Remittances, market size, and foreign direct investment: a case of sub-Saharan Africa

Abstract

This study covers the period 1981–2014 and uses an unbalanced panel data set for 85 developing countries. It assesses the effect of remittances through per capita GDP on FDI inflows to Sub-Saharan Africa (SSA) and compares its performance in attracting FDI with the other developing regions. The results show a positive effect of remittances on FDI, but it depends on the level of per capita GDP of the host country. That is, an increase in remittances by one standard deviation, on average, increases FDI inflows by 0.09% a year. Remittances have a positive effect on FDI in 43 countries, and eight of them are in SSA. In addition, a SSA country receives about 0.8% more FDI than the average country in ASIA, but there is no difference between SSA and Latin America and the Caribbean, and SSA and the Middle East and North Africa. Further, the growth rate of the host country’s GDP has a positive effect on FDI, which supports the market size hypothesis.

Appendices

Appendix 1

1.1 Theoretical Model

The model assumes a TNC’s operations at home and abroad, 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 c_h and q_h are unit costs and the output level at the home plant, c_f and q_f are unit costs and the output level at the foreign plant, and subscripts h and f represent home and foreign, respectively.

Total output demand is given as

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

(7)

Hence, the Lagrangean function is

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

(8)

and the first order conditions for the cost minimization problem are

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

(9)

$$ \frac{\partial L}{\partial {q}_f}={c}_f^{\prime}\left({q}_f\right){q}_f+{c}_f\left({q}_f\right)-\lambda =0,\kern0.5em \mathrm{and} $$

(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 the marginal costs at the home and foreign plants, respectively.

By equating (9) and (10) and solving for the home plant output (q_h) and then substituting this result into eq. (11), we obtain the foreign plant’s output. That is, foreign production is given by

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

(12)

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

Next, the TNC has to determine the level of inputs for producing at the foreign plant. Based on a Cobb-Douglas production function, foreign production is given as

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

(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 the real wage and the real user cost of capital, respectively.

Assuming that the foreign plant’s costs are minimized, the Lagrangean function is defined by

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

(15)

Then, 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)

$$ \partial L/{\partial K}_f={r}_f-\lambda\ \beta\ \left({q}_f/{K}_f\ \right)=0,\kern0.5em \mathrm{and} $$

(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 equation (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 equation (12) into (20) yields the final expression for the TNC’s optimal capital stock at the foreign plant as

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

(21)

Therefore, the TNC’s optimal capital stock at the foreign plant can be specified as

$$ {K}_t^{\ast }=f\left({q}_f, RUC\right) $$

(22)

where the host country’s demand (q_f) and relative unit costs (RUC) between the home and host countries have a positive effect on ${K}_t^{\ast }$.

Appendix 2

Table 5 Variable Definitions and Data Sources

Appendix 3

Table 6 Summary statistics. Annual values for the period 1981–2014