International Saving, Investment and Trade

Abstract

Feldstein and Horioka (Econ J 90:314–329, 1980) observed that saving and investment move closely together in the major OECD countries. This finding is a puzzle if national economies are characterized by one sector neoclassical production functions—with diminishing returns to capital, a high level of savings in a country should create an incentive to export capital. In this paper, we show that this incentive disappears in the presence of multiple sectors with differing capital intensities. In a high saving country, national capital can be absorbed domestically without a decline in its marginal product through a shift in the sectoral composition of national production towards capital intensive sectors. This is nothing but the well-known Rybczynski effect. We present a modified version of the standard Heckscher–Ohlin (HO) Model to show that very small barriers to capital mobility are enough to force national savings to stay within the country of origin. We also argue that, while the assumptions of this model may appear special, they are not unrealistic for the developed countries in the Feldstein Horioka study. Some historical economic trends are also consistent with the picture presented in this paper. Finally, the paper shows that the conventional insights from the one sector neoclassical model can be completely overturned in a multi-sector setting when technological differences are introduced.

Appendix

The following proposition states that, starting from a situation with identical returns to capital in the two countries, the change in r is the same in response to a change in prices in the case of Cobb–Douglas production functions with multiplicative technological differences.

Proposition

Suppose that r=r*, and the production functions in each sector of the home and foreign country are, respectively,

$$ F_{{i\,}} {\left( {K_{i} ,L_{i} } \right)} = A_{i} K^{{\alpha _{1} }}_{i} L^{{1 - \alpha _{1} }}_{i} \;{\text{and}}\;F^{*}_{i} {\left( {K_{i} ,L_{i} } \right)} = A^{*}_{i} K^{{\alpha _{1} }}_{i} L^{{1 - \alpha _{1} }}_{i} $$

(4)

where i=1, 2 is the index for the sectors. Then ${\vartheta r} \mathord{\left/ {\vphantom {{\vartheta r} {\vartheta p_{2} = {\vartheta r^{ * } } \mathord{\left/ {\vphantom {{\vartheta r^{ * } } {\vartheta p_{2} }}} \right. \kern-\nulldelimiterspace} {\vartheta p_{2} }}}} \right. \kern-\nulldelimiterspace} {\vartheta p_{2} = {\vartheta r^{ * } } \mathord{\left/ {\vphantom {{\vartheta r^{ * } } {\vartheta p_{2} }}} \right. \kern-\nulldelimiterspace} {\vartheta p_{2} }}$.

Proof

For a given price p _i and factor prices w and r, the revenue function is $p_{i} A_{i} K^{{\alpha _{i} }}_{i} L^{{1 - \alpha _{i} }}_{i}$ and the profit function in sector i can be written as $\pi _{i} {\left( {K_{i} ,L_{i} } \right)} = p_{i} A_{i} K^{{\alpha _{i} }}_{i} L^{{1 - \alpha _{i} }}_{i} - wL_{i} - rK_{i}$. Maximization of π _i (K _i , L _i ) with respect to K _i and L _i yields

$$ K_{i} = \frac{{\alpha _{i} }} {{1 - \alpha _{i} }}\frac{w} {r}L_{i} . $$

(5)

With perfect competition and constant returns to scale production functions, profits will be zero in the equilibrium, i.e., π _i (K _i , L _i )=0. Substituting Eq. 5 in π _i (K _i , L _i )=0 and solving for w, we obtain

$$ w = {\left( {1 - \alpha _{i} } \right)}\alpha ^{{\frac{{\alpha _{i} }} {{1 - \alpha _{i} }}}}_{i} {\left(\kern1.5pt {p_{i} A_{i} } \right)}^{{\frac{{1}} {{1 - \alpha _{i} }}}} r^{{ \kern1pt- \kern1pt\frac{{\alpha _{i} }} {{1 - \alpha _{i} }}}} . $$

(6)

Equation 6 will hold for both of the sectors, i=1, 2, with the same w and r:

$$ w = {\left( {1 - \alpha _{1} } \right)}\alpha _{1} ^{{\frac{{\alpha _{1} }} {{1 - \alpha _{1} }}}} {\left(\kern1.5pt {p_{1} A_{1} } \right)}^{{\frac{{1 }} {{1 - \alpha _{1} }}}} r^{{ \kern1pt-\kern1pt \frac{{\alpha _{1} }} {{1 - \alpha _{1} }}}} ,\;{\text{and}}\;w = {\left( {1 - \alpha _{2} } \right)}\alpha _{2} ^{{\frac{{\alpha _{1} }} {{1 - \alpha _{2} }}}} {\left(\kern1.5pt {p_{2} A_{2} } \right)}^{{\frac{{1 }} {{1 - \alpha _{2} }}}} r^{{ \kern1pt-\kern1pt \frac{{\alpha _{2} }} {{1 - \alpha _{2} }}}} . $$

(7)

Using the pair of Eq. 6, one can solve for r as

$$r = {c{\left( {p_{2} A_{2} } \right)}^{{\beta _{2} }} } \mathord{\left/ {\vphantom {{c{\left( {p_{2} A_{2} } \right)}^{{\beta _{2} }} } {{\left( {p_{1} A_{1} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {p_{1} A_{1} } \right)}}^{{\beta _{1} }} ,$$

(8)

where ${\left( {{\text{letting}}\,\,\gamma = {\left( {\frac{{\alpha _{2} }}{{1 - \alpha _{2} }} - \frac{{\alpha _{1} }}{{1 - \alpha _{1} }}} \right)}} \right)}$ $\beta _{i} = {\left[ {\gamma {\left( {1 - \alpha _{i} } \right)}} \right]}^{{ - 1}}$, i=1, 2, and $c = \frac{{\alpha ^{{\alpha _{2} \beta _{2} }}_{2} }} {{\alpha ^{{\alpha _{1} \beta _{1} }}_{1} }}{\left( {\frac{{1 - \alpha _{2} }} {{1 - \alpha _{1} }}} \right)}^{{\frac{1} {\gamma }}}$. Without loss of generality, consider a change in p ₂, From Eq. 8, the partial response of r is

$$ \frac{{\partial r}} {{\partial p_{2} }} = c\frac{{\beta _{2} p_{2} ^{{\beta _{2} - 1}} A_{2} ^{{\beta _{2} }} }} {{p^{{\beta _{1} }}_{1} A^{{\beta _{1} }}_{1} }} $$

(9)

Similarly, for the foreign country, we have

$$ r^* = {c{\left(\kern1.5pt {p_{2} A^{*}_{2} } \right)}^{{\beta _{2} }} } \mathord{\left/ {\vphantom {{c{\left( {p_{2} A^{*}_{2} } \right)}^{{\beta _{2} }} } {{\left( {p_{1} A^{*}_{1} } \right)}^{{\beta _{1} }} }}} \right. } {{\left(\kern1.5pt {p_{1} A^{*}_{1} } \right)}^{{\beta _{1} }} }, $$

(10)

and

$$ \frac{{\partial r^*}} {{\partial p_{2} }} = c\frac{{\beta _{2} p_{2} ^{{\beta _{2} - 1}} A^{{*\beta _{2} }}_{2} }} {{p^{{\beta _{1} }}_{1} A^{{*\beta _{1} }}_{1} }}. $$

(11)

Since r=r* initially, we equate the right hand sides of Eqs. 8 and 10. That yields

$$ \frac{{A^{{\beta _{2} }}_{2} }} {{A^{{\beta _{1} }}_{1} }} = \frac{{A^{{*\beta _{2} }}_{2} }} {{A^{{*\beta _{1} }}_{1} }}. $$

(12)

Finally, Eqs. 9, 11 and 12 imply that ${\partial r} \mathord{\left/ {\vphantom {{\vartheta r} {\vartheta p_{2} = {\vartheta r^{ * } } \mathord{\left/ {\vphantom {{\vartheta r^{ * } } {\vartheta p_{2} }}} \right. } {\vartheta p_{2} }}}} \right. } {\partial p_{2} = {\partial r^{ * } } \mathord{\left/ {\vphantom {{\vartheta r^{ * } } {\vartheta p_{2} }}} \right. } {\partial p_{2} }}$. □