Do Market Size and Remittances Explain Foreign Direct Investment Flows to Sub-Sahara Africa?

Abstract

The paper analyzes the effect of remittances in attracting foreign direct investment (FDI) to Sub-Saharan Africa (SSA). We apply an unbalanced panel data set for 40 African countries for the period 1981–2013. The results indicate positive and significant impacts of remittances on net FDI inflows to SSA conditioned on the level of per capita GDP in the host country. Therefore, a threshold of per capita GDP is needed for a SSA country to benefit from the positive impact of remittances on net FDI inflows. In addition, host country demand positively affects net FDI inflows to Africa, which supports the market size hypothesis.

Paper submitted to the Sixth Annual Conference on Regional Integration in Africa (ACRIA 6), July 1–2, 2015, Lagos, Nigeria

Appendices

Appendix 1

1.1 Derivation of the Econometric Model

The model assumes that the TNC decides first on whether or not to undertake FDI which requires a decision on the output level in the foreign country. Then, for the TNC undertaking FDI, total costs are defined as a function of costs of production in both the TNC’s home and foreign plants. So, total costs are given by:

$$ TC={c}_h\left({q}_h\right){q}_h+{c}_f\left({q}_f\right){q}_f $$

(6)

where TC is total costs, ${c}_h$ and ${q}_h$ are unit costs and output level in the home plant, ${c}_f$ and ${q}_f$ are unit costs and output level in the foreign plant, subscripts h and f are for home and foreign.

The constraint for total cost minimization is given by total output demand (TD) as:

$$ TD={q}_h+{q}_f $$

(7)

The associated Lagrangian function is defined as:

$$ L={c}_h\left({q}_h\right){q}_h+{c}_f\left({q}_f\right){q}_f+\lambda\;\left(TD-{q}_h - {q}_f\right) $$

(8)

and the first order conditions for the cost minimization problem are given by:

$$ \partial L/\partial {q}_h={c}_h^{\prime}\;\left({q}_h\right){q}_h+{c}_h\left({q}_h\right)-\lambda =0, $$

(9)

$$ \frac{\partial L}{\partial {q}_f}={c}_f^{\prime}\left({q}_f\right){q}_f+{c}_f\left({q}_f\right)-\lambda =0,\mathrm{and} $$

(10)

$$ \partial L/\partial \lambda =TD-{q}_h - {q}_f=0 $$

(11)

where ${c}_h^{\prime }=\partial {c}_h/\partial {q}_h$ and ${c}_f^{\prime }=\partial {c}_f/\partial {q}_f$. Equations (9) and (10) are marginal costs in the home and foreign plants respectively.

By equating (9) and (10) and solving for home output (${q}_h\Big)$ and then substituting this result into Eq. (11), we obtain the equilibrium output at the foreign plant. Therefore, foreign production is given as:

$$ {q}_f={\varnothing}_1\;TD+{\varnothing}_2\;RUC $$

(12)

where ${\varnothing}_1={c}_h^{\prime }/\left({c}_h^{\prime }+{c}_f^{\prime}\right)$ and ${\varnothing}_2=1/\left({c}_h^{\prime }+{c}_f^{\prime}\right)$ which are assumed to be positive, and $RUC={c}_h-{c}_f$ which represents relative unit costs between home country and host country. Equation (12) shows that the foreign plant’s output is positively related to both total demand and relative unit costs.

Next, the TNC has to determine the level of inputs for producing in the foreign plant. A Cobb-Douglas production function is assumed to represent foreign production as follows:

$$ {q}_f={L}_f^{\propto}\;{K}_f^{\beta } $$

(13)

Then, the costs associated with foreign production are given by:

$$ {C}_f={w}_f\;{L}_f+{r}_f\;{K}_f $$

(14)

where w and r are real wage and real user cost of capital respectively.

Assuming the foreign plant’s costs are minimized, the Lagrangian function is defined as:

$$ L={w}_f\;{L}_f+{r}_f\;{K}_f+\lambda\;\left({q}_f - {L}_f^{\propto}\;{K}_f^{\beta}\right) $$

(15)

The first order conditions for the cost minimization problem are given by:

$$ \partial L/\partial {L}_f={w}_f-\lambda \propto \left({q}_f/{L}_f\right)=0, $$

(16)

$$ \frac{\partial L}{{\partial K}_f}={r}_f-\lambda\;\beta\;\left(\frac{q_f}{K_f}\right)=0,\mathrm{and} $$

(17)

$$ \partial L/\partial \lambda ={q}_f - {L}_f^{\propto}\;{K}_f^{\beta }=0 $$

(18)

Dividing Eq. (16) by Eq. (17) and then rearranging yields:

$$ {w}_f\;{L}_f/\propto {q}_f={r}_f\;{K}_f/\beta {q}_f $$

(19)

Taking ${L}_f$ from Eq. (18) and substituting it into (19) yields ${K}_f$ as:

$$ {K}_f={\left[\left(\beta /\propto \right)\left({w}_f/{q}_f\right)\right]}^{\propto /\left(\propto +\beta \right)}\;{q_f}^{1/\left(\propto +\beta \right)} $$

(20)

Plugging Eq. (12) into Eq. (20) yields the final expression for the TNC’s desired capital stock (a capital stock level that solves the cost minimization problem) at the foreign plant as:

$$ {K}_f^{*}={\left[\left(\beta /\propto \right)\left({w}_f/{q}_f\right)\right]}^{\propto /\left(\propto +\beta \right)}\;{\left[{\varnothing}_1\;TD+{\varnothing}_2\;RUC\right]}^{1/\left(\propto +\beta \right)} $$

(21)

Appendix 2

1.1 Variable Definitions and Data Sources

Variable name	Variable definition	Source
FDI/GDP	Ratio of real net FDI inflows to real GDP	Own calculations
Net FDI inflows	Net FDI inflows balance of payment values in current U.S. dollars	World Development Indicators online version, World Bank (2014)
Real GDP	Host country real GDP at 2005 constant prices	Penn World Table Version 7.1, 2014
Real per capita GDP	Real per capita GDP at 2005 constant prices	Penn World Table Version 7.1, 2014
Remittances	Workers’ remittances and compensation of employees received in current U.S. dollars	World Development Indicators online version, World Bank (2014)
Remittances/GDP* real per capita GDP	Interaction of the Ln of real remittances/real GDP and Ln of real per capita GDP	Own calculations
Real exchange rate	Real exchange rate. Dollars per unit of foreign currency. It is defined as in Waldkirch (2003). It is computed by multiplying the nominal exchange rate by the ratio of the host country CPI to the U.S. CPI plus 0.001	Own calculations
Ln Imports/GDP	Natural log of the ratio imports to GDP	World Development Indicators online version, World Bank (2014)
Ln inflation	Natural log of 1 plus the annual change of the GDP deflator	Own calculations from International Financial Statistics CD-ROM, IMF, 2014
Ln U.S. r-Ln Host Country r	U.S. real interest rate and host country real interest rate differential	Own calculations. Real interest rate data is from the World Development Indicators online version, World Bank (2014)
Foreign capital stock	Host country foreign capital stock	UNCTAD, Division on Investment and Enterprise. http://unctadstat.unctad.org/ReportFolders/reportFolders.aspx
GDP deflator	GDP deflator	World Development Indicators online version, World Bank (2012)
Nominal exchange rate	U.S. dollars per unit of host country currency	International Financial Statistics CD-ROM, IMF, 2014.
CPI	Consumer price index	World Development Indicators online version, World Bank (2014)

Appendix 3

1.1 Summary Statistics, Annual Values for the Period 1981–2013

Variable	N	Mean	Std. Dev.	Minimum	Maximum
FDI/GDP	863	0.0347	0.0864	−0.0859	1.6182
Ln per capita GDP	863	6.6359	1.0990	4.7351	9.6075
Ln remittances/GDP	863	−4.6722	2.1461	−14.7571	0.0628
Ln real exchange rate	863	−4.3062	2.3364	−9.4712	3.6465
Ln imports/GDP	860	−0.9880	0.5549	−3.5126	1.4465
Ln inflation	863	0.1017	0.1318	−0.3449	1.0348
Ln foreign capital stock/GDP	863	−2.0508	1.3018	−8.1593	2.0712
Remittances/GDP	863	0.0487	0.1241	0.0000	1.0648

The SSA countries included in the study are Angola, Burundi, Benin, Burkina Faso, Botswana, Central African Republic, Chad, Cote d’Ivoire, Cameroon, Comoros, Cape Verde, Ethiopia, Gabon, Ghana, Guinea, The Gambia, Guinea-Bissau, Equatorial Guinea, Kenya, Liberia, Lesotho, Madagascar, Mali, Mozambique, Mauritania, Mauritius, Malawi, Namibia, Niger, Nigeria, Rwanda, Sudan, Senegal, Sao Tome and Principe, Swaziland, Seychelles, Togo, Uganda, South Africa and Zambia.