negative impact on FDI inflows to developing
countries is long-term especially when disaster damages are severe. We utilize country-level
data on FDI in 1991–2015 from the World Bank Development Indicators (WDI) and dataon natural disasters in 1976–2015 from the Emergency Disasters Database (EM-DAT) maintained by the Centre for Research on the Epidemiology of Disasters.8 Detailed information
on data sources is provided in Data Appendix.
Following Escaleras and Register (2011), we regress FDI inflows (as a percent of GDP)
from the world to country i in year t on the total number of natural-disaster events that hit
country i in t − 1 to t − τ years:
FDIi,t = α + βτX(No. of natural disasters)i,t−s + x0i,t γ + ui,t ,

s=1

where τ takes 5, 10, or 15; xi,t is a column vector of control variables; and ui,t is the error term.9 We reexamine their analysis by updating the sample period and splitting thesample based on whether a country is a developing/developed one.10 The estimates of β indeveloping-countries sample are shown in columns (1) to (3) of Table 1, all of which show
a negative sign with strong statistical significance. Although the absolute magnitude of theestimate gets smaller as the time span is longer (from columns (1) to (3)), there seems along-term impact. The estimates in developed-countries sample are in columns (4) to (6), allof which show a negative sign but without statistical significance. These results suggest that
8

The EM-DAT database is commonly used in studies on natural disasters (e.g., Escaleras and Register,
2011; Felbermayr and Gröschl, 2013, 2014; Hallegatte, 2015; Doytch, 2019; Kikkawa and Sasahara, 2020)
9
Control variables include: population growth, inflation, corporate tax and an index of financial development. See Data Appendix for variable descriptions and full regression results.
10
Following the classification of the World Bank, a developed country is defined as one that belongs to thehigh-income group, while a developing country as one that falls in the other income groups.

6the negative impact of natural disasters is more articulated in developing countries.

7

Table 1. Disaster impact on FDI: developing vs. developed countries(1)
No. of disasters in theprior 5 years

Dependent variable: FDI (as % of GDP)
Developing countries
Developed countries
(2)
(3)
(4)
(5)
(6)

−0.031∗∗−0.056(0.014)
No. of disasters in theprior 10 years(0.052)−0.027∗∗∗−0.020(0.007)(0.024)

No. of disasters in theprior 15 years
Country fixed effects
Year fixed effects
Controls
Number of countries
Number of observations
R2

X
X
X
112
2,000
0.513

X
X
X
112
2,000
0.515

−0.020∗∗∗−0.007(0.005)(0.014)

X
X
X
112
2,000
0.515

X
X
X
41
655
0.426

X
X
X
41
655
0.424

X
X
X
41
655
0.423

Notes: Standard errors clustered by country are in parentheses. Developed countries are those belonging to the high-income group, while developing countries to the other income groups, according
to the classification of the World Bank. We exclude tax haven countries identified by Hines andRice (1994) and countries that never experienced natural disasters in 1976–2015. We drop the top
1% and the bottom 1% of the observations of the dependent variable as outliers.
∗ Significant at 10% level; ∗∗ Significant at 5% level; ∗∗∗ Significant at 1% level.

Let us check whether disasters have indeed long-lasting effects on the current FDI performance. We explore this by decomposing the number of disaster events in the prior 15 years
into recent and past ones. Namely, the modified estimation equation includes three disastervariables such that (i)the number of events in the prior 5 years; (ii)that in the prior 6 to 10
years; and (iii)that in the prior 11 to 15 years, or two variables such that (i)the number of
events in the prior 5 years; and (ii)that in the prior 6 to 15 years. We further consider theheterogeneous effect of disasters depending on their intensity. A disaster event is defined asa severe one if it records financial damage as a share of GDP exceeding its median value forall countries that have ever suffered from disasters in 1976–2015. Hence, a non-severe event
is defined as one if it is equal to or below the median. Table 2 provides regression resultsfor developing countries. In all columns, the number of disasters more than 5 years ago havenegative effect with in general statistical significance, while that in the prior 5 years does
show any statistically significant effect. These suggest a long-term negative impact. The
8negative coefficients in columns (1) to (2) are consistently greater in magnitude than theircounterparts in columns (3) to (4), telling that the severe events discourage FDI inflows more.
These observations guide our theory in a way such that the long-term (and perhaps
irreversible) impact could be modeled as shifts between multiple equilibria of industrial configurations in the host country. Important aspects are that such shifts may likely be to occur
in developing counties and to be brought especially by severe disasters. Building a model
describing these aspects, our aim is then to characterize the conditions under which FDI indeveloping countries shows resilience against substantial disasters.

Table 2. Disaster impact on FDI in developing countries: severe vs. non-severe disasters
Dependent variable: FDI (as % of GDP)
Severe disasters
Non-severe disasters
(1)
(2)
(3)
(4)
No. of disasters in theprior 5 years
No. of disasters in theprior 6 to 10 years
No. of disasters in theprior 11 to 15 years

0.013

0.014

0.019

0.018

(0.055)(0.056)(0.024)(0.024)−0.081∗−0.053∗∗(0.049)(0.022)−0.095∗∗∗−0.031(0.034)(0.028)

No. of disasters in theprior 6 to 15 years
Country dummies
Year dummies
Number of countries
Number of observations
R2

X
X
112
2,000
0.516

−0.088∗∗∗−0.042∗∗∗(0.022)(0.013)

X
X
112
2,000
0.516

X
X
112
2,000
0.515

X
X
112
2,000
0.515

Notes: Standard errors clustered by country are in parentheses. A severe disaster in country i inyear t is defined as one that records financial damages as a share of GDP exceeding its median for
all countries that have ever experienced natural disasters in 1976–2015. A non-severe disaster incountry i in year t is defined as one that is not severe. We exclude tax haven countries identified
by Hines and Rice (1994) and countries that never experienced natural disasters during the sample
period. We drop the top 1% and the bottom 1% of the observations of the dependent variable as
outliers.
∗ Significant at 10% level; ∗∗ Significant at 5% level; ∗∗∗ Significant at 1% level.

9The remainder of the paper is structured as follows. The next section describes the modeland characterizes conditions under which different industrial configurations emerge. Section
3 examines the impact of natural disasters and characterizes the conditions under which
multinationals show resilience. Section 4 presents two extensions of the basic model. The
final section concludes the paper.

2

The model

Consider the host country and the foreign country, comprising the rest of the world. There
are two sectors: a differentiated-product sector and a homogeneous-product sector. In the
differentiated sector, there are three types of firms: domestic, multinational, and foreign firms.
The last two are foreign-owned firms. Differentiated varieties have two roles: final goods
for consumers in the two countries and intermediate inputs for domestic and multinationalfirms. To best fit our model in the context of developing-countries, the host-country market
is assumed to be small and localized and thus served by only domestic firms, while theforeign-owned firms serve the non-host country market.11 Foreign capital used as fixed costsof setting up foreign-owned firms is free to choose between the host and the foreign countries.
Fig. 1 presents the structure of our model.
In the homogeneous sector, firms use labor to produce a homogeneous good. We assume
that the good is freely traded and the unit labor requirement is unity. These imply that the
good’s price is equal to both a constant world price and wage. We choose the homogeneous
good as the numéraire, so that both the good price and the wage are unity. Labor is freely
mobile between two sectors, which equalize wages between the sectors.
11

In an earlier working paper, we analyze the situation where foreign-owned firms serve the host-country
market and obtain similar results (Kato and Okubo, 2017).

10

Fig. 1. Model structure.

2.1

Tastes and production

Consumers.

The representative consumer in the host country has the following utility

function:u = Qα (q O )1−α ,
σ
Z
 σ−1
σ−1
σ
q(ω) dω,where Q =(1)

and where Q is the composite of the differentiated final goods and q(ω) is the demand
for an individual variety of ω produced by the domestic firms. q O is the demand for thenuméraire good, α is the expenditure share on final goods, and σ > 1 measures the elasticity of
substitution between them. We solve the first-order condition (FOC) of utility maximization
to obtain demand function for variety ω:

q=

p(ω)
P

−σ

E
,
P

Z
where P =

p(ω)

(2)
1−σ

1
 1−σ

dω

,

and where p is the price of the variety and E is the aggregate expenditure on differentiatedgoods, which is equal to α share of income. The income of the representative consumer
11

consists of labor income and excess profits repatriated by domestic firms (if not zero). Notingthat domestic firms are symmetric, the price index, P , reduces to 1
1
P = N p1−σ 1−σ = N 1−σ p,(3)where N is the number (or mass) of domestic firms. We will suppress the variety index of ωin what follows.
Our focus is on the host country; hence, we do not fully model the market in the rest of
the world, whom multinational and foreign firms serve. The demand functions for a typicalvariety produced by multinational firms, i = m, and foreign firms, i = f , areqi = p −σ E ∗
i
P∗

P∗

∗
≡ p−σ
i D ,

i ∈ {m, f },(4)

where P ∗ and E ∗ are respectively the price index and the total expenditure on differentiatedgoods in the rest of the world. The market size of the rest of the world is summarized by aconstant D∗ ≡ E ∗ (P ∗ )σ−1 .
Domestic firms.

Each domestic firm requires F amounts of labor for setup costs. Onceestablished, they use ea units of a Cobb-Douglas composite input for each unit of output they
produce. The composite input comprises foreign intermediates (with share 1 − µ) and local
intermediates produced by the differentiated sector itself (with share µ). The price of foreignintermediates is exogenously given by τ p∗u , where p∗u ≥ 1 is a constant free-on-board priceand τ ≥ 1 represents trade costs between the host country and the rest of the world. The
minimized total cost to produce q units of a typical variety is thenC(q) = P µ w1−µe
aq + wF = P µe
aq + F,(5)

noting that the wage is equal to one: w = 1. As the demand elasticity is given by σ, which
we will see later, the FOCs for profit maximization yield the usual constant-markup pricing:
σe
aP µ
p=
= aP µ ,σ−1(6)where we choose ea such that ea = (σ − 1)a/σ. From Eqs. (3) and (6), we can rewrite the12price index as
1

1

P = a 1−µ N (1−σ)(1−µ) ,(7)which decreases with N because σ > 1 and µ ∈ (0, 1),
Multinationals.

Each multinational firm needs one unit of foreign capital to start

operation and e
am units of a composite input per unit of output. The composite input
for multinationals is different from that for domestic firms and is made up of intermediates
produced abroad (with share 1 − µm ) and intermediates produced by domestic firms (withshare µm ). The cost function for a typical multinational is thenCm (qm ) = P µm (τ p∗u )1−µm e
am qm + rm ,(8)

where qm is given by Eq. (4) and πm is the rental rate of foreign capital. The FOCs give theoptimal price:pm =σeam P µm (τ p∗u )1−µm= am P µm (τ p∗u )1−µm ,
σ−1

(9)

where eam is chosen such that eam = (σ − 1)am /σ.
Foreign firms.

Each foreign firm needs one unit of foreign capital for setup costs andeam units of foreign intermediates per unit of output. They source all inputs from the world
market and do not incur trade costs. The cost function for a typical foreign firm is
Cf (qf ) = p∗ue
am qf + rf ,(10)

where rf is the rental rate of foreign capital for foreign firms. The optimal price for thevariety is simply given by pf = am p∗u .
Finally, we need to consider clearing conditions for goods and labor markets. The total
output for the variety produced by each domestic firm, q, must be equal to the sum of
consumer demand and the input requirement of domestic and multinational firms. By using
Eq. (2) and applying Shepard’s lemma to Eqs. (5) and (7), we obtainq= p −σ E

=p

P
−σ

+N

∂C(q)
∂Cm (qm )
+ Nm
∂p
∂p

P
 σ−1

P
E + N µP σ+µ−1e
aq + Nm µm P σ+µm −1 (τ p∗u )1−µm e
am q m ,13(11)

noting that the demand elasticity is equal to the elasticity of substitution between varietiesσ.
Similarly, the labor demand in the differentiated sector can be derived from using Sheprad’s lemma as N · ∂C(q)/∂w = N [(1 − µ)P µe
aq + F ]. The labor-market clearing requiresthat the sum of the labor demand in both the differentiated and the numéraire sectors must
be equal to the total workforce in the host country, L. It determines the upper bound of Nsuch that N ≤ N ≡ L/F [σ(1 − µ) + µ] (see Appendix 1). In the numéraire sector, its labordemand and thus its output are adjusted in a way such that imports/exports of the good arebalanced.

2.2

Industry equilibrium

All three types of firms freely enter and exit from the differentiated sector. Let Π ≡ pq −C(q)be the excess profit of domestic firms, i.e., operating profits minus fixed costs. Then, entry
occurs when Π > 0, while exit occurs when Π < 0. This adjustment process stops at the
point where domestic firms break even, that is, Π = 0. Using Eqs. (5), (6), and (10), we canderive the combinations of N and Nm that satisfy Π = 0 as
Π = pq − C(q) = pq − P µe
aq − F = 0,µm
→ Nm = ΘN − 1−µ N − αN ,
h
iσ−1
µm
σF [σ(1 − µ) + µ] am a 1−µ (τ p∗u )1−µm
where Θ ≡,µm D∗ (σ − 1)

(12)
N≡

L
,
F [σ(1 − µ) + σ]noting that N represents the maximum number of domestic firms the host country can
support, which depends on its workforce, L. We draw a typical Π = 0 locus in Fig. 2(a).
The locus has an upward slope under a reasonable condition that the expenditure share on
varieties is not sufficient small such that α > 1−(1−µ)/µm , which we will assume throughout
the paper.12
We assume a gradual entry-and-exit process such that the entry cost is proportional to
the number of existing domestic firms: Ṅ = Π, where the dot denotes the time derivative.13µm

The Π = 0 locus increases with N if ∂Nm /∂N = N −1− 1−µ [µm αN + (1 − µ − µm )N ]/(1 − µd ) < 0, or
equivalently µm αN +(1−µ−µm )N > 0 holds. A sufficient condition for this inequality is α > 1−(1−µ)/µm .
13More rigorous dynamic analyses of location models can be found in Baldwin (2001), Ottaviano (2001),
Boucekkine et al. (2013), and Fujishima and Oyama (2021).
12

14

The arrows in Fig. 2 indicate the direction of motions. Above the curve, Π < 0 holds anddomestic firms exit. Meanwhile, below the curve, Π > 0 holds and domestic firms enter.
It has an upward slope because an increase in the number of multinationals and hence inlocal intermediate demand induces the entry of domestic firms. When N is small such thatN ∈ [0, αN ], the costs of sourcing local intermediates, P , are too high for a positive numberof domestic firms to survive. The domestic firms may use up all labor in the host country,
that is, N = N , in which case no further entry is allowed and incumbents make positive
profits.
We turn to multinational and foreign firms. Let Πi = pi qi − Ci (qi ) be the excess profit
of firm i ∈ {m, f }. Then, free entry and exit lead to Πi = 0, where the rental rate offoreign capital is exactly covered by operating profits: ri = pi qi /σ. As a result of thearbitrage behavior of foreign investors, foreign capital chooses the type of firms that generates
higher rental rate/operating profits. Foreign capital becomes indifferent between becoming
a multinational and a foreign firm when the capital-return differential is zero:∆rm ≡ rm − rf = pm qm /σ − pf qf /σ = 0,h 1−µmi(σ−1)(1−µ)→ N = aσ−1 τ µm (p∗u )−1≡ N0 ,(13)

where we used Eqs. (4), (8) to (10) and pf = am p∗u . A typical ∆rm = 0 locus is drawn
in Fig. 2(b) with arrows indicating the direction of motion, where Kf is the total amountof foreign capital. The locus does not depend on the mass of multinationals, Nm , because
the operating profits of both types of firms are independent of Nm . What only matters forthe location decision of foreign capital is the price index of local intermediates, P , which
is a decreasing function of N . The ∆rm = 0 locus, or equivalently the N = N0 line is thethreshold number of local firms above which foreign capital chooses to enter the host country.
When N > N0 holds, multinationals can produce at a lower marginal cost than foreign firms,
and thus foreign capital can choose to become a multinational. The opposite is true when
N < N0 holds.
Following the gradual relocation process such that Ṅm = ∆rm as in the entry-and-exitof local firms, the movement of foreign capital stops at either one of the three points: (i)∆rm = 0; (ii) ∆rm > 0 and all foreign capital becomes a multinational, i.e., Nm = Kf ; and(iii) ∆rm < 0 and all foreign capital becomes a foreign firm, i.e., Nm = 0.

15

Fig. 2. Equilibrium curves.

Industry equilibrium, in which both the adjustments of N and Nm are completed, isdetermined by the relative positions of the two curves. When N0 < αN holds, foreign
capital finds it more profitable to become a multinational than to become a foreign firmeven if there are few local firms and hence P is high. More multinationals demand local
intermediates, inducing more domestic firms to enter. Consequently, the economy reaches
point S1 : (N, Nm ) = (N , Kf ), a stable equilibrium where both domestic and multinationalfirms coexist.
Meanwhile, when N0 > N holds, no foreign capital prefers to become a multinational.
The unique stable equilibrium is point S2 : (N, Nm ) = (αN , 0), where only domestic firms
operate in the host country. Since there are no intermediate demand by multinationals, thenumber of domestic firms, αN = αL/F [σ(1 − µ) + σ], is constrained solely by the local
expenditure on differentiated goods, E = αL.
When N0 is in between αN and N , both points, S1 and S2 , are stable equilibria. Fig.
3 shows this situation. The foreign-capital-return differential is not large enough; hence,
whether becoming a multinational or a foreign firm has no definite answer. Rather, theanswer depends on the number of local firms currently prevailing in the host country. This
complementarity between multinationals and local firms creates a coordination problem.
Foreign capital will enter the host country if local production is expected to expand. If
there exists a prospect of multinationals rising intermediate demand, more domestic firms
will enter, leading the economy to point S1 . The same reasoning applies to point S2 : local
intermediate production is never expected to expand, if no prospect of multinational entry
16exists. Which of the two equilibria arises depends on the expectations of firms/investors andthe initial industry configuration (Krugman, 1991; Matsuyama, 1991). Point U is a saddle
but an unstable equilibrium, because our model does not include any jump variables to put
the economy on the saddle path.

Fig. 3. Multiple equilibria.

As N is a function of fixed labor input F , it is convenient to characterize industry equilibrium using F . We assume that (a) the expenditure share on varieties is not too small suchthat α > 1 − (1 − µ)/µm , in which case the Π = 0 locus has an upward slope, and (b) itnever touches the upper limit of Nm , that is, a sufficiently large amount of foreign capitalsuch that Kf > ΘN

1−µ−µm1−µ(1 − α) (see Eq. (12)). Then we obtain the following proposition.

Proposition 1 (Industry equilibrium). Using the fixed labor requirement for a domestic
firm, F , industry equilibrium is characterized as follows:(i) If F is small such that F < Fa ≡ αL/N0 [σ(1 − µ) + µ], the configuration in whichdomestic and multinational firms coexist, S1 : (N, Nm ) = (N , Kf ), is the only stableequilibrium.
(ii) If F is large such that F > Fb ≡ L/N0 [σ(1 − µ) + µ], the configuration in which all
multinational firms leave, S2 : (N, Nm ) = (αN , 0), is the only stable equilibrium.
(iii) If F is intermediate such that Fa ≤ F ≤ Fb , both configurations are stable equilibria.

173Natural disasters and the resilience of FDI

3.1

Adverse shock to local firms

Let us now consider natural disasters in the host country. A natural disaster to local firms
is modeled as an adverse shock to the fixed labor input F , that is, an increase from F toF + ∆F with ∆F > 0. We examine (i) whether the natural disaster changes the equilibrium
configuration, and if so (ii) when such a change is less likely to occur: that is, when the hosteconomy is more likely to be resilient.
Suppose F is in between Fa and Fb and that the economy is at point S1 : (N, Nm ) =(N , Kf ). Fig. 4(a) depicts this situation and marks the initial point with a double circle. As
shown by the thin dashed line in Fig. 4(b), an increase in F raises labor used in each domestic
firm and hence reduces the maximum number of firms the host country can support, i.e., a0decrease from N to N . It means that more domestic firms become unprofitable, moving also
the Π = 0 locus left. The ∆rm = 0 locus does not change, however, as F does not directly
enter the operating profits of multinational and foreign firms.
0

In Fig. 4(b), the shock is so substantial that the new N = N line is located to theleft of the ∆rm = 0 locus. The decline in local supplying industry raises input prices andthus makes multinationals unprofitable. If such an adverse effect reaches a certain threshold,multinationals suddenly start leaving the host country. Multinational exits in turn decreases
demand for local input and causes a further decline in local industry. The dotted arrow in
Fig. 4(b) traces the industry evolution: it moves left horizontally up to N0 and then moves
0lower left, heading for a new equilibrium at point S20 : (N, Nm ) = (αN , 0), as indicated by adouble mark in Fig. 4(c).

18Fig. 4. Equilibrium switch due to a natural disaster (from panel (a) to (c)).

The condition for the equilibrium switch to occur is
h 1−µmi(σ−1)(1−µ)
L< N0 ≡ aσ−1 τ µm (p∗u )−1,(F + ∆F )[σ(1 − µ) + µ]
L
→ F + ∆F > Fb ≡,N0 [σ(1 − µ) + µ]0N ≡→ ∆F > Fb − F ≡ ∆Fmin .

(14)

A natural disaster causes a shift in equilibrium only if the magnitude of shock exceeds acertain threshold. In addition, as long as myopic location decision is assumed, the equilibrium
shift is permanent.14 This result echoes the long-lasting negative impact of severe disasters
on FDI found by Toner-Rodgers and Friedt (2020) and the motivational observations we laidout in Table 2.
We can see that the threshold level of shock, ∆Fmin , increases with the Cobb-Douglas
share of local intermediate for multinationals µm , and decreases with trade costs τ . Put
differently, as µm is higher or τ is lower, the equilibrium switch is less likely to occur. Multinationals more dependent on low-price local intermediates (higher µm ) make greater profits,
so that they are more likely to stay in the host country despite the decreased number of local
suppliers.15 Lower trade costs play a similar role by reducing the import price of foreign
14

We consider forward-looking location decision in Section 4.2.
Under the situation where point S1 can be an equilibrium, the sourcing costs of local intermediates are
not higher than those of foreign intermediates, i.e., P ≤ τ p∗u (see Appendix 2 for the proof). In contrast toµm , the effect of domestic firm’s input share of local intermediates, µ, on ∆Fmin is ambiguous. Higher µ1519intermediates and thus making multinationals more profitable. Contrary to the concern of
the Bank of Thailand, the 2011 flood did not cause drastic long-run changes in the locationand production of manufacturing MNEs (Haraguchi and Lall, 2015). This may reflect thefact that Thailand had already established strong linkages with multinationals and engaged
in trade liberalization (Milner et al., 2006; Feliciano and Doytch, 2020).
Assuming (a) α > 1 − (1 − µ)/µm and (b) Kf > ΘN

1−µ−µm1−µ(1 − α) as in Proposition 1,

we can prove the following proposition (see Appendix 2 for the proof).
Proposition 2 (Natural disaster). Suppose that the fixed labor input, F , is intermediateso that multiple equilibria arise, i.e., F ∈ [Fa , Fb ], and that the host economy is initially at
point S1 , where multinationals and local firms coexist. If F increases to F + ∆F due to anatural disaster, then the following holds:(i) If the level of shock is substantial such that F +∆F > Fb , or equivalently ∆F > ∆Fmin ,the equilibrium switches from S1 to S20 , where the host country loses all multinationals.
(ii) The threshold level of shock increases with the share of local intermediates for multinationals and decreases with trade costs, i.e., ∂(∆Fmin )/∂µm ≥ 0 and ∂(∆Fmin )/∂τ ≤ 0.
That is, the natural disaster is less likely to trigger the equilibrium switch if multinationals are more dependent on local intermediates or they face lower trade costs.

3.2

Other types of shock

The essence of the above analysis is that the negative shock to local firms raises the cost of
local sourcing and hence discourages foreign capital to stay in the host country. Other types ofshocks that directly or indirectly raises the local-input price would give qualitatively the same
result. For example, one can think of additional intra-trade costs that local suppliers have toincur when delivering varieties to multinationals and consumers. Through the destruction ofdomestic transportation infrastructure, natural disasters may raise intra-trade costs, leading
to a higher local-input price. This translates into an upward shift of the Π = 0 locus andmeans that local firms use more roundabout technologies based on intermediates and use less labor. Morelabor can be devoted to the fixed labor input for potential local firms, leading to more entry and thus making
the price index of local intermediates lower. However, higher µ may push the price index up if the local
intermediates are more expensive than labor. If the productivity of domestic firms are sufficiently high such1
1that a ≤ e σ (αN ) σ−1 , the former effect dominates the latter, so that ∂(∆Fmin )/∂µ > 0 holds. See Appendix
2 for details.

20a rightward shift of the ∆rm = 0 locus (i.e., the N = N0 line); however, it does not change
the N = N line unlike the case in Section 3.1.16 Our main results would maintain in thiscase. That is, if the level of shock is substantial, the equilibrium switches from the one
with both local and multinational firms to the one with only local firms (Proposition 2(i)).
Multinationals are more likely to stay in the disaster-hit host country if they rely more on
local inputs or they face lower trade costs (Proposition 2(ii)).
A more straightforward way to model natural disasters is direct shocks to multinationals,
as documented in a number of disaster experiences in developing countries. Supposing thatthe fixed cost of capital for setting up a multinational increases from one to ∆Fm , otherthings being equal, the capital return multinationals generate decreases and foreign capital
finds it more profitable to leave the host country. This effect results in a rightward shift ofthe ∆rm = 0 locus.17 Applying an analogous reasoning, we can confirm qualitatively thesame results as Proposition 2.

4

Extensions

We provide two extensions of the basic model.

4.1

Multinationals with heterogeneous productivity

In the basic model, multinationals are all homogeneous in productivity. In reality, however,productivity differs from multinationals, which may lead to heterogeneous response to disasters. For example, Hayakawa et al. (2015) report that in the aftermath of the Thailand 2011
floods, changes in sourcing patterns of multinationals differ by their age and size, which is16

If intra-trade costs are modeled as an iceberg cost, denoted by τe ≥ 1, the price index is modified as
1
1
1
P = [N (eτ p)1−σ ] 1−σ = (eτ a) 1−µ N (1−σ)(1−µ) from Eqs. (3) and (7). Since τe and a enter in a multiplicative
form, both terms have the same effect on the Π = 0 curve and the ∆rm = 0 line (see Eqs. (12) and (13)). An
increase in τe as a result of a natural disaster shifts the Π = 0 curve upward and the N = N0 line rightward.
If the increase is so substantial that the N = N0 line goes beyond the N = N line, the equilibrium switchesfrom point S1 to S20 (Proposition 2(i)). Higher µm and lower τ would move the N = N0 line left (see Eq.
(13)) and hence make the switch less likely to occur (Proposition 2(ii)).
17
As a result of the disaster, the cost function of a typical multinational is modified as C(qm ) =µm
P (τ p∗u )1−µm e
am qm + rm ∆Fm and the capital return as rm = pm qm /(σ∆Fm ). The ∆rm = 0 locus afh 1−µmi(σ−1)(1−µ)
1−µm(∆Fm ) µm . It can be seen that an increaseter shock is thus given by N0 = aσ−1 τ µm (p∗u )−1
in ∆Fm moves the ∆rm = 0 locus right and higher µm and lower τ make the rightward shift smaller, leading
to qualitatively the same results as Proposition 2.

21

often associated with their productivity. We will see that the introducing heterogeneous productive multinationals into the basic model would give richer implications and more realistic
equilibrium configurations.
Heterogeneity comes from a stochastic draw of unit input requirements, e
am = am (σ−1)/σ,
as in the literature on heterogeneous firm models (Melitz, 2003; Baldwin and Okubo, 2006).
We assume that the cumulative density function of am ∈ [am , am ] takes a truncated Pareto
distribution. Namely, the probability of a multinational drawing productivity lower than amisG(am ) =aρm − 1aρm − aρm=,aρm − aρmaρm − 1

where ρ ≥ 1 is the shape parameter. We set am to one without loss of generality. In addition,
it is reasonable to assume that high-productive MNEs (lower am ) enjoy lower trade costs(lower τ ) per-unit of ship than low-productive firms due to scale economies in transportation(Forslid and Okubo, 2015, 2016):18
τ (am ) = aγm ,implying that most productive firms with am = 1 is free from trade costs: τ (1) = 1.
The return to foreign capital depends on its productivity and thus its relocation incentive
also differs by productivity. Given the number of domestic firms N , Fig. 5 shows a typicalcapital-return differential: ∆rm (am ) ≡ rm (am ) − rf (am ), which captures the incentive tolocate in the host country. The advantage of locating in the host country is a low costof sourcing local inputs, whereas its disadvantage is a high cost of sourcing foreign inputs.
For multinationals with lower am , the advantage is more beneficial because of their larger
amount of production, whereas the disadvantage is smaller thanks to scale economies oftransportation. Hence more productive multinationals have a greater ∆rm (am ) and thus astronger incentive to locate in the host country, as shown in Fig. 5.
18

Forslid and Okubo (2016) document that the export-to-sales ratio of Japanese firms differs greatly amongfirms and is systematically higher for larger exporters.

22

Fig. 5. Location incentives of multinationals.

As in the basic model, we consider a gradual relocation process. Namely, each foreign
capital, initially located in the foreign country, incurs migration costs χ to move to the hostcountry. The migration costs is assumed to be proportional to the flow of migrating capital,i.e., χ = Ṅm (Baldwin and Okubo, 2006). Fig. 5 tells that the first capital ready to pay
the relocation costs will be those that have the most to gain, i.e., the most efficient foreign
capital. In industry equilibrium where the capital movement ceases, foreign capital withRam ≤ aRm becomes a multinational in the host country, whereas foreign capital with am > amremains in the foreign country as a foreign exporter, where aR
m is the cut-off productivity at
which the two locations are indifferent. The number of multinationals is thus given by
Nm = G(aRm )Kf =

ρ(aRm) − 1· Kf ,aρm − 1

which is proportional to aRm : Nm increases as the host country allows less productive foreign
capital to come.19
Taking the migration of foreign capital into account, the entry and exit of local firms
gradually take place. Fig. 6 illustrates industry equilibria in the (N, Nm ) plane, corresponding to Fig. 3. Noteworthily, unlike the basic model, the ∆rm (aRm ) = 0 locus is no longer a
vertical line. Its upward slope comes from heterogeneous productivity: as the local supplying industry expands and the local-sourcing cost is lower, less productive foreign capital can
ρ−1
The migration costs are thus given by χ = Ṅm = ρamȧm Kf /(aρm − 1) and aR
m is the solution ofR∆rm (am ) = χ. See Appendix 3 for details.
19

23

enter. As a result, a few but very productive multinationals remain in point S2 . In Appendix
3, we can check that multiple equilibria arise if the fixed labor requirement for setting up adomestic firm, F , takes an intermediate value, just like the basic model (Proposition 1(iii)).

Fig. 6. Industrial configurations under heterogeneous multinationals.

Considering the effect of an increase in F due to a natural disaster as in Section 3.1,
we can see in Fig. 7 qualitatively the same changes and the same intuition behind them asin the basic model. That is, the Π = 0 curve moves up simply because lower profitability
shrinks the area where local firms can survive. The total number of local firms that the hostcountry can accommodate decreases so that the N = N moves left. As a result of theseshifts, the new Π0 = 0 curve may no longer intersect at point U with the ∆rm (aRm ) = 0 curve,
in which case the equilibrium would switch from S1 with many multinationals to S20 withfew multinationals. The unique but interesting difference from the basic model is clear fromthe new equilibrium S20 : the most efficient multinationals are the ones that remain in thedisaster-hit country.20
20This relocation pattern holds also when the disaster does not trigger the equilibrium switch. An increasein F moves the N = N line left, thereby decreasing Nm at equilibrium S1 along the ∆rm (aRm ) = 0 locus.
R
The decrease in Nm = G(aRm )Kf is equivalent with an decrease in am , implying that the least efficient
multinationals are the first to leave the host country.

24

Fig. 7. Impact of a natural disaster under heterogeneous multinationals.

It can also be checked that if multinationals are more dependent on local suppliers (higherµm ), the disaster is less likely to trigger the equilibrium switch.21 By imposing assumptions
similar to those in Propositions 1 and 2, we can formally prove the following proposition.
The proof and explicit expressions are given in Appendix 3.
Proposition 3 (Heterogeneous multinationals).

Assume that multinationals are het-

erogeneous in a way that is specified in the text. Suppose that the fixed labor input, F , isintermediate so that multiple equilibria arise, i.e., F ∈ (Fea , Feb ], and that the host economy isinitially at point S1 with many multinationals. Consider an increase in F due to a natural
disaster, then the following holds:(i) Multinationals with higher productivity are more likely to stay in the host country.
(ii) The natural disaster is less likely to trigger the equilibrium switch from S1 to S20 , where
the host country loses most of multinationals, if multinationals are more dependent on
local intermediates (higher µm ).

4.2

Reconstruction from disasters

We have so far modeled a disaster as a permanent shock. Let us instead consider a temporalshock and uncover under what conditions foreign capital reenters the gradually recovering
host country. To come to the point, the host country re-attract multinationals earlier, as (a)it
21This result comes from the fact that a higher µm makes smaller the upward shift of the Π = 0 curve.

25

recovers from the disaster more quickly, (b)they are more dependent on local intermediatesor (c)they face lower trade costs. These conditions have in common with those in Proposition
2(ii) and 3(ii).
As long as myopic relocation decision is assumed as before, no foreign capital relocatesto the host country even if it fully recovers from the disaster. To allow for the possibilityof reentering, we need to consider far-sighted decision making of foreign capital: it chooses
whether to become a multinational or a foreign firm to maximize its lifetime return.22
Consider the situation where the host country is hit by a natural disaster at time s = 0
and all multinationals leave there, corresponding to point S20 in Fig. 4(c). Suppose then thatthe increased fixed-labor input due to the disaster gradually gets back to the pre-shock level
after some time T . Specifically, the fixed labor input at time s, denoted by F (s), is given by

F (s) =

F eδ(T −s)

for s ∈ [0, T )Ffor s ∈ [T, ∞),where δ is the recovery rate and F (0) = F eδT > Fb ≡ L/N0 [σ(1 − µ) + µ] and F ≤ Fb are
assumed to ensure the situation in Fig. 4(c). Letting t (≤ T ) be the time at which foreign
capital moves from the foreign to the host country, the lifetime capital return, v(t), is givenbyZ tv(t) ≡

e
|0

−θs

Z T

rf ds +{z} |t0e−θs rm(s)ds +Z ∞T{z

Locate in foreign

Locate in hoste−θs rm ds,}

where θ > 0 is the discount rate. For s ∈ [0, t), foreign capital becomes a foreign exporterand makes the flow return rf . It locates in the host country from time t onward. The flow0
return during recovery period s ∈ [t, T ) is rm(s) and is fully recovered to the pre-shock level0
rm (≥ rm(s)) for s ∈ [T, ∞). The optimal timing of relocation can be derived from maximizingv(t) with respect to t.
One naturally expects that if reconstruction takes very long time (high T ), foreign capitalwith positive discount rate θ never relocates to the host country, i.e., t = ∞. Furthermore,
22

We note that under the forward-looking behavior multiple equilibria disappear. If the fixed labor input
F takes a value in between Fa and Fb and the situation is like Fig. 3, foreign capital chooses point S1 atwhich it earns a higher flow return than at S2 , so that S1 is the unique stable equilibrium. Domestic firms
also prefer S1 to S2 because they make positive profits at S1 and zero profits at S2 . Point S1 is better thanS2 in the Pareto sense.

26

discussions in Section 3.1 tell that multinationals make greater profits as the share of local
inputs in multinational production, µm , is higher or trade costs, τ , are lower. This should
imply that higher µm or lower τ would push up the timing of multinationals’ reentering, i.e.,lower t. Assuming (a) α > 1 − (1 − µ)/µm and (b) Kf > ΘN

1−µ−µm1−µ(1 − α) as in Propositions

1 and 2, we can establish these arguments in Proposition 4 and formally prove them inAppendix 4.
Proposition 4 (Recovery from disaster). Consider the situation where the host country
is hit by a natural disaster and hosts no multinationals at time s = 0. Suppose that the fixedlabor input at time s < T is given by F (s) = F eδ(T −s) with F (0) = F eT > Fb and is fully
recovered to the pre-shock level F ≤ Fb from time s = T onward. On the optimal timing t ofmultinational reentering, the following holds:(i) Multinationals never reenter the host country, i.e., t = ∞, if the recovery time fromthe disaster is too long such that T >> T , where T is a bundle of parameters distinct
from T .
(ii) Assuming a range of parameters that ensure interior solutions of optimal timing t ∈(0, ∞), multinationals reenter the host country more quickly, as the recovery time isshorter (lower T ), multinationals are more dependent on local intermediates (higherµm ) or they face lower trade costs (lower τ ), i.e., ∂t/∂T > 0; ∂t/∂µm < 0; and∂t/∂τ > 0.

5

Conclusion

This paper has developed a theoretical framework to address the resilience of multinationals
against a severe shock such as natural disasters. Our focus is on two notable aspects ofmultinationals, footloose-ness and input-output linkages with local suppliers. These aspects
give rise to multiple equilibria, one in which multinationals help local industry develop and theother in which multinationals never enter. When a natural disaster seriously damages local
firms and thus raises the price of local intermediate inputs, the equilibrium switch occurs:
multinationals leave the host country and shall never return. We have then identified underwhat conditions multinationals are more likely to stay in the disaster-hit host country. The
27

key parameters are the share of local intermediates in multinational production and trade
costs of foreign intermediates. In particular, as multinationals rely more on local suppliers
and make greater profits through low sourcing costs, a decline in the local supplying industry
due to natural disasters is less likely to affect their relocation decision. This insight carries
over to the case where multinationals are heterogeneous and the analysis of the timing ofdisaster reconstruction.
We believe that our model yields rich analytical outcomes, yet remains sufficiently simple
to produce new insights into the nexus between natural disasters and multinationals. The
analysis can be enriched in many ways. One way is to explicitly introduce local upstream
and downstream firms and allow them to benefit from technology spillovers from multinationals. Using the extended model, one can distinguish between inter-industry (i.e., horizontal)
and intra-industry (i.e., vertical) spillovers and examine their interactions with natural disasters. The degree of spillovers may decrease when greater disaster risk discourages MNEs’commitment to local procurement. We leave this and other possible extensions to future
research.

Appendices
Appendix 1.

Derivations

We here provide detailed derivations of cost function C(q), total demand for a differentiatedproduct q, and free entry conditions.
A1-1.

Cost function

The cost-minimization problem for a typical domestic firm producing variety ω isZ
minp(ω 0 )qu (ω 0 )dω 0 + wl + wF,
0{qu (ω )},l"Z
 σ #µs.t. eaq(ω) = z

σ−1qu (ω 0 ) σ dω 0σ−1l1−µ ,

where qu (ω 0 ) is intermediate demand for variety ω 0 . The symmetry of firms implies q(ω) = q.
The problem can be solved in two steps. First, we consider the cost-minimization problem

28

for the differentiated inputs:Z
min0{qu (ω )}p(ω 0 )qu (ω 0 )dω 0 ,Zs.t. Qu =0qu (ω )

σ−1
σ

dω

0

σ
 σ−1

.

The FOCs yield qu (ω 0 ) = [p(ω 0 )/P ]−σ Qu . Using this, we formulate the original problem as
min pQu + wl + wF,

Qu ,qus.t. eaq = zP µ w1−µ ,The FOCs for the above minimization problem give demand functions for both domestic andforeign intermediates:
Qu = µzµ−µ (1 − µ)−(1−µ) P µ−1 w1−µeaq,
qu = (1 − µ)zµ−µ (1 − µ)−(1−µ) P µ w−µeaq.
By using these results and choosing z as z = µµ (1 − µ)1−µ , we obtain the cost function forthe domestic firm in the text. The cost function for the multinational firm is obtained in asimilar way.
A1-2.

Total demand

We apply Shephard’s lemma to the cost function given in Eq. (5) to obtain input demandby domestic firms for variety ω:
∂P µ
∂C(q)
=
· w1−µeaq∂p(ω 0 )∂p(ω 0 )
µ
 1−σ
Z
∂
=
p(ω 0 )1−σ dω·eaq∂p(ω 0 )µ=(1 − σ)p(ω 0 )−σ P µ−1eaq
1−σ= µp(ω 0 )−σ P σ+µ−1eaq,
noting that w = 1. As all domestic firms are symmetric, the intermediate demand for thevariety by them becomes N µp−σ P σ+µ−1e
aq. Similarly, we derive intermediate demand by all−σ σ+µm −1∗ 1−µmmultinationals as Nm µm pm P(τ pu )eam qm . The total demand for the variety is thesum of these input demand and final-good demand (Eq.(2)):
 p −σ E+ N µp−σ P σ+µ−1 w1−µe
aq + Nm µm p−σ P σ+µm −1 (τ p∗u )1−µm e
am q m= p−σ P σ−1 E + N µP σ+µ−1e
aq + Nm µm P σ+µm −1 (τ p∗u )1−µm e
am q m .

q=

P

P

29

(11)

which is given in the text.
A1-3.

Free entry conditions

The following expressions are useful for later reference:
1

1

P = a 1−µ N (1−σ)(1−µ) ,

(A1)
1−σ
1−µ

1
1−µ

,
p1−σ = (aP µ )1−σ = a Nhi1−σ µmµmµm∗ 1−µm 1−σ1−µ (τ p∗ )1−µm
=
a
a
p1−σ
=
a
P
(τ
p
)
N 1−µ .
m
m
m
u
u

(A2)
(A3)

Free entry and exit of domestic firms imply that no domestic firms enter if their excess
profits are negative, Π = pq − C(q) < 0, while if Π ≥ 0 there are positive entries. As typicaldomestic firm breaks even if
0 = Π = pq − C(q)= pq − P µe
aq − Fσ − 1 σP µea= pq −
q−F
σ σ−1
σ−1
pq − F= pq −σ= pq/σ − F,where we used Eq. (6) from the third to the fourth line. The break-even level of sales ofdomestic firms are thus pq = σF . They make positive excess profits if the differentiatedsector uses up local labor so that no further entry into the sector is possible, that is, if
N = N ≡ L/F [σ(1 − µ) + µ], which will be derived later.
We multiply both sides of Eq. (11) by p to get p 1−σ p 1−σ p 1−σ

P µm (τ p∗u )1−µm e
am q mP
PPE
σ − 1 σeaP µNm σ − 1 σeam P µm (τ p∗u )1−µm=+µ
q + µm
qm
N
σ σ−1
N σ
σ−1
E
σ−1
σ − 1 Nm
=
+
µpq +
µm
pm qm ,
N
σ
σ
N

pq =

E + NµP µe
aq + Nm µm

where we used Eq. (3) from the first to the second line and Eqs. (6) and (9) from the second
to the last line. Solving this equation for pq givesσEµm (σ − 1) Nm
pq =
+
pm qm
σ − µ(σ − 1) N
σ
N


σ
E
µm (σ − 1) Nm 1−σ ∗
=
+
p D .
σ(1 − µ) + µ N
σ
N m

30

When there are no excess profits for domestic firms, the aggregate expenditure on differentiated goods is α share of total labor income: E = αwL = αL. Substituting the above
expression, Eq. (A3) and E = αL into the break even level of sales yields
pq = σF,o1−σ 
nµmµm
σαL µm (σ − 1) Nm 1−µ∗ 1−µm1−µam a (τ pu )D∗ = σF,→+N
σ(1 − µ) + µ Nσ
Ni1−σ µmµmµm D∗ (σ − 1) h
→ αL +
N 1−µ Nm = N F [σ(1 − µ) + µ],
am a 1−µ (τ p∗u )1−µm
σµm→ Nm = ΘN − 1−µ N − αN ,
(12)
i
h
σ−1
µm
σF [σ(1 − µ) + µ] am a 1−µ (τ p∗u )1−µm
Lwhere Θ ≡, N≡,∗
µm D (σ − 1)
F [σ(1 − µ) + µ]which is given in the text.
Free entry and exit of multinational and foreign firms drive their excess profits to zero,
which determines their rental rate of foreign capital:
Πm = pm qm − Cm (qm ) = pm qm − P µm (τ p∗u )1−µm e
am qm − rm = 0,1−σ ∗→ rm = pm qm /σ = pm D /σ,Πf = pf qf − Cf (qf ) = pf qf − p∗ue
am qf − rf = 0,1−σ ∗→ rf = pf qf /σ = pf D /σ.
Foreign capital is indifferent between becoming a multinational and a foreign firm if the
return differential is zero:1−σ∆rm ≡ rm − rf = D∗ (p1−σ)/σ
m − pfhi
∗µm∗ 1−µm 1−σ∗ 1−σ=D
am P (τ pu )− (am pu )/σ,no1−σ µmµm∗ 1−µm
∗ 1−σ
∗
1−µ
1−µ
− (am pu )N/σ=D
am a (τ pu )no1−σ µm
µm
1−µ
∗
−µ
∗
∗ 1−σ
m
m
N 1−µ − 1 /σ = 0.
= D (am pu )a 1−µ τ
(pu )

(A4)

Solving this for N givesi(σ−1)(1−µ)
h 1−µm≡ N0 ,
N = aσ−1 τ µm (p∗u )−1
which is given in the text.

31

(13)

A1-4.

Upper bound of the number of domestic firms

Aggregate labor demand in the differentiated sector is the product of the labor demand byindividual local firms and the number of local firms, N . Applying Shephard’s lemma to Eq.
(5), we obtainN∂(P µ w1−µe
aq + wF )
∂C(q)
=N
∂w
∂w


= N (1 − µ)P µ w−µe
aq + F= N [(1 − µ)P µe
aq + F ] .

We evaluate this at the break-even level of sales, pq = σF , to get
N [(1 − µ)P µe
aq + F ] = N [(1 − µ)(σ − 1)pq/σ + F ]= N [(1 − µ)(σ − 1)σF/σ + F ]= N F [σ(1 − µ) + µ].
The labor demand must be smaller than the total workforce in the host country, L:
N F [σ(1 − µ) + µ] ≤ L,
L
≡ N,
→N ≤
F [σ(1 − µ) + µ]which determines the upper bound of N .

Appendix 2.
A2-1.

Impact of natural disaster

Proof of Proposition 2

Since Proposition 2(i) is established in the text, here we prove Proposition 2(ii): ∂(∆Fmin )/∂µm ≥0; ∂(∆Fmin )/∂τ ≤ 0. Differentiating ∆Fmin defined in Eq. (14) with respect to µm yields
∂(∆Fmin )
∂
L
=
−F
∂µm
∂µm N0 {σ(1 − µ) + µ}
∂N0
L
=− 2
·
N0 [σ(1 − µ) + µ] ∂µm
n 1−µmo(σ−1)(1−µ) 
L
∂
−1
σ−1
∗
=− 2
·
a
τ µm (pu )N0 [σ(1 − µ) + µ] ∂µmL(σ − 1)(1 − µ)=− 2
· N0 −ln τ
N0 [σ(1 − µ) + µ]µ2m
L(σ − 1)(1 − µ) ln τ
= 2
≥ 0,µm τ N0 [σ(1 − µ) + µ]32where equality holds at τ = 1.
Similarly, differentiating ∆Fmin with respect to τ gives∂N0
L∂(∆Fmin )·=− 2∂τN0 [σ(1 − µ) + µ] ∂τ
N0 (σ − 1)(1 − µ)(1 − µm )
L
·
=− 2
·
N0 [σ(1 − µ) + µ] τ
µmL(σ − 1)(1 − µ)(1 − µm ) ln τ
≤ 0,=−
µm N0 [σ(1 − µ) + µ]where equality holds at τ = 1. These establish Proposition 2(ii).

A2-2.

Other issues

We derive the condition for ∂(∆Fmin )/∂µ > 0 if F ∈ (Fa , Fb ):∂(∆Fmin )
∂
L
=
−F
∂µ
∂µ N0 {σ(1 − µ) + µ}L(σ − 1)
L
∂N0
=
− 2
2
N0 [σ(1 − µ) + µ]
N0 [σ(1 − µ) + µ] ∂µo
n 1−µmL(σ − 1)1∗
−1
+ ln τ µm (pu )=N0 [σ(1 − µ) + µ] σ(1 − µ) + µn 1−µmoF N (σ − 1)1∗−1=
+ ln τ µm (pu )N0σ(1 − µ) + µn 1−µmo
1∗−1µ+ ln τ m (pu )> F (σ − 1)
≡ RHS(µ).
σ(1 − µ) + µ
where from the second-to-last to the last line we used the fact that F < Fb , or equivalently
N0 < N . A sufficient condition for ∂(∆Fmin )/∂µ > 0 is RHS(µ) ≥ 0 for µ ∈ (0, 1). Whilenoting that RHS 0 (µ) > 0 holds. we use the expression of N0 given in Eq. (13) to rewrite
RHS(µ) as1ln (a1−σ N0 )+RHS(µ) = F (σ − 1)σ(1 − µ) + µ (σ − 1)(1 − µ)
1 ln (a1−σ N0 )≥ RHS(0) = F (σ − 1)
+
σ
σ−1
"
#
1−σ
1 ln a αN+.
≥ F (σ − 1)
σ
σ−1

33

The expression in the last line is positive if
1 ln a1−σ αN
+
≥ 0,
σ
σ−1
1
1
→ a ≤ e σ (αN ) σ−1 .
which is a sufficient condition for ∂(∆Fmin )/∂µ > 0.
Next we show P ≤ τ p∗u if there exists N0 ≥ 0 that satisfies Eq. (13) (or equivalently Eq.
(A4)). Let us first look at Eq. (A4):∆rm = D∗ (am p∗u )1−σ [g(N ; µm ) − 1]/σ = 0,h µmi1−σ µm
N 1−µ .
where g(N ; µm ) ≡ a 1−µ τ 1−µm (p∗u )−µm

(A4)

We consider a range of parameters that ensure the existence of N0 ≥ 0 satisfying Eq. (A4).
Because g(N ; 0) = τ 1−σ ≤ 1 and g(N ; µm ) > 0, we must have ∂g(N ; µm )/∂µm ≥ 0 in orderfor Eq. (13) to have a solution for N = N0 ≥ 0. This condition results in τ p∗u /P ≥ 1:
σ−11
− 1−µ
1∂g(N ; µm )∗1−σ= g(N ; µm ) · ln τ pu aN
≥ 0,
∂µm

σ−1
1
− 1−µ1∗≥ 0,→ ln τ pu aN 1−σ→ τ p∗u



aN

1
1−σ

1
− 1−µ= τ p∗u /P ≥ 1,

 0
0
noting that the derivative of f (x) = aA(x) bB(x) is given by f 0 (x) = f (x) ln aA (x) bB (x) .

Appendix 3.
A3-1.

Multinationals with heterogeneous productivity

Location condition of multinationals

Using the results in Appendix A1-3, we can write the return differential of foreign capital as∆rm (am ) = rm (am ) − rf (am )= pm (am )qm (am )/σ − pf (am )qf (am )/σ= D∗ pm (am )1−σ − pf (af )1−σ
n
o1−σ µmµm
γ 1−µm ∗ −µm
∗
∗ 1−σ
1−µ
1−µ
N
(pu )
− 1 /σa (am )= D (am pu )no1−σ µm
µm
∗
−µ
∗
∗ 1−σ
γ
1−µ
m
m
= D (am pu )a 1−µ (am )(pu )N 1−µ − 1 /σ,

34

R
noting that τ (am ) = aγm . The cut-off productivity, aRm , is given by the solution of ∆rm (am ) =0. Since the big square bracket term in the above expression decreases with am becauseRγ(1−µm )(1−σ) < 0, the return differential is positive (or negative) if am < aRm (or am > am ).
We can explicitly solve for the cut-off productivity:∆rm (aRm ) = 0,n µmo1−σ µmγ(1−µm )(1−σ)
1−µ (p∗ )−µm
)
a
→ (aR
N 1−µ − 1 > 0,muo−(1−σ)n µmµm
γ(1−µm )(1−σ)
1−µ (p∗ )−µm
→ (aR
)
=
a
N − 1−µ ,muµm
o− γ(1−µn 1µmm)
1−µ (p∗ )−1
N γ(σ−1)(1−µ)(1−µm ) .
→ aR
=
a
u
m
On the other hand, the mass of multinationals is expressed as a function of the cut-off
productivity:
R
Nm = Pr(bam ≤ aRm ) = G(am )Kf =Kf (aρm − 1),aρm − 1

ρ
1/ρ
→ aR
.
m = [Nm (am − 1)/Kf + 1]

(A5)

Substituting this into the explicit solution of aRm givesµm
n 1
o− γ(1−µ
ρµm
m)
∗ −1
1−µ
a (pu )N γ(σ−1)(1−µ)(1−µm ) ,ρµmn 1o− γ(1−µ
ρµm
m)
ρ
∗ −1
1−µ
→ Nm (am − 1)/Kf + 1 = a (pu )N γ(σ−1)(1−µ)(1−µm ) ,nρµmo− γ(1−µ
ρµm
1
Kf
m)
∗
−1
γ(σ−1)(1−µ)(1−µ)
m − 1 ,
a 1−µ (pu )N→ Nm = ρam − 1[Nm (aρm − 1)/Kf + 1]1/ρ =(A6)which increases with N because ρµm /[γ(σ − 1)(1 − µ)(1 − µm )] > 0. Fig. A1(b) draws thee∆rm (aRm ) = 0-locus defined in Eq. (A6), where N0 , at which Nm = 0, is given by
Nm = 0,(σ−1)(1−µ)
e0 ,→ N = aσ−1 (p∗u )−1≡Ne0 > 1. The arrows indicates the direction ofwhich is assumed to be greater than one: Nmotion of foreign capital. As in the basic model, the area where foreign capital moves to thehost country (upper arrow) expands as N increases and thus local suppliers develops. Unlike
the basic model, however, the locus is not a vertical line but a upward-sloping curve because
the relocation incentive differs in productivity. High-productive foreign capital is ready tomove to the host country with small number of suppliers, whereas for low-productive one to
move, a sufficient number of local suppliers is necessary.

35

A3-2.

Zero-profit conditions of domestic firms

The goods market clearing condition requires that the total sales must be equal to totalpurchase by consumers, domestic firms and multinationals:pq = p 1−σP

E + Nµ p 1−σPµP eaq + Kf µm

 p 1−σ Z aRm
P

1

Z aRm

P µm [τ (am )p∗u ]1−µm e
am qm (am )dG(am )σ − 1 σeaP
Kf σ − 1σeam P [τ (am )p∗u ]1−µm
E+µq + µmqm (am )dG(am )
N
σ σ−1
N σ
σ−1
1
Z R
E
σ−1
σ − 1 Kf am
=
+
µpq +
µm
pm (am )qm (am )dG(am ),
N
σ
σ
N 1
µ

µm

=

noting that multinationals with am ∈ [1, aR
m ] are in the host country. The integral part in
the right-hand side is
Z aRm

Z aRm
pm (am )qm (am )dG(am ) =pm (am )1−σ D∗ ·

1

1

ρD∗
= ρ
am − 1

Z aRm h

am a

ρaρ−1
m
dam
aρm − 1µm
1−µ(aγm p∗u )1−µm

i1−σ

µm

N 1−µ · aρ−1
m dam

1

i1−σ µm Z aRm
µm
ρD
∗
1−µ
m )]
= ρ
aρ−1−(σ−1)[1+γ(1−µdam
a 1−µ (pu ) m
N 1−µm
am − 11i1−σ µm (aR )ρe − 1µm
ρD∗ h 1−µa (p∗u )1−µm,= ρ
N 1−µ mam − 1ρe∗h

1−σis given by Eq. (A3).
where ρe ≡ ρ − (σ − 1)[1 + γ(1 − µm )] and pm
As in Appendix A1-3, we substitute these expressions into the zero-profit condition ofdomestic firms, pq = σF , to obtain

pq = σF,
"
#
Z R
σ
E
µm (σ − 1) Kf am→+
pm (am )qm (am )dG(am ) = σF,σ − µ(σ − 1) Nσ
N 1
o1−σ µm (aR )ρe − 1 µm
σαL µm (σ − 1) Kf ρD∗ n 1−µ∗ 1−µm→+a (pu )
N 1−µ m= σF,ρσ(1 − µ) + µ NσN am − 1ρeµm
ρee − 1−µ→ Kf [(aR(N − αN ),m ) − 1] = Θ0 N
where ρe ≡ ρ − (σ − 1)[1 + γ(1 − µm )],
e0 ≡
Θ

h µm
i1−σ
ρe(aρm − 1)σF [σ(1 − µ) + µ] a 1−µ (p∗u )1−µm
ρµm

D∗ (σ − 1)

,

N≡

L
,
F [σ(1 − µ) + µ]

noting that the upper bound of the number of domestic firms, N , is the same as that in the36basic model.
Using Eq. (A5), we can rewrite the above equation as
h
i
µm
ρe/ρ
ρ
e 0 N − 1−µKf {Nm (am − 1)/Kf + 1} − 1 = Θ(N − αN ),
n

oρ/eρ
µm
Kf
− 1−µ
e
(N − αN ) + 1−1 ,→ Nm = ρΘNam − 1i1−σh µm
ρe(aρm − 1)σF [σ(1 − µ) + µ] a 1−µ (p∗u )1−µm
e ≡Θ
e 0 /Kf =where Θ,ρµm D∗ Kf (σ − 1)

(A7)which increases as we have assumed α > 1 − (1 − µ)/µm . Fig. A1(b) draws the Π = 0 locus
with arrows indicating the direction of motion of domestic firms.

Fig. A1. Equilibrium curves under heterogeneous multinationals.

A3-3.

Conditions for multiple equilibria

We can know from Figs. 6 and A1 that multiple equilibria occur if the two equilibrium curvesintersect twice. The sufficient conditions for this are as follows. First, the N -intercept of theeΠ = 0 curve is greater than or equal to that of the ∆rm (aRm ) = 0 curve, that is, αN ≥ N0 .
R
Second, the Π = 0 curve is located above the ∆rm (am ) = 0 curve for some N ∈ [αN , N ].
Finally, the ∆rm (aRm ) = 0 curve is located above the Π = 0 curve at N = N .
The first condition reduces toαL
e0 ≡ aσ−1 (p∗ )−1 (σ−1)(1−µ) ,≥NuF [σ(1 − µ) + µ]αL→F ≤≡ Feb .
e0 [σ(1 − µ) + µ]
N

αN ≡

37

The second condition requires that for some N ∈ [αN , N ], the following must hold:
n
n


ρµm
o− γ(1−µ
oρ/eρ
ρµm
µm
1
Kf
Kf
m)
− 1−µ
∗ −1
e
γ(σ−1)(1−µ)(1−µ)
1−µm − 1 ,(N − αN ) + 1
Na (pu )
ΘN
−1 > ρ
aρm − 1am − 1ρµm
o− γ(1−µnoρ/eρ n 1
ρµm
µmm)
e − 1−µ→ ΘN(N − αN ) + 1
N γ(σ−1)(1−µ)(1−µm ) ,> a 1−µ (p∗u )−1
ρ
eµm
n 1
o− γ(1−µ
ρ
eµm
µm
m)
− 1−µ
∗ −1
e
1−µ
(N − αN ) + 1 > a (pu )N γ(σ−1)(1−µ)(1−µm ) ,
→ ΘN


ρ
eµm
n 1
o− γ(1−µ
ρ
eµm
µm
αL
m)
−
e 1 N 1−µ F N −N γ(σ−1)(1−µ)(1−µm ) ,→Θ+ 1 > a 1−µ (p∗u )−1σ(1 − µ) + µ→ F > max{F1 , 0} ≡ Fea ,
n

ρ
eµm
o− γ(1−µ
ρ
eµm
µm
1
αL
m)
−1
−1
∗ −1
e
γ(σ−1)(1−µ)(1−µ
)
1−µ
1−µ
m
a (pu )
N,
where F1 ≡ Θ1 N
−1 +σ(1 − µ) + µ
e 1 ≡ Θ/Fe .
and ΘThe third condition implies


n
n
ρµm
oρ/eρ
o− γ(1−µ
ρµm
µm
1
K
Kf
1− 1−µm)f∗−1
γ(σ−1)(1−µ)(1−µ)
me−1 > ρ
(1 − α) + 1−1 ,a 1−µ (pu )NΘNaρm − 1am − 1

ρ/eρ
ρµm
n 1
o− γ(1−µρµm
1−µ−µmm)∗−1
γ(σ−1)(1−µ)(1−µ
)
1−µ
m
e
→ a 1−µ (pu )> ΘN(1 − α) + 1
,
N
ρ
eµm
n 1
o− γ(1−µρeµm
1−µ−µmm)∗ −1
e 0 N 1−µ (1 − α) + 1,
1−µ→ a (pu )N γ(σ−1)(1−µ)(1−µm ) > Kf−1 Θ


ρ
eµm
h 1
i γ(1−µ1−µ−µmρeµm− γ(σ−1)(1−µ)(1−µ
m)
∗
−1
)
1−µ
m
e 0N
ef .
→ Kf > a 1−µ (pu )NΘ(1 − α) + 1 ≡ K

In sum, the multiple equilibria occurs if the fixed labor input takes an intermediate valuee f holds.
such that Fea < F ≤ Feb and the amount of foreign capital is so large that Kf > K

A3-4.

Proof of Proposition 3

Since Proposition 3(i) is evident from Fig. 7 and the discussions in the text, here we provee0 ≡ [a(p∗ )−(1−µ) ]σ−1 > 1; (c)Proposition 3(ii). Assume that (a) α > 1 − (1 − µ)/µm ; (b) Nue f ; (d) F ∈ (Fea , Feb ]; and (e) ρe ≡ ρ − (σ − 1)[1 + γ(1 − µm )]. All assumptions are
Kf > K
necessary for considering the possibility of equilibrium switch due to natural disasters. The
first three are sort of regularity conditions. Assumption (a) guarantees the upward slope ofthe Π = 0 locus in the (N, Nm ) plane. Assumptions (b) and (c) respectively ensures a finite
value of expectation and a sufficient number of local suppliers at point S2 . If (c) did not hold,the comparative statics with respect to the exponent of N would yield meaningless results(see Eq. (A7)). Under the last two assumptions, (d) and (e), multiple equilibria arise.
Consider an increase in the fixed labor input F due to a natural disaster. As in the basic
38

model, this shock results in (A) a leftward shift of the vertical line N = N ; (B) an upward
shift of the Π = 0 curve upward; (C) no change in the ∆rm (aRm ) = 0 curve. Fig. 7 illustrates
00these shifts of curves, where the Π = 0 curve and the N = N line are the corresponding
curves after the shock.
It can be seen from from observations (B) and (C) that point S1 in Fig. 7 is no longer astable equilibrium if the upward shift of the Π = 0 curve is so large that the new Π0 = 0 andthe ∆rm (aRm ) = 0 curves do not intersect at point U . From Eq. (A7), the shift of the Π = 0
curve is proportional to



i
µm
µm
∂ h e − 1−µ∂ e − 1−µ
αL
∂Nm
∝
ΘN
(N − αN ) =
Θ1 N
FN −
0<
∂F
∂F
∂F
σ(1 − µ) + µ
1−µ−µme 1 N 1−µ
=Θ
i1−σ
h µm
ρ
∗ 1−µm1−µρe(am − 1)σ[σ(1 − µ) + µ] a (pu )=.
ρµm D∗ Kf (σ − 1)As ∂Nm /∂F is greater, point S1 is less likely to be an stable equilibrium. The magnitudeof the upward shift depends on the share of local inputs for multinational production, µm ,entering both the numerator and the denominator of the term in the last line. Under oure0 > 1 or ln N
e0 > 1, the numerator decreases with µm :assumption that No1−σ  h µm
i1−σ h 1
i1−σµm∂ n 1−µ∗ 1−µma (pu )
ln a 1−µ (p∗u )−1= a 1−µ (p∗u )1−µm∂µm
i1−σ 
h µm
1−σln a(p∗u )−(1−µ)= (1 − µ)−1 a 1−µ (p∗u )1−µm
i1−σ
h µm
∗ 1−µm−1
e −1
1−µ= (1 − µ)a (pu )
ln N
0
i1−σ
h µm
e0 < 0.
ln N= −(1 − µ)−1 a 1−µ (p∗u )1−µm
Since the denominator unambiguously increases with µm , the whole term decreases with µm :i
µm
∂ 2 h e − 1−µ∂ 2 Nm∝ΘN(N − αN )∂F ∂µm∂F ∂µmn µmo1−σ 
ρe(aρm − 1)σ[σ(1 − µ) + µ] ∂−1
∗ 1−µm1−µ=µa (pu )
ρD∗ Kf (σ − 1)
∂µm m

o1−σ
n µm
o1−σ 
µm
ρe(aρm − 1)σ[σ(1 − µ) + µ] −1 ∂ n 1−µ∗ 1−µm−2∗
1−µm− µm a 1−µ (pu )
< 0.
=
µm
a (pu )
ρD∗ Kf (σ − 1)∂µmThat is, the upward shift of the Π = 0 curve is smaller as µm is higher. This establishes
Proposition 3(ii), stating that multinationals emphasizing local sourcing show the resilienceto natural disasters.

39

Appendix 4.

Reconstruction from disasters

Supposing that a natural disaster strikes at an initial time s = 0, the fixed labor input attime s ≥ 0 is specified as F (s) = F eδ(T −s) . The fixed input returns to the pre-shock level
F after time T . At point S1 , capital return of becoming a multinational at time s (≤ T ),denoted by rm (s), is then
i1−σ
h
µm
µm
rm (s) = (D∗ /σ) am a 1−µ (τ p∗u )1−µm
N (s) 1−µµm
 1−µi1−σ 
hµm
L∗∗ 1−µm1−µ= (D /σ) am a (τ pu )F (s){σ(1 − µ) + µ}
µm

 1−µ
i1−σ
h
µm
L
∗
∗ 1−µm1−µ= (D /σ) am a (τ pu )F eδ(T −s) {σ(1 − µ) + µ}
h
i
µm
1−σ
δµm (T −s)µm= (D∗ /σ) am a 1−µ (τ p∗u )1−µm
N 1−µ e− 1−µ= rm e−δµm (T −s)
1−µfor s < T,which becomes the pre-shock level rm after time T . Note that in equilibrium S1 the numberof domestic firms is given by N = N .
Letting t (≤ T ) be the time at which foreign capital moves from the foreign to the hostcountry, the lifetime return it generates is given by
Z t
Z ∞
−θs
0
v(t) ≡
e rf ds +e−θs rm
(s)ds
0
t
Z t
Z T
Z ∞
θδµm (T −s)
−
−θs
1−µ
=
e rf ds +erm ds +e−θs rm ds, for t ≤ T,
0tT

where θ > 0 is the discount rate. The optimal timing of entering the host country is derived
from the following first-order condition:v 0 (t) = e−θt rf − e−θδµm (T −t)
1−µrm = 0,θδµm (T − t)
→ −θt + ln rf = −+ ln rm ,1−µ θ(1 − µ + δµm )tθδµm T
rf
→
=
+ ln
,
1−µ
1−µ
rm

 
1−µ
rm

b

if T ≤ T ≡
ln
0
θδµm
rf

 
→t=
,
1
1
−
µ
r

m
b

b
δT −
ln
≡ t (> 0) if T > T
1 − µ + δµm
θ
rf
(A8)

noting that rm > rf , or equivalently ln(rm /rf ) > 0 holds at point S1 . We can immediately
40

see from Eq. (A8) that the optimal timing weakly increases with the recovery time, i.e.,∂t/∂T ≥ 0. This optimal timing is indeed smaller than T :

 
1
−
µ
rm
1
−
µ
T+
ln
> 0.
T −b
t=
1 − µ + δµm
θrf
The second-order condition (SOC) is(T −t)
θδµm − θδµm
1−µv 00 (t) = −θe−θt rf +erm < 0,
1−µ
 

δµm
δµm (T − t)rf→
· exp θ t −
<
,
1−µ
1−µ
rm



 

δµm (t − T )
rf
δµm
+θ t+
< ln
.
→ ln
1−µ
1−µ
rm

If the SOC does not hold, the objective function v(t) exhibits a convex one and foreign capitalnever moves to the host country, i.e., t = ∞. The inequality in the last line always holds if
the following sufficient condition holds:








 
δµm
δµm (t − T )δµm
δµm (T − T )
rf
ln
+θ t+
≤ ln
+θ T +
< ln
,
1−µ
1−µ
1−µ
1−µ
rm

 

rf
δµm
+ θT < ln
,
→ ln
1−µ
rm


1 − µ rf1
→ T < T ≡ ln·,θ
δµm rmwhere T is defined over a parameter range that ensures T > 0. If T is sufficiently higher
than T , the SOC is not satisfied and the time of reentering never comes, i.e., t = ∞, which
establishes Proposition 4(i).
Assuming the existence of interior solutions, that is, a parameter range that satisfies
Tb < T and T ∈ (Tb, T ), we can check that the optimal timing t = b
t decreases with µm :



 
∂b
t
1
1 − µ ∂ ln(rm /rf )
1−µ
rm
−
=
· (1 − µ + δµm ) − δ δT −ln
2∂µm
(1 − µ + δµm )
θ
∂µm
θ
rf

  


 
1
(1 − µ)(1 − µ + δµm ) rf rm
rm
1−µ
rm
1−σ
=
−
ln
−
ln
τ
−
δ
δT
−
ln
(1 − µ + δµm )2
θµm
rm rf
rf
θ
rf

 
(1 − µ)(1 − µ + δµm )1
rm=ln τ 1−σ − δ 2 T − (1 − µ)2 ln< 0.
2(1 − µ + δµm )
θµm
rf

41

From the first to the second line, the following relations were used:
n
µm
o1−σ
1
1
rm
∗ −1
1−µ
1−µ
N
= a (τ pu )
τ 1−σ > 1,
rf
n

o1−σ
1
1
∂(rm /rf )∗−11−µ= rm ln a 1−µ (τ pu )
N
,
∂µm

  
1 rm
rm
1−σ
> 0.
=
ln
− ln τ
µm rf
rf
Similarly, it can be checked that ∂ bt/∂τ < 0. These establish Proposition 4(ii).

42

Data Appendix for“The Resilience of FDI to Natural Disasters through Industrial
Linkages”
Hayato KatoToshihiro Okubo

Osaka University

Keio University

This appendix provides supplementary tables for empirical examples in Introduction.

43

Table A1. Description of variables
Variable

Description

SourceNo. of natural disasters

Number of natural disasters that record
positive financial damages.

EM-DAT

FDI (as % of GDP)

FDI net inflows (new investment inflows
less disinvestment) divided by GDP.

WDI

Population growth rate (%)
Inflation rate (%)
Corporate tax rate (%)

Financial depth

Annual population growth rate.
Inflation as measured by the annual
growth rate of the GDP deflator.
Statutory corporate tax rate.
Score measures of the depth of stock market and international debt securities, ranging from zero to one (FMD: Financial
Market Depth).

WDI
WDI
Asen (2020)

IMF

Notes: EM-DAT: Emergency Events Database by the Centre for Research on the Epidemiology ofDisasters, https://www.emdat.be/ WDI: World Development Indicators by the World Bank,

https://datatopics.worldbank.org/world-development-indicators/ Statutory tax
rates collected by Asen (2020) and the Tax Foundation, https://taxfoundation.org/
publications/corporate-tax-rates-around-the-world/ IMF: Financial Development
Index Database by the International Monetary Fund,
https://data.imf.org/?sk=F8032E80-B36C-43B1-AC26-493C5B1CD33B

44

Table A2. List of countries
Developing countries #112
AngolaAlbania
Argentina
Armenia
Azerbaijan
BurundiBenin
Burkina Faso
Bangladesh
Bulgaria
Bosnia and Herzegovina
Belarus
Bolivia
BrazilBhutanBotswana
Chile
China
Cameroon
Congo, Dem. Rep.
Congo, Rep.
Colombia
Comoros
Costa Rica
Czech Republic
Dominica
Dominican Republic
Algeria
EcuadorEgypt, Arab Rep.
Estonia
EthiopiaFiji
Micronesia, Fed. Sts.
Georgia
Ghana
Guatemala
GuyanaHonduras
Croatia
Haiti

Hungary
Indonesia
India
Iran, Islamic Rep.
Jamaica
JordanKazakhstan
Kenya
Kyrgyz Republic
Cambodia
Korea, Rep.
Lao PDR
St. Lucia
Sri Lanka
Lithuania
LatviaMoroccoMoldova
Madagascar
Maldives
MexicoMyanmarMongolia
Mozambique
Mauritania
Mauritius
MalawiMalaysia
Namibia
Niger
Nigeria
Nicaragua
Nepal
Oman
Pakistan
Peru
Philippines
Papua New Guinea
PolandParaguay
Romania

Developed countries #41
Russian Federation
RwandaSaudi Arabia
Sudan
SenegalSolomon Islands
El Salvador
SerbiaSlovak Republic
Slovenia
Seychelles
Chad
ThailandTajikistan
Turkmenistan
Tonga
Trinidad and Tobago
Tunisia
TurkeyTanzania
UgandaUkraineUruguay
Uzbekistan
Venezuela, RB
VietnamSamoa
Yemen, Rep.
South Africa
ZambiaArgentina
Australia
Austria
Belgium
Brunei Darussalam
CanadaChile
Czech Republic
Germany
Denmark
Spain
Estonia
FinlandFranceUnited Kingdom
GreeceCroatia
Hungary
IcelandIsraelItaly
Japan
Korea, Rep.
Lithuania
LatviaNetherlands
NorwayNew Zealand
Oman
PolandPortugal
Russian Federation
Saudi Arabia
Slovak Republic
Slovenia
SwedenSeychelles
Trinidad and Tobago
Uruguay
United States
Venezuela, RB

Notes: Developing countries are those belonging to low-income, lower-middle-income, or uppermiddle-income groups at some point in 1996 to 2015, according to the World Bank. See: https://
datatopics.worldbank.org/world-development-indicators/the-world-by-income-and-region.
html Developed countries are those belonging to high-income group at some point in 1996 to 2015.
The list does not include countries identified as tax havens (“big seven” and “dots”) by Hines andRice (1994).

45

Table A3. Summary statisticsN

Mean St. Dev.

Min

Max

Developing countries
FDI

2,000 3.601

3.477−2.49921.687

No. of disasters in the prior 5 years

2,000 3.861

9.280

0

112

No. of disasters in the prior 10 years 2,000 6.833

16.6030199

No. of disasters in the prior 15 years 2,000 8.921

22.1500

273

Population growth rate

2,000 1.417

1.226−3.848

5.432

Inflation rate

2,000 44.108

Corporate tax rate

2,000 29.615

8.640

0

55

Financial depth

2,000 0.118

0.159

0.000

0.837

FDI

655

3.270

4.706

−5.61636.953

No. of disasters in the prior 5 years

655

6.476

12.815088

No. of disasters in the prior 10 years 655 11.812

23.3910165

No. of disasters in the prior 15 years 655 15.789

31.572

0

236

Population growth rate

655

0.695

0.911

−1.854

7.350

Inflation rate

655

2.609

4.860 −27.632

40.440

Corporate tax rate

655 30.446

8.240

12

58

Financial development

655

0.290

0.004

0.999

631.813 −26.300 26,765.860

Developed countries

46

0.500

Table A4. Disaster impact on FDI: developing vs. developed countries(1)
No. of disasters in theprior 5 years

Dependent variable: FDI (as % of GDP)
Developing countries
Developed countries
(2)
(3)
(4)
(5)
(6)

−0.031∗∗−0.056(0.014)
No. of disasters in theprior 10 years(0.052)−0.027∗∗∗−0.020(0.007)
No. of disasters in theprior 15 years
Population growth rate
Inflation rate
Corporate tax rate
Financial depthCountry fixed effects
Year fixed effects
Controls
Number of countries
Number of observations
R2

0.535∗∗∗(0.196)−0.0001∗∗∗(0.00004)−0.049∗∗∗(0.018)0.910(1.581)
X
X
X
112
2,000
0.513

0.519∗∗∗(0.197)−0.0001∗∗∗(0.00004)−0.047∗∗∗(0.018)1.276(1.536)
X
X
X
112
2,000
0.515

(0.024)−0.020∗∗∗−0.007(0.005)(0.014)0.509∗∗(0.198)−0.0001∗∗∗(0.00004)−0.047∗∗∗(0.018)1.498(1.529)
X
X
X
112
2,000
0.515

0.576
(1.060)−0.017(0.028)−0.093(0.081)
3.477(2.707)
X
X
X
41
655
0.426

0.579
(1.066)−0.017(0.028)−0.096(0.081)
3.479(2.761)
X
X
X
41
655
0.424

0.607
(1.071)−0.017(0.027)−0.102(0.082)3.629(2.734)
X
X
X
41
655
0.423

Notes: Standard errors clustered by country are in parentheses. Developed countries are those belonging to the high-income group, while developing countries to the other income groups, according
to the classification of the World Bank. We exclude tax haven countries identified by Hines andRice (1994) and countries that never experienced natural disasters in 1976–2015. We drop the top
1% and the bottom 1% of the observations of the dependent variable as outliers.
∗ Significant at 10% level; ∗∗ Significant at 5% level; ∗∗∗ Significant at 1% level.

47

Table A5. Disaster impact on FDI in developing countries: severe vs. non-severe disasters
Dependent variable: FDI (as % of GDP)
Severe disasters
Non-severe disasters
(1)
(2)
(3)
(4)
No. of disasters in theprior 5 years
No. of disasters in theprior 6 to 10 years
No. of disasters in theprior 11 to 15 years

0.013

0.014

0.019

0.018

(0.055)(0.056)(0.024)(0.024)−0.081∗−0.053∗∗(0.049)(0.022)−0.095∗∗∗−0.031(0.034)(0.028)

No. of disasters in theprior 6 to 15 years
Population growth rate
Inflation rate
Corporate tax rate
Financial development
Country dummies
Year dummies
Number of countries
Number of observations
R2

0.488∗∗(0.199)−0.0001∗∗∗(0.00004)−0.046∗∗∗(0.018)1.196(1.555)
X
X
112
2,000
0.516

−0.088∗∗∗−0.042∗∗∗(0.022)(0.013)0.489∗∗(0.199)−0.0001∗∗∗(0.00004)−0.046∗∗∗(0.018)1.182(1.566)
X
X
112
2,000
0.516

0.519∗∗∗(0.198)−0.0001∗∗∗(0.00004)−0.049∗∗∗(0.018)1.622(1.528)
X
X
112
2,000
0.515

0.517∗∗∗(0.198)−0.0001∗∗∗(0.00004)−0.049∗∗∗(0.018)1.652(1.518)
X
X
112
2,000
0.515

Notes: Standard errors clustered by country are in parentheses. A severe disaster in country i inyear t is defined as one that records financial damages as a share of GDP exceeding its median for
all countries that have ever experienced natural disasters in 1976–2015. A non-severe disaster incountry i in year t is defined as one that is not severe. We exclude tax haven countries identified
by Hines and Rice (1994) and countries that never experienced natural disasters during the sample
period. We drop the top 1% and the bottom 1% of the observations of the dependent variable as
outliers.
∗ Significant at 10% level; ∗∗ Significant at 5% level; ∗∗∗ Significant at 1% level.

48

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