Multinational Firms and Economic Integration: The Role of Global Uncertainty

Abstract

This paper develops a three-country, two-sector, two-factor general-equilibrium trade model in which multinational firms’ FDI decisions are influenced by global uncertainty level. We investigate the effects of economic integration under uncertainty, and highlight an important new type of FDI which is certainty-seeking. A numerical general-equilibrium model has been explored to study in depth the endogenous regime changes with six different firm types. Among others, we show that multinational firms are highly influenced by global uncertainty level, so that even the same economic integration process leads to significantly different global market structure.

1. Introduction

Multinational firms have been key players in globalization processes. During the last decades, extensive research has been conducted to understand their characteristics and roles in the globalizing world. It is now largely reported that multinational firms are larger, more skill-intensive, and more productive. In particular, multinational firms are more R&D intensive and technology transfers by multinational firms have played an important role for economic development and sustainable economic growth in many countries (see, e.g., [1,2,3,4,5]).

Consequently, governments in many countries have pursued various forms of economic integration to attract multinational activities and foreign direct investment (FDI), as well as to promote exports. In particular, free trade agreements (FTAs) have been used extensively and have become a major part of the global trading and investment system [6]. Traditional trade theories have been extended in various ways to incorporate multinational firms and their investment behaviors. A standard basic framework to analyze the effects of multinational activities has been the two-country, two-good, two-factor Heckscher–Ohlin model (see, e.g., [7,8,9]). By extending the basic framework with various FDI motives, such as market-seeking, resource-seeking, and efficiency-seeking, new trade theories have significantly enriched our understanding of trade/investment patterns and gains from globalization in the presence of multinational firms. Though many important links between location characteristics and multinational firm activities have been revealed, all these approaches are, however, limited in studying the role of uncertainty.

Firms are very sensitive to any kinds of uncertainty when they make decisions on investment. In particular, for the multinational firms who have to incur large sunk costs to enter the market, global uncertainty level should be crucial when they decide where to locate their headquarters as well as where to add additional affiliate branches. Traditional investment theories have stressed that a great deal of waiting (inertia) should be optimal when dynamic decisions are made in an uncertain environment. The irreversible nature of investment should be particularly important for multinational firms when they choose their headquarter and branch locations.

Figure 1 shows the World Uncertainty Index, which is very volatile and even increasing. The World Uncertainty Index (WUI) is a measure indicator that tracks uncertainty level across the world. Ahir et al. [10] construct the WUI for a panel of 143 individual countries (with a population of at least two million) using a text mining approach which counts the frequency of the word “uncertainty” (and its variants) in the quarterly Economist Intelligence Unit (EIU) country reports, provided by a leading company in the field of country intelligence on a regular basis for 189 countries. Since uncertainty is a nebulous and broad concept, researchers have used different methods to measure uncertainty. Typically, there have been two methods: (i) an approach based on the volatility of key economic and financial variables, and (ii) an approach based on text-searching (mining) newspaper archives. Using the latter approach and a single source (EIU country reports), Ahir et al. provide an uncertainty index which is comparable for a large set of advanced and developing economies and updated quarterly. Figure 1 is the World Uncertainty Index over time (GDP weighted average), where the vertical scale represents the number of times uncertain (or its variants) is mentioned in EIU country reports per thousand words multiplied by 100,000. Based on the index, they highlight among others that global uncertainty has increased significantly since 2012 and uncertainty spikes are more synchronized in advanced economies, which would largely affect the multinational firms with multiple plants in multiple countries.

The aim of this paper is to study the role of uncertainty in the global trade and investment pattern. We develop a three-country, two-sector, general-equilibrium trade model in which multinational firms’ FDI decisions are influenced by global uncertainty level. Depending on the global uncertainty level, six types of firms have emerged endogenously and compete in the global market. Conventional proximity-concentration tradeoff determines firms’ foreign market entry mode: exporting vs. FDI. Multinational firms base their headquarters in one of the three countries and operate production plants in each country to meet the local demands, while national firms in each country face marginal trade costs to export to other countries.

Given this basic setup, we investigate the effects of economic integration (trade liberalization) between two of the three countries, and the role of global uncertainty level. In particular, we analyze in depth the emergence of each firm type by constructing and solving a trade-cost-uncertainty box. The numerical simulation results show that multinational firms are highly influenced by global uncertainty level so that even the same economic integration (globalization) process leads to significantly different global market structure.

The rest of the paper is organized as follows. Section 2 discusses the related literature. In Section 3, we present the basic setup of the model. In Section 4, we present a parameterized general-equilibrium model and show the trade-cost-uncertainty box in the case of three symmetric countries. In Section 5, we investigate asymmetric-country cases. Section 6 and Section 7 provide a brief discussion and concluding remarks.

2. Related Literature

This study relates to several literature branches. The theoretical literature of investment under uncertainty has stressed that a great deal of waiting (inertia) should be optimal when decisions are made in a dynamic and uncertain environment (see, e.g., [11,12,13,14,15,16]). In general, investors are very sensitive to any kind of uncertainty, and this is particularly the case for the firms who have to incur large investment to enter the market. Although all investment would be highly exposed to market uncertainties, it has been widely found that multinational firms were typically more sensitive to uncertainty than national firms. Various reasons have been given. Related to recent firm heterogeneity literature in international trade, multinational firms are typically larger and more productive than national firms (see, e.g., [17,18,19,20,21]). These two facts imply that multinational firms are expected to incur higher investment for international market entry/operation and various innovation (R&D). The irreversible nature of investment would then lead multinational firms to adopt the wait-and-see strategy. Additionally, multinational firms face various foreignness costs, as well as expropriation risks for some cases, to operate in multiple countries [22].

Though widely treated in the literature, uncertainty is a broad concept which includes various economic, political, and social factors. Among others, previous studies have focused on the political and institutional uncertainty of the host country and its impact on the FDI inflows. For example, Julio and Yook [23] show that foreign investments are significantly deterred by political uncertainty during election periods. Additionally, numerous studies have highlighted the negative relationships between political uncertainty and FDI flows (see, e.g., [24,25,26,27,28,29]). In the same vein, Hermes and Lensink [30] highlighted also the significant correlation between political uncertainty and the outflow of domestic capital. With the close relationship between the overall uncertainty and the institutional quality of the host country, many studies have also studied the institutional-quality-FDI links, and identified overall positive relationship between good institutional quality and FDI flows (see, e.g., [31,32]). Consequently, for example, Dixit [33] concludes that FDI may be influenced the most sensitively by the political uncertainty and the institutions.

Though many systematic links between uncertainty and FDI flows have been uncovered, previous studies have focused mainly on the country-specific uncertainty of the host country. On the other hand, country-specific uncertainties should also be highly interrelated given that today’s globalization process occurs at a much finer level of disaggregation and complexifies increasingly by forming a global market and global supply chain with many different countries included. Recently, on the empirical side, numerous studies have analyzed and identified the international spillover of uncertainty across countries (see, e.g., [34,35,36,37,38]). For example, currently the Russia–Ukraine war shows well how global uncertainty is closely interrelated and affects simultaneously the global economy. We have also observed how the US–China trade conflict has affected the global economy by increasing global uncertainty. In such an environment, multinational firms’ investment decisions might be better explained by global uncertainty rather than country-specific uncertainty, since, in contrast to national firms, multinational firms operate their affiliates in many countries and the locations are strategically and closely interrelated. Related to this issue, for example, a recent work by Jardet et al. [39] finds an interesting result. Using panel data of 129 countries over 1995–2019 (pre-COVID-19), they find that inward FDI is influenced by global uncertainty rather than host country uncertainty: higher global uncertainty significantly decreases inward FDI, while the effect of the host country uncertainty is not statistically significant.

Trade theories have largely been developed and studied the international trade and investment patterns by incorporating multinational firms and by considering the competition between national firms and multinational firms. Even though many important insights have been gained, traditional trade theories implicitly assume that multinational firms and national firms face zero or at least the same uncertainty levels. However, since, in contrast to the national firms, multinational firms operate their affiliates in many countries simultaneously, multinational firms should be exposed more to the international uncertainty and affected more. Based on this assumption as well as recent evidence, in this paper we revisit the effect of economic integration (trade liberalization) on the international trade and investment patterns when multinational firms’ investment and/or entry decisions are influenced by global uncertainty level rather than one country-specific uncertainty level.

3. The Model

In this section, we construct a three-country, two-sector, general-equilibrium trade model. The world is composed of three countries (regions), $r,u\in \left\{i,j,k\right\}$, and in each country there are two sectors: a homogeneous-good sector $Y$ and a differentiated-good sector $X$. Consumers in each country have Cobb–Douglas preferences over the two goods: $U=Y^{\alpha }{X}^{\beta }$, with respective demands $Y=\alpha \frac{Inc}{P_Y}$ and $X=\beta \frac{Inc}{P_X}$. There are two factors of production: $\overline{S}$ (skilled labor) and $\overline{L}$ (composite factor); a fixed composite factor $\overline{L}$ includes unskilled labor and others. For simplicity of notation, we will omit the country index when no confusion arises.

3.1. Homogeneous Good Sector

Y is produced using S and L by a competitive industry with constant returns to scale. We assume a CES production function: $Y={\left[{\alpha }_Y{L}_Y^{{\rho }_Y}+{\beta }_Y{S}_Y^{{\rho }_Y}\right]}^{\frac{1}{{\rho }_Y}}$. Solving producer’s optimization problem yields the demand for each factor at given factor prices (wage rates) $w_L$ and $w_S$, associated with an aggregate price index $P_Y$:

$$L_Y={\tilde{\alpha }}_Y{\left(\frac{P_Y}{w_L}\right)}^{{\sigma }_Y}Y \mathrm{and} S_Y={\tilde{\beta }}_Y{\left(\frac{P_Y}{w_S}\right)}^{{\sigma }_Y}Y,$$

(1)

$$P_Y={\left[{\tilde{\alpha }}_Y{w}_L^{1-{\sigma }_Y}+{\tilde{\beta }}_Y{w}_S^{1-{\sigma }_Y}\right]}^{1/\left(1-{\sigma }_Y\right)},$$

(2)

where ${\tilde{\alpha }}_Y={\alpha }_Y^{{\sigma }_Y}$ and ${\tilde{\beta }}_Y={\beta }_Y^{{\sigma }_Y}$, and ${\sigma }_Y=1/\left(1-{\rho }_Y\right)$ is the elasticity of substitution between factors. Y is freely traded between countries.

3.2. Differentiated Good Sector

3.2.1. Demands

There is a continuum of varieties and consumers have Dixit–Stiglitz preferences: $X={\left[{{\displaystyle \int }}_{n\in N}x{(n)}^{\rho }dn\right]}^{\frac{1}{\rho }}$, $0<\rho <1$, where $N$ represents the mass of available varieties and the index $n$ denotes individual varieties. Solving consumers’ optimization problem yields the demand schedule for each variety associated with an aggregate price index $P_X$:

$$x\left(n\right)={\left(\frac{p\left(n\right)}{P_X}\right)}^{-\sigma }X,$$

(3)

$$P_X={\left[{{\displaystyle \int }}_{n\in N}p{(n)}^{1-\sigma }dn\right]}^{\frac{1}{1-\sigma }},$$

(4)

where $\sigma =1/\left(1-\rho \right)$ is the elasticity of substitution among varieties; $p\left(n\right)$ is the market price of each variety.

3.2.2. Competition and Foreign Market Entry Modes

X is produced by a monopolistic competition industry with increasing returns to scale, using S. Firms charge a constant markup over marginal production costs:

$$p_i=\frac{\sigma }{\sigma -1}{w}_{si}c, p_j=\frac{\sigma }{\sigma -1}{w}_{sj}c \mathrm{and} p_k=\frac{\sigma }{\sigma -1}{w}_{sk}c,$$

(5)

where c is the unit production cost measured in efficiency units of skill labor.

Firms in industry X choose their entry mode to serve foreign markets. Firms can export goods produced in the home country, or build foreign branches to meet the local demands. Firms face a trade-off (proximity-concentration trade-off): exports to foreign markets are associated with iceberg trade costs $\tau >1$ per unit of goods, whereas additional local branches incur addition fixed setup costs per market. We index the domestic exporting firms and the multinational firms engaging in horizontal FDI using d and h, respectively. Consequently, six different firm-types may arise endogenously:

• $N_i^d$, $N_j^d,$ and $N_k^d$: domestic exporting firms in a country {$i, j, k$}
• $N_i^h$, $N_j^h$, and $N_k^h$: multinational firms based in a country {$i, j, k$}, and having foreign branches in other countries.

Consumers in each country have demands for each variety. In country-I, the demands for each variety are:

$$x_{ii}^d=x_{ii}^h=x_{ji}^h=x_{ki}^h={\left(\frac{p_i}{P_{Xi}}\right)}^{-\sigma }{X}_i,$$

(6)

$$x_{ji}^d={\tau }_{ij}^{1-\sigma }{\left(\frac{p_j}{P_{Xi}}\right)}^{-\sigma }{X}_i \mathrm{and} x_{ki}^d={\tau }_{ik}^{1-\sigma }{\left(\frac{p_j}{P_{Xi}}\right)}^{-\sigma }{X}_i,$$

(7)

where $x_{ii}^d$, $x_{ii}^h$, $x_{ji}^h$, $x_{ki}^h$, $x_{ji}^d$, and $x_{ki}^d$ denote each type of X-goods:

• $x_{ii}^d$: produced by country-i national firms
• $x_{ii}^h$: produced by multinational firms headquartered in country-i
• $x_{ji}^h$: produced by multinational firms headquartered in country-j and having an affiliate in country-i
• $x_{ki}^h$: produced by multinational firms headquartered in country-k and having an affiliate in country-i
• $x_{ji}^d$: produced by country-j national firms and exporting to country-i
• $x_{ki}^d$: produced by country-k national firms and exporting to country-i.

With six different firm-types, the aggregate consumption price index can be written as:

$$P_{Xi}={\left[N_i^d{p}_i{}^{1-\sigma }+N_j^d{\left({\tau }_{ij}{p}_j\right)}^{1-\sigma }+N_k^d{\left({\tau }_{ik}{p}_k\right)}^{1-\sigma }+N_i^h{p}_i{}^{1-\sigma }+N_j^h{p}_i{}^{1-\sigma }+N_k^h{p}_i{}^{1-\sigma }\right]}^{\frac{1}{1-\sigma }},$$

(8)

where $N_i^d$, $N_j^d$, $N_k^d$, $N_i^h$, $N_j^h$, and $N_k^h$ represent the number of each firm type. In the same way, the demands and the consumption price index can be derived for country j and k.

Entering the market requires two types of fixed setup costs: a firm-specific fixed setup cost $f_f$ and plant-specific fixed costs $f_p$ for each plant they build, which are also measured in units of skilled labor S. Thus, domestic exporting firms incur $f_f+f_p$ in their home country, while multinational firms having separate branches in each country incur $f_f+f_p+f_p+f_p$.

3.2.3. Global Uncertainty and Investment Cost

Firms are very sensitive to any kinds of uncertainty. It is particularly the case for the multinational firms when they choose their headquarter and branch locations. Traditional theories have highlighted that a great deal of inertia (waiting) should be optimal when dynamic decisions were made in an uncertain environment. The irreversible nature of investment should particularly be important for multinational firms.

Among others, Dixit [12] derives such positive value of waiting in a simple formulation. The traditional Marshallian investment trigger is multiplied by a factor of $\gamma /\left(\gamma -1\right)$, so that the investment trigger under uncertainty is $H=\frac{\gamma }{\gamma -1}M$, where $\gamma$ is dependent on the discount rate $\delta$ and the volatility (uncertainty) $v$ of the future revenue:

$$\gamma =\frac{1}{2}\left[1+\sqrt{1+\frac{8\delta }{v^2}}\right]>1.$$

(9)

We incorporate the uncertain nature of investment into the model by assuming that:

$$f_{fi}^h=\frac{{\gamma }_i}{{\gamma }_i-1}{f}_{fi}^{h0}, f_{fj}^h=\frac{{\gamma }_j}{{\gamma }_j-1}{f}_{fj}^{h0} \mathrm{and} f_{fk}^h=\frac{{\gamma }_k}{{\gamma }_k-1}{f}_{fk}^{h0},$$

(10)

$$f_{pi}^h=\frac{{\gamma }_i}{{\gamma }_i-1}{f}_{pi}^{h0}, f_{pj}^h=\frac{{\gamma }_j}{{\gamma }_j-1}{f}_{pj}^{h0} \mathrm{and} f_{pk}^h=\frac{{\gamma }_k}{{\gamma }_k-1}{f}_{pk}^{h0},$$

(11)

where $f_f$ and $f_p$ are the uncertainty-adjusted firm-specific and plant-specific fixed setup costs, respectively. Thus, global uncertainty plays an important role for investment decision of multinational firms. Higher uncertainty (an increase of $v$) induces higher fixed setup (investment) costs, whereas lower uncertainty (a fall in $v$) leads to lower fixed setup (investment) costs.

3.3. Equilibrium

3.3.1. Goods Market

Y goods are homogeneous and freely traded. The price $P_Y$ is determined by world demand and supply:

$$Y_i+Y_j+Y_k\ge {\alpha }_i\frac{In{c}_i}{P_Y}+{\alpha }_j\frac{In{c}_j}{P_Y}+{\alpha }_k\frac{In{c}_k}{P_Y}.$$

(12)

We choose $P_Y$ as our numeraire.

In the monopolistically competitive industry X, firms are free to enter the market. In equilibrium, markup revenues exactly cover the fixed setup costs. Following zero-profit conditions determine the equilibrium number of each firm type $N_r^d$ and $N_r^h$, $r,u\in \left\{i,j,k\right\}$:

$$\left(p_r-w_{Sr}c\right)\left(x_{rr}^d+{\displaystyle \sum }_{r\ne u}{x}_{ru}^d\right)\le w_{Sr}\left(f_{fr}^d+f_{pr}^d\right) \left({\mathit{N}}_{\mathit{r}}^{\mathit{d}}\right)$$

(13)

$$\left(p_r-w_{Sr}c\right)x_{rr}^h+{\displaystyle \sum }_{r\ne u}\left(p_u-w_{Su}c\right)x_{ru}^h\le w_{Sr}\left(f_{fr}^h+f_{pr}^h\right)+{\displaystyle \sum }_{r\ne u}{w}_{Su}{f}_{pu}^h \left({\mathit{N}}_{\mathit{r}}^{\mathit{h}}\right)$$

(14)

Equations (13) and (14) are written in complementary slackness form. A non-negative variable to be solved is associated with each inequality. In mathematical programming, this is referred to as a complementarity problem: equations hold with strict equality if the associated firm types are active with positive production (zero profits), while firms are inactive (exit from the market) if inequalities hold with negative profits.

3.3.2. Labor Market

From the assumed Y industry technology, following labor market clearing condition (written in complementary slackness form) determines $w_L$ (the wage rate of L) in each country:

$${\overline{L}}_i\ge L_{Yi}, {\overline{L}}_j\ge L_{Yj} \mathrm{and} {\overline{L}}_k\ge L_{Yk}.$$

(15)

Similarly, the wage rate of $w_S$ in each country, $r,u\in \left\{i,j,k\right\}$ is determined by following labor market clearing condition for S (written in complementary slackness form):

$$\begin{gathered} {\overline{S}}_r\ge S_{Yr}+S_r^d{N}_i^d+S_r^h{N}_r^h+{\displaystyle \sum }_{r\ne u}{S}_{ur}^h{N}_u^h, \\ {S}_r^d={\displaystyle \sum }_{r}c{x}_{rr}^d+(f_{fr}^d+f_{pr}^d), \\ {S}_r^h=c{x}_{rr}^h+f_{fr}^h+f_{pr}^h, \\ {S}_{ur}^h=c{x}_{ur}^h+f_{pr}^h, \end{gathered}$$

(16)

where $S_{Yr}$ is the industry-Y skilled-labor demands in country-$r$, while $S_r^d$, $S_r^h$, and $S_{ur}^h$ are the skilled-labor demands in the industry-X:

• $S_r^d$: skilled-labor demands of country-$r$ national firms
• $S_r^h$: skilled-labor demands of multinational firms headquartered in country-$r$
• $S_{ur}^h$: skilled-labor demands of multinational firms headquartered in other countries and operating an affiliate in country-$r$.

3.3.3. Income

Finally, national incomes follow from employment:

$$In{c}_i=w_{Li}{\overline{L}}_i+w_{Si}{\overline{S}}_i, In{c}_j=w_{Lj}{\overline{L}}_j+w_{Sj}{\overline{S}}_j \mathrm{and} In{c}_k=w_{Lk}{\overline{L}}_k+w_{Sk}{\overline{S}}_k.$$

(17)

4. The Numerical General-Equilibrium Model

The model developed in Section 3 contains many dimensions and many inequalities, which makes it difficult to use traditional comparative statics analyses. Changing a parameter value generally affects the strict inequality and equality conditions simultaneously, and may lead to abrupt regime changes with different firm types emerging and exiting endogenously.

In this section, we present a parameterized version of the model and solve the nonlinear complementarity problem using numerical simulation methods. The GAMS (General Algebraic Modeling System) software has been used to solve the numerical general-equilibrium model [40]. In our model, we have 43 equations and 43 endogenous variables, which should be solved simultaneously. $P_Y$ is chosen as the numeraire. Analyzing endogenous entry and/or exit of each firm type needs to solve simultaneously all the corner solutions of the mixed complementarity problem (MCP) for each firm type. For example, in Equations (13) and (14), equations hold with strict equality if the associated firm types are active with positive production (zero profits), while firms are inactive (exit from the market) if inequalities hold with negative profits. In the same way, if any supply is larger than demand, the associated price variable will be zero, while the equilibrium price levels will be determined when the relevant market clearing conditions hold (supply equals demand).

For the benchmark, we assume that the world is endowed with 1500 units of L and 4500 units of S, which are divided between countries i, j, and k. Initially, we calibrate the model so that the three countries are symmetric, with each having 500 units of L and 1500 units of S.

Table 1. Benchmark parameter and variable values.

$\alpha$	$\beta$	$\sigma$	${\tilde{\alpha }}_Y$	${\tilde{\beta }}_Y$	${\sigma }_Y$	$c$	$f_f^{d0}$	$f_p^{d0}$	$f_f^{h0}$	$f_p^{h0}$
0.50	0.50	5.00	0.50	0.50	3.00	1.00	10.00	5.00	12.00	2.50
$\delta$	$v$	$\overline{L}$	$\overline{S}$	$w_L$	$w_S$	$Y$	$P_Y$	$p$	$Inc$	$P_X$
0.05	0.00	500	1500	1.00	1.00	1000	1.00	1.25	2000	0.53
${\tau }_{ij}$	${\tau }_{ik}$	${\tau }_{jk}$	$x_{ii}^d$	$x_{jj}^d$	$x_{kk}^d$	$x_{ij}^d$	$x_{ik}^d$	$x_{ji}^d$	$x_{jk}^d$	$x_{ki}^d$
1.50	1.50	1.50	26.00	26.00	26.00	5.14	5.14	5.14	5.14	5.14
$x_{kj}^d$	$x_{ii}^h$	$x_{ij}^h$	$x_{ik}^h$	$x_{jj}^h$	$x_{ji}^h$	$x_{jk}^h$	$x_{kk}^h$	$x_{ki}^h$	$x_{kj}^h$	$N_i^d$
5.14	26.00	26.00	26.00	26.00	26.00	26.00	26.00	26.00	26.00	0.00
$N_j^d$	$N_k^d$	$N_i^h$	$N_j^h$	$N_k^h$
0.00	0.00	10.26	10.26	10.26

shows the benchmark parameter and variable values. Initially, all prices are normalized to one as far as possible; thus, from Equation (17) each country has the same income of 2000 with the same endowments. We set $\sigma =5$, which is one of the values commonly used in the monopolistic competition models in the literature: with $\sigma =5$, the markup of monopolistically competitive firms ($1/\sigma$) is 20%; this, in turn, leads to $p=1.25$ from Equation (5).

Recent firm heterogeneity literature in international trade has highlighted that multinational firms are more productive, larger, and associated with better technologies compared to their national competitors. Though we do not model explicitly such heterogeneity in this paper, our assumptions on the fixed costs partly reflect such important features. The firm-level fixed cost (knowledge-capital) is higher for multinational firms, while once paid such higher setup cost multinational firms can add individual plants more cheaply than national competitors: $f_f^{h0}>f_f^{d0}$, and $f_p^{h0}<f_p^{d0}$. That is, the higher knowledge-capital of multinational firms yields higher internal economies of scale. However, note that the total fixed cost for multinational firms is higher since they have at least more than two plants in different countries. Changing fixed cost values under these basic assumptions would of course change the results quantitatively, particularly in the number of firms, but would not affect our main qualitative results.

Initially, we assume that no uncertainty prevails in the world with $v=0.00$, so that $f_f^h=f_f^{h0}$ and $f_p^h=f_p^{h0}$. On the other hand, exporting requires high trade costs: ${\tau }_{ij}={\tau }_{ik}={\tau }_{jk}=1.50$. Consequently, in the benchmark case we have only multinational firms producing while national firms are inactive; initially, 10.26 multinational firms headquartered in each country, respectively, are operating.

We are interested in the different effects of economic integration depending on the global uncertainty levels. Take, for example, an economic integration (trade liberalization) between country i and j. Holding other parameter values constant, we can solve the model by altering the trade cost between i and j (${\tau }_{ij}$) and the global uncertainty level ($v$). Figure 2 shows the equilibrium regimes in such ${\tau }_{ij}-v$ box.

The vertical axis in Figure 2 represents the trade cost between country i and j (${\tau }_{ij}$), while the horizontal axis represents the global uncertainty level ($v$). The lowest ${\tau }_{ij}$ and $v$ are measured from the southwest corner, in which ${\tau }_{ij}=1.0$ and $v=0.0$. Along the horizontal axis, $v$ increases from 0.0 to 0.2, while ${\tau }_{ij}$ increases from 1.0 to 1.5 along the vertical axis.

The numbers inside the box indicate the emergence of each firm type: {100, 10, 1, 0.1, 0.01, 0.001} are associated with {$N_i^h$, $N_j^h$, $N_k^h$, $N_i^d$, $N_j^d$, $N_k^d$}, respectively. For example, in the northwest corner in which ${\tau }_{ij}=1.5$ and $v=0.0$, $N_i^h$, $N_j^h$, and $N_k^h$ are active (denoted by 111.000). In such a way, Figure 2 displays all the equilibrium regimes with different values of ${\tau }_{ij}$ and $v$. In general, we can distinguish three different areas: multinational firm only regimes (colored in green), mixed regimes of national and multinational firms (colored in white), and national firm only regimes (colored in yellow).

We see that multinational firms are more active with lower $v$ and higher ${\tau }_{ij}$, while domestic exporting firms are more active with lower ${\tau }_{ij}$ and higher $v$. Along the southwest–northeast diagonal, mixed regimes of both multinational and national firms are observed. Among others, Figure 2 highlights that global uncertainty plays an important role in investment decisions of multinational firms and the effects of economic integration may greatly differ depending on the global uncertainty level.

It is widely documented that in this type of monopolistic competition models the elasticity of substitution is important for the results. Therefore, we also perform sensitivity analyses for alternative values of $\sigma$. The equilibrium regimes in the ${\tau }_{ij}-v$ box for alternative values of $\sigma$ are reported in Figure A1 and Figure A2 in the Appendix A. Compared to the benchmark case (Figure 2), we find the same pattern, but with lower value of $\sigma$ the area of the emergence of multinational firms is reduced, while with higher value of $\sigma$ the area of the emergence of multinational firms is expanded. This is because of the different magnitude of fixed costs in the total revenue of multinational firms. Lower value of $\sigma$ implies higher markup, $1/\sigma$, and higher fixed-cost proportion in the total revenue of multinational firms. Thus, other things being equal, e.g., at the same ${\tau }_{ij}$, lower value of $\sigma$ relatively increases the negative impacts of higher $v$ on multinational firms.

5. Asymmetric Countries

So far, we have assumed that the three countries are symmetric in endowments and market size. In this section, we investigate also asymmetric cases. Figure 3 presents the equilibrium regimes in the ${\tau }_{ij}-v$ box, when the two integrating countries are large. Both country i and j have 40% of world endowments, respectively. We observe overall that domestic exporting firms are more active compared to Figure 2. Other things being equal, a larger market promotes the concentration incentive over proximity incentive. However, we have the same qualitative insights as before.

Finally, Figure 4 presents the equilibrium regimes in the ${\tau }_{ij}-v$ box, when the two integrating countries are relatively small. Each of country i and j has 20% of world endowments, respectively. In this case, we observe that firms are mainly located in country $k$, having the largest market. $N_k^h$ and $N_k^d$ are active in most areas. Again, previous qualitative insights remain valid.

Global uncertainty plays an important role in investment decisions of multinational firms and the effects of economic integration may greatly differ depending on the global uncertainty level. To see this more in depth, let us take one specific column and one specific row in the ${\tau }_{ij}-v$ box. Consider the case in which both country i and j have 40% of world endowments, respectively.

Figure 5 shows first the effects of trade liberalization between country i and j when $v=0.09$. As ${\tau }_{ij}$ falls from 1.4 to 1.0, $N_i^d$ and $N_j^d$ increase, while $N_i^h$ and $N_j^h$ decrease. At the end, $N_k^h$ and $N_k^d$ emerge too, due to the exit of $N_i^h$ and $N_j^h$.

On the other hand, Figure 6 shows the effects of a fall in $v$ when ${\tau }_{ij}=1.15$. As $v$ falls from 0.13 to 0.00, we observe an inverse pattern. As global uncertainty reduces, $N_i^h$ and $N_j^h$ increase, while $N_i^d$ and $N_j^d$ decrease. Other things being equal, multinational firms base their headquarters in large countries with large markets.

6. Discussion

It is now widely documented that there is a significant and positive relationship between FDI and economic development and growth. In particular, multinational firms have been at the very core of the globalization process and their global investments have yielded many positive effects through induced technology transfers between countries. In many countries, government authorities have pursued various forms of trade and investment liberalization to attract multinational activities as well as to promote trade and overall investment. Recently, many countries have also been pursuing mega-FTAs which include many different countries to form a global market and global supply chain. How such movements will change the international trade and investment patterns is of great interest for policy makers. In particular, understanding the links between global uncertainty and global market structure should be an important research direction.

In this study, we developed a three-country, two-sector, two-factor general-equilibrium trade model in which multinational firms’ FDI decisions are influenced by global uncertainty level. The traditional theoretical framework of the two-country, two-good, two-factor Heckscher-Ohlin model has been extended by incorporating multinational firms and a third country to study the effects of economic integration between two of the three countries and the role of global uncertainty level. By constructing and solving in detail the trade-cost-uncertainty box, the paper shows that multinational firms are indeed highly influenced by the global uncertainty level, so that even the same economic integration process leads to significantly different global market structure. Traditionally, three types of FDI motives (market-seeking, resource-seeking, and efficiency-seeking) have been identified. This paper may add an important new type which is certainty-seeking FDI.

This paper’s results are in line with recent empirical evidence. The negative relationship between FDI flows and uncertainty is now widely documented in the literature. As FDI flows are closely related to the political and institutional uncertainty of the host country [33], as well as because of the measurement problem of uncertainty [39], most studies have focused on identifying the relationship between FDI flows and political uncertainty or institutional quality. Julio and Yook [23], among others, highlight that the FDI flows are significantly reduced by the political uncertainty during the election periods. See also Azzimonti [41], Chen et al. [42], and Honig [43] for evidence of the negative relationship between political uncertainty and FDI inflows. Given the close relationship between the institutional variables (such as corruption, financial system, law and order, etc.) and overall uncertainty, many researchers have also used a variety of institutional variables to identify the effect on FDI flows. See, for example, Wei [44], Buchanan et al. [45], Benassy-Quere et al. [46], and Daude and Stein [47]. Though previous literature has mainly focused on the country-specific uncertainty and FDI inflows, recent work by Jardet et al. [39] also highlights that FDI flows are influenced by global uncertainty rather than host country-specific uncertainty. This paper contributes to the literature by theoretically analyzing the links between global uncertainty and FDI flows and the resulting global market structure.

We are of course not the first to theoretically analyze the impact of uncertainty on the firms’ investment behavior. The classical literature of investment under uncertainty has highlighted that uncertainty increases the value of waiting to invest, and in particular it is optimal for the firms who have to incur irreversible sunk investments to take the “wait-and-see” strategy until the uncertainty is resolved (see, e.g., [11,12,13,14,15,16]). Such basic insights and mechanisms have also been adapted and explored in the context of foreign direct investment (see, e.g., [48,49,50]). Though such models also study the effect of uncertainty on the firms’ foreign direct investment, mostly they are limited to the investment decisions of one representative firm in a partial equilibrium framework. This paper contributes to the literature by providing a unified theoretical general equilibrium framework where different firm types emerge endogenously and compete in the global market. In ours, each firm decides where to base and how to enter the foreign market, which enables us to analyze the links between global uncertainty and global trade/investment pattern.

As a purely theoretical model, the specific implications are rather general and may be limited. Additionally, the certainty-seeking behavior of multinational firms are not fully considered for individual country levels. In our model, we distinguish mainly two types of foreign market entry modes: exporting vs. FDI by multinational firms, and multinational firms are defined as firms operating local plants and producing locally to meet the demands of foreign countries. Consequently, given the three-country (region) setup, there are three types of multinational firms that are based (headquartered) in one of the three countries and have local plants in the other two countries. Following recent evidence of the international spillover of uncertainty across countries, and also as a simplification of the theoretical model, we consider a situation of the same uncertainty variations across counties. In this sense, our certainty-seeking FDIs are more related to the global uncertainty level. Though the basic insights would be the same, our model can easily be extended to address the country-specific uncertainty differences with more types of multinational firms. With the same three-country setup, nine different multinational firms may emerge: three types of multinational firms that are headquartered in one of the three countries and which have local plants in the other two countries, and six types of multinational firms that are headquartered in one of the three countries and have a local plant in one of the other two foreign countries. With such setup, we then may study the impact of uncertainty level change in one specific country and address country-specific uncertainty rather than global uncertainty. Though the model becomes much more complicated, the main theoretical insights would be the same. Since multinational firms require higher setup cost and higher investment cost needs to be incurred in the headquartered country, an increase of uncertainty level in one specific country would first result in the exit of multinational firms headquartered in that country. Such an uncertainty issue may be applied to the case of demand uncertainty too. Suppose for example that the model’s uncertainty factor enters in the marginal cost of each firm type. An increase of demand uncertainty perceived by firms would act so that the marginal cost rises. In the same mechanisms, a rise in the global uncertainty would affect in general the multinational firms since they produce globally.

Though there has been a huge amount of research on the effects of economic integration (trade and investment liberalization), previous theoretical models have implicitly assumed that all firms face zero or at least the same uncertainty levels. By incorporating the uncertainty factor in the firms’ decision function, the results of this paper highlight that uncertainty plays an important role in the determination of international trade/investment patterns. The policy makers in the negotiation may need to focus on how to decrease the overall uncertainty perceived by firms rather than simply reducing tariffs or other taxes. The regional and global uncertainty issue should be included in the policy agenda of all the countries and requires a global cooperation between countries since such an issue is not in the hands of any single country. We are living in a world where global uncertainty and risks are increasingly growing. Moreover, today’s globalization process occurs at a much finer level of disaggregation, as it complexifies increasingly by forming a global market and global supply chain with many different countries included [51,52]. If the purpose of the government would be to attract and promote multinational firm activities, reducing any kind of uncertainty in the market might be a more important factor than any other policy measures.

Though widely treated and mentioned in the literature, uncertainty is a nebulous and broad concept including various factors and branches of economic activities. Depending on the different uncertainty types, the impact on each sector or economic activity may be largely different. For example, the uncertainty raised by the COVID-19 pandemic severely affected the global tourism industry and the economy of countries where the tourism industry is important. On the other hand, the uncertainty raised by the Russia–Ukraine war increased global energy prices and, among others, the energy-intensive industries were affected the most negatively. Additionally, the uncertainty caused by the US–China trade war and Brexit has caused many firms to relocate their economic activities to other countries. Though it is beyond the scope of this paper, the financial sector should also be the most responsive to any kind of uncertainty and affect the real economy in a close mutual relationship. The degree of dependence on external finance is largely different sector by sector and the effect of uncertainty may be larger in sectors with higher external financial dependence (see, e.g., [53,54]). Even though the effect of uncertainty might be largely different sector by sector and in various contexts of uncertainty, the main results of this paper would remain valid as long as multinational activities need higher investment in multiple countries and multinational firms are exposed more to international uncertainties for any decision making. Currently, the world is characterized by two forces. On the one hand, economic integration (globalization) proceeds more and more intensively, such as the RCEP and the CPTPP. However, on the other hand, various forms of uncertainty are rising at the global level, as shown in Figure 1. In such an environment, this study may provide a theoretical basis for further research and applications in this field.

7. Conclusions

In this paper, we highlighted the links between FDI and global uncertainty within a unified theoretical general equilibrium framework. By focusing on the global uncertainty rather than one host country-specific uncertainty, we have investigated the effects of economic integration (trade liberalization) between two countries and analyzed the endogenous global market structures (regime changes) depending on the global uncertainty levels. By numerically solving the mixed complementarity problem for each firm type, we derived full trade-cost-uncertainty boxes under plausible parameter values. By considering the global uncertainty dimension in addition to the trade cost dimension, the results have shown that multinational firms are indeed highly influenced by global uncertainty level so that even the same economic integration process leads to significantly different global market structure. At a given trade cost, a rise in the global uncertainty harms the multinational firms relatively more and decreases the global FDI flows, whereas, at a given global uncertainty level, a rise in the trade cost favors the multinational firms and increases the global FDI flows. Additionally, we investigated the trade-cost-uncertainty box in the case of asymmetric countries in the market sizes, as well as for alternative values of the elasticity of substitution between varieties. Altering other parameter values changes the picture more or less, but the same patterns were obtained.

Though new implications for the role of global uncertainty in the international trade and investment patterns may be obtained from this study, several limitations and possible future works are noteworthy. With its dominance during the past decades, this study has focused on the horizontal FDI. However, it is also widely reported that vertical FDI is growing rapidly and the global supply chain is being increasingly complexified by forming global supply networks. Extending and adapting the model in the context of vertical specialization of multinational firms would make it possible to address, for example, the import content of export and multinational production. As a first theorical development, this paper has focused on the role of uncertainty. However, there should be many other factors influencing the trade and investment. Undoubtedly, extending and adapting the model’s setup to consider other various factors in the context of political economics might lead to interesting and even different results. Additionally, with the very broad concept of uncertainty, more specified various forms of uncertainty may be considered to analyze different effects in both magnitude and direction and how they differently affect multinational firms’ investment decisions. Finally, following conventional frameworks of trade models, in this paper we have in mind the manufacturing sector in general. However, taking into accounts the specificities of other sectors and other economic activities would also be an interesting future research direction. I leave them for future research.