The role of FDI along transitional dynamics of the host country in an endogenous growth model

Over the past few decades, opening up to the global economy and attracting foreign direct investment (FDI) have been significant policy priorities in developing countries to promote their economic development. The main argument is that multinational enterprises (MNEs) would boost investment, bring new technologies and (management) skills, and generate FDI spillovers on domestic firms. However, the effects of FDI on the host country’s development are far from clear.

Overall, empirical literature finds that the effect of FDI on the host country’s economic growth is relatively weak (Carkovic and Levine, 2005; Gunby et al., 2017) and the link between FDI and growth varies over time (Bénétrix et al., 2023). More precisely, whether this effect is significant or not depends on local conditions such as the host country’s income levels, institutional strength (Baiashvili and Gattini, 2020), the level of human capital (Li and Liu, 2005), or the development of local financial markets (Alfaro et al., 2004, 2010). For instance, the impact is positive in countries with high development level of human capital or financial markets (Borensztein et al., 1998; Alfaro et al., 2004). Besides, there is an inverted-U sharped connection between the extent of FDI impact and the host country’s income-levels. The effect is larger for low- to middle-income countries, before declining from transition to high-income ones (Baiashvili and Gattini, 2020).¹¹1See, for example, Almfraji and Almsafir (2014) for a literature review on the FDI-growth’s relationship.

Despite substantial empirical research on the nexus FDI-growth,²²2Over the five decades of research on FDI, the link FDI-GDP (economic growth) is the most often investigated. Indeed, 107 of 500 published articles considered in Paul and Feliciano-Cestero (2021) study the impacts of FDI on the host country’s economic growth. there is still a lack of theoretical analysis. Hence, our paper aims to understand the role of FDI along the transitional dynamics of the host economy by investigating fundamental questions:

• (i)

  What is the optimal strategy of a country receiving FDI?

• (ii)

  How can FDI help the host country escape the middle-income trap and potentially achieve economic growth in the long run?

We address these questions by using an optimal growth model with FDI and endogenous growth. Let us briefly describe the ingredients of our model. The host country is assumed to be a small open economy with three goods: consumption, physical capital, and new goods. These commodities are freely tradable with the rest of the world. There are two agents: a representative agent of the host country and an MNE. The representative agent has three choices for investment: (1) buy physical capital to produce consumption good, (2) invest in training to improve her/his skills and then work for MNE in order to get a salary, and (3) invest in research and development (R&D) to get innovations. If innovations are good enough, they will improve the productivity of domestic firms.

First, we show that if the host country has a low initial resource and a weak research process efficiency, it should never invest in R&D but focus on FDI. In this case, its economy converges to a steady state, which is higher than that of the economy without FDI.

Second, consider a low-income country so that the country cannot immediately invest in R&D and new technology (because the fixed cost in R&D is so high). In this situation, we prove that if the leverage of new technology is high enough or the country has good potential in R&D, the optimal strategy of the country should be as follows:

• -

  Stage 1: the country should train specific workers.

• -

  Stage 2: specific workers will work for the MNE to get a favorable salary and improve the country’s income and capital accumulation.

• -

  Stage 3: once the country’s income is high enough, it should focus on R&D to create new technology that increases the domestic firms’ total factor productivity (TFP). Thanks to this, its economy may have economic growth in the long run.

Our model also shows that a country may get economic growth in the long run without FDI. Our analyses suggest that FDI only plays a role as a catalyst for the host country’s economic growth, especially in the first stages of the host country’s development process.

This research has two significant contributions to the literature. First, we theoretically advance the understanding of how FDI affects economic growth. The existing literature provides some theoretical models to study the effect of FDI on growth. Looking back to history, Findlay (1978) examines the role of FDI in a dynamic framework by assuming that the sequences of domestic and foreign firms’ capital stocks are determined by a continuous time dynamical system.³³3This system’s parameters include domestic and foreign firms’ technological efficiency that are exogenous. A key insight in Findlay (1978) is his assumption of the ‘contagion’ effect: the level of efficiency of domestic firms depends on (but is lower than) that of the advanced part of the world. Wang (1990) develops this idea by assuming that there is technology diffusion: the host country’s human capital stock is an increasing function of the ratio of foreign investment to domestically owned capital. By using this modeling of FDI and a two-country model with free capital mobility and exogenous propensities to save, Wang (1990) shows that opening to FDI has beneficial implications for the host country.

Notice, nevertheless, that in Wang (1990), the propensity to save is exogenous. Some other research considers models with endogenous saving rates. In a continuous time model with a continuum of varieties of capital goods,⁴⁴4For this kind of growth models, see Romer (1990), Grossman and Helpman (1991). Borensztein et al. (1998) model FDI as the fraction of varieties produced by foreign firms in the total varieties of products. Under specific setups (Cobb-Douglas production and CRRA utility functions), they compute the rate of growth in the steady state equilibrium, which is an increasing function of the fraction of varieties produced by foreign firms in the total varieties of products. Berthélemy and Démurger (2000) extend Borensztein et al. (1998)’s model by endogenizing the numbers of varieties produced by domestic and foreign firms. As in Borensztein et al. (1998), Berthélemy and Démurger (2000) focus on the steady state equilibrium and compute the growth rate of the host country in the case of Cobb-Douglas production and CRRA utility functions. Using a continuous time product variety-based endogenous growth, Alfaro et al. (2010) study the role of local financial markets in enabling FDI to promote growth through backward linkages.⁵⁵5In Alfaro et al. (2010), the development level of the local financial market is modeled by the difference between the instantaneous borrowing rate and the lending rate. They focus on the balanced growth path and their calibration shows that an increase in FDI leads to higher growth rates in financially developed countries compared to those observed in financially poorly developed ones.

Unlike the above studies, we focus neither on the steady state nor on the balanced growth path with specific functions. Instead, we explore the global and transitional dynamics of the optimal paths in endogenous growth models with FDI and without restrictions on the utility function.⁶⁶6Nguyen-Huu and Pham (2018, 2024) study the nexus between FDI spillovers and industrial policy of a host country in a two-period and an exogenous growth models respectively. However, they do not consider endogenous growth. To be best of our knowledge, we are the first to do so. Consequently, our results seem to be more robust. Moreover, our analyses of transitional dynamics allow us to better understand the optimal strategy for the host countries (as we have explained), while the existing literature does not.

Second, our paper also contributes to the literature on optimal growth with thresholds (see Azariadis and Drazen, 1990; Bruno et al., 2009; Le Van et al., 2010, 2016 among others) and increasing returns (see Romer, 1986; Jones and Manuelli, 1990; Kamihigashi and Roy, 2007 among others). Our added value is to show the role of FDI. We point out that FDI may partially contribute to the capital accumulation of the host country and hence enable the country to overcome the threshold at the first stage of its development process. However, whether a host country can obtain growth in the long run does not depend on FDI but on the local conditions (mainly its innovation capacity and the efficiency of its investment in R&D). From a technical point of view, our analysis is far from trivial because of the presence of both domestic and foreign firms. For instance, the method used in Bruno et al. (2009), Le Van et al. (2010) cannot be directly applied in our model.

The paper is structured as follows. Section 2 introduces an endogenous growth model with FDI. Section 3 investigates the interplay between FDI, R&D, and economic growth of the host country. Section 4 concludes. Formal proofs are presented in the Appendix.

Let us start with a benchmark model in which there is a small open economy with three kinds of goods: consumption, physical capital, and so-called new goods. The consumption good is taken as numéraire. The price (in terms of consumption good) of physical capital is exogenous and denoted by $p$.

In each period, there is an MNE in the host country. It produces the new good by using two inputs: physical capital and specific labor. We assume that there is no domestic firm in this sector.

At each date $t$, the foreign firm (without market power) chooses $K_{e,t}$ units of physical capital and $L^{D}_{e,t}$ units of specific labor in order to maximize its profit:

where $p_{n}$ is the exogenous price (in terms of consumption good) of the new good.

There is a representative agent in the host country. Taking prices and wages as given, the agent chooses the allocation of resources to maximize the intertemporal welfare of the whole population.

The host country has three choices for investment at each date $t$. First, it can buy $K_{c,t+1}$ units of physical capital to produce $A_{c}K_{c,t+1}^{\alpha}$ units of the consumption good at period $t+1$, where $\alpha\in(0,1)$.

Second, it can use $H_{t+1}$ units of the consumption good for training to generate $A_{h}H_{t+1}^{\alpha_{h}}$ units of specific labor, where $\alpha_{h}\in(0,1)$. The latter works for the MNE to get a total wage of $w_{t+1}A_{h}H_{t+1}^{\alpha_{h}}$ (units of the consumption good).

The last choice is to invest in R&D to create new technology: If the host country invests $N_{t+1}$ units of the consumption good in R&D at period $t$, it will obtain $bN_{t+1}^{\sigma}$ units of new technology in period $t+1$, where $b$ represents the efficiency of the research process. We assume that $\sigma\in(0,1)$. The new technologies can improve the old sector’s productivity, but only if the amount of investment in R&D exceeds a critical threshold such that $bN_{t+1}^{\sigma}>\bar{x}$, where $\bar{x}>0$ represents a fixed cost. In this case, the productivity goes up to $A_{c}+a(bN_{t+1}^{\sigma}-\bar{x})$ where the parameter $a$ indicates the efficiency or the leverage of the new technology.⁷⁷7To introduce R&D, we can also write, for example, $A_{c}+\gamma((N_{t+1}-N^{*})^{+})^{\sigma}$ instead of $A_{c}+a(bN_{t+1}^{\sigma}-\bar{x})^{+}$. However, the main results have similar insights.

To sum up, the representative agent solves the dynamic growth problem below:

subject to

for every $t\geq 1$. Here, $\beta\in(0,1)$ is a rate of time preference while $u$ is the instantaneous utility function.

We require the following assumption.

We provide a formal definition of equilibrium.

At equilibrium, we have $L^{D}_{e,t}=L_{e,t}>0$. Hence, the first order conditions of the problem $(F_{t})$ imply that, for every $t$:

Wage $w$ depends not only on the foreign firm TFP but also on the prices of physical capital and new goods.

Denote $S_{t+1}=pK_{c,t+1}+N_{t+1}+H_{t+1}$ the total savings of the host country. In our framework, it is equal to the aggregate investment. By using Equation (4), the problem $(P)$ can be rewritten as follows:

for any $t\geq 1$, and $c_{0}+S_{1}\leq X_{0},$ where $X_{0}\equiv A_{c}K_{c,0}^{\alpha}+w_{0}L_{e,0}$ and $G(S)$ is defined by

Notice that the function $G(\cdot)$ is continuous, strictly increasing and $G(0)=0$. However, it may be non-concave and non-smooth.

Let us now consider a case where there is the MNE but no R&D. In this case, the problem $(P)$ becomes

where the function $F(S)$ is defined by

We can check that $F(S)$ is strictly increasing, strictly concave, smooth and satisfies Inada condition $F^{\prime}(0)=\infty$. By using the standard argument in the dynamic programming, we obtain the following result.

The property ${S}_{b}>{S}_{a}$ means that with the presence of the MNE, the economy’s investment stock converges to a steady state which is higher than that of the economy without FDI. Moreover, the steady state level $S_{b}$ is increasing in the TFP of the old sector, wage, as well as the TFP of the MNE. It implies that the effect of FDI on the steady state output depends on both FDI and the host country’s circumstances. This is consistent with several studies mentioned in the Introduction section.

We now investigate the global dynamics of the allocation to explore the role of FDI. We first provide some static analysis (Subsection 3.1) and then global dynamic analysis (Subsection 3.2).

We have investigated the nexus between FDI, R&D and growth in a host country by using infinite-horizon optimal growth models. According to our results, the very question does not rely on whether or not developing countries should attract inward FDI, but instead on how they implement policies to benefit from FDI spillovers. We have proved that FDI can act as a catalyst, helping a host developing country to avoid a middle income trap and potentially attain a higher income. However, to reach sustained economic growth in the long run, the host country should focus on domestic investment and R&D.