The Theory of Horizontal FDI and the Gravity Equation

Seminar Paper, 2015

20 Pages, Grade: 2,0


Table of Contents


2.Theory of Horizontal FDI
2.1 Theory of symmetric firms and intermediate inputs
2.2 Theory of heterogeneous firms and fixed costs increasing with distance ...

3.Gravity equation
3.1 From aggregate affiliate sales to the gravity equation
3.2 The gravity equation and its application for the empirical analysis


5.Critical reception


1. Introduction

The gravity equation is a common and often used empirical technique to analyse bilat- eral trade. The relationship between the theoretical background of multinational firms and findings from the empirical research with the gravity equation, however, had not been proven to be strong. This results from the fact that gravity equations which try to explain foreign affiliate sales are ad hoc and therefore the coefficients estimated by them are hard to interpret. That is why Kleinert and Toubal (2010), from now on re- ferred to as K&T, further elaborate the theoretical origin of the structural gravity equa- tion by Redding and Venables (2003) which they use to analyse exports and FDI. In their paper they focus on three different theoretical models. Two models on horizontal FDI by Brainard (1997) and by Helpman et al. (2004) and one on vertical FDI by Ve- nables (1999). After the theoretical part they try to apply the gravity equations they derived on a dataset on affiliate sales to analyse if these equations hold true in the empirical analysis.

In our paper we will focus on the theoretical origins of the two models on horizontal FDI, since these are the models who hold in the empirical test. Our focus lies on the derivation of these models. We show the differences among the models themselves, as well as the similarities and differences between the original models and the revised models by K&T. We will further show how these models lead to the gravity equations by analysing its connections with the structural gravity equation by Redding and Vena- bles (2003) in greater detail.

Summing up, the paper of K&T is very rich in information but rather short considering the scope. This is why they abbreviate some of the theoretical underpinnings behind the models. With our paper we want to give some further insides concerning the horizontal FDI models to ensure a better understanding of the paper by K&T and the intuitions behind their elaborations.

2. Theory of Horizontal FDI

2.1 Theory of symmetric firms and intermediate inputs

Considering symmetric firms, the presented paper by K&T refers to the contribution by Brainard (1997). In her paper, she analyzes the so-called proximity-concentration trade-off and the extent to which location decisions reflect this trade-off. In detail this means that a firm can serve the foreign market via exporting or via FDI by setting up affiliates. When serving via exports, a firm can profit from concentrating its production in one location and thus achieving economies of scale. In contrast to that, a firm that produces via affiliates can benefit from the proximity to its customers. Therefore, it can avoid the shipping costs that occur when a firm exports to another location.

In the model Brainard uses, firms are more likely to serve foreign markets via FDI the higher transport costs and trade barriers are and the lower investment barriers and the plant-level economies of scale relative to the firm-level economies of scale are. According to the proximity-concentration hypothesis, a firm should serve markets via FDI if the already mentioned benefits of proximity outweigh the benefits of producing in one location and exporting the products from there. She introduces a model with two factors, two countries and two sectors. The first sector produces a homogeneous good, whereas the second sector produces differentiated goods. While the first sector uses constant-returns-to-scale technology, the second sector uses increasing-returns-to- scale technology.

Afterwards, she makes various assumptions in order to simplify the model. She implies symmetry in factor endowments and consumer preferences, a demand function of the CES type (constant elasticity of substitution below one) among the different varieties of the product and homothetic preferences across the two aggregate goods. The model assumes that the technology in the differentiated sector is characterized by increasing firm-level returns. That is because in this sector corporate activities like R&D are prevalent, which can be distributed among the production facilities without losing value, no matter on how many of those facilities they are applied. However, every new variety of the product induces a fixed cost (∙) as a function of the local wage in market , . As already described, there further exist plant-level economies of scale, so unit costs decrease with concentrating production in one location. The production opera- tions are described by a fixed cost () per plant and a constant marginal cost (). As can be seen easily, both cost forms are again functions of the local wage. The 2 model additionally assumes that the geographic separation of production activities from headquarter activities does not incur any costs. Therefore producing quantity in market , regardless of where the headquarter is located, costs

illustration not visible in this excerpt

Additionally, a firm that performs exporting faces per-unit costs due to trade barriers on the one hand and transportation costs on the other hand. The latter increase with distance, a crucial factor when the derivation of the gravity equation is considered later on. Transport costs are modeled as iceberg trade costs, which means that for a given amount that is produced in market = , “the amount that survives shipment to the foreign market is decreasing in the distance between the two markets, , and the transport cost, : ି(+)” (Brainard, 1997, p. 522).

Furthermore in the first sector, the homogeneous good sector, the wage - given that factor endowments are the same - is equal across all countries, = , . Therefore firms only base their decision if they serve foreign markets via exports or via FDI on the trade-off between the variable cost of exporting and the fixed cost when opening an affiliate in another market.

Now Brainard argues that in the model she provides there exist three possible equilibria. Firstly, one in which all firms have plants in both countries (FDI). Secondly, one in which all firms have one plant in the home country and export to the foreign market. And thirdly, one in which both multinational firms and exporting firms exist. This is a crucial point regarding the paper by K&T. As will be shown later, in their adaption of the model, only the first and the second equilibrium can exist, since there are no extensive margins due to the implementation of intermediate goods.

However, the described characteristics of the Brainard model lead to the following conditions for the three equilibria:

illustration not visible in this excerpt

Intuitively, the higher are transport costs and trade barriers and the lower are plant- level fixed costs relative to firm-level fixed costs, the more likely is an equilibrium where all firms perform FDI (pure multinational equilibrium) and vice versa for the pure trade equilibrium.

Brainard argues, that in the former equilibrium, no trade of final goods exist at all (pure equilibrium) and that trade only occurs in invisible corporate services. Again it should be mentioned, that K&T change this assumption. Since the focus lies on the paper by K&T, this fact will be explained not now, but in the following section. As already noted, in the Brainard model there is a third possible equilibrium for an intermediate range of parameter values where both firm types exist at the same time. Thus there is a fraction of firms in each market that operates a single plant and exports, and a fraction 1 െ with plants in both countries (mixed equilibrium). In this mixed equilibrium the share of exports relative to total sales is higher, the lower are transport costs and trade barriers and the higher are the plant-level fixed costs. The reverse is true for multinational activity :

illustration not visible in this excerpt

Brainard already mentions that the model she provides can be expanded and may include multiple stages of production by incorporating intermediate goods. For her em- pirical purposes however, this would unnecessarily complicate the interpretation of her results.

As mentioned, K&T rely heavily on the above presented model. They are also placed in a world with two sectors, agriculture producing a homogeneous good and manu- facturing producing a set of heterogeneous goods . Again, a Cobb-Douglas function with subutility functions of the CES type is used to describe customers’ utility:

illustration not visible in this excerpt

0 1. The subutility function of the CES type looks as follows:

illustration not visible in this excerpt


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The Theory of Horizontal FDI and the Gravity Equation
University of Hohenheim  (Institute of Economics)
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Tobias Maurer (Author)Roman Hartinger (Author), 2015, The Theory of Horizontal FDI and the Gravity Equation, Munich, GRIN Verlag,


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